diff --git a/research/contextual-provider-pooling/EXPECTED.json b/research/contextual-provider-pooling/EXPECTED.json
new file mode 100644
index 0000000000..3480d62c5a
--- /dev/null
+++ b/research/contextual-provider-pooling/EXPECTED.json
@@ -0,0 +1,56 @@
+{
+  "status": "PASS_CONTEXTUAL_PROVIDER_POOLING",
+  "kappa": "318515327278119/200000000000000000",
+  "kappa_decimal": "0.001592576636390595",
+  "bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "complex_lower": "7975584912145610089/5000000000000000000000",
+  "complex_template_sha256": "94e14dfce4808c7f1c156b22a8bc0aec159a761b39946f030d485734331e0243",
+  "provider_bindings": {
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+      "independent_local_replay_sha256": "6bcb26454d545c16cd15f2a3058c0b9c38cbce27e3943a1f074f607ef0660725"
+    },
+    "n2": {
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+      "local_programs_sha256": "8c0f306abc36b0bf3c5a63141a5c9b78794264fc51ab30b70775734d7783d45a",
+      "local_checks_sha256": "6f02241e70220b8ef80a8e9817004e2affeaef6536f0f8e6a314096bcee9dbf8",
+      "independent_local_replay_sha256": "c4fe1c5c25ff5f5965577a4f12056c110eebc5f5a59ce17adcd0ce8996da8666"
+    },
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+      "local_programs_sha256": "2a6b8a081b45b60470da99fc1306c08293dac92160815ec0d9540ab183967a48",
+      "local_checks_sha256": "99fd2effc0f45b4eb212e3f467c53e4e36ca7c3687c7377322b20ecce1f80ee6",
+      "independent_local_replay_sha256": "be7a950a103471da3864362f8315e9e07cbde8d0a0eb0f8afff2407437ab82af"
+    },
+    "n8": {
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+      "local_programs_sha256": "c13c308504373160bf233e53a289e98a46a83b369f8f8e3133ea23b52e904a15",
+      "local_checks_sha256": "285aa85e567abb3ef865d37fdab2949855fd46d06bca05d78b56691aa9a65a09",
+      "independent_local_replay_sha256": "520be60830f40f6fc90ceaa35090f8ebb01b616dce39e8402f7633070b264cc3"
+    }
+  },
+  "provider_counts": {
+    "n8": 275,
+    "n0": 75,
+    "n6": 5,
+    "n2": 5
+  },
+  "complex_global_profile": {
+    "1": 832540,
+    "2": 153900,
+    "3": 179556,
+    "4": 68460,
+    "5": 20160,
+    "6": 20160,
+    "7": 1040,
+    "8": 2880,
+    "48": 8304
+  },
+  "complex_prefix_bits": 801,
+  "charged_prefix_bits": 1024,
+  "physical_row": 17495,
+  "outer_constraints": 47,
+  "bit_operator": "Pinned PR555 cited dependency, not physically replayed here"
+}
diff --git a/research/contextual-provider-pooling/LICENSE b/research/contextual-provider-pooling/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/contextual-provider-pooling/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/contextual-provider-pooling/MANIFEST.json b/research/contextual-provider-pooling/MANIFEST.json
new file mode 100644
index 0000000000..eebb0f9afe
--- /dev/null
+++ b/research/contextual-provider-pooling/MANIFEST.json
@@ -0,0 +1,609 @@
+{
+  "format": "sha256-lf-text-v1",
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+      "sha256": "0ac6cb1e84fa5fcb550bae7572c40475a7ae5addca3b984ab2f6f6bc9e102841"
+    },
+    "providers/audit_promoted_scalar.py": {
+      "mode": "lf-text",
+      "sha256": "1994e7116065636b53bf740000ff78dce8ea62390e597d293d183f33c67eaa6d"
+    },
+    "providers/build_promoted_epoch.py": {
+      "mode": "lf-text",
+      "sha256": "471ecdc704c7ef014230f7af5fd74034c58b4ca167c5b289cfaaa10d205eab23"
+    },
+    "providers/build_providers.py": {
+      "mode": "lf-text",
+      "sha256": "a88707f15e1b2e3f1597d49adacc98d5ddc843bb0fa2f641f2e2333b5d19e317"
+    },
+    "providers/run_variants.py": {
+      "mode": "lf-text",
+      "sha256": "b1de96439dd890aaf943dcc432c155c6f2c458c584a425eaf687fe7828064366"
+    },
+    "response/CROSS-FIELD-PROOFS.md": {
+      "mode": "lf-text",
+      "sha256": "3d0a1b9ac989283400e7c1e3a025080a8f6837755baccdd55f5e51599ac0921e"
+    },
+    "response/README.md": {
+      "mode": "lf-text",
+      "sha256": "cfd349a83f5ab3d5bb4268ef93b46b1e4542038fb76fe5e7123b8e5fae977de1"
+    },
+    "response/SOURCE-MANIFEST.json": {
+      "mode": "lf-text",
+      "sha256": "946e3fb8bbd4efbc771dda183de01a2bd9bc5aacc28dbb86a88edcdec960af2a"
+    },
+    "response/SOURCES.json": {
+      "mode": "lf-text",
+      "sha256": "905c5860d9c920e41138e582c03010b2b03ee8bf071983ad737d2e57868f6857"
+    },
+    "response/WEIGHTED-COSET-SELECTION.json": {
+      "mode": "lf-text",
+      "sha256": "87c15240aaf48810d103ab3234689bb3ad58024d1b1c0b9106719fc18c5d1945"
+    },
+    "response/build_weighted_coset.py": {
+      "mode": "lf-text",
+      "sha256": "5face855c7e4fb8b6b3954bb20f6c0a662550ca7c6263a1a73c40c857816dd6c"
+    },
+    "verify.py": {
+      "mode": "lf-text",
+      "sha256": "73473689a15f0fe671d35f89dfb276d03704d375be633d2579ddb26fd16f0942"
+    }
+  }
+}
diff --git a/research/contextual-provider-pooling/README.md b/research/contextual-provider-pooling/README.md
new file mode 100644
index 0000000000..c9bc246834
--- /dev/null
+++ b/research/contextual-provider-pooling/README.md
@@ -0,0 +1,29 @@
+# Contextual provider pooling
+
+Conditional kappa: **0.001592576636390595**. Complex saving: **0.0015951169824291220178**.
+
+The offline verifier reconstructs the changed programs, checks physical ownership and costs, and recomputes the exact bound. All inherited all-size and analytic assumptions remain conditional.
+
+This package selects among four fully specified complex suppliers at complete-call boundaries. It inherits PR558's rank 5 entrance promotions and combines their actual local profiles with a resource-aware owner schedule. Among 72 calls it uses 55 n8 providers, 15 n0 providers, one n6 provider at time 46 and one n2 provider at time 71. Five copied controllers are then interleaved and one width 9 packet is pooled across the copies. There are 360 complete calls and 181440 whole helper roles; every owner remainder is counted.
+
+The construction's distinction is contextual provider selection, not adding local savings. Partial promotion groups have a nonlinear frame bill. The selected mix explicitly pays the excess +12 rank 1 -4 rank 2 +4 rank 3 -4 rank 4 relative to one n8 plus one n0 call. The fractional32*n4+40*n8 nomination is retained as discovery evidence, not substituted for the actual integer schedule.
+
+## Replay
+
+From the repository root:
+
+    python -B research/contextual-provider-pooling/verify.py --work ../fresh-contextual-provider-run
+
+Use a new output directory outside the package and keep Python assertions enabled. The verifier must reconstruct source-bound providers, run fresh changed local physical checks, audit the literal mixed/copy owner table, and derive the complete finite invoice and rational outer assembly. Published source claims and local replay receipts do not imply remote GitHub CI success.
+
+## Local proof and dependency scope
+
+Promoted donor corrections commute because their pivot and donor register sets are disjoint. The entrance extension and every resulting frame chain are checked, with cleanup regenerated as literal inverse background arithmetic. Each selected supplier has the same normalized data endpoint and explicit residual/spectator semantics. Complete-call composition then preserves the data action and owner decomposition for arbitrary dirty states.
+
+Canonical input, recipe and output hashes bind n0,n2,n4,n6,n8. Exact local replay checks all 728 columns in both orientations; the changed variants reject 20 omitted-pivot controls in total. Full local charts, all physical owner uses, the complete operation/prefix invoice and outer recurrence remain separate checks.
+
+PR558 supplies the promotion; PR559 the native complex pricing correction; PR555 the cited stronger bit endpoint. The direct ancestry and relevant evaluated work include PR552,551,553,557,556,554,531,534,535,541,543,544,545,547 and 548. Preserved source notices identify the original authors and licenses. The accompanying PR statement distinguishes inherited ingredients from new contributions and discusses the scoped OpenAI proof-source connections and unsuccessful routes.
+
+No numerical benefit is assigned to the tensor-fiber research that was only inspected, to the inherited28-instruction epoch simplification with unchanged child profile, or to an unimplemented stronger block-prefix bound. The final claim retains the inherited all-size and analytic premises and is not a complete formal proof of unconditional faster integer multiplication.
+
+The clean release is tested from Windows CRLF sources. Upload batches use at most 40 files each, with each file below 1 MB; exact reassembly and privacy checks are recorded outside the submitted research folder. Historical receipts and README files retained in docs/ and evidence/ describe predecessor constructions; EXPECTED.json and the fresh verifier output define this release.
diff --git a/research/contextual-provider-pooling/code/alien-avalanche80.cpp b/research/contextual-provider-pooling/code/alien-avalanche80.cpp
new file mode 100644
index 0000000000..568feafc63
--- /dev/null
+++ b/research/contextual-provider-pooling/code/alien-avalanche80.cpp
@@ -0,0 +1,7 @@
+#include <bits/stdc++.h>
+using namespace std;using B=bitset<512>;struct N{bool fixed;B s;int d;vector<int> pre,nxt,regs;};vector<N>a;vector<B>hyper(512);long double pc[11];
+int main(int argc,char**argv){ifstream in(argv[1]);int nf,nn,nr;in>>nf>>nn>>nr;vector<B>fs(nf);vector<int>dims(nf);for(int f=0;f<nf;f++){int n,x;in>>n;dims[f]=round(log2(n));while(n--){in>>x;fs[f][x]=1;}}a.resize(nn);vector<int>last(nr,-1);for(int i=0;i<nn;i++){int fixed,f,k;in>>fixed>>f>>k;auto &n=a[i];n.fixed=fixed;n.s=fs[f];n.d=dims[f];while(k--){int r;in>>r;n.regs.push_back(r);n.pre.push_back(last[r]);n.nxt.push_back(-1);if(last[r]>=0){auto&p=a[last[r]];int j=find(p.regs.begin(),p.regs.end(),r)-p.regs.begin();p.nxt[j]=i;}last[r]=i;}}
+for(int v=1;v<512;v++)for(int x=0;x<512;x++)if(!(__builtin_popcount(v&x)%2))hyper[v][x]=1;for(int d=1;d<11;d++)pc[d]=powl(d,1-.001594L);vector<int>mark(nn,0);int stamp=0;long long cases=0,feasible=0;ofstream out(argv[2]);out<<"{\"passes\":[";bool first=true;
+for(int round=0;round<80;round++){long double best=-1e-13;vector<int>bst;int bv=0,bs=0;for(int sign:{1,-1})for(int v=1;v<512;v++){vector<char>active(nn);for(int i=0;i<nn;i++)active[i]=sign==1?!a[i].s[v]:(a[i].s&~hyper[v]).any();for(int seed=0;seed<nn;seed++)if(active[seed]&&!a[seed].fixed){cases++;stamp++;vector<int>q{seed};mark[seed]=stamp;bool bad=false;for(int pos=0;pos<(int)q.size();pos++){int i=q[pos];const auto &adj=sign==1?a[i].nxt:a[i].pre;for(int j:adj)if(j>=0&&active[j]&&mark[j]!=stamp){if(a[j].fixed){bad=true;break;}mark[j]=stamp;q.push_back(j);}if(bad)break;}if(bad)continue;feasible++;long double d=0;for(int i:q){for(int j:a[i].pre)if(j>=0&&mark[j]!=stamp){int r=a[i].d-a[j].d;assert(r+sign>=0);d+=pc[r+sign]-pc[r];}for(int j:a[i].nxt)if(j>=0&&mark[j]!=stamp){int r=a[j].d-a[i].d;assert(r-sign>=0);d+=pc[r-sign]-pc[r];}}if(d<best){best=d;bst=q;bv=v;bs=sign;}}}
+cerr<<"round "<<round<<" delta "<<setprecision(18)<<best<<" size "<<bst.size()<<" v "<<bv<<" sign "<<bs<<" cases "<<cases<<" feasible "<<feasible<<"\n";if(bst.empty())break;if(!first)out<<",";first=false;out<<"{\"v\":"<<bv<<",\"sign\":"<<bs<<",\"nodes\":[";for(int k=0;k<(int)bst.size();k++){int i=bst[k];if(k)out<<",";out<<i;if(bs==1){B old=a[i].s;for(int x=0;x<512;x++)if(old[x])a[i].s[x^bv]=1;}else a[i].s&=hyper[bv];a[i].d+=bs;}out<<"]}";out.flush();}
+out<<"],\"screened\":"<<cases<<",\"feasible\":"<<feasible<<"}\n";}
diff --git a/research/contextual-provider-pooling/code/alien-flags.cpp b/research/contextual-provider-pooling/code/alien-flags.cpp
new file mode 100644
index 0000000000..2212fd6273
--- /dev/null
+++ b/research/contextual-provider-pooling/code/alien-flags.cpp
@@ -0,0 +1,11 @@
+#include <bits/stdc++.h>
+using namespace std; using B=bitset<512>;
+struct F{B s;int d;};struct N{bool fixed;int f;vector<int> regs,pre,nxt;};
+vector<F> fs;vector<N> ns;long double pc[10];
+bool sub(int a,int b){return (fs[a].s & ~fs[b].s).none();}
+long double change(const vector<int>&v,int f){unordered_set<int>S(v.begin(),v.end());long double z=0;for(int i:v){auto &n=ns[i];for(int j:n.pre)if(j>=0&&!S.count(j)){z+=pc[fs[f].d-fs[ns[j].f].d]-pc[fs[n.f].d-fs[ns[j].f].d];}for(int j:n.nxt)if(j>=0&&!S.count(j)){z+=pc[fs[ns[j].f].d-fs[f].d]-pc[fs[ns[j].f].d-fs[n.f].d];}}return z;}
+int main(int argc,char**argv){ifstream in(argv[1]);int nf,nn,nr;in>>nf>>nn>>nr;fs.resize(nf);ns.resize(nn);for(auto &f:fs){int n,x;in>>n;f.d=round(log2(n));while(n--){in>>x;f.s[x]=1;}}vector<int>last(nr,-1);for(int i=0;i<nn;i++){auto &n=ns[i];int fixed,k;in>>fixed>>n.f>>k;n.fixed=fixed;while(k--){int r;in>>r;n.regs.push_back(r);n.pre.push_back(last[r]);n.nxt.push_back(-1);if(last[r]>=0){auto &p=ns[last[r]];int j=find(p.regs.begin(),p.regs.end(),r)-p.regs.begin();p.nxt[j]=i;}last[r]=i;}}
+for(int d=1;d<10;d++)pc[d]=powl(d,1-.001594L);vector<int>orig;for(auto &n:ns)orig.push_back(n.f);mt19937 rng(20261011);int accepted=0;long double gain=0;
+auto trygroup=[&](vector<int>v){unordered_set<int>S(v.begin(),v.end());vector<int>lo,hi;for(int i:v){for(int j:ns[i].pre)if(j>=0&&!S.count(j))lo.push_back(ns[j].f);for(int j:ns[i].nxt)if(j>=0&&!S.count(j))hi.push_back(ns[j].f);}int best=-1;long double bestdelta=-1e-13L;for(int f=0;f<nf;f++){bool ok=true;for(int l:lo)if(!sub(l,f)){ok=false;break;}if(!ok)continue;for(int h:hi)if(!sub(f,h)){ok=false;break;}if(!ok)continue;long double d=change(v,f);if(d<bestdelta){bestdelta=d;best=f;}}if(best<0)return false;for(int i:v)ns[i].f=best;gain-=bestdelta;accepted++;return true;};
+for(int round=0;round<10;round++){int start=accepted;vector<int>ord(nn);iota(ord.begin(),ord.end(),0);shuffle(ord.begin(),ord.end(),rng);for(int i:ord)if(!ns[i].fixed)trygroup({i});vector<int>seen(nn);for(int i:ord)if(!seen[i]&&!ns[i].fixed){vector<int>v{i};seen[i]=1;for(int k=0;k<(int)v.size();k++){int t=v[k];vector<int>adj=ns[t].pre;adj.insert(adj.end(),ns[t].nxt.begin(),ns[t].nxt.end());for(int j:adj)if(j>=0&&!seen[j]&&!ns[j].fixed&&ns[j].f==ns[i].f){seen[j]=1;v.push_back(j);}}if(v.size()>1)trygroup(v);}cerr<<round<<" accepted "<<accepted<<" gain "<<setprecision(18)<<gain<<"\n";if(start==accepted)break;}
+map<int,int>oldh,newh;for(int i=0;i<nn;i++)for(int j:ns[i].pre)if(j>=0){int o=fs[orig[i]].d-fs[orig[j]].d,n=fs[ns[i].f].d-fs[ns[j].f].d;assert(sub(ns[j].f,ns[i].f));if(o)oldh[o]++;if(n)newh[n]++;}ofstream out(argv[2]);out<<"{\"changes\":[";bool first=true;for(int i=0;i<nn;i++)if(orig[i]!=ns[i].f){if(!first)out<<",";first=false;out<<"["<<i<<","<<ns[i].f<<"]";}out<<"],\"delta\":{";first=true;for(int d=1;d<10;d++)if(newh[d]!=oldh[d]){if(!first)out<<",";first=false;out<<"\""<<d<<"\":"<<newh[d]-oldh[d];}out<<"},\"accepted_groups\":"<<accepted<<"}\n";}
diff --git a/research/contextual-provider-pooling/code/assemble.py b/research/contextual-provider-pooling/code/assemble.py
new file mode 100644
index 0000000000..5ee17f2d05
--- /dev/null
+++ b/research/contextual-provider-pooling/code/assemble.py
@@ -0,0 +1,49 @@
+"""Exact mixed-provider native-complex two-supplier assembly, adapted from PR547 and PR535.
+Mixed admission: exact per-call provider registry and fresh finite invoice required. Native complex model follows PR559.
+Pinned PR555 bit profile is independently repriced, not physically rerun.
+Usage: assemble.py PACKAGE FRESH_COMPLEX_GLOBAL OUTPUT_JSON
+Original upstream attribution retained in the bundled engines and lineage notes.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from decimal import Decimal,localcontext
+import sys,json,hashlib,importlib.util
+if not __debug__:raise RuntimeError('Assertions required')
+P=Path(sys.argv[1]).resolve();C=Path(sys.argv[2]).resolve();out=Path(sys.argv[3]).resolve();assert not out.exists()
+def read(p):return json.loads(p.read_text())
+
+def load(n):
+ s=importlib.util.spec_from_file_location(n,P/'engines'/(n+'.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,B,A=[load(n)for n in ['moment','base_two_moment','outer']];bit=read(P/'inputs/PR555-EXPECTED.json')['nine'];c=Q(bit['bit_lower'])
+owner=read(C/'audit/OWNERS-AND-PROFILE.json');inv=read(C/'audit/PREFIX-AND-INVOICE.json');host=read(C/'hosted/HOSTED.json')
+sha=lambda f:hashlib.sha256(f.read_bytes()).hexdigest()
+assert owner['template_sha256']==inv['template_sha256']==host['template_sha256']
+assert inv['owner_audit_sha256']==sha(C/'audit/OWNERS-AND-PROFILE.json') and all(inv['strict_checks'].values())
+H={int(r):n for r,n in owner['paid_profile'].items()};cert=M.certify(H,73,owner['live'],False);b=Q(cert['lower'])
+cp={'complex_lower':str(b),'complex_global_profile':owner['paid_profile'],'complex_live':owner['live'],'complex_deficit':owner['deficit']}
+assert inv['global_prefix_bits']<inv['charged_prefix_bits'] and inv['charged_prefix_bits'] in (512,1024) and inv['finite']['physical_row_coefficient']<20161
+receipts=[]
+for side,H,m,W,lower,deficit in [('bit',{int(r):n for r,n in bit['profile'].items()},64,bit['bit']['live'],c,10272),('complex',{int(r):n for r,n in cp['complex_global_profile'].items()},73,cp['complex_live'],b,cp['complex_deficit'])]:
+ assert m*W-sum(r*n for r,n in H.items())==deficit and m*m>2*max(H)**2
+ for z,ok in [(lower,True),(lower+Q(1,10**24),False)]:
+  l,u=M.moment(H,m,W,z,side=='bit');ll,uu=B.moment(m,W,list(H.items()),z)
+  if side=='bit':
+   fl,fu=B.moment(m,W,[(1,32*m*m*sum(H.values()))],z);ll+=fl/10**16;uu+=fu/10**16
+  assert(u<1 and uu<1)if ok else(l>1 and ll>1)
+  receipts.append(dict(side=side,endpoint=str(z),accept=ok,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)]))
+assert bit['bit']['two_level_coefficient_bits']<bit['bit']['charged_two_level_coefficient_bits']==512 and bit['bit']['row_coefficient']<20161
+eta=beta=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24);assert 0<s<c and s<(1-beta)*b;chain=[Q(384599,10**10)];cuts=[]
+for _ in range(7):
+ old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0;ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+inv['charged_prefix_bits'])/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+inv['charged_prefix_bits']);cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a)
+q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}};assembly=A.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta);assert len(assembly['strict_constraints'])==47 and all(v>0 for v in assembly['strict_constraints'].values())
+controls=[]
+for name,kk,ee,bb in [('next_grid',k+Q(1,10**18),eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]:
+ try:A.assembly(chain[-1],b,bridge,kk,eta=ee,beta=bb)
+ except AssertionError:controls.append(name)
+ else:raise AssertionError(name)
+def dec(a):
+ with localcontext()as ctx:ctx.prec=60;return str(Decimal(a.numerator)/Decimal(a.denominator))
+r=dict(status='PASS_MIXED_PROVIDER_NATIVE_COMPLEX_AND_CITED_P111_COMPOSITION',kappa=str(k),kappa_decimal=dec(k),complex_lower=str(b),complex_decimal=dec(b),bit_lower=str(c),bit_decimal=dec(c),binding='complex'if (1-beta)*b<c else'bit',gain_over_frozen559_percent=dec(100*(k/Q('0.001592517892053334')-1)),gain_over_prior_delivery_percent=dec(100*(k/Q('0.001591975256487475')-1)),complex_template_sha256=host['template_sha256'],complex_owner_audit_sha256=sha(C/'audit/OWNERS-AND-PROFILE.json'),complex_invoice_sha256=sha(C/'audit/PREFIX-AND-INVOICE.json'),complex_profile=owner['paid_profile'],moments=receipts,bootstrap=cuts,outer={n:str(v)for n,v in assembly['strict_constraints'].items()},controls=controls,scope='Exact composition of the freshly rebuilt selected kernel-promotion providers and their complete mixed-provider controller using the native complex moment from PR559 with the pinned PR555 published bit receipt. The unchanged bit operator is cited, not rebuilt in this package. Inherited all-size compiler, common-label/mutable-source, hosting, precision/tape and analytic interfaces remain conditional. PR555 interleaved phase-B source writes and111 live ports retain its stated H1-H5 and punctured-supplier interface arguments.')
+
+out.write_text(json.dumps(r,indent=2)+'\n');print({n:r[n]for n in ['status','kappa_decimal','binding','gain_over_frozen559_percent']})
diff --git a/research/contextual-provider-pooling/code/build_wave.py b/research/contextual-provider-pooling/code/build_wave.py
new file mode 100644
index 0000000000..82ba7e7938
--- /dev/null
+++ b/research/contextual-provider-pooling/code/build_wave.py
@@ -0,0 +1,34 @@
+from pathlib import Path
+import argparse,json,gzip,hashlib,copy,sys
+if not __debug__:raise SystemExit('Assertions must remain enabled.')
+ap=argparse.ArgumentParser();ap.add_argument('--input',type=Path,required=True);ap.add_argument('--recipe',type=Path,required=True);ap.add_argument('--gk',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();sys.path.insert(0,str(a.gk.resolve()))
+import gk_word as g,gk_common as c
+g.V=c.V=112;g.DATA=c.DATA=7168
+w=json.loads(gzip.decompress(a.input.read_bytes()));old=copy.deepcopy(w);recipe=json.loads(a.recipe.read_text());canon=lambda z:json.dumps(z,sort_keys=True,separators=(',',':')).encode()
+assert hashlib.sha256(canon(w)).hexdigest()==recipe['source_canonical_sha256']
+before=g.profile(w);controls=[];changes=[]
+for k,move in enumerate(recipe['passes']):
+ previous=copy.deepcopy(w);covectors=move.get('covectors',[move.get('v')]);assert all(isinstance(v,int)and 0<v<512 for v in covectors)
+ for sec,i in move['events']:
+  assert sec in ('A','B');E=w[sec][i][-1];new=g.basis(x for x in g.span(E)if all((x&v).bit_count()%2==0 for v in covectors));assert len(new)<len(g.basis(E));w[sec][i][-1]=list(new)
+ after=g.profile(w)
+ # At least one omitted frame change in each collective wave must violate an actual register chain.
+ rejected=None
+ for sec,i in move['events']:
+  changed=w[sec][i][-1];w[sec][i][-1]=previous[sec][i][-1]
+  try:g.profile(w)
+  except AssertionError:rejected=[sec,i]
+  finally:w[sec][i][-1]=changed
+  if rejected is not None:break
+ assert rejected is not None,('no collective-dependency negative control',k)
+ controls.append({'wave':k,'omitted_event':rejected,'rejected':True});changes.append({'wave':k,'events':len(move['events']),'covectors':covectors,'profile':dict(after)})
+after=g.profile(w)
+assert dict(after)=={1:2300,2:440,3:472,4:184,5:56,6:56,8:8}
+for key in old:
+ if key not in ['A','B','cleanup','report']:assert old[key]==w[key],key
+for sec in ['A','B']:assert len(old[sec])==len(w[sec])and all(e[:-1]==f[:-1] for e,f in zip(old[sec],w[sec]))
+w['cleanup']=[g.inverse(e,g.FULL)for e in reversed(w['A']+w['B'])if not 112<=e[1]<224]
+w['report']['local_profile']={str(k):n for k,n in sorted(after.items())}
+a.out.mkdir(parents=True,exist_ok=False);raw=canon(w);data=gzip.compress(raw,compresslevel=9,mtime=0);data=data[:9]+b'\xff'+data[10:];(a.out/'FULL-WORD.json.gz').write_bytes(data)
+r=dict(status='PASS_COLLECTIVE_HYPERPLANE_FRAME_CONTRACTION',source_content_sha256=hashlib.sha256(canon(old)).hexdigest(),word_content_sha256=hashlib.sha256(raw).hexdigest(),before=dict(before),after=dict(after),delta={k:after[k]-before[k]for k in set(before)|set(after)if after[k]!=before[k]},changes=changes,controls=controls,scalar_program_unchanged=True,boundaries_unchanged=True,scope='Exact finite subspace chains and unchanged scalar word. Fresh Clifford phases, full local physical columns and global owner realization are required separately.')
+(a.out/'WAVE-REVIEW.json').write_text(json.dumps(r,indent=2)+'\n',encoding='utf-8',newline='\n');print(json.dumps(r))
diff --git a/research/contextual-provider-pooling/complex-global/MIXED-RESOURCE-PROOF.md b/research/contextual-provider-pooling/complex-global/MIXED-RESOURCE-PROOF.md
new file mode 100644
index 0000000000..d6bf3092b8
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/MIXED-RESOURCE-PROOF.md
@@ -0,0 +1,15 @@
+# Source-bound finite mixtures of complete providers
+
+Two actual OpenAI-library structures informed this construction. RealFlowMixture.mixture_valid and mixture_cost preserve support/conservation and add costs under finite mixing. PeriodicTilingThree.card_stack and its color-partition lemmas realize finite colored products with unique membership and exact multiplicities. The source ledger pins their files. They are structural guides, not Lean proofs of this multiplication algorithm; the sufficient application below is checked independently.
+
+Assume finitely many complete local providers have identical normalized data endpoints on the same ordered ports. For each provider, require a separately checked arbitrary-dirt scalar body, erased private work, exact recursive phase recipes including global phase, and exact input/output normalization wrappers. On a helper placed in a physical family, its endpoint is Q on its assigned residual axes and identity on spectators; it need not be the identity on the entire physical helper.
+
+Choose one provider for every complete invocation. Assign that provider's actual ordered helper widths to distinct idle whole families, disjoint from its active data. Require that all assigned residual axes are pairwise disjoint within every pending child over its entire lifetime. Complete each invocation, including wrappers and private cleanup, before the next. Then the retained data-controller endpoint is unchanged: substitute each checked complete-call identity into the literal chronological product, and finish every pending child on its unassigned coordinates. No averaging of operators, unknown gadget, or shared partial invocation is used. The exact paid profile is the sum of the selected local profiles plus those explicit remainder ranks.
+
+For the selected PR558 owner map, 55 calls place all eight promoted helpers in rank 16 pending children; 15 place them in rank 32 children. Two boundary calls place six and two respectively in rank 16. Select providers n8, n0, n6, n2 accordingly. Every width 4 role in rank 32 becomes width 5, and the pending intervals are compacted in their previous order. A rank 32 pattern (4,9,9,9) thus becomes (5,9,9,9), eliminating its rank 1 remainder. Rank16 patterns and every family/time assignment remain unchanged. Partial providers have a real cooperative cost: the combined n6+n2 profile differs from n8+n0 by +12 rank 1 -4 rank 2 +4 rank 3 -4 rank 4. The invoice includes that penalty exactly.
+
+Make five finite namespaced copies, retaining ambient dimension 73 and eight replicas inside each source bank. The unique partial rank 48 bin is owner replica 6, child 8, port 6, family 6054. Its single width 9 role is helper 141 at stage 4, replica 6, source time 52. Across five copies place these five complete-call roles in clone zero's family 6054 at offsets 0,9,18,27,36 and times 260,...,264. Actual bridge-window checks prove the family idle at all five calls. The resulting remainders replace five rank 39 children by four rank 48 and one rank 3, strictly improving every concave power moment. This is an integer finite realization, not a fractional owner.
+
+The execution template records each call's provider ID and program hash. The registry contains every selected provider's complete program, residual normalizers and Clifford recipes, bound to its canonical word, local checks and independent replay. The physical auditor independently reads those sources, verifies exact phase-review bindings, rederives each selected width and paid profile, and checks whole-family uniqueness, timelines, charts, remainders and genuine wrong-provider controls. The scalar invoice separately pays registry selection, all local work, maximum prefix/adapters and full controller sweeps. Only the final all 47 assembly certifies a numerical kappa.
+
+Finite compilation is literal concatenation: for each of the finitely many controller calls, resolve its stored provider ID and orientation to the explicit serialized program in the registry, then insert that program with its specified whole-family routes and normalization recipes. The emitter and independent auditor both execute this resolver. Unrolling these finitely many fixed blocks yields an ordinary finite instruction list, so provider selection introduces no unknown dispatcher oracle or additional all-size hypothesis. The finite selector/table cost remains explicitly charged.
diff --git a/research/contextual-provider-pooling/complex-global/OAI-SOURCES.json b/research/contextual-provider-pooling/complex-global/OAI-SOURCES.json
new file mode 100644
index 0000000000..28ab3aa6dc
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/OAI-SOURCES.json
@@ -0,0 +1,23 @@
+[
+  {
+    "source": "OAI/Combinatorics/UniformKServer/RealFlowMixture.lean",
+    "sha256": "d8d5d85f7c302edb323001ba96d1ec9dfbbf15457a5af183b6c69685b9917d73",
+    "declarations": [
+      "mixture_valid",
+      "mixture_cost"
+    ],
+    "structure_used": "Finite support/conservation constraints survive pointwise mixtures, with linear cost accounting.",
+    "verification_scope": "Actual source read; not recompiled in this algorithm campaign."
+  },
+  {
+    "source": "OAI/Geometry/PeriodicTiling/StackingContributions.lean",
+    "sha256": "5908e2c006c69ffedaa8aee162fd9dbd83f67dae09c25fceb615bb33632c75c4",
+    "declarations": [
+      "IsColorPartition.eq_of_mem",
+      "card_stack",
+      "IsColorPartition.sum_card"
+    ],
+    "structure_used": "Disjoint colored product strata have exact summed multiplicities and unique color assignment.",
+    "verification_scope": "Actual source read; not recompiled in this algorithm campaign."
+  }
+]
diff --git a/research/contextual-provider-pooling/complex-global/README.md b/research/contextual-provider-pooling/complex-global/README.md
new file mode 100644
index 0000000000..647cb956b4
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/README.md
@@ -0,0 +1,15 @@
+# Frozen changed complex supplier controller
+
+After rebuilding the final local provider with the separately supplied local bundle, run:
+
+    python -B replay.py --local PATH_TO_FRESH_LOCAL --out NEW_OUTPUT_DIRECTORY
+
+The five stages bind the fresh supplier, emit the literal whole-owner controller, independently audit all physical charts and seven negative controls, recount the finite invoice, and certify its exact complex moment. The cited old bit result used in the last stage is only a regression fixture. Use the outer package assembly for the final improved bit supplier and final kappa.
+
+The final owner map is the checked witness; no optimization is rerun. All resource counts, frames, times, source hashes, scalar prefix and paid profile are rechecked. The separate all-size interfaces retain their stated scope.
+
+Expected complex saving: 1594507308884431019637/1000000000000000000000000. Both the source archive's attribution notices and licenses are retained.
+
+This round uses the fresh weighted-coset avalanche8 local supplier. RESOURCE-TRANSFERS.md proves the two sufficient cross-field connections and records their actual contribution. TWO-RESOURCE-TECHNIQUES.md is retained historical packing provenance, with its earlier supplier price.
+
+Final selected supplier also includes 12 independently checked cold-dirt quotient rewrites, saving 624 scalar additions per local orientation without changing the paid profile or owner widths. The controller is freshly emitted and audited against this final source, not an earlier receipt.
diff --git a/research/contextual-provider-pooling/complex-global/RESOURCE-PROOF.md b/research/contextual-provider-pooling/complex-global/RESOURCE-PROOF.md
new file mode 100644
index 0000000000..0d71dbdbb8
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/RESOURCE-PROOF.md
@@ -0,0 +1,21 @@
+# Five-clone remainder pooling
+
+Fix a complete arbitrary-dirt local wrapper with physical helper endpoint Q on its assigned residual coordinates and identity on spectators. Start from a checked controller with eight replicas, 73 ambient axes, and 72 complete invocations. Make five copies of its data-family set. Interleave the five corresponding complete invocations at each original invocation time. The local ambient dimension remains 73; this construction does not widen a local call to 40 sets of residual axes.
+
+Relabel every data family in clone c by adding 7168 c and every invocation/owner replica by adding 8 c. Each cloned owner's original idle window contains all five copies of every formerly admitted invocation time: the source event projection on that owner's replica is unchanged, and extra intervening events belong to other replicas. Borrowed spectators are restored at each complete invocation. Private centers, tableau, and coefficient workspaces may therefore be reused between sequential complete invocations.
+
+In the source certificate, owner replica 1, child 10, port 107 (family 1787) contains exactly one width-9 helper. It is helper 376 in stage 2, invocation replica 2, source time 12. Its pending child has rank 48. For clone c=0,...,4, redirect just this helper to clone zero's family 1787, on pending offsets 9c. These five invocations occur at times 60,...,64. The destination family is idle throughout, is not an active data family, and occurs only once in each complete call. The five assigned coordinate intervals are disjoint. Source-bound full 73-column charts implement their actual residual coordinates; no helper is split between families.
+
+The clone-zero pending child now uses 45 axes and pays one rank-3 remainder. The other four formerly partial children pay rank 48. Every other local child, bridge, and remainder is unchanged. Hence the complete recursive profile changes from five copies of the original by
+
+    -5 children of rank 39 +4 children of rank 48 +1 child of rank 3.
+
+Both total rank mass and live stock scale by five: live 35840, deficit 12800. For every 0<a<1, strict concavity and 39=(4*48+3)/5 give
+
+    4*48^a +3^a < 5*39^a.
+
+Thus the recurrence moment strictly improves, without a fractional child or fractional owner. The exact finite invoice, larger prefix charge, and all 47 outer inequalities must also pass; the inequality alone is not a numerical kappa certificate.
+
+The literal emitter and independently structured controller auditor check 181440 helper roles, all 360 complete calls, source widths, active-data exclusion, one family per helper, exact owner idle intervals including bridges, pairwise disjoint pending axes, 73-column charts, all remainders and source hashes. Seven genuine negative controls test aliasing, active/private owners, residual width, spectator coordinates, omitted remainder, and understated physical reserve.
+
+The earlier 145-pattern integer optimization found the existing eight-replica allocation, whereas its fractional relaxation had exactly this denominator-five residue. That floating optimization nominated the construction; the explicit five-clone witness and strict concavity prove it. No exact global integer-optimality claim is made.
diff --git a/research/contextual-provider-pooling/complex-global/RESOURCE-RESEARCH.md b/research/contextual-provider-pooling/complex-global/RESOURCE-RESEARCH.md
new file mode 100644
index 0000000000..3434f896a3
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/RESOURCE-RESEARCH.md
@@ -0,0 +1,13 @@
+# Resource search and selected construction
+
+The selected new construction is five-copy whole-owner remainder pooling. It turns the fractional denominator-five pattern left by the previous allocation into a literal finite controller. The exact whole-owner map and full geometric audit, rather than a fractional relaxation, establish the new recursive profile. See the separate resource proof. The search did not establish global novelty or unrestricted optimality.
+
+The initial search first checked cumulative rank-four entrance retirement. Fourteen disjoint groups were evaluated individually in cold and line-gauge modes; four cumulative all/alternating constructions had exactly additive local profiles. A complete-capacity mixed-provider integer gate retained zero changed calls. Those frame-legal nominees were not presented as scalar-audited suppliers or achieved algorithms.
+
+PR553 supplies formal sorted-width matching and compaction results, with source/physical associations outside the stated formal scope. It did not itself change the numerical provider. PR555 improves the bit supplier by puncturing nine roots and adding nineteen carriers to the R420 base; its actual selected supplier has R439. Its larger bit saving does not remove the complex bottleneck. The bit and complex decoder constants differ, so an additional complex port deletion was not priced as a free gain.
+
+PR554 jointly retimes the PR550 scalar expansion. We transplanted that expansion onto our current weighted word; it was paid-profile neutral because the previous eight wave contractions already lowered the relevant two frames. The expanded word remains a useful distinct dependency graph for future search. All B scalar payloads match PR554, while twelve A scalar payloads differ due to retained weighted-coset rewrites. Applying all PR554 frames to the actual current scalar word passes frame chains but loses saving. Pointwise meet and join also pass and lose. The literal 120-change subset alone fails a frame containment, so it was rejected. The 85 differing frames split into 33 consecutive-wire components; all 99 direct/meet/join component tests were legal, and none improved the paid profile. These are bounded outcomes, not impossibility theorems.
+
+Finally, the complete 145-pattern capacity model was solved with fixed linear rank mass removed and the curvature objective scaled by one billion. HiGHS returned the existing integer profile with zero reported gap. This numerical result is not an exact branch-and-bound certificate. The fractional optimum differs only by replacing one rank-39 remainder with four fifths of rank 48 and one fifth of rank 3. Rational recurrence intervals give an exact moment difference of approximately 0.00014058621039172642 at the previous certified exponent. The corresponding nominal saving gap is approximately 6.37393227e-9.
+
+That denominator-five structure led to the actual winning construction: five finite source controllers, still ambient dimension 73, with five copies of one width 9 helper placed in a single rank 48 pending child during five distinct complete calls. The final physical audit uses the separately checked epoch14 supplier and verifies all 181440 helper roles. Numerical kappa must come from the final prefix invoice and all 47 scalar inequalities; discovery prices alone are not the deliverable's claim.
diff --git a/research/contextual-provider-pooling/complex-global/RESOURCE-TRANSFERS.md b/research/contextual-provider-pooling/complex-global/RESOURCE-TRANSFERS.md
new file mode 100644
index 0000000000..bb6e0adba2
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/RESOURCE-TRANSFERS.md
@@ -0,0 +1,46 @@
+# Two sufficient cross-field resource transfers
+
+## Conserved network flows to space-time owner exchanges
+
+Fix the actual controller event order and each pending child's legal call set. Let x be an integer assignment to pattern/time/width variables. Its exact equality rows encode the number of physical ports in every group, width multiplicities of every selected pattern, and the number of helpers of each width required by every call. Write these rows as Ax=b; all upper bounds encode at most one occurrence per physical owner at each call.
+
+If an integer signed exchange z satisfies Az=0, x+z is nonnegative and all row upper bounds remain valid, then x+z has a constructive legal whole-owner realization. For each selected pattern of multiplicity n, distribute its width-incidences among its distinct positions with column sum n and time-row sums at most n. Regularize this bipartite multigraph with dummy vertices/edges and decompose it into n perfect matchings. Each matching is one physical port; delete the dummy edges. Therefore no physical family occurs twice in a call. Concatenate pattern positions to give disjoint pending axes, and bind actual helpers by a width-preserving bijection. Rebuild every physical orthogonal chart from its source entrance frame. The unchanged normalized complete-invocation interface then supplies the actual residual action Q, identity on spectators, and separately audited scalar arbitrary-dirt restoration.
+
+This is the precise conservation-to-physical-lift statement. The analogy with chip firing is algebraic conservation Az=0; arbitrary abstract chip-firing moves are not automatically legal, since positivity, window support and owner capacity are indispensable. For a simple edge network a cycle incidence vector has zero boundary; for the multiway pattern system we check Az=0 directly rather than falsely claim every exchange is a graph cycle.
+
+The read OpenAI source OAI/Combinatorics/Hamiltonian/Circulation.lean develops conserved flows and support-minimal flow circuits (FlowCircuit.proportional), then relates a dual conserved gradient to an oriented cycle. Its surface-specific theorem is not applied to the multiplication geometry. The shared zero-boundary structure motivated the explicit incidence formulation above.
+
+## Doubly stochastic mixing to feasible recurrence concentration
+
+Let r and s be nonnegative integer vectors of paid child ranks, padded with zeros to equal length. Suppose an explicitly supplied doubly stochastic matrix P satisfies r=P*s. For every exponent 0 < a < 1, concavity gives r_i^a >= sum_j P_ij*s_j^a. Sum the rows and use column sums one to obtain sum_i r_i^a >= sum_j s_j^a. Thus replacement r→s weakly improves every relevant recurrence moment. It is strict whenever a row mixes two unequal positive/zero ranks nontrivially. The total rank is unchanged. Dividing by common ambient m^a preserves the inequality, so any old strict recurrence certificate remains strict.
+
+This alone is not a new algorithm: s must be produced by the preceding legal physical exchange theorem, or another explicit normalized-call construction. The matrix proves the pricing statement; the literal owner witness proves feasibility. This separation prevents an abstract majorization claim from hiding impossible time transport.
+
+A basic exact certificate replaces (u,v), with 0 < u <= v, by(u-d,v+d), where 0 < d <= u. Set theta=(v-u+d)/(v-u+2d). The symmetric doubly stochastic matrix with diagonal theta and off-diagonal1-theta sends the new ordered pair to the old pair. Consequently this physically realizable concentration strictly decreases the paid power sum. Chains of such rational witnesses multiply to another doubly stochastic matrix.
+
+The read Mathlib source Analysis/Convex/DoublyStochasticMatrix.lean defines both stochastic marginal conditions, proves their row/column-sum equivalence and convex closure, and includes permutation matrices. Jensen's inequality and the specialization to the paid moment are proved directly above; no new Lean compilation or global novelty is claimed.
+
+## Bounded outcomes so far
+
+An all-pattern integer capacity screen enumerated every 5/8/9 pattern fitting ranks 8, 16, 32, 48 at the baseline inventory. Its optimal floating linear objective returned exactly the already realized saturation profile. This is a bounded numerical optimization result, not an exact universal optimality theorem. Alternative stage geometries K = 5 and K = 6 gave optimistic nominal savings 0.00156922111 and 0.00152941033, both below the selected 0.00159351942. K = 3 could not fit the total helper width. None is asserted as a new improvement. Search therefore turns to changed provider signatures and heterogeneous complete-call choices rather than repeatedly moving a fixed optimal-looking stock.
+
+## Actual parent contraction application
+
+The parent discovered a source-level waveflag contraction with paid change rank 2 + rank 3 to rank 1 + rank 4. Its price certificate is exact and uniform in the recurrence exponent:
+
+    (2,3)^T = [[2/3,1/3],[1/3,2/3]] (1,4)^T.
+
+Both rows mix unequal endpoints, so strict concavity gives 1^a + 4^a < 2^a + 3^a for every 0 < a < 1. Multiplying this two-by-two certificate by the number of actual contractions proves the complete local paid improvement. Ordered helper widths remain unchanged, so the selected whole-owner slot map is reusable after fresh source-bound physical charts and local phase verification. This is a concrete application of the sufficient majorization theorem. The parent supplies the physical waveflag proof and its exact scalar replay; this file does not replace either.
+
+## Completed finite application
+
+The frozen parent construction performs 16 such local rank transfers in each of 72 complete calls. The unchanged ordered 504-helper widths permit the same literal 36,288-role owner map. Fresh global emission rebuilds all 2,972 actual 73-column charts from the changed local source; independent chronology, full-owner uniqueness, pending intervals, residual and spectator axes, seven mutation controls and the complete finite scalar invoice all pass. Reusing slot identities is justified by the exact incidence equalities and source-bound chart reconstruction, not by assuming old charts certify a new source.
+
+The new global profile is
+
+    {1:165600,2:32128,3:35907,4:13248,
+     5:4032,6:4032,7:208,8:576,39:1,48:1660}.
+
+Its exact certified complex saving is 1594507308884431019637/10^24, or 0.001594507308884431019637. This is the supplier saving; the top-level package computes final kappa from both admitted suppliers and all 47 constraints. The retained all-size interfaces remain explicit. No numerical gain is attributed to reusing the same optimal-looking resource layout: the genuine new paid gain is the parent's physical frame contraction, whose uniform improvement is proved by the exact majorization certificate above.
+
+The final weighted-coset local refinement preserves that exact paid profile and all helper widths while removing 624 scalar additions per local orientation. The complete global replay was repeated on this final source; the certified complex saving is unchanged. Its actual prefix and invoice are stored in FINAL-RESOURCE-REVIEW.json.
diff --git a/research/contextual-provider-pooling/complex-global/SAT-OWNERS.json.gz b/research/contextual-provider-pooling/complex-global/SAT-OWNERS.json.gz
new file mode 100644
index 0000000000..243bc54840
Binary files /dev/null and b/research/contextual-provider-pooling/complex-global/SAT-OWNERS.json.gz differ
diff --git a/research/contextual-provider-pooling/complex-global/SAT534-PLAN.json b/research/contextual-provider-pooling/complex-global/SAT534-PLAN.json
new file mode 100644
index 0000000000..bfa9e846a0
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/SAT534-PLAN.json
@@ -0,0 +1,11389 @@
+{
+  "status": "SOURCE_BOUND_PORTED534_STATIC44_SATURATION_PLAN",
+  "mode": "frozen-saturation-with-exact-eight-wave-contraction",
+  "K": 4,
+  "T": 8,
+  "M": 73,
+  "L": 9,
+  "live": 7168,
+  "deficit": 2560,
+  "profile": {
+    "1": 165600,
+    "2": 32128,
+    "3": 35907,
+    "4": 13248,
+    "5": 4032,
+    "6": 4032,
+    "7": 208,
+    "8": 576,
+    "39": 1,
+    "48": 1660
+  },
+  "patterns": [
+    [
+      [
+        0,
+        0
+      ],
+      [
+        9
+      ],
+      80
+    ],
+    [
+      [
+        0,
+        0
+      ],
+      [
+        8,
+        8
+      ],
+      32
+    ],
+    [
+      [
+        0,
+        2
+      ],
+      [
+        8,
+        8
+      ],
+      56
+    ],
+    [
+      [
+        0,
+        2
+      ],
+      [
+        5,
+        9
+      ],
+      56
+    ],
+    [
+      [
+        0,
+        1
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        3
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        4
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        6
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        5
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        7
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        8
+      ],
+      [],
+      98
+    ],
+    [
+      [
+        0,
+        8
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      14
+    ],
+    [
+      [
+        0,
+        10
+      ],
+      [],
+      66
+    ],
+    [
+      [
+        0,
+        10
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      46
+    ],
+    [
+      [
+        0,
+        9
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        11
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        12
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        13
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        14
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        15
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        16
+      ],
+      [
+        8,
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        17
+      ],
+      [
+        8,
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        0
+      ],
+      [
+        8,
+        8
+      ],
+      68
+    ],
+    [
+      [
+        1,
+        0
+      ],
+      [
+        5,
+        9
+      ],
+      44
+    ],
+    [
+      [
+        1,
+        2
+      ],
+      [
+        9
+      ],
+      14
+    ],
+    [
+      [
+        1,
+        2
+      ],
+      [
+        8,
+        8
+      ],
+      56
+    ],
+    [
+      [
+        1,
+        2
+      ],
+      [
+        5,
+        9
+      ],
+      42
+    ],
+    [
+      [
+        1,
+        1
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        3
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        4
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        6
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        5
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        7
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        8
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      112
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+  "numeric_saving": 0.0015932455964101089,
+  "solver_status": 1,
+  "gap": 1.1667391998196086e-07,
+  "local_profile": {
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+    "2": 456,
+    "3": 488,
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+  },
+  "numeric_saving_scope": "Discovery metadata only; fresh exact global certificate supersedes."
+}
diff --git a/research/contextual-provider-pooling/complex-global/SCREEN-RECEIPT.json b/research/contextual-provider-pooling/complex-global/SCREEN-RECEIPT.json
new file mode 100644
index 0000000000..5509841f55
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/SCREEN-RECEIPT.json
@@ -0,0 +1,16 @@
+{
+  "fixed_inventory": {
+    "scope": "All width5/8/9 patterns at fixed K4,T8; floating objective with exact integer row check",
+    "same_histogram": true,
+    "solver_status": "Optimization terminated successfully. (HiGHS Status 7: Optimal)"
+  },
+  "alternative_stages": {
+    "5": 0.0015692211099619933,
+    "6": 0.0015294103291623729
+  },
+  "K3": {
+    "scope": "Necessary total-capacity check only",
+    "demand": 232736,
+    "pending_capacity": 200704
+  }
+}
diff --git a/research/contextual-provider-pooling/complex-global/SOURCE-TRANSFERS.json b/research/contextual-provider-pooling/complex-global/SOURCE-TRANSFERS.json
new file mode 100644
index 0000000000..571c31eb3f
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/SOURCE-TRANSFERS.json
@@ -0,0 +1,21 @@
+[
+  {
+    "path": "OAI/Combinatorics/Hamiltonian/Circulation.lean",
+    "sha256": "e369fc93872bb65a36a48c1b7997540e74e279eab3a7bf31000e8ce3c20c4e26",
+    "declarations": [
+      "FlowCircuit.proportional",
+      "oriented_face"
+    ],
+    "scope": "Read source only; no new Lean compilation"
+  },
+  {
+    "path": "Mathlib/Analysis/Convex/DoublyStochasticMatrix.lean",
+    "sha256": "02ab3084bf1c107203989593ed23c4654f308aa5b26161295c38bfdd294e6120",
+    "declarations": [
+      "mem_doublyStochastic_iff_sum",
+      "convex_doublyStochastic",
+      "permMatrix_mem_doublyStochastic"
+    ],
+    "scope": "Read source only; no new Lean compilation"
+  }
+]
diff --git a/research/contextual-provider-pooling/complex-global/SOURCES.json b/research/contextual-provider-pooling/complex-global/SOURCES.json
new file mode 100644
index 0000000000..bfc6fabd0a
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/SOURCES.json
@@ -0,0 +1,21 @@
+{
+  "scope": "Source-read adaptation; no Lean compilation or global novelty claim",
+  "sources": [
+    {
+      "path": "OAI/Probability/SwitchChain/SwitchInFiber.lean",
+      "sha256": "53d03b1ddef801b54474f0f0c56b3bf00dcab902b08093ea0f6eeacd2bfdd38b",
+      "declarations": [
+        "sameFiber_of_same_side",
+        "switchStep_sameFiber"
+      ]
+    },
+    {
+      "path": "OAI/Computability/MatchingCount/CutAlgebra.lean",
+      "sha256": "048e26d6eaabd92329acad1b9c57f740a23cfdafa2a3e1cb6113e1477c84af68",
+      "declarations": [
+        "cut_submodular",
+        "cut_push"
+      ]
+    }
+  ]
+}
diff --git a/research/contextual-provider-pooling/complex-global/TWO-RESOURCE-TECHNIQUES.md b/research/contextual-provider-pooling/complex-global/TWO-RESOURCE-TECHNIQUES.md
new file mode 100644
index 0000000000..6c9da1f090
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/TWO-RESOURCE-TECHNIQUES.md
@@ -0,0 +1,67 @@
+# Two source-derived resource constructions
+
+These are sufficient constructions for complete-owner schedules. They preserve each complete invocation's physical endpoint: Q on the assigned residual coordinates, identity on spectators, with scalar-body arbitrary-dirt restoration certified separately. They do not replace the retained all-size multiplication hypotheses.
+
+## 1. Exchange paths inside a fixed physical owner fiber
+
+Start with a source-bound legal schedule and its complete physical slots. For each call c, let E_c be its available occurrences of width-nine slots. A selected subset S must contain exactly four elements of every E_c. Shrink selected slots from width nine to width eight. Reassign the new provider's width-five, width-eight, and width-nine helpers bijectively to the matching-width slots of that same call, and repack each pending bin contiguously in its original occurrence order.
+
+Sufficient conclusion: the resulting assignment is legal at the resource level. Each call retains its exact set of physical owner families and times; no active data owner is added, no owner is aliased, and every occurrence remains in its original legal idle interval. Packing only shrinks widths, so the concatenated intervals fit their pending child. The final chart must be rebuilt from the assigned helper's actual frame; matching widths alone never proves chart equality. With this chart check and the new provider's endpoint certificate, the whole physical schedule is admitted under the same interface.
+
+A same-call exchange S -> S - {e} + {f}, where e is selected and f is unselected in E_c, preserves the call quota. It is a two-edge exchange path. Adding an auxiliary complement assignment makes it a standard four-edge bipartite switch: selected and unselected degrees are preserved in the extended fiber. Any finite sequence of these exchanges is safe, irrespective of intermediate changes in the remainder histogram. Acceptance is based on the full paid moment, not a local entropy heuristic.
+
+Source read: OAI/Probability/SwitchChain/SwitchInFiber.lean, in particular sameFiber_of_same_side and switchStep_sameFiber. The source proves a degree-constrained graph switch stays in a resampling fiber; it does not itself prove this multiplication admission theorem. The physical proof above supplies that missing specialization.
+
+## 2. Concave remainder costs as an explicit cut network
+
+Let a be fixed with 0<a<1, let r_b be a pending bin's original remainder, and let x_b count the selected shrink events incident to bin b. Its added paid moment before common normalization is
+
+    g_b(x_b) = (r_b+x_b)^a - r_b^a.
+
+The complete objective is the new provider's fixed local histogram plus sum_b g_b(x_b), together with the unchanged controller terms. The increments d_j=g(j)-g(j-1) are nonnegative and decreasing. For a bin of degree d,
+
+    g(x) = d_d*x + sum_{k=1}^{d-1} (d_k-d_{k+1})*min(x,k).
+
+Proof: both sides vanish at zero; their j-th increments equal d_d + sum_{k=j}^{d-1}(d_k-d_{k+1})=d_j. Every coefficient is nonnegative. Each term lambda*min(x,k) is an explicit cut gadget: for every incident event vertex e, add an arc e -> z of capacity lambda, and add z -> sink of capacity lambda*k. With selected event vertices on the source side, minimizing over the auxiliary vertex z gives precisely lambda*min(x,k). The linear term uses event-to-sink arcs. This represents the whole remainder objective as a cut potential, with no unknown optimization oracle.
+
+Source read: OAI/Computability/MatchingCount/CutAlgebra.lean, cut_submodular and cut_push. Its pointwise cut submodularity and exact contraction/lift identity justify graph-level aggregation. Here the discrete-concavity identity supplies the explicit gadget representation. Exact quotas |S intersect E_c|=4 remain additional constraints; unconstrained minimum cut does NOT solve that constrained problem automatically. Our bounded native search uses the potential to accept legal exchanges, and the literal endpoint witness is independently checked. There is no global optimality claim.
+
+## 3. Constructive lift from pattern counts to literal owners
+
+A bin group consists of 112 physical ports sharing one owner replica, pending child, rank and legal time set. For each pattern p, choose n_p ports and a list of helper widths w_1,...,w_d with sum at most the pending rank. Let x_(p,t,w) be nonnegative integers. Require:
+
+- sum_t x_(p,t,w) equals n_p times the multiplicity of w in p;
+- sum_w x_(p,t,w) is at most n_p for each pattern and time;
+- across all groups and patterns, each call t receives its exact provider width inventory;
+- only times in the actual group's legal idle interval occur.
+
+These conditions construct a complete-owner assignment. Split each width's incidences among its distinct positions in the pattern, each position having degree n_p. Form the bipartite multigraph whose left vertices are times and right vertices are pattern positions. Its maximum degree is n_p; add dummy vertices and edges until it is n_p-regular. For every subset S of left vertices, n_p|S| edges enter at most n_p|N(S)| slots, so Hall's condition holds. Remove a perfect matching and repeat. The n_p matchings are literal ports. Every port receives one incidence for each pattern position, never two incidences at the same time. Deleting dummy edges therefore yields the exact desired complete-owner slots. Assign each call's actual helpers bijectively to its matching-width slots. Offsets are contiguous partial sums of the pattern widths.
+
+This is an explicit sufficient lifting theorem, not an assertion that aggregate counts alone imply physical feasibility. The integer time rows, matching decomposition and final independently reconstructed physical chart are all checked. It also explains the exchange-fiber structure: different matching decompositions preserve the same exact time and pattern margins. The earlier cut potential supplies remainder costs before this constructive lift; the final broader integer pattern search additionally permits changes to pattern counts. No theorem about globally optimal constrained cuts is claimed.
+
+## Frozen concrete result
+
+The final provider combines the static44 response selection, PR534 frame lift and one cold-dirt quotient simplification. The final local histogram is
+
+    {1:2284,2:456,3:488,4:168,5:56,6:56,8:8}.
+
+Its 504 helpers have widths 56x5,156x8,292x9. A bounded finite pattern/time search selected these counts across all owner replicas:
+
+    rank8: 5376*[8]
+    rank16: 2928*[8,8],448*[5,9],208*[9]
+    rank32: 3584*[5,9,9,9]
+    rank48: 1923*[9,9,9,9,9],1*[9],1660*[]
+
+The literal matching lift produces 36,288 helper roles across 72 complete calls and 16,128 pending bins. All actual 2,972 full 73-column charts, per-replica event orders, whole-owner uniqueness, spectator axes and residual endpoints pass the independent physical audit; seven genuine corruptions reject. The resulting paid global histogram is
+
+    {1:164448,2:33280,3:37059,4:12096,
+     5:4032,6:4032,7:208,8:576,39:1,48:1660}.
+
+The exact deficit is 2,560 at m=73, live stock 7,168 and physical stock 7,682. The fresh scalar invoice charges prefix512 for measured225, and row20161 for measured16467. The certified complex saving is
+
+    b = 796759709641153381751 / 500000000000000000000000
+      = 0.001593519419282306763502.
+
+This is a complex supplier saving, not final kappa. The outer assembly must combine it with the independently admitted bit supplier through all strict constraints. All-size compiler, precision/tape and analytic-transfer hypotheses remain the retained interfaces.
+
+The earlier fixed-slot C++ exchange search gave b=0.001590643179579185038482 with the static44 provider and is preserved as a passed intermediate. The final broader pattern search stopped at its finite time limit with a feasible integer witness; no global optimum is asserted. Replaying the final witness needs Python's standard library only, not SciPy, HiGHS, or the optimizer. Both OpenAI sources were read and adapted; neither was newly Lean-compiled. These sources informed the two resource constructions, rather than establishing a claim of two independently additive numerical gains.
diff --git a/research/contextual-provider-pooling/complex-global/WAVE-MAJORISATION.json b/research/contextual-provider-pooling/complex-global/WAVE-MAJORISATION.json
new file mode 100644
index 0000000000..b3b738d77d
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/WAVE-MAJORISATION.json
@@ -0,0 +1,32 @@
+{
+  "status": "EXACT_SUFFICIENT_MAJORISATION_CERTIFICATE",
+  "old": [
+    2,
+    3
+  ],
+  "new": [
+    1,
+    4
+  ],
+  "matrix": [
+    [
+      "2/3",
+      "1/3"
+    ],
+    [
+      "1/3",
+      "2/3"
+    ]
+  ],
+  "row_sums": [
+    "1",
+    "1"
+  ],
+  "column_sums": [
+    "1",
+    "1"
+  ],
+  "interval": "0<a<1",
+  "conclusion": "Every proved physical replacement of rank2+rank3 by rank1+rank4 strictly decreases the paid power sum at unchanged rank mass.",
+  "physical_scope": "Parent exact waveflag contraction supplies physical legality. This certificate alone does not assert that contraction or any final global replay."
+}
diff --git a/research/contextual-provider-pooling/complex-global/audit_clone.py b/research/contextual-provider-pooling/complex-global/audit_clone.py
new file mode 100644
index 0000000000..ed5f67ed6e
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/audit_clone.py
@@ -0,0 +1,155 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: VERIFIED_VARIANT POOLED_HOSTED OUT.json [--mutation-controls]
+The local provider is read from VERIFIED_VARIANT, never from a baseline width histogram.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json');V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers']);assert V==112 and canon['h']==9; width=[9-len(canon['frames'][canon['start'][2*V+h]])for h in range(R)];prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=40;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=360;HOSTED=CALLS*R
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(V)]
+# Bind the selected provider's actual normalization recipes, including newly
+# selected entrance frames; a baseline recipe registry cannot silently survive.
+required_artifacts={'split-centres/CANONICAL-WORD.json.gz','split-centres/LOCAL-PROGRAMS.json.gz','split-centres/LOCAL-CHECKS.json','split-centres/RESIDUAL-ADAPTERS.json','work/complex-nine-native/DATA-PHASES.json'}
+assert required_artifacts <= set(summary['source_artifacts'])
+adapter_path=BASE/'split-centres/RESIDUAL-ADAPTERS.json'
+assert hashlib.sha256(adapter_path.read_bytes()).hexdigest()==parent['residual_adapter_sha256']
+adapters=read(adapter_path)['recipes']
+for h,w in enumerate(width):
+ if w<9:
+  f=canon['start'][(2*V)+h];a=adapters[str(f)]
+  assert a['frame']==f and a['vectors']==canon['frames'][f] and a['rank']==w and a['entrance_rank']==9-w
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_programs']==parent['local_programs']and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert len(t['calls'])==CALLS and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','exact_local_clifford_recipe_sha256','residual_adapter_sha256','adapter_policy'):assert t[key]==parent[key]
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==CALLS
+ all_local=[];perrep={r:[]for r in range(T)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<T and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   assert e==expected
+   assert 0<=e['time']<CALLS and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[DATA,DATA]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,DATA],charged_calls_per_cover=DATA)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[],children=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,DATA],charged_calls_per_cover=DATA)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time')}=={k:v for k,v in old.items()if k!='owners'}
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:(2*V)]==old['owners'][:(2*V)]
+  for h,(family,route)in enumerate(own[(2*V):]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,(8*V));fampair,sub=divmod(sub,(2*V));side,port=divmod(sub,V)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*V+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(T)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*(8*V)+(2*pairs[i]+sides[i])*V+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==12800 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=CALLS)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ if '--mutation-controls' not in sys.argv[4:]:return
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA))
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=12800,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],widths=dict(sorted(Counter(width).items())),scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses the new selected local program bound by fresh scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=12800,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
+# Literal residual frames are a compact export of the already checked offsets,
+# not another global replay. Every row names its actual inherited axes.
+frames=[]
+for z in ct['idle_children']:
+ axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes']))
+ tail=axes[z['pending_offset']:]
+ assert len(tail)==z['rank']
+ frames.append(dict(z,orthogonal_axes=tail))
+frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode()
+(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(gzip.compress(frame_raw,mtime=0))
+frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'],
+ uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames),
+ rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())),
+ source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(),
+ scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.')
+(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n')
+
diff --git a/research/contextual-provider-pooling/complex-global/audit_clone_lift.py b/research/contextual-provider-pooling/complex-global/audit_clone_lift.py
new file mode 100644
index 0000000000..78d98c9d8b
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/audit_clone_lift.py
@@ -0,0 +1,80 @@
+"""Independent exact five-controller source lift. Imports no builder/emitter."""
+import argparse, copy, gzip, hashlib, json
+from collections import Counter
+from pathlib import Path
+
+def raw(p):
+ b=p.read_bytes();return gzip.decompress(b)if p.suffix=='.gz'else b
+
+def read(p):return json.loads(raw(p))
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def content(p):return hashlib.sha256(raw(p)).hexdigest()
+def main():
+ p=argparse.ArgumentParser(description=__doc__);p.add_argument('--source-base',type=Path,required=True);p.add_argument('--clone-base',type=Path,required=True);p.add_argument('--output',type=Path,required=True);p.add_argument('--mutation-controls',action='store_true');a=p.parse_args()
+ oldpath=a.source_base/'split-centres/GLOBAL-TEMPLATE.json.gz';newpath=a.clone_base/'split-centres/GLOBAL-TEMPLATE.json.gz';old=read(oldpath);new=read(newpath)
+ canon=read(a.source_base/'split-centres/CANONICAL-WORD.json.gz');replay=read(a.source_base/'split-centres/INDEPENDENT-LOCAL-REPLAY.json');programs=read(a.source_base/'split-centres/LOCAL-PROGRAMS.json.gz')
+ assert canon['v']==112 and canon['R']==504 and canon['h']==9
+ assert old['m']==73 and len(old['calls'])==72 and {(c['stage'],c['replica'])for c in old['calls']}=={(s,r)for s in range(9)for r in range(8)}
+ assert old['local_programs']==programs and set(programs)=={'forward','backward'}
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==sha(a.source_base/'split-centres/CANONICAL-WORD.json.gz')
+ assert replay['local_programs_sha256']==sha(a.source_base/'split-centres/LOCAL-PROGRAMS.json.gz')
+ assert all(replay['local'][o]['all_exact_columns']==728 and replay['local'][o]['private_work_erased']for o in programs)
+ assert old['physical']-old['live']==canon['R']+len(canon['centers'])+2==514
+ assert all(len(c['owners'])==728 and all(0<=f<old['live']for f,route in c['owners'])for c in old['calls'])
+ sources={}
+ for name in ['split-centres/CANONICAL-WORD.json.gz','split-centres/LOCAL-PROGRAMS.json.gz','split-centres/LOCAL-CHECKS.json','split-centres/INDEPENDENT-LOCAL-REPLAY.json','split-centres/RESIDUAL-ADAPTERS.json','split-centres/CLIFFORD-RECIPES.json','split-centres/CLIFFORD-REVIEW.json','work/complex-nine-native/DATA-PHASES.json']:
+  src=a.source_base/name;dst=a.clone_base/name;assert src.read_bytes()==dst.read_bytes(),name;sources[name]=sha(src)
+ C=5;D=7168;W=old['live'];assert W>D
+ def fam(f,c):
+  assert 0<=c<C and 0<=f<old['physical']
+  if f<D:return c*D+f
+  if f<W:return C*D+c*(W-D)+f-D
+  return C*W+f-W
+ changed={'calls','live','physical','private_namespace','idle_children','bank_padding','cover_final_correction','execution_schedule'}
+ expected=copy.deepcopy(old)
+ expected['live']=C*W;expected['physical']=C*W+514
+ expected['calls']=[]
+ for oc in old['calls']:
+  for c in range(C):
+   nc=copy.deepcopy(oc);nc['replica']=oc['replica']+8*c;nc['owners']=[[fam(f,c),rt]for f,rt in oc['owners']];expected['calls'].append(nc)
+ expected['private_namespace']={k:[C*W+x-W for x in interval]for k,interval in old['private_namespace'].items()}
+ expected['idle_children']=[]
+ for item in old['idle_children']:
+  assert item['replicas']==8;expected['idle_children'].append(item|{'replicas':40})
+ expected['bank_padding']['families']=[fam(f,c)for c in range(C)for f in old['bank_padding']['families']]
+ expected['bank_padding']['children']=[item|{'family':fam(item['family'],c)}for c in range(C)for item in old['bank_padding']['children']]
+ expected['cover_final_correction']=old['cover_final_correction']|{'families':[0,C*W],'charged_calls_per_cover':C*W}
+ for e in expected['execution_schedule']:
+  if 'replicas'in e:
+   assert e['replicas']==list(range(8));e['replicas']=list(range(40))
+  if e['kind']=='bank_padding_cover_sweep':e['families']=[C*D,C*W]
+  elif e['kind']=='translate_every_live_family':e.update(expected['cover_final_correction'])
+ def audit(t):
+  assert set(t)==set(old)
+  assert {k:t[k]for k in t if k not in changed}=={k:old[k]for k in old if k not in changed}
+  assert t==expected,'not the literal namespaced fivefold source'
+  bank=set(t['bank_padding']['families']);counts=Counter(f for c in t['calls']for f,rt in c['owners']if f in bank)
+  assert set(counts)==bank and set(counts.values())=={8},'each bank remains an eight-replica bank'
+  assert len(t['calls'])==360 and len({(c['stage'],c['replica'])for c in t['calls']})==360
+  for r in range(40):
+   assert [(c['stage'],c['orientation'],c['pair'])for c in t['calls']if c['replica']==r]==[(c['stage'],c['orientation'],c['pair'])for c in old['calls']if c['replica']==r%8]
+  assert all(len({f for f,rt in c['owners']})==728 for c in t['calls'])
+ audit(new);controls=[]
+ if a.mutation_controls:
+  def reject(name,mut):
+   q=copy.deepcopy(new);mut(q);assert q!=new
+   try:audit(q)
+   except(AssertionError,KeyError,IndexError,TypeError,ValueError):controls.append(name)
+   else:raise AssertionError('accepted '+name)
+  reject('collapse clone data namespace',lambda q:q['calls'][1]['owners'][0].__setitem__(0,q['calls'][0]['owners'][0][0]))
+  reject('share eight-replica bank across clones',lambda q:q['calls'][1]['owners'][224].__setitem__(0,q['calls'][0]['owners'][224][0]))
+  reject('change bank axis-copy route',lambda q:q['calls'][1]['owners'][224][1].__setitem__(-1,39))
+  reject('omit cloned bank complement',lambda q:q['bank_padding']['children'].pop())
+  reject('understate shared private reserve',lambda q:q.__setitem__('physical',q['physical']-1))
+  reject('change immutable ambient rank',lambda q:q.__setitem__('m',74))
+  reject('change source replica schedule',lambda q:next(e for e in q['execution_schedule']if 'replicas'in e)['replicas'].pop())
+  reject('omit final family correction',lambda q:q['cover_final_correction'].__setitem__('charged_calls_per_cover',q['live']-1))
+ report={'status':'PASS_INDEPENDENT_LITERAL_FIVEFOLD_SOURCE_LIFT','ambient_m':73,'clones':5,'replicas_per_clone':8,'replicas_total':40,'calls':360,'literal_owner_entries_checked':262080,'parent_live':W,'cloned_parent_live':5*W,'shared_private_reserve':514,'eight_replicas_per_dedicated_bank':True,'private_work_erasure_bound_to_fresh_replay':True,'immutable_metadata_keys':sorted(set(old)-changed),'source_template_sha256':content(oldpath),'clone_template_sha256':content(newpath),'source_artifacts':sources,'mutations_rejected':controls,'mutation_controls_run':a.mutation_controls,'scope':'Exact finite source lift with shared erased work, disjoint data and separate eight-replica banks. New hosted allocation, coefficient invoice and all-size compiler admission are separate; retained conditional interfaces are unchanged.'}
+ a.output.parent.mkdir(parents=True,exist_ok=True);a.output.write_text(json.dumps(report,indent=2)+'\n',encoding='utf-8');print(json.dumps(report,indent=2))
+if __name__=='__main__':main()
diff --git a/research/contextual-provider-pooling/complex-global/audit_mixed.py b/research/contextual-provider-pooling/complex-global/audit_mixed.py
new file mode 100644
index 0000000000..0b673c918a
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/audit_mixed.py
@@ -0,0 +1,186 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: VERIFIED_VARIANT POOLED_HOSTED OUT.json [--mutation-controls]
+The local provider is read from VERIFIED_VARIANT, never from a baseline width histogram.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json');V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers']);assert V==112 and canon['h']==9; width=[9-len(canon['frames'][canon['start'][2*V+h]])for h in range(R)];prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=40;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=360;HOSTED=CALLS*R
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(V)]
+provider_file=Path(sys.argv[sys.argv.index('--providers')+1]);locations=read(provider_file);providers={};expected_registry={}
+for pid,name in locations.items():
+ d=Path(name);w=read(d/'CANONICAL-WORD.json.gz');programs=read(d/'LOCAL-PROGRAMS.json.gz');lc=read(d/'LOCAL-CHECKS.json');rr=read(d/'INDEPENDENT-LOCAL-REPLAY.json');ad=read(d/'RESIDUAL-ADAPTERS.json');cl=read(d/'CLIFFORD-RECIPES.json')
+ fhash=lambda file:hashlib.sha256((d/file).read_bytes()).hexdigest()
+ assert set(programs)=={'forward','backward'}
+ phase_review=read(d/'CLIFFORD-REVIEW.json');assert phase_review['canonical_word_sha256']==fhash('CANONICAL-WORD.json.gz')and phase_review['recipe_sha256']==fhash('CLIFFORD-RECIPES.json')and phase_review['all_child_equalities_include_global_phase']
+ assert(w['v'],w['R'],w['h'],w['ports'])==(V,R,9,canon['ports'])
+ assert rr['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert rr['canonical_word_sha256']==fhash('CANONICAL-WORD.json.gz')and rr['local_programs_sha256']==fhash('LOCAL-PROGRAMS.json.gz')
+ assert all(rr['local'][o]['all_exact_columns']==2*V+R and rr['local'][o]['private_work_erased']for o in programs)
+ ww=[9-len(w['frames'][w['start'][2*V+h]])for h in range(R)]
+ for h,r in enumerate(ww):
+  if r<9:
+   fr=w['start'][2*V+h];a=ad['recipes'][str(fr)]
+   assert(a['frame'],a['vectors'],a['rank'],a['entrance_rank'])==(fr,w['frames'][fr],r,9-r)
+ providers[pid]=dict(widths=ww,checks=lc,canonical=w)
+ expected_registry[pid]=dict(canonical_word_sha256=fhash('CANONICAL-WORD.json.gz'),local_programs_sha256=fhash('LOCAL-PROGRAMS.json.gz'),local_checks_sha256=fhash('LOCAL-CHECKS.json'),independent_local_replay_sha256=fhash('INDEPENDENT-LOCAL-REPLAY.json'),residual_adapter_sha256=fhash('RESIDUAL-ADAPTERS.json'),exact_local_clifford_recipe_sha256=fhash('CLIFFORD-RECIPES.json'),local_programs=programs,residual_adapters=ad,clifford_recipes=cl)
+
+# Bind the selected provider's actual normalization recipes, including newly
+# selected entrance frames; a baseline recipe registry cannot silently survive.
+required_artifacts={'split-centres/CANONICAL-WORD.json.gz','split-centres/LOCAL-PROGRAMS.json.gz','split-centres/LOCAL-CHECKS.json','split-centres/RESIDUAL-ADAPTERS.json','work/complex-nine-native/DATA-PHASES.json'}
+assert required_artifacts <= set(summary['source_artifacts'])
+adapter_path=BASE/'split-centres/RESIDUAL-ADAPTERS.json'
+assert hashlib.sha256(adapter_path.read_bytes()).hexdigest()==parent['residual_adapter_sha256']
+adapters=read(adapter_path)['recipes']
+for h,w in enumerate(width):
+ if w<9:
+  f=canon['start'][(2*V)+h];a=adapters[str(f)]
+  assert a['frame']==f and a['vectors']==canon['frames'][f] and a['rank']==w and a['entrance_rank']==9-w
+
+def resolve_program(template,call):
+ registry=template['provider_registry'];entry=registry[call['provider']]
+ code=entry['local_programs'][call['orientation']]
+ assert isinstance(code,list)and code
+ return code
+
+def audit(t):
+ assert t['provider_registry']==expected_registry
+ assert set(c['provider']for c in t['calls'])==set(providers)
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_programs']==parent['local_programs']and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert len(t['calls'])==CALLS and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','exact_local_clifford_recipe_sha256','residual_adapter_sha256','adapter_policy'):assert t[key]==parent[key]
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==CALLS
+ all_local=[];perrep={r:[]for r in range(T)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<T and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   assert e==expected
+   assert 0<=e['time']<CALLS and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[DATA,DATA]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,DATA],charged_calls_per_cover=DATA)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[],children=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,DATA],charged_calls_per_cover=DATA)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  pid=call['provider'];width=providers[pid]['widths'];selected_checks=providers[pid]['checks']
+  assert resolve_program(t,call)==expected_registry[pid]['local_programs'][call['orientation']]
+  assert call['local_program_sha256']==selected_checks[call['orientation']]['sha256']
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time','provider','local_program_sha256')}=={k:v for k,v in old.items()if k not in('owners','local_program_sha256')}
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:(2*V)]==old['owners'][:(2*V)]
+  for h,(family,route)in enumerate(own[(2*V):]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,(8*V));fampair,sub=divmod(sub,(2*V));side,port=divmod(sub,V)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*V+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in selected_checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(T)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*(8*V)+(2*pairs[i]+sides[i])*V+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==12800 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=CALLS)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ if '--mutation-controls' not in sys.argv[4:]:return
+ q=copy.deepcopy(ct);mut(q);assert q!=ct
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4)
+reject('wrong selected provider',lambda q:q['calls'][0].__setitem__('provider',next(k for k in providers if k!=q['calls'][0]['provider'])))
+reject('wrong provider program registry',lambda q:q['provider_registry'][q['calls'][0]['provider']]['local_programs'].__setitem__('forward',[]))
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA))
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=12800,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],provider_widths={pid:dict(sorted(Counter(z['widths']).items()))for pid,z in providers.items()},provider_counts=dict(Counter(c['provider']for c in ct['calls'])),scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses the new selected local program bound by fresh scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=12800,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
+# Literal residual frames are a compact export of the already checked offsets,
+# not another global replay. Every row names its actual inherited axes.
+frames=[]
+for z in ct['idle_children']:
+ axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes']))
+ tail=axes[z['pending_offset']:]
+ assert len(tail)==z['rank']
+ frames.append(dict(z,orthogonal_axes=tail))
+frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode()
+(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(gzip.compress(frame_raw,mtime=0))
+frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'],
+ uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames),
+ rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())),
+ source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(),
+ scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.')
+(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n')
+
diff --git a/research/contextual-provider-pooling/complex-global/build_clone.py b/research/contextual-provider-pooling/complex-global/build_clone.py
new file mode 100644
index 0000000000..2190632451
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/build_clone.py
@@ -0,0 +1,65 @@
+"""Five finite controller copies, interleaved at each source invocation; m stays73."""
+from pathlib import Path
+from collections import Counter,defaultdict
+import argparse,copy,gzip,hashlib,json,shutil
+ap=argparse.ArgumentParser();ap.add_argument('--base',type=Path,required=True);ap.add_argument('--owners',type=Path,required=True);ap.add_argument('--plan',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args()
+assert not a.out.exists();a.out.mkdir(parents=True)
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+def dump(p,x):
+ raw=json.dumps(x,sort_keys=True,separators=(',',':')).encode();p.write_bytes(gzip.compress(raw,mtime=0)if p.suffix=='.gz'else raw+b'\n');return hashlib.sha256(raw).hexdigest()
+C=5;T0=8;T=40;V=112;D0=7168;DATA=D0*C
+old=read(a.base/'split-centres/GLOBAL-TEMPLATE.json.gz');roles=read(a.owners);plan=read(a.plan)
+assert len(old['calls'])==72 and plan['T']==8 and plan['M']==73 and len(roles)==36288
+B=a.out/'base';shutil.copytree(a.base,B)
+t=copy.deepcopy(old);oldlive=old['live'];newlive=oldlive*C;reserve=old['physical']-oldlive;assert reserve==514
+# Dedicated bank controls remain five independent 8-replica banks, never one 40-replica bank.
+def fam(f,c):
+ if f<D0:return f+c*D0
+ if f<oldlive:return DATA+(f-D0)+c*(oldlive-D0)
+ return newlive+(f-oldlive)
+t['calls']=[]
+for oc in old['calls']:
+ for cl in range(C):
+  q=copy.deepcopy(oc);q['replica']+=8*cl;q['owners']=[[fam(f,cl),rt]for f,rt in q['owners']];t['calls'].append(q)
+t['live']=newlive;t['physical']=newlive+reserve
+for k,(l,u)in t['private_namespace'].items():t['private_namespace'][k]=[newlive+l-oldlive,newlive+u-oldlive]
+for q in t['idle_children']:assert q['replicas']==8;q['replicas']=40
+oldbank=old['bank_padding'];t['bank_padding']['families']=[fam(f,c)for c in range(C)for f in oldbank['families']]
+t['bank_padding']['children']=[]
+for c in range(C):
+ for q in oldbank['children']:
+  z=copy.deepcopy(q);z['family']=fam(q['family'],c);t['bank_padding']['children'].append(z)
+t['cover_final_correction'].update(families=[0,newlive],charged_calls_per_cover=newlive)
+for e in t['execution_schedule']:
+ if 'replicas'in e:e['replicas']=list(range(T))
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,newlive]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+parent_hash=dump(B/'split-centres/GLOBAL-TEMPLATE.json.gz',t)
+p=copy.deepcopy(plan)
+for stale in ('patterns','stage_assignments','numeric_saving','solver_status','gap','numeric_saving_scope'):p.pop(stale,None)
+p.update(T=40,live=DATA,deficit=12800,mode='five finite interleaved clones with one pooled remainder packet')
+p['order']=[[s,r+8*c]for s,r in plan['order']for c in range(C)]
+p['windows']={}
+for k,(rank,times)in plan['windows'].items():
+ r,i=map(int,k.split(','))
+ for cl in range(C):p['windows'][f'{r+8*cl},{i}']=[rank,[5*t+c for t in times for c in range(C)]]
+h=Counter({int(r):5*n for r,n in plan['profile'].items()});h[39]-=5;h[48]+=4;h[3]+=1;p['profile']={r:n for r,n in sorted(h.items())if n};assert 73*DATA-sum(r*n for r,n in h.items())==12800
+out=[];witness=[]
+for q in roles:
+ for cl in range(C):
+  z=copy.deepcopy(q);z['replica']+=8*cl;z['owner_replica']+=8*cl;z['family']+=D0*cl;z['copy']+=8*V*cl;z['time']=5*q['time']+cl
+  if(q['owner_replica'],q['child'],q['port'])==(1,10,107):
+   assert(q['time'],q['stage'],q['replica'],q['helper'],q['width'],q['offset'],q['family'])==(12,2,2,376,9,0,1787)
+   z.update(owner_replica=1,family=1787,copy=219,offset=9*cl);witness.append(z)
+  out.append(z)
+out.sort(key=lambda z:(z['time'],z['helper']));assert len(witness)==5
+# Literal independent width/time/whole-family check before the geometric auditor.
+bycall=defaultdict(set);used=defaultdict(set)
+for z in out:
+ key=(z['stage'],z['replica']);assert z['family']not in bycall[key];bycall[key].add(z['family']);rank,times=p['windows'][f"{z['owner_replica']},{z['child']}"];assert z['time']in times
+ k=(z['owner_replica'],z['child'],z['port']);cells=set(range(z['offset'],z['offset']+z['width']));assert max(cells)<rank and not used[k]&cells;used[k]|=cells
+assert all(len(s)==504 for s in bycall.values()) and len(bycall)==360
+for cells in used.values():assert cells==set(range(len(cells)))
+ph=dump(a.out/'PLAN.json',p);oh=dump(a.out/'OWNERS.json.gz',out)
+receipt={'status':'FIVE_FINITE_CLONES_LITERAL_RESOURCE_WITNESS','ambient_m':73,'replicas_per_clone':8,'clones':5,'calls':360,'helper_roles':len(out),'profile':p['profile'],'live':DATA,'deficit':12800,'pooled_roles':witness,'parent_semantic_sha256':parent_hash,'plan_semantic_sha256':ph,'owners_semantic_sha256':oh,'sources':{str(x.name):hashlib.sha256(x.read_bytes()).hexdigest()for x in [a.owners,a.plan,a.base/'split-centres/GLOBAL-TEMPLATE.json.gz']},'scope':'Literal resource construction; fresh full physical audit and finite scalar invoice required.'}
+dump(a.out/'CLONE-CONSTRUCTION.json',receipt);print(json.dumps(receipt,indent=2))
diff --git a/research/contextual-provider-pooling/complex-global/build_mixed72.py b/research/contextual-provider-pooling/complex-global/build_mixed72.py
new file mode 100644
index 0000000000..cd83aec231
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/build_mixed72.py
@@ -0,0 +1,37 @@
+"""Select each complete provider from actual rank16 slot availability; compact literal owner intervals."""
+from pathlib import Path
+from collections import Counter,defaultdict
+import argparse,gzip,hashlib,json
+ap=argparse.ArgumentParser();ap.add_argument('--owners',type=Path,required=True);ap.add_argument('--plan',type=Path,required=True);ap.add_argument('--providers',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();assert not a.out.exists();a.out.mkdir(parents=True)
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+z=read(a.plan);roles=read(a.owners);locations=read(a.providers);records={}
+for pid,name in locations.items():
+ d=Path(name);cw=read(d/'CANONICAL-WORD.json.gz');checks=read(d/'LOCAL-CHECKS.json');assert(cw['v'],cw['R'],cw['h'])==(112,504,9)
+ H={int(r):n for r,n in checks['forward']['paid_profile'].items()};assert H=={int(r):n for r,n in checks['backward']['paid_profile'].items()}
+ records[pid]={'widths':[9-len(cw['frames'][f])for f in cw['start'][224:]],'profile':H}
+assert set(records)=={'n0','n2','n6','n8'}
+c=Counter()
+for q in roles:
+ if q['width']==4 and z['windows'][f"{q['owner_replica']},{q['child']}"][0]==16:c[q['time']]+=1
+selector={f'{s},{rep}':'n'+str(c[t])for t,(s,rep)in enumerate(z['order'])};assert Counter(selector.values())=={'n8':55,'n0':15,'n6':1,'n2':1}
+bins=defaultdict(list)
+for q in roles:
+ pid=selector[f"{q['stage']},{q['replica']}"];w=records[pid]['widths'][q['helper']]
+ assert w==q['width']or(q['width']==4 and w==5)
+ q['width']=w;bins[q['owner_replica'],q['child'],q['port']].append(q)
+for k,rs in bins.items():
+ off=0
+ for q in sorted(rs,key=lambda q:q['offset']):q['offset']=off;off+=q['width']
+ assert off<=z['windows'][f'{k[0]},{k[1]}'][0]
+h=Counter()
+for pid in selector.values():h.update(records[pid]['profile'])
+for key,(rank,times)in z['windows'].items():
+ rep,ch=map(int,key.split(','))
+ for port in range(112):
+  left=rank-sum(q['width']for q in bins[rep,ch,port]);assert left>=0
+  if left:h[left]+=1
+assert 73*7168-sum(r*n for r,n in h.items())==2560
+z.update(status='SOURCE_BOUND_MIXED_PROVIDER_LITERAL_PLAN',mode='selected promotion only in rank16 owner slots',provider_for_call=selector,profile=dict(sorted(h.items())),local_profiles={k:v['profile']for k,v in records.items()})
+for key in ['patterns','stage_assignments','numeric_saving','solver_status','gap','local_profile','numeric_saving_scope']:z.pop(key,None)
+raw=json.dumps(roles,sort_keys=True,separators=(',',':')).encode();(a.out/'OWNERS.json.gz').write_bytes(gzip.compress(raw,mtime=0));(a.out/'PLAN.json').write_text(json.dumps(z,indent=2)+'\n',encoding='utf8',newline='\n')
+r={'status':'PASS_LITERAL_PROVIDER_SELECTION_AND_OFFSET_COMPACTION','provider_counts':dict(Counter(selector.values())),'profile':dict(sorted(h.items())),'source_owners_sha256':hashlib.sha256(a.owners.read_bytes()).hexdigest(),'source_plan_lf_sha256':hashlib.sha256(a.plan.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),'owner_content_sha256':hashlib.sha256(raw).hexdigest(),'scope':'Provider widths/profile read from actual canonical/local receipts. Independent chronology, source lift, charts and invoice follow.'};(a.out/'MIXED-CONSTRUCTION.json').write_text(json.dumps(r,indent=2)+'\n',encoding='utf8',newline='\n');print(json.dumps(r,indent=2))
diff --git a/research/contextual-provider-pooling/complex-global/build_mixed_clone.py b/research/contextual-provider-pooling/complex-global/build_mixed_clone.py
new file mode 100644
index 0000000000..473b1f46ab
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/build_mixed_clone.py
@@ -0,0 +1,66 @@
+"""Five finite controller copies, interleaved at each source invocation; m stays73."""
+from pathlib import Path
+from collections import Counter,defaultdict
+import argparse,copy,gzip,hashlib,json,shutil
+ap=argparse.ArgumentParser();ap.add_argument('--base',type=Path,required=True);ap.add_argument('--owners',type=Path,required=True);ap.add_argument('--plan',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args()
+assert not a.out.exists();a.out.mkdir(parents=True)
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+def dump(p,x):
+ raw=json.dumps(x,sort_keys=True,separators=(',',':')).encode();p.write_bytes(gzip.compress(raw,mtime=0)if p.suffix=='.gz'else raw+b'\n');return hashlib.sha256(raw).hexdigest()
+C=5;T0=8;T=40;V=112;D0=7168;DATA=D0*C
+old=read(a.base/'split-centres/GLOBAL-TEMPLATE.json.gz');roles=read(a.owners);plan=read(a.plan)
+assert len(old['calls'])==72 and plan['T']==8 and plan['M']==73 and len(roles)==36288
+B=a.out/'base';shutil.copytree(a.base,B)
+t=copy.deepcopy(old);oldlive=old['live'];newlive=oldlive*C;reserve=old['physical']-oldlive;assert reserve==514
+# Dedicated bank controls remain five independent 8-replica banks, never one 40-replica bank.
+def fam(f,c):
+ if f<D0:return f+c*D0
+ if f<oldlive:return DATA+(f-D0)+c*(oldlive-D0)
+ return newlive+(f-oldlive)
+t['calls']=[]
+for oc in old['calls']:
+ for cl in range(C):
+  q=copy.deepcopy(oc);q['replica']+=8*cl;q['owners']=[[fam(f,cl),rt]for f,rt in q['owners']];t['calls'].append(q)
+t['live']=newlive;t['physical']=newlive+reserve
+for k,(l,u)in t['private_namespace'].items():t['private_namespace'][k]=[newlive+l-oldlive,newlive+u-oldlive]
+for q in t['idle_children']:assert q['replicas']==8;q['replicas']=40
+oldbank=old['bank_padding'];t['bank_padding']['families']=[fam(f,c)for c in range(C)for f in oldbank['families']]
+t['bank_padding']['children']=[]
+for c in range(C):
+ for q in oldbank['children']:
+  z=copy.deepcopy(q);z['family']=fam(q['family'],c);t['bank_padding']['children'].append(z)
+t['cover_final_correction'].update(families=[0,newlive],charged_calls_per_cover=newlive)
+for e in t['execution_schedule']:
+ if 'replicas'in e:e['replicas']=list(range(T))
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,newlive]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+parent_hash=dump(B/'split-centres/GLOBAL-TEMPLATE.json.gz',t)
+p=copy.deepcopy(plan)
+for stale in ('patterns','stage_assignments','numeric_saving','solver_status','gap','numeric_saving_scope'):p.pop(stale,None)
+p.update(T=40,live=DATA,deficit=12800,mode='five finite interleaved clones with one pooled remainder packet')
+p['order']=[[s,r+8*c]for s,r in plan['order']for c in range(C)]
+p['provider_for_call']={f'{s},{r+8*c}':plan['provider_for_call'][f'{s},{r}']for s,r in plan['order']for c in range(C)}
+p['windows']={}
+for k,(rank,times)in plan['windows'].items():
+ r,i=map(int,k.split(','))
+ for cl in range(C):p['windows'][f'{r+8*cl},{i}']=[rank,[5*t+c for t in times for c in range(C)]]
+h=Counter({int(r):5*n for r,n in plan['profile'].items()});h[39]-=5;h[48]+=4;h[3]+=1;p['profile']={r:n for r,n in sorted(h.items())if n};assert 73*DATA-sum(r*n for r,n in h.items())==12800
+out=[];witness=[]
+for q in roles:
+ for cl in range(C):
+  z=copy.deepcopy(q);z['replica']+=8*cl;z['owner_replica']+=8*cl;z['family']+=D0*cl;z['copy']+=8*V*cl;z['time']=5*q['time']+cl
+  if(q['owner_replica'],q['child'],q['port'])==(6,8,6):
+   assert(q['time'],q['stage'],q['replica'],q['helper'],q['width'],q['offset'],q['family'])==(52,4,6,141,9,0,6054)
+   z.update(owner_replica=6,family=6054,copy=678,offset=9*cl);witness.append(z)
+  out.append(z)
+out.sort(key=lambda z:(z['time'],z['helper']));assert len(witness)==5
+# Literal independent width/time/whole-family check before the geometric auditor.
+bycall=defaultdict(set);used=defaultdict(set)
+for z in out:
+ key=(z['stage'],z['replica']);assert z['family']not in bycall[key];bycall[key].add(z['family']);rank,times=p['windows'][f"{z['owner_replica']},{z['child']}"];assert z['time']in times
+ k=(z['owner_replica'],z['child'],z['port']);cells=set(range(z['offset'],z['offset']+z['width']));assert max(cells)<rank and not used[k]&cells;used[k]|=cells
+assert all(len(s)==504 for s in bycall.values()) and len(bycall)==360
+for cells in used.values():assert cells==set(range(len(cells)))
+ph=dump(a.out/'PLAN.json',p);oh=dump(a.out/'OWNERS.json.gz',out)
+receipt={'status':'FIVE_FINITE_CLONES_LITERAL_RESOURCE_WITNESS','ambient_m':73,'replicas_per_clone':8,'clones':5,'calls':360,'helper_roles':len(out),'profile':p['profile'],'live':DATA,'deficit':12800,'pooled_roles':witness,'parent_semantic_sha256':parent_hash,'plan_semantic_sha256':ph,'owners_semantic_sha256':oh,'sources':{str(x.name):hashlib.sha256(x.read_bytes()).hexdigest()for x in [a.owners,a.plan,a.base/'split-centres/GLOBAL-TEMPLATE.json.gz']},'scope':'Literal resource construction; fresh full physical audit and finite scalar invoice required.'}
+dump(a.out/'CLONE-CONSTRUCTION.json',receipt);print(json.dumps(receipt,indent=2))
diff --git a/research/contextual-provider-pooling/complex-global/emit_clone.py b/research/contextual-provider-pooling/complex-global/emit_clone.py
new file mode 100644
index 0000000000..b86fecd132
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/emit_clone.py
@@ -0,0 +1,100 @@
+"""Punctured 112-port whole-owner derivative, adapted for icekylinx with GPT-6 Astra.
+Based on PR514 and its credited PR484/507 lineage.
+CLI: --base VERIFIED_VARIANT --owners ASYNC-OWNERS.json.gz --plan ASYNC-PLAN.json --out OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy,argparse
+from pathlib import Path
+from collections import Counter,defaultdict
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--base',type=Path,required=True);parser.add_argument('--owners',type=Path,required=True);parser.add_argument('--plan',type=Path,required=True);parser.add_argument('--out',type=Path,required=True)
+a=parser.parse_args();BASE,MAP,PLAN,OUT=(p.resolve()for p in(a.base,a.owners,a.plan,a.out));assert not OUT.exists();OUT.mkdir(parents=True)
+class OH:
+ @staticmethod
+ def idle_basis(q):
+  z=next(i for i in range(9)if not(q>>i)&1);u=q^(1<<z);order=list(range(9));order[0],order[z]=order[z],order[0]
+  return[(1<<i)^(u if u>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ @staticmethod
+ def spectators(q,pending,off,w):
+  B=OH.idle_basis(q);occ=[B.index(v)for v in pending[off:off+w]]
+  return[j for j in range(73)if j not in occ][:9-w]
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+plan=read(PLAN);call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==360;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);T=40;V=canon['v'];M=73;R=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)
+assert(len(roles),len(canon['start']),len(ph['recipes']))==(360*R,2*V+R,V)
+widths=[9-len(canon['frames'][canon['start'][(2*V)+h]])for h in range(R)];assert widths==plan['baseline_widths'], 'source-bound selected provider widths'
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==widths[h] and 0<=orp<T
+ assert f==orp*(8*V)+(2*pairs[i]+side[i])*V+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f<DATA for f,r in c['owners'])
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in checks[c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*(8*V)+(2*pairs[i]+side[i])*V+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==12800
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='round20-R504-asynchronous-whole-owner-v1',live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['bank_padding']['children']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert t['local_programs']==parent['local_programs']
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',template_sha256=hashlib.sha256(raw).hexdigest(),parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),rank_mass=sum(r*n for r,n in paid.items()),deficit=12800,maxchild=max(paid),hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),source_artifacts={p.relative_to(BASE).as_posix():hashlib.sha256(p.read_bytes()).hexdigest()for p in [BASE/'split-centres/CANONICAL-WORD.json.gz',BASE/'split-centres/LOCAL-PROGRAMS.json.gz',BASE/'split-centres/LOCAL-CHECKS.json',BASE/'split-centres/RESIDUAL-ADAPTERS.json',BASE/'split-centres/CLIFFORD-RECIPES.json',BASE/'split-centres/CLIFFORD-REVIEW.json',BASE/'split-centres/INDEPENDENT-LOCAL-REPLAY.json',BASE/'work/complex-nine-native/DATA-PHASES.json']},scope='New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/contextual-provider-pooling/complex-global/emit_mixed.py b/research/contextual-provider-pooling/complex-global/emit_mixed.py
new file mode 100644
index 0000000000..6d54049c38
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/emit_mixed.py
@@ -0,0 +1,127 @@
+"""Punctured 112-port whole-owner derivative, adapted for icekylinx with GPT-6 Astra.
+Based on PR514 and its credited PR484/507 lineage.
+CLI: --base VERIFIED_VARIANT --owners ASYNC-OWNERS.json.gz --plan ASYNC-PLAN.json --out OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy,argparse
+from pathlib import Path
+from collections import Counter,defaultdict
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--base',type=Path,required=True);parser.add_argument('--owners',type=Path,required=True);parser.add_argument('--plan',type=Path,required=True);parser.add_argument('--out',type=Path,required=True)
+parser.add_argument('--providers',type=Path,required=True)
+a=parser.parse_args();BASE,MAP,PLAN,OUT=(p.resolve()for p in(a.base,a.owners,a.plan,a.out));assert not OUT.exists();OUT.mkdir(parents=True)
+class OH:
+ @staticmethod
+ def idle_basis(q):
+  z=next(i for i in range(9)if not(q>>i)&1);u=q^(1<<z);order=list(range(9));order[0],order[z]=order[z],order[0]
+  return[(1<<i)^(u if u>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ @staticmethod
+ def spectators(q,pending,off,w):
+  B=OH.idle_basis(q);occ=[B.index(v)for v in pending[off:off+w]]
+  return[j for j in range(73)if j not in occ][:9-w]
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+plan=read(PLAN);call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==360;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);T=40;V=canon['v'];M=73;R=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)
+assert(len(roles),len(canon['start']),len(ph['recipes']))==(360*R,2*V+R,V)
+locations=read(a.providers);providers={};registry={}
+for pid,location in locations.items():
+ d=Path(location);cw=read(d/'CANONICAL-WORD.json.gz');lc=read(d/'LOCAL-CHECKS.json');lp=read(d/'LOCAL-PROGRAMS.json.gz');ad=read(d/'RESIDUAL-ADAPTERS.json');cr=read(d/'CLIFFORD-RECIPES.json');rv=read(d/'INDEPENDENT-LOCAL-REPLAY.json')
+ assert(cw['v'],cw['R'],cw['h'],cw['ports'])==(V,R,9,canon['ports'])
+ fh=lambda n:hashlib.sha256((d/n).read_bytes()).hexdigest()
+ assert set(lp)=={'forward','backward'}
+ phase_review=read(d/'CLIFFORD-REVIEW.json');assert phase_review['canonical_word_sha256']==fh('CANONICAL-WORD.json.gz')and phase_review['recipe_sha256']==fh('CLIFFORD-RECIPES.json')and phase_review['all_child_equalities_include_global_phase']
+ assert rv['canonical_word_sha256']==fh('CANONICAL-WORD.json.gz')and rv['local_programs_sha256']==fh('LOCAL-PROGRAMS.json.gz')
+ widths=[9-len(cw['frames'][cw['start'][2*V+h]])for h in range(R)]
+ providers[pid]=dict(canonical=cw,checks=lc,widths=widths)
+ registry[pid]=dict(canonical_word_sha256=fh('CANONICAL-WORD.json.gz'),local_programs_sha256=fh('LOCAL-PROGRAMS.json.gz'),local_checks_sha256=fh('LOCAL-CHECKS.json'),independent_local_replay_sha256=fh('INDEPENDENT-LOCAL-REPLAY.json'),residual_adapter_sha256=fh('RESIDUAL-ADAPTERS.json'),exact_local_clifford_recipe_sha256=fh('CLIFFORD-RECIPES.json'),local_programs=lp,residual_adapters=ad,clifford_recipes=cr)
+assert set(plan['provider_for_call'].values())==set(providers)
+
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];pid=plan['provider_for_call'][f'{s},{rep}'];widths=providers[pid]['widths'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==widths[h] and 0<=orp<T
+ assert f==orp*(8*V)+(2*pairs[i]+side[i])*V+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);pid=plan['provider_for_call'][f'{k[0]},{k[1]}'];c['provider']=pid;c['local_program_sha256']=providers[pid]['checks'][c['orientation']]['sha256'];assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f<DATA for f,r in c['owners'])
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in providers[c['provider']]['checks'][c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*(8*V)+(2*pairs[i]+side[i])*V+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==12800
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='round20-R504-asynchronous-whole-owner-v1',live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['provider_registry']=registry
+t['provider_semantics']='Every call must execute provider_registry[call.provider].local_programs[call.orientation] and that provider residual/Clifford recipes; the top-level original programs identify the data-controller anchor only.'
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['bank_padding']['children']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert t['local_programs']==parent['local_programs']
+assert all(c['provider']in registry for c in t['calls'])
+def resolve_program(template,call):
+ entry=template['provider_registry'][call['provider']]
+ assert call['orientation']in('forward','backward')
+ program=entry['local_programs'][call['orientation']]
+ assert isinstance(program,list)and program
+ return program
+# A finite concatenation of already serialized programs; no new runtime oracle.
+for call in t['calls']:
+ actual=resolve_program(t,call)
+ assert actual==registry[call['provider']]['local_programs'][call['orientation']]
+
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',template_sha256=hashlib.sha256(raw).hexdigest(),parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),rank_mass=sum(r*n for r,n in paid.items()),deficit=12800,maxchild=max(paid),hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),source_artifacts={p.relative_to(BASE).as_posix():hashlib.sha256(p.read_bytes()).hexdigest()for p in [BASE/'split-centres/CANONICAL-WORD.json.gz',BASE/'split-centres/LOCAL-PROGRAMS.json.gz',BASE/'split-centres/LOCAL-CHECKS.json',BASE/'split-centres/RESIDUAL-ADAPTERS.json',BASE/'split-centres/CLIFFORD-RECIPES.json',BASE/'split-centres/CLIFFORD-REVIEW.json',BASE/'split-centres/INDEPENDENT-LOCAL-REPLAY.json',BASE/'work/complex-nine-native/DATA-PHASES.json']},scope='New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/contextual-provider-pooling/complex-global/inputs558/OWNERS.json.gz b/research/contextual-provider-pooling/complex-global/inputs558/OWNERS.json.gz
new file mode 100644
index 0000000000..eeb01317d7
Binary files /dev/null and b/research/contextual-provider-pooling/complex-global/inputs558/OWNERS.json.gz differ
diff --git a/research/contextual-provider-pooling/complex-global/inputs558/PLAN.json b/research/contextual-provider-pooling/complex-global/inputs558/PLAN.json
new file mode 100644
index 0000000000..f48def86c4
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/inputs558/PLAN.json
@@ -0,0 +1,12546 @@
+{
+  "status": "FRESH_INTEGER_MATCHED_RANK5_EIGHT_PIVOT_OWNER_PLAN",
+  "mode": "frozen-saturation-pattern-time-matching",
+  "K": 4,
+  "T": 8,
+  "M": 73,
+  "L": 9,
+  "live": 7168,
+  "deficit": 2560,
+  "profile": {
+    "1": 166880,
+    "2": 30528,
+    "3": 35779,
+    "4": 13824,
+    "5": 4032,
+    "6": 4032,
+    "7": 208,
+    "8": 576,
+    "39": 1,
+    "48": 1660
+  },
+  "patterns": [
+    [
+      [
+        0,
+        0
+      ],
+      [
+        9
+      ],
+      10
+    ],
+    [
+      [
+        0,
+        0
+      ],
+      [
+        8,
+        8
+      ],
+      102
+    ],
+    [
+      [
+        0,
+        2
+      ],
+      [
+        8,
+        8
+      ],
+      88
+    ],
+    [
+      [
+        0,
+        2
+      ],
+      [
+        4,
+        9
+      ],
+      24
+    ],
+    [
+      [
+        0,
+        1
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        3
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        4
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        6
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        5
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        7
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        8
+      ],
+      [],
+      46
+    ],
+    [
+      [
+        0,
+        8
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      66
+    ],
+    [
+      [
+        0,
+        10
+      ],
+      [],
+      112
+    ],
+    [
+      [
+        0,
+        9
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        11
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        12
+      ],
+      [],
+      79
+    ],
+    [
+      [
+        0,
+        12
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      33
+    ],
+    [
+      [
+        0,
+        13
+      ],
+      [],
+      94
+    ],
+    [
+      [
+        0,
+        13
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      18
+    ],
+    [
+      [
+        0,
+        14
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        15
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        16
+      ],
+      [
+        8,
+        8
+      ],
+      112
+    ],
+    [
+      [
+        0,
+        17
+      ],
+      [
+        8,
+        8
+      ],
+      48
+    ],
+    [
+      [
+        0,
+        17
+      ],
+      [
+        4,
+        9
+      ],
+      64
+    ],
+    [
+      [
+        1,
+        0
+      ],
+      [
+        9
+      ],
+      104
+    ],
+    [
+      [
+        1,
+        0
+      ],
+      [
+        4,
+        9
+      ],
+      8
+    ],
+    [
+      [
+        1,
+        2
+      ],
+      [
+        9
+      ],
+      16
+    ],
+    [
+      [
+        1,
+        2
+      ],
+      [
+        8,
+        8
+      ],
+      88
+    ],
+    [
+      [
+        1,
+        2
+      ],
+      [
+        4,
+        9
+      ],
+      8
+    ],
+    [
+      [
+        1,
+        1
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        3
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        4
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        6
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        5
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        7
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        8
+      ],
+      [],
+      112
+    ],
+    [
+      [
+        1,
+        10
+      ],
+      [],
+      112
+    ],
+    [
+      [
+        1,
+        9
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        11
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        12
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        13
+      ],
+      [],
+      112
+    ],
+    [
+      [
+        1,
+        14
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        15
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        1,
+        16
+      ],
+      [
+        8,
+        8
+      ],
+      100
+    ],
+    [
+      [
+        1,
+        16
+      ],
+      [
+        4,
+        9
+      ],
+      12
+    ],
+    [
+      [
+        1,
+        17
+      ],
+      [
+        8,
+        8
+      ],
+      106
+    ],
+    [
+      [
+        1,
+        17
+      ],
+      [
+        4,
+        9
+      ],
+      6
+    ],
+    [
+      [
+        2,
+        0
+      ],
+      [
+        9
+      ],
+      68
+    ],
+    [
+      [
+        2,
+        0
+      ],
+      [
+        8,
+        8
+      ],
+      44
+    ],
+    [
+      [
+        2,
+        2
+      ],
+      [
+        8,
+        8
+      ],
+      112
+    ],
+    [
+      [
+        2,
+        1
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        2,
+        3
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        2,
+        4
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        2,
+        6
+      ],
+      [
+        5,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        2,
+        5
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        2,
+        7
+      ],
+      [
+        8
+      ],
+      112
+    ],
+    [
+      [
+        2,
+        8
+      ],
+      [
+        9,
+        9,
+        9,
+        9,
+        9
+      ],
+      112
+    ],
+    [
+      [
+        2,
+        10
+      ],
+      [],
+      112
+    ],
+    [
+      [
+        2,
+        9
+      ],
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+    8,
+    8,
+    8,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    4,
+    8,
+    4,
+    4,
+    4,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    4,
+    8,
+    4,
+    4,
+    4,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5
+  ],
+  "solver_status": "literal_integer_flow_and_per_window_matching",
+  "gap": null,
+  "local_profile": {
+    "1": 2316,
+    "2": 424,
+    "3": 464,
+    "4": 192,
+    "5": 56,
+    "6": 56,
+    "8": 8
+  }
+}
diff --git a/research/contextual-provider-pooling/complex-global/invoice_clone.py b/research/contextual-provider-pooling/complex-global/invoice_clone.py
new file mode 100644
index 0000000000..aac9e222de
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/invoice_clone.py
@@ -0,0 +1,304 @@
+"""Recount the five-copy changed controller and its actual asynchronous finite invoice.
+Five copies enlarge the family namespace, not the per-family ambient dimension73.
+The previous invoice implementation is retained below with explicit copy-count,
+deficit and payload changes; no bit or row charge is omitted.
+
+Prepared for icekylinx with OpenAI Codex assistance. Apache-2.0.
+Adapted from the attributed Round19 audit_async_invoice.py and its PR484/514
+ancestry. Uses the fresh hash-bound independent local replay for exact scalar
+endpoints; independently recounts emitted Horner work, prefix envelopes,
+paid local calls, wrappers and finite charges. Does not rerun the old baseline
+or read an old INTEGRATION.json as evidence for the changed word.
+"""
+import argparse
+import gzip
+import hashlib
+import json
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def filehash(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def contenthash(path):
+    data = path.read_bytes()
+    return hashlib.sha256(gzip.decompress(data) if path.suffix == '.gz' else data).hexdigest()
+
+
+def run(base, hosted, audit, out, retained_invoice=None):
+    local_dir = base / 'split-centres'
+    cp = local_dir / 'CANONICAL-WORD.json.gz'
+    pp = local_dir / 'LOCAL-PROGRAMS.json.gz'
+    rp = local_dir / 'INDEPENDENT-LOCAL-REPLAY.json'
+    w, programs, replay = read(cp), read(pp), read(rp)
+    checks = read(local_dir / 'LOCAL-CHECKS.json')
+    parent = read(local_dir / 'GLOBAL-TEMPLATE.json.gz')
+    template_path = hosted / 'GLOBAL-TEMPLATE.json.gz'
+    template = read(template_path)
+    owners = read(audit / 'OWNERS-AND-PROFILE.json')
+    control = read(audit / 'ASYNC-AUDIT.json')
+    template_hash = contenthash(template_path)
+    assert template_hash == control['complex_template_sha256'] == owners['template_sha256']
+    assert owners['status'] == 'PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+    assert replay['status'] == 'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+    assert replay['canonical_word_sha256'] == filehash(cp)
+    assert replay['local_programs_sha256'] == filehash(pp)
+    assert template['local_programs'] == parent['local_programs'] == programs
+    assert template['recipe'] == parent['recipe']
+    assert Counter(c['orientation'] for c in template['calls']) == Counter(c['orientation'] for c in parent['calls'])
+
+    v, helpers, h, m = w['v'], w['R'], w['h'], template['m']
+    assert v == 112 and h == 9 and m == 73
+    assert replay['v'] == v and replay['helpers'] == helpers
+    n = 2*v + helpers
+    stages, replicas, blocks_per_stream = 9, 40, 4
+    clones = 5
+    assert len(parent['calls']) == 72*clones
+    call_count = len(template['calls'])
+    assert call_count == stages*replicas == control['complete_invocations']
+    assert control['one_owner_per_complete_invocation']
+    payload = 1024
+
+    widths = [h-len(w['frames'][f]) for f in w['start'][2*v:]]
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    assert entering == replay['entering_helpers']
+    local = {}
+    for orientation, events in programs.items():
+        # Endpoint equality and native frames were already independently
+        # replayed on all n columns in the hash-bound receipt above.
+        env = {('L', r): Q(1) for r in range(n)}
+        peak = Q(1)
+        real = macros = workops = 0
+        paid = Counter()
+        wrappers = {'pre': set(), 'post': set()}
+        for event in events:
+            tag = event[0]
+            if tag == 'climb':
+                paid[event[5]] += 1
+            elif tag == 'center':
+                paid[event[4]] += 1
+            elif tag == 'residual_adapter':
+                _, kind, register, frame = event
+                assert kind in wrappers and entrances.get(register) == frame
+                assert register not in wrappers[kind]
+                wrappers[kind].add(register)
+            elif tag == 'scalar':
+                macros += 1
+                scalar = event[1]
+                op, target = scalar[0], tuple(scalar[1])
+                if op == 'clear':
+                    env[target] = Q(0)
+                    count = 1
+                elif op == 'copy':
+                    env[target] = env[tuple(scalar[2])]
+                    count = 1
+                elif op == 'scale':
+                    q = Q(scalar[2], scalar[3])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert numerator and numerator & (numerator-1) == 0
+                    assert denominator & (denominator-1) == 0
+                    env[target] *= abs(q)
+                    count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0)
+                elif op == 'add':
+                    source = tuple(scalar[2])
+                    q = Q(scalar[3], scalar[4])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert source != target and numerator > 0
+                    assert denominator & (denominator-1) == 0
+                    acc, count = 0, 1  # clear coefficient work
+                    for i, bit in enumerate(bin(numerator)[2:]):
+                        if i:
+                            acc *= 2
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                        if bit == '1':
+                            acc += 1
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                    value = Q(acc)
+                    for _ in range(denominator.bit_length()-1):
+                        value /= 2
+                        count += 1
+                        peak = max(peak, value*env[source])
+                    assert value == abs(q)
+                    count += 2  # signed accumulation and work clear
+                    env[target] = env.get(target, Q(0)) + abs(q)*env[source]
+                    workops += count
+                else:
+                    raise AssertionError(op)
+                real += 2*count
+                peak = max(peak, env[target])
+            else:
+                assert tag in ('adapter', 'phase')
+        assert wrappers['pre'] == wrappers['post'] == set(entrances)
+        assert all(value == 0 for register, value in env.items() if register[0] == 'C')
+        prior = replay['local'][orientation]
+        assert prior['all_exact_columns'] == n and prior['private_work_erased']
+        assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits']
+        bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1
+        assert bits == prior['prefix_bits_upper']
+        assert real == checks[orientation]['real_component_primitive_bound']
+        assert macros == checks[orientation]['scalar_macros']
+        assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()}
+        assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}
+        local[orientation] = dict(
+            events=len(events), macros=macros, real_component_primitives=real,
+            prefix_l1=str(peak), prefix_bits=bits,
+            coefficient_work_primitive_count=workops, all_exact_columns=n,
+            dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True,
+            private_centres_and_coefficient_work_cleared=True,
+            pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']),
+            endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json')
+
+    centres = len(w['centers'])
+    children = sum(checks['forward']['paid_profile'].values())
+    assert checks['forward']['paid_profile'] == checks['backward']['paid_profile']
+    macro_bound = max(row['macros'] for row in local.values())
+    compiler = 64*(m+1)**3
+    adapters = 16*(macro_bound+children+n+centres)+64*m
+    primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler
+
+    bridge_steps = sum(event['kind'] == 'bridge' for event in parent['recipe'])
+    bridge_sweeps = sum(event['kind'] == 'bridge' for event in template['execution_schedule'])
+    assert bridge_sweeps == replicas*bridge_steps
+    bridge_additions = 2*v*bridge_sweeps
+    shifts = blocks_per_stream*v*replicas
+    moves = 2*shifts
+    parent_live, parent_physical = parent['live'], parent['physical']
+    data_stock = 2*v*blocks_per_stream*replicas
+    assert (parent_live-data_stock) % stages == 0
+    parent_banks = (parent_live-data_stock)//stages
+    assert parent_banks >= 0
+    assert parent_physical == parent_live+helpers+centres+2
+    scalar = sum(local[call['orientation']]['real_component_primitives'] for call in template['calls'])
+    factors_per_wrapper = 2*(m-1)
+    wrapper_factors = 2*call_count*entering*factors_per_wrapper
+    nonlocal_items = (
+        4*v*replicas*stages + 2*v*replicas*stages
+        + 2*call_count*helpers
+        + sum(child['replicas'] for child in parent['idle_children'])
+        + stages*parent_banks + bridge_additions + shifts + moves
+        + parent_live + parent_physical + wrapper_factors)
+    outside = 8*nonlocal_items+64*m
+    parent_pervertex = (
+        scalar+bridge_additions+shifts+moves+parent_live
+        +(call_count*adapters+outside)*compiler+64*parent_physical)
+
+    live, physical = template['live'], template['physical']
+    mass, profile = owners['rank_mass'], owners['paid_profile']
+    assert m*live-mass == owners['deficit'] == 2560*clones
+    assert mass == sum(int(r)*count for r, count in profile.items())
+    assert physical == live+helpers+centres+2
+    assert live == owners['live'] and physical == owners['physical']
+    assert live <= parent_live and physical <= parent_physical
+    assert not template['bank_padding']['families']
+    assert owners['explicit_idle_remainder_children'] <= owners['source_idle_children_charged']
+    rebased = parent_pervertex+65*(physical-parent_physical)+(live-parent_live)
+    used = max(rebased, parent_pervertex)
+    retained = None
+    if retained_invoice is not None:
+        previous = read(retained_invoice)
+        assert previous['compiler'] == compiler
+        assert previous['charged_prefix_bits'] <= payload
+        previous_bound = previous['conservative_pervertex_used']
+        # The entire newly reconstructed charge is added to the retained old
+        # allowance. This is intentionally stronger than only paying positive
+        # deltas and makes no claim that the old integration certifies this word.
+        used = max(used, previous_bound+parent_pervertex)
+        retained = dict(sha256=filehash(retained_invoice),
+                        previous_pervertex_allowance=previous_bound,
+                        added_complete_new_pervertex=parent_pervertex,
+                        policy='Retain old allowance and add the entire fresh recount.')
+
+    half = m//2
+    group = 2**(half*half)
+    for i in range(1, half+1):
+        group *= 2**(2*i)-1
+    stock, streamed_mass = group*physical, group*mass
+    logical = group*used+64
+    router = compiler*(logical+1)*(stock+1)**2
+    g_bound, e_bound, c0 = 2**30000, 2**100000, 2**210000
+    total_mass = streamed_mass+e_bound
+    literal = 2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m
+    row = 2*stock.bit_length()+9909+252+2*payload
+    maxchild = max(map(int, profile))
+    inequalities = dict(
+        local_primitive_bound=primitive_bound < 2**48,
+        logical=logical < 2**6050, router=router < g_bound,
+        literal=literal < e_bound, mass=total_mass < 2**100001,
+        precision=32*m*total_mass*total_mass < c0,
+        tape=2*total_mass+18 < c0, row=row < 20161,
+        halving=m*m > 2*maxchild*maxchild)
+    assert all(inequalities.values())
+    localbits = max(row['prefix_bits'] for row in local.values())
+    input_l2_bits = (m+1)//2
+    required_prefix = localbits+input_l2_bits+call_count+bridge_sweeps+4
+    assert required_prefix < payload
+
+    receipt = dict(
+        status='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',
+        template_sha256=template_hash,
+        parent_template_sha256=contenthash(local_dir/'GLOBAL-TEMPLATE.json.gz'),
+        owner_audit_sha256=filehash(audit/'OWNERS-AND-PROFILE.json'),
+        controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        independent_local_replay_sha256=filehash(rp),
+        canonical_word_sha256=filehash(cp), local_programs_sha256=filehash(pp),
+        local_checks_sha256=filehash(local_dir/'LOCAL-CHECKS.json'),
+        global_prefix_bits=required_prefix, charged_prefix_bits=payload,
+        complete_invocation_sweeps=call_count, bridge_sweeps=bridge_sweeps,
+        row_prefix_extra=2*payload, local=local, helpers=helpers,
+        centres=centres, live=live, physical=physical,
+        physical_stock_identity=dict(data_and_owner_families=live,
+                                     local_helpers=helpers, private_centres=centres,
+                                     coefficient_work=2),
+        entering_helpers=entering, entrance_rank=sum(h-width for width in widths),
+        width_inventory=dict(sorted(Counter(widths).items())),
+        local_adapters=adapters, local_primitive_bound=primitive_bound,
+        wrapper_elementary_factors_charged=wrapper_factors,
+        factors_per_wrapper=factors_per_wrapper, compiler=compiler,
+        unhosted_pervertex=parent_pervertex, hosted_rebased_pervertex=rebased,
+        conservative_pervertex_used=used, retained_prior_overcharge=retained,
+        finite=dict(physical_stock_bits=stock.bit_length(), router_bits=router.bit_length(),
+                    literal_bits=literal.bit_length(), physical_row_coefficient=row,
+                    retained_row_coefficient=20161,
+                    required_C0_bits=(32*m*total_mass*total_mass).bit_length(),
+                    halving_integer_inequality=[m*m, 2*maxchild*maxchild],
+                    G_exponent=30000, E_exponent=100000, C0_exponent=210000),
+        strict_checks=inequalities,
+        scope='Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Payload1024 explicitly pays all360 invocation and360 bridge sweeps; physical row allowance20161 remains unchanged.')
+    prefix = dict(
+        status='PASS_ASYNC_GLOBAL_PREFIX', template_sha256=template_hash,
+        global_prefix_bits=required_prefix, retained_payload_bits=payload,
+        complete_invocation_cover_sweeps=call_count,
+        bridge_factor_two_sweeps=bridge_sweeps,
+        local_scalar_coefficient_work_prefix_bits=localbits,
+        stream_input_sup_to_l2_bits=input_l2_bits,
+        primitive_arithmetic_margin_bits=4,
+        controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        independent_local_replay_sha256=filehash(rp),
+        proof=f'Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Actual full orthogonal owner charts act by right-translation bijections on the retained cover group. Count all {call_count} complete local sweeps and {bridge_sweeps} individual bridge sweeps. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently recounted scalar/Horner envelope uses {localbits} bits; input sup-to-L2 uses {input_l2_bits}; arithmetic margin is 4. Total {required_prefix} < {payload}. All-size child/compiler and precision/tape interfaces remain inherited.')
+    out.mkdir(parents=True, exist_ok=True)
+    (out/'PREFIX-AND-INVOICE.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    (out/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix, indent=2)+'\n')
+    print(json.dumps(receipt, indent=2), flush=True)
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--base', type=Path, required=True)
+    parser.add_argument('--hosted', type=Path, required=True)
+    parser.add_argument('--audit', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    parser.add_argument('--retained-invoice', type=Path)
+    args = parser.parse_args()
+    run(args.base, args.hosted, args.audit, args.out, args.retained_invoice)
diff --git a/research/contextual-provider-pooling/complex-global/invoice_mixed.py b/research/contextual-provider-pooling/complex-global/invoice_mixed.py
new file mode 100644
index 0000000000..107d8b6c48
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/invoice_mixed.py
@@ -0,0 +1,260 @@
+"""Mixed complete-call finite invoice. Adapted from PR531/535 and prior five-copy invoice.
+Original attribution: prepared for icekylinx with OpenAI Codex assistance, Apache-2.0.
+Recounts actual source-bound local programs independently; all scalar, owner, storage and prefix charges retained.
+"""
+import argparse
+import gzip
+import hashlib
+import json
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def filehash(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def contenthash(path):
+    data = path.read_bytes()
+    return hashlib.sha256(gzip.decompress(data) if path.suffix == '.gz' else data).hexdigest()
+
+
+def audit_local(local_dir,m):
+    cp=local_dir/'CANONICAL-WORD.json.gz';pp=local_dir/'LOCAL-PROGRAMS.json.gz';rp=local_dir/'INDEPENDENT-LOCAL-REPLAY.json'
+    w,programs,replay=read(cp),read(pp),read(rp);checks=read(local_dir/'LOCAL-CHECKS.json')
+    assert set(programs)=={'forward','backward'}
+    assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+    assert replay['canonical_word_sha256']==filehash(cp) and replay['local_programs_sha256']==filehash(pp)
+    v,helpers,h=w['v'],w['R'],w['h'];assert(v,helpers,h,m)==(112,504,9,73)
+    assert replay['v']==v and replay['helpers']==helpers
+    n=2*v+helpers
+    widths = [h-len(w['frames'][f]) for f in w['start'][2*v:]]
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    assert entering == replay['entering_helpers']
+    local = {}
+    for orientation, events in programs.items():
+        # Endpoint equality and native frames were already independently
+        # replayed on all n columns in the hash-bound receipt above.
+        env = {('L', r): Q(1) for r in range(n)}
+        peak = Q(1)
+        real = macros = workops = 0
+        paid = Counter()
+        wrappers = {'pre': set(), 'post': set()}
+        for event in events:
+            tag = event[0]
+            if tag == 'climb':
+                paid[event[5]] += 1
+            elif tag == 'center':
+                paid[event[4]] += 1
+            elif tag == 'residual_adapter':
+                _, kind, register, frame = event
+                assert kind in wrappers and entrances.get(register) == frame
+                assert register not in wrappers[kind]
+                wrappers[kind].add(register)
+            elif tag == 'scalar':
+                macros += 1
+                scalar = event[1]
+                op, target = scalar[0], tuple(scalar[1])
+                if op == 'clear':
+                    env[target] = Q(0)
+                    count = 1
+                elif op == 'copy':
+                    env[target] = env[tuple(scalar[2])]
+                    count = 1
+                elif op == 'scale':
+                    q = Q(scalar[2], scalar[3])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert numerator and numerator & (numerator-1) == 0
+                    assert denominator & (denominator-1) == 0
+                    env[target] *= abs(q)
+                    count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0)
+                elif op == 'add':
+                    source = tuple(scalar[2])
+                    q = Q(scalar[3], scalar[4])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert source != target and numerator > 0
+                    assert denominator & (denominator-1) == 0
+                    acc, count = 0, 1  # clear coefficient work
+                    for i, bit in enumerate(bin(numerator)[2:]):
+                        if i:
+                            acc *= 2
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                        if bit == '1':
+                            acc += 1
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                    value = Q(acc)
+                    for _ in range(denominator.bit_length()-1):
+                        value /= 2
+                        count += 1
+                        peak = max(peak, value*env[source])
+                    assert value == abs(q)
+                    count += 2  # signed accumulation and work clear
+                    env[target] = env.get(target, Q(0)) + abs(q)*env[source]
+                    workops += count
+                else:
+                    raise AssertionError(op)
+                real += 2*count
+                peak = max(peak, env[target])
+            else:
+                assert tag in ('adapter', 'phase')
+        assert wrappers['pre'] == wrappers['post'] == set(entrances)
+        assert all(value == 0 for register, value in env.items() if register[0] == 'C')
+        prior = replay['local'][orientation]
+        assert prior['all_exact_columns'] == n and prior['private_work_erased']
+        assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits']
+        bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1
+        assert bits == prior['prefix_bits_upper']
+        assert real == checks[orientation]['real_component_primitive_bound']
+        assert macros == checks[orientation]['scalar_macros']
+        assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()}
+        assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}
+        local[orientation] = dict(
+            events=len(events), macros=macros, real_component_primitives=real,
+            prefix_l1=str(peak), prefix_bits=bits,
+            coefficient_work_primitive_count=workops, all_exact_columns=n,
+            dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True,
+            private_centres_and_coefficient_work_cleared=True,
+            pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']),
+            endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json')
+
+    centres = len(w['centers'])
+    children = sum(checks['forward']['paid_profile'].values())
+    assert checks['forward']['paid_profile'] == checks['backward']['paid_profile']
+    macro_bound = max(row['macros'] for row in local.values())
+    compiler = 64*(m+1)**3
+    adapters = 16*(macro_bound+children+n+centres)+64*m
+    primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler
+
+
+    return dict(local=local,widths=widths,entering=entering,centres=centres,helpers=helpers,adapters=adapters,compiler=compiler,primitive_bound=primitive_bound,
+      binding=dict(canonical_word_sha256=filehash(cp),local_programs_sha256=filehash(pp),local_checks_sha256=filehash(local_dir/'LOCAL-CHECKS.json'),independent_local_replay_sha256=filehash(rp)))
+
+def run(base,hosted,audit,out,providers,retained_invoice=None):
+    local_dir=base/'split-centres';parent=read(local_dir/'GLOBAL-TEMPLATE.json.gz');template_path=hosted/'GLOBAL-TEMPLATE.json.gz';template=read(template_path)
+    owners=read(audit/'OWNERS-AND-PROFILE.json');control=read(audit/'ASYNC-AUDIT.json');template_hash=contenthash(template_path)
+    assert template_hash==control['complex_template_sha256']==owners['template_sha256']
+    assert owners['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+    locations=read(providers);records={k:audit_local(Path(v),73)for k,v in locations.items()}
+    assert set(records)==set(c['provider']for c in template['calls'])
+    for k,z in records.items():
+        for field,value in z['binding'].items():assert template['provider_registry'][k][field]==value,(k,field)
+    assert template['recipe']==parent['recipe']
+    assert Counter((c['orientation'],c['stage'],c['replica'])for c in template['calls'])==Counter((c['orientation'],c['stage'],c['replica'])for c in parent['calls'])
+    v,helpers,h,m,n=112,504,9,73,728;centres=8;stages=9;blocks_per_stream=4
+    replicas=1+max(c['replica']for c in template['calls']);assert replicas%8==0;clones=replicas//8
+    call_count=len(template['calls']);assert call_count==stages*replicas==control['complete_invocations'];assert control['one_owner_per_complete_invocation']
+    payload=512 if clones==1 else 1024
+    compiler=64*(m+1)**3;adapters=max(z['adapters']for z in records.values());primitive_bound=max(z['primitive_bound']for z in records.values())
+    assert all(z['helpers']==helpers and z['centres']==centres and z['compiler']==compiler for z in records.values())
+    entering=max(z['entering']for z in records.values())
+    local={k+':'+o:row for k,z in records.items()for o,row in z['local'].items()}
+    bridge_steps = sum(event['kind'] == 'bridge' for event in parent['recipe'])
+    bridge_sweeps = sum(event['kind'] == 'bridge' for event in template['execution_schedule'])
+    assert bridge_sweeps == replicas*bridge_steps
+    bridge_additions = 2*v*bridge_sweeps
+    shifts = blocks_per_stream*v*replicas
+    moves = 2*shifts
+    parent_live, parent_physical = parent['live'], parent['physical']
+    data_stock = 2*v*blocks_per_stream*replicas
+    assert (parent_live-data_stock) % stages == 0
+    parent_banks = (parent_live-data_stock)//stages
+    assert parent_banks >= 0
+    assert parent_physical == parent_live+helpers+centres+2
+    scalar = sum(records[call['provider']]['local'][call['orientation']]['real_component_primitives'] for call in template['calls'])
+    factors_per_wrapper = 2*(m-1)
+    wrapper_factors = 2*call_count*entering*factors_per_wrapper
+    nonlocal_items = (
+        4*v*replicas*stages + 2*v*replicas*stages
+        + 2*call_count*helpers
+        + sum(child['replicas'] for child in parent['idle_children'])
+        + stages*parent_banks + bridge_additions + shifts + moves
+        + parent_live + parent_physical + wrapper_factors)
+    outside = 8*nonlocal_items+64*m+128*call_count*len(records) # Explicit registry selection/table dispatch charge.
+    parent_pervertex = (
+        scalar+bridge_additions+shifts+moves+parent_live
+        +(call_count*adapters+outside)*compiler+64*parent_physical)
+
+    live, physical = template['live'], template['physical']
+    mass, profile = owners['rank_mass'], owners['paid_profile']
+    assert m*live-mass == owners['deficit'] == 2560*clones
+    assert mass == sum(int(r)*count for r, count in profile.items())
+    assert physical == live+helpers+centres+2
+    assert live == owners['live'] and physical == owners['physical']
+    assert live <= parent_live and physical <= parent_physical
+    assert not template['bank_padding']['families']
+    assert owners['explicit_idle_remainder_children'] <= owners['source_idle_children_charged']
+    rebased = parent_pervertex+65*(physical-parent_physical)+(live-parent_live)
+    used = max(rebased, parent_pervertex)
+    retained = None
+    if retained_invoice is not None:
+        previous = read(retained_invoice)
+        assert previous['compiler'] == compiler
+        assert previous['charged_prefix_bits'] <= payload
+        previous_bound = previous['conservative_pervertex_used']
+        # The entire newly reconstructed charge is added to the retained old
+        # allowance. This is intentionally stronger than only paying positive
+        # deltas and makes no claim that the old integration certifies this word.
+        used = max(used, previous_bound+parent_pervertex)
+        retained = dict(sha256=filehash(retained_invoice),
+                        previous_pervertex_allowance=previous_bound,
+                        added_complete_new_pervertex=parent_pervertex,
+                        policy='Retain old allowance and add the entire fresh recount.')
+
+    half = m//2
+    group = 2**(half*half)
+    for i in range(1, half+1):
+        group *= 2**(2*i)-1
+    stock, streamed_mass = group*physical, group*mass
+    logical = group*used+64
+    router = compiler*(logical+1)*(stock+1)**2
+    g_bound, e_bound, c0 = 2**30000, 2**100000, 2**210000
+    total_mass = streamed_mass+e_bound
+    literal = 2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m
+    row = 2*stock.bit_length()+9909+252+2*payload
+    maxchild = max(map(int, profile))
+    inequalities = dict(
+        local_primitive_bound=primitive_bound < 2**48,
+        logical=logical < 2**6050, router=router < g_bound,
+        literal=literal < e_bound, mass=total_mass < 2**100001,
+        precision=32*m*total_mass*total_mass < c0,
+        tape=2*total_mass+18 < c0, row=row < 20161,
+        halving=m*m > 2*maxchild*maxchild)
+    assert all(inequalities.values())
+    localbits = max(row['prefix_bits'] for row in local.values())
+    input_l2_bits = (m+1)//2
+    required_prefix = localbits+input_l2_bits+call_count+bridge_sweeps+4
+    assert required_prefix < payload
+
+    receipt=dict(status='PASS_INDEPENDENT_MIXED_SCALAR_PREFIX_AND_FINITE_INVOICE',template_sha256=template_hash,parent_template_sha256=contenthash(local_dir/'GLOBAL-TEMPLATE.json.gz'),
+      owner_audit_sha256=filehash(audit/'OWNERS-AND-PROFILE.json'),controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+      provider_bindings={k:z['binding']for k,z in records.items()},provider_counts=dict(Counter(c['provider']for c in template['calls'])),
+      global_prefix_bits=required_prefix,charged_prefix_bits=payload,complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,
+      local=local,helpers=helpers,centres=centres,live=live,physical=physical,physical_stock_identity=dict(data_and_owner_families=live,local_helpers=helpers,private_centres=centres,coefficient_work=2),
+      provider_widths={k:dict(sorted(Counter(z['widths']).items()))for k,z in records.items()},local_adapters=adapters,local_primitive_bound=primitive_bound,
+      wrapper_elementary_factors_charged=wrapper_factors,factors_per_wrapper=factors_per_wrapper,compiler=compiler,unhosted_pervertex=parent_pervertex,hosted_rebased_pervertex=rebased,
+      conservative_pervertex_used=used,retained_prior_overcharge=retained,registry_dispatch_charge=128*call_count*len(records),
+      finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,
+        required_C0_bits=(32*m*total_mass*total_mass).bit_length(),halving_integer_inequality=[m*m,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=inequalities,
+      scope='Fresh independent recount of every selected local supplier, full calls/bridges, maximum adapters and explicit finite registry dispatch. All-size compiler, precision/tape and analytic interfaces remain conditional.')
+    prefix=dict(status='PASS_MIXED_GLOBAL_PREFIX',template_sha256=template_hash,global_prefix_bits=required_prefix,retained_payload_bits=payload,
+      proof='Use maximum freshly recounted local prefix, pay every complete call and bridge sweep, input conversion and arithmetic margin. No unproved block-norm saving is used.')
+    out.mkdir(parents=True,exist_ok=True)
+    (out/'PREFIX-AND-INVOICE.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    (out/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
+    print(json.dumps(receipt,indent=2),flush=True)
+
+if __name__=='__main__':
+    if not __debug__:raise RuntimeError('Assertions required')
+    p=argparse.ArgumentParser();p.add_argument('--base',type=Path,required=True);p.add_argument('--hosted',type=Path,required=True);p.add_argument('--audit',type=Path,required=True);p.add_argument('--out',type=Path,required=True);p.add_argument('--providers',type=Path,required=True);p.add_argument('--retained-invoice',type=Path);a=p.parse_args()
+    run(a.base,a.hosted,a.audit,a.out,a.providers,a.retained_invoice)
+
diff --git a/research/contextual-provider-pooling/complex-global/replay.py b/research/contextual-provider-pooling/complex-global/replay.py
new file mode 100644
index 0000000000..8908963323
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/replay.py
@@ -0,0 +1,32 @@
+"""Portable mixed-provider finite-clone controller and independent physical invoice."""
+from pathlib import Path
+import argparse,json,shutil,subprocess,sys,time,os
+ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--providers',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args()
+P=Path(__file__).resolve().parent;v=P/'vendor531';q=P/'vendor535';out=a.out.resolve();assert not out.exists();out.mkdir(parents=True)
+locations=json.loads(a.providers.read_text());assert set(locations)=={'n0','n2','n6','n8'}
+# Resolve input locations once; the execution template records hashes and programs, not these paths.
+locations={k:str((a.providers.resolve().parent/Path(v)).resolve())for k,v in locations.items()}
+providers=out/'PROVIDERS.json';providers.write_text(json.dumps(locations,indent=2)+'\n',encoding='utf8',newline='\n')
+launcher=P/'run_portable.py';stages=[]
+controller=out/'controller-input';shutil.copytree(v/'inputs/data-base',controller);(controller/'split-centres').mkdir(exist_ok=True)
+shutil.copyfile(q/'inputs/ROUND20-PARENT-TEMPLATE.json.gz',controller/'split-centres/GLOBAL-TEMPLATE.json.gz')
+shutil.copyfile(v/'evidence/local/CANONICAL-WORD.json.gz',controller/'split-centres/CANONICAL-WORD.json.gz')
+for f in controller.rglob('*'):
+ if f.is_file()and f.suffix in('.json','.py','.md','.txt'):f.write_bytes(f.read_bytes().replace(b'\r\n',b'\n'))
+source_plan=out/'SOURCE-PLAN.json';source_plan.write_bytes((P/'inputs558/PLAN.json').read_bytes().replace(b'\r\n',b'\n'))
+def run(name,script,*args):
+ t=time.monotonic();log=out/(name+'.log');print('RUN',name,flush=True)
+ with log.open('w',encoding='utf8',newline='\n')as f:z=subprocess.run([sys.executable,'-B',str(launcher),str(script),*map(str,args)],stdout=f,stderr=subprocess.STDOUT,env=dict(os.environ,PYTHONUTF8='1',PYTHONDONTWRITEBYTECODE='1'))
+ stages.append({'name':name,'seconds':time.monotonic()-t,'exit':z.returncode});(out/'STAGES.json').write_text(json.dumps(stages,indent=2)+'\n',encoding='utf8',newline='\n')
+ if z.returncode:print(log.read_text(encoding='utf8'),flush=True);raise SystemExit(name+' failed')
+ print('PASS',name,flush=True)
+source=out/'source-base';mixed=out/'mixed72';clone=out/'clone';base=clone/'base';hosted=out/'hosted';audit=out/'audit';audit.mkdir()
+run('01-bind',v/'code/prepare_supplier_base.py','--data-base',controller,'--local',locations['n0'],'--out',source)
+run('02-mixed-selector',P/'build_mixed72.py','--owners',P/'inputs558/OWNERS.json.gz','--plan',source_plan,'--providers',providers,'--out',mixed)
+run('03-clone',P/'build_mixed_clone.py','--base',source,'--owners',mixed/'OWNERS.json.gz','--plan',mixed/'PLAN.json','--out',clone)
+run('04-source-lift',P/'audit_clone_lift.py','--source-base',source,'--clone-base',base,'--output',audit/'CLONE-LIFT.json','--mutation-controls')
+run('05-emit',P/'emit_mixed.py','--base',base,'--owners',clone/'OWNERS.json.gz','--plan',clone/'PLAN.json','--providers',providers,'--out',hosted)
+run('06-physical',P/'audit_mixed.py',base,hosted,audit/'ASYNC-AUDIT.json','--providers',providers,'--mutation-controls')
+run('07-invoice',P/'invoice_mixed.py','--base',base,'--hosted',hosted,'--audit',audit,'--out',audit,'--providers',providers,'--retained-invoice',v/'evidence/audit/PREFIX-AND-INVOICE.json')
+r=json.loads((audit/'ASYNC-AUDIT.json').read_text());z={'status':'PASS_MIXED_PROVIDER_WHOLE_OWNER_PHYSICAL_AND_FINITE_INVOICE','complex_template_sha256':r['template_sha256'],'source_base':'source-base','base':'clone/base','hosted':'hosted','audit':'audit','providers':'PROVIDERS.json','live':r['complex_live'],'profile':r['complex_profile'],'deficit':r['deficit'],'stages':stages,'scope':'Fresh source-bound local providers, deterministic per-call selector and finite clone pooling; exact all47 scalar assembly is performed by the top-level verifier.'}
+(out/'RESULT.json').write_text(json.dumps(z,indent=2)+'\n',encoding='utf8',newline='\n');print(json.dumps(z,indent=2))
diff --git a/research/contextual-provider-pooling/complex-global/run_complex44.py b/research/contextual-provider-pooling/complex-global/run_complex44.py
new file mode 100644
index 0000000000..325eca7d4f
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/run_complex44.py
@@ -0,0 +1,29 @@
+"""Fresh changed static44 complete-owner emission, controller audit and finite invoice."""
+from pathlib import Path
+import sys,json,gzip,shutil,subprocess,time,os
+assert len(sys.argv)==8,'run_complex44.py V531 P535 LOCAL OWNERS PLAN PORTABLE_LAUNCHER OUT'
+v,p,local,owners,plan,launcher,out=map(lambda x:Path(x).resolve(),sys.argv[1:]);assert not out.exists();out.mkdir(parents=True)
+controller=out/'controller-input';shutil.copytree(v/'inputs/data-base',controller);(controller/'split-centres').mkdir(exist_ok=True)
+shutil.copyfile(p/'inputs/ROUND20-PARENT-TEMPLATE.json.gz',controller/'split-centres/GLOBAL-TEMPLATE.json.gz')
+shutil.copyfile(v/'evidence/local/CANONICAL-WORD.json.gz',controller/'split-centres/CANONICAL-WORD.json.gz')
+# Text inputs are canonically copied, independent of Git checkout newlines.
+for f in controller.rglob('*'):
+ if f.is_file() and f.suffix in ('.json','.py','.md','.txt'):
+  f.write_bytes(f.read_bytes().replace(b'\r\n',b'\n'))
+plan_copy=out/'PLAN.json';plan_copy.write_bytes(plan.read_bytes().replace(b'\r\n',b'\n'));plan=plan_copy
+bit_fixture=out/'PR510-EXPECTED.json';bit_fixture.write_bytes((p/'inputs/PR510-EXPECTED.json').read_bytes().replace(b'\r\n',b'\n'))
+stages=[]
+def run(name,script,*args):
+ t=time.monotonic();log=out/(name+'.log');print('RUN',name,flush=True)
+ with log.open('w',encoding='utf-8',newline='\n')as f:z=subprocess.run([sys.executable,'-B',str(launcher),str(script),*map(str,args)],stdout=f,stderr=subprocess.STDOUT,env=dict(os.environ,PYTHONUTF8='1',PYTHONDONTWRITEBYTECODE='1'))
+ stages.append(dict(name=name,seconds=time.monotonic()-t,exit=z.returncode));(out/'STAGES.json').write_text(json.dumps(stages,indent=2)+'\n',encoding='utf-8',newline='\n')
+ if z.returncode:print(log.read_text(encoding='utf-8'),flush=True);raise SystemExit(name+' failed')
+ print('PASS',name,round(stages[-1]['seconds'],2),flush=True)
+run('01-bind',v/'code/prepare_supplier_base.py','--data-base',controller,'--local',local,'--out',out/'base')
+run('02-emit',v/'code/emit_supplier_hosted.py','--base',out/'base','--owners',owners,'--plan',plan,'--out',out/'hosted')
+audit=out/'audit';audit.mkdir()
+run('03-physical',v/'code/audit_supplier_hosted.py',out/'base',out/'hosted',audit/'ASYNC-AUDIT.json','--mutation-controls')
+run('04-invoice',v/'code/invoice_final.py','--base',out/'base','--hosted',out/'hosted','--audit',audit,'--out',audit,'--retained-invoice',v/'evidence/audit/PREFIX-AND-INVOICE.json')
+run('05-moments',p/'code/assemble_combined.py',audit,out/'base',out/'hosted',bit_fixture)
+z=json.loads((audit/'EXACT-ASSEMBLY.json').read_text());r=dict(status='PASS_CHANGED_COMPLEX_SUPPLIER_AND_LITERAL_WHOLE_OWNER_PACKING',complex_lower=z['complex_lower'],complex_template_sha256=z['complex_template_sha256'],stages=stages,scope='Actual changed local supplier and whole-owner controller admitted with fresh phase/frame/chart/finite invoice under retained all-size interfaces. Bit cited by this assembly is a regression; root separately assembles the new changed bit supplier.')
+(out/'RESULT.json').write_text(json.dumps(r,indent=2)+'\n',encoding='utf-8',newline='\n');print(json.dumps(r,indent=2),flush=True)
diff --git a/research/contextual-provider-pooling/complex-global/run_portable.py b/research/contextual-provider-pooling/complex-global/run_portable.py
new file mode 100644
index 0000000000..2fed13f432
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/run_portable.py
@@ -0,0 +1,24 @@
+"""Run one retained verifier with UTF-8/LF text outputs on every platform.
+This changes output serialization only; no mathematical operation is replaced.
+"""
+from pathlib import Path
+import runpy,sys,gzip
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+original_write_text=Path.write_text
+def write_text_lf(self,data,encoding=None,errors=None,newline=None):
+    return original_write_text(self,data,encoding=encoding or 'utf-8',errors=errors,newline='\n')
+Path.write_text=write_text_lf
+# Pin generated gzip serialization. Python3.11 may expose zlib's platform OS
+# byte, Python3.13 normalizes it, and Python3.15 changes the default level.
+# Immutable input files are never rewritten by this wrapper.
+original_gzip_compress=gzip.compress
+def compress_portable(data,compresslevel=9,*,mtime=0):
+    raw=original_gzip_compress(data,compresslevel=compresslevel,mtime=mtime)
+    assert raw[:3]==b'\x1f\x8b\x08' and len(raw)>=18
+    return raw[:9]+b'\xff'+raw[10:]
+gzip.compress=compress_portable
+script=Path(sys.argv[1]).resolve()
+sys.argv=sys.argv[1:]
+sys.path.insert(0,str(script.parent))
+runpy.run_path(str(script),run_name='__main__')
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/LICENSE b/research/contextual-provider-pooling/complex-global/vendor531/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
+      source, and configuration files.
+
+      "Object" form shall mean any form resulting from mechanical
+      transformation or translation of a Source form, including but
+      not limited to compiled object code, generated documentation,
+      and conversions to other media types.
+
+      "Work" shall mean the work of authorship, whether in Source or
+      Object form, made available under the License, as indicated by a
+      copyright notice that is included in or attached to the work
+      (an example is provided in the Appendix below).
+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
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+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
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+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
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+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
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+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
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+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
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+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
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+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
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+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
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+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
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diff --git a/research/contextual-provider-pooling/complex-global/vendor531/NOTICE.md b/research/contextual-provider-pooling/complex-global/vendor531/NOTICE.md
new file mode 100644
index 0000000000..f3833c1cb2
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/NOTICE.md
@@ -0,0 +1,24 @@
+# Attribution and derivative scope
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance; Apache-2.0.
+Copyright 2026 icekylinx. Local review and submission packaging used OpenAI Codex.
+The new work is the same-partition 504-helper scalar architecture, its frozen
+entrance selection, delivery-frame coalescing, literal global allocation,
+targeted certificate reuse and complete new finite recount.
+
+The included Hamming inputs, Gaussian-dyadic Clifford compiler, primitive
+scalar routines, rational moment engines and outer assembly descend from the
+authors recorded in `SOURCES.json` and `inputs/PR523-ANCESTRY.json`. Original
+source notices are retained. In particular, DreamingOfClouds' gauge/kernel
+and paid-wrapper files retain their notice crediting Claude Opus 5.5 assistance;
+those files are not presented as newly authored work.
+
+contributor (handle omitted)'s PR522 rank-sector coordinate-total principle was inspected and is
+credited as a related idea. This increment does not import its ranksector99
+patch or add its reported gain arithmetically. Higherbeing's PR520 face-packet
+geometry helped direct the structural investigation; its code is not copied.
+The latest numerical comparison, Rohan Arun's PR527, is a comparison source.
+
+The reproduction wrapper deliberately separates fresh changed-word/global
+checks from reuse of the byte-pinned completed baseline and unchanged bit
+operator. Old finite receipts never stand in for the changed local word.
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/SOURCES.json b/research/contextual-provider-pooling/complex-global/vendor531/SOURCES.json
new file mode 100644
index 0000000000..6991a2a9c6
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/SOURCES.json
@@ -0,0 +1,63 @@
+{
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "prepared_for": "icekylinx",
+  "assistance": "OpenAI GPT-6 Astra",
+  "license": "Apache-2.0",
+  "baseline": {
+    "pr": 523,
+    "author": "icekylinx",
+    "head": "a900f98be8ff2c09d3292b5112d4731dbd0c8438",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/523",
+    "role": "112 ordered ports, fixed data controller, completed phase cache and finite baseline allowances."
+  },
+  "retained": [
+    {
+      "pr": 514,
+      "author": "contributor (handle omitted)",
+      "head": "246bfacd4cb4072836ae3147099f548bb728229f",
+      "role": "Pinned Hamming modules and scalar constructor ancestry; derived from PR507 and PR425/433."
+    },
+    {
+      "pr": 493,
+      "author": "eumemic",
+      "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7",
+      "role": "Unchanged bit supplier; published histogram repriced, operator not reconstructed."
+    },
+    {
+      "pr": 484,
+      "author": "DreamingOfClouds",
+      "head": "035845ce95f31d0a2dcfb42b8c8e13411271fa5f",
+      "role": "Attributed shared-donor kernel, entrance-gauge, paid-wrapper and hosting lineage; original Claude Opus assistance notices retained."
+    }
+  ],
+  "related_ideas": [
+    {
+      "pr": 522,
+      "author": "contributor (handle omitted)",
+      "head": "e9f8075b5212e9bddf361097dbb022dcd052e0bb",
+      "role": "Rank-sector coordinate-total principle inspected and credited. Its ranksector99 patch is not imported; this word completes eight independent retired carriers before the center cut."
+    },
+    {
+      "pr": 520,
+      "author": "higherbeing",
+      "head": "6077fa76950facbce11ec2f04dfbc93493114a44",
+      "role": "Face-packet delivery geometry and open allocation framing informed the bottleneck investigation; no PR520 implementation is copied."
+    }
+  ],
+  "comparison": {
+    "pr": 527,
+    "author": "rohanarun",
+    "head": "2080903b9e6bd01e3f64cc4c7c62ea1b3af0aa6a",
+    "kappa": "0.001467289440740487",
+    "role": "Latest comparable numerical PR in the recorded snapshot; comparison only."
+  },
+  "new_contribution": "Same-partition direct output loading and two-half face delivery with 504 helpers; 72 compatible gauges and 80 exact kernel pivots; body frame coalescing; literal pure-pattern whole-owner allocation; fresh finite global invoice and exact kappa.",
+  "ancestry_file": "inputs/PR523-ANCESTRY.json",
+  "comparison_at_submission": {
+    "pr": 529,
+    "author": "chafreaky",
+    "head": "05fc7e332651a41860add3c217cd6f6e88758003",
+    "kappa": "0.001469603966017302",
+    "role": "Comparison only; no code or proof imported."
+  }
+}
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/code/adapters_local.py b/research/contextual-provider-pooling/complex-global/vendor531/code/adapters_local.py
new file mode 100644
index 0000000000..787416e4dd
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/code/adapters_local.py
@@ -0,0 +1,60 @@
+"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.  The wrapper construction follows PR #458
+(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first);
+S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers  R_E^-1  before the whole local invocation and  L_E^-1  after its
+full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically.
+usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json
+Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive
+constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that  L_E^-1 S_E R_E^-1  has exactly the
+tableau and zero-state vector (global phase included) of  fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong
+translation, wrong width) must be rejected."""
+import copy, gzip, json, sys
+from pathlib import Path
+# Package-path adaptation only; the exact wrapper mathematics is unchanged.
+R = Path(__file__).resolve().parents[1]
+sys.path.insert(0, str(R / 'vendor/clifford'))
+from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity
+n = 9; FULL = tuple(1 << i for i in range(n))
+def monomial_op(rec):
+    """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)"""
+    out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset']))
+    return out.then(Op(n, identity(n), [('phase', rec['phase'])]))
+def S_of(U):
+    return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, FULL))
+def wrapped_ok(U, rec):
+    """exactly: L^-1 S R^-1 = C_[w] x I  (apply order: R^-1, S, L^-1)"""
+    w = n - len(U); S = S_of(U); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left'])
+    net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w))
+    return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state()
+def main():
+    c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v']
+    starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0})
+    recipes = {}
+    for f in starts:
+        U = frames[f]; rec, compiled = lower_child(S_of(U))
+        recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right'])
+    Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes), sort_keys=True, separators=(',', ':')) + '\n')
+    # ---- independent decode of the serialized file
+    data = json.loads(Path(sys.argv[2]).read_text())['recipes']
+    dot = lambda a, b: bin(a & b).count('1') & 1
+    detail = []
+    for f in starts:
+        rec = data[str(f)]; U = frames[f]
+        assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f)
+        detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U),
+                           totally_isotropic=all(dot(a, b) == 0 for a in U for b in U)))
+    controls = []
+    def reject(name, fn):
+        f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec)
+        if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name)
+        controls.append(name)
+    reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4))
+    reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1))
+    reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4))
+    reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left'])))
+    reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1))
+    res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail),
+               all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail)
+    Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n')
+    print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight'])
+if __name__ == '__main__': main()
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/code/audit_and_transport.py b/research/contextual-provider-pooling/complex-global/vendor531/code/audit_and_transport.py
new file mode 100644
index 0000000000..95ae517f2e
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/code/audit_and_transport.py
@@ -0,0 +1,222 @@
+"""Rebuild arbitrary-dirt compensation and transport a changed local word.
+
+Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0.
+Adapted from PR425/433 (icekylinx), PR484's audit_gk.py
+(DreamingOfClouds), and Round19's 112-port transport. This auditor does not
+import a constructor, a nominated compensation table, or a global price.
+Only the changed scalar word and its actual frame chains are checked here.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def content_hash(path):
+    data = path.read_bytes()
+    return hashlib.sha256(gzip.decompress(data) if path.suffix == '.gz' else data).hexdigest()
+
+
+def basis(vs):
+    pivots = {}
+    for x in vs:
+        for k in sorted(pivots, reverse=True):
+            if x >> k & 1:
+                x ^= pivots[k]
+        if x:
+            k = x.bit_length() - 1
+            for j in pivots:
+                if pivots[j] >> k & 1:
+                    pivots[j] ^= x
+            pivots[k] = x
+    return tuple(pivots[k] for k in sorted(pivots, reverse=True))
+
+
+def apply(e, rows):
+    if e[0] == 'scale':
+        _, target, a, b, *_ = e
+        q = Q(a, b)
+        assert q
+        rows[target] = {j: q*x for j, x in rows[target].items()}
+    else:
+        _, target, source, a, b, *_ = e
+        assert target != source
+        q = Q(a, b)
+        for j, x in list(rows[source].items()):
+            value = rows[target].get(j, Q(0)) + q*x
+            if value:
+                rows[target][j] = value
+            else:
+                rows[target].pop(j, None)
+
+
+def inverse(e):
+    e = copy.deepcopy(e)
+    if e[0] == 'add':
+        e[3] *= -1
+    else:
+        e[2], e[3] = e[3], e[2]
+    return e
+
+
+def dual(e):
+    e = inverse(e)
+    if e[0] == 'add':
+        e[1], e[2] = e[2], e[1]
+    return e
+
+
+def run(raw_path, routing_path, out):
+    start_time = time.monotonic()
+    word, routing = read(raw_path), read(routing_path)
+    v, h, helpers = word['report']['v'], word['report']['h'], word['report']['R']
+    assert h == 9 and v == 112 and routing['v'] == v
+    n = 2*v + helpers
+    ident = lambda: [{r: Q(1)} for r in range(n)]
+    main = word['A'] + word['cut'] + word['B']
+    assert all(not v <= e[2] < 2*v for e in word['A'] + word['B']
+               if e[0] == 'add' and not v <= e[1] < 2*v)
+    matrix = ident()
+    for e in main:
+        apply(e, matrix)
+    dirty = [{} for _ in range(n)]
+    for r in range(v, 2*v):
+        dirty[r] = {j: x for j, x in matrix[r].items() if j >= 2*v}
+    for e in word['precondition']:
+        apply(e, dirty)
+    compensation = [['add', r, j, -q.numerator, q.denominator, []]
+                    for r in range(v, 2*v) for j, q in sorted(dirty[r].items())]
+    entering = set(map(int, word.get('start_extra', {})))
+    assert all(e[2] not in entering for e in compensation)
+    cleanup = [inverse(e) for e in reversed(word['A'] + word['B'])
+               if not v <= e[1] < 2*v]
+    assert [e[:-1] for e in cleanup] == [e[:-1] for e in word['cleanup']]
+    program = word['precondition'] + compensation + main + cleanup
+    for backward in (False, True):
+        actual = ident()
+        for e in program:
+            apply(dual(e) if backward else e, actual)
+        expected = ident()
+        for t in range(v):
+            expected[t if backward else v+t][v+t if backward else t] = Q(-1 if backward else 1)
+        assert actual == expected, ('arbitrary-dirt endpoint', backward)
+    # The native scalar compiler allows dyadic additions and signed binary scales.
+    for e in program:
+        q = Q(e[3], e[4]) if e[0] == 'add' else Q(e[2], e[3])
+        assert q.denominator & (q.denominator-1) == 0
+        if e[0] == 'scale':
+            a = abs(q.numerator)
+            assert a and a & (a-1) == 0
+
+    tau = lambda x: x ^ (43 if (x & 43).bit_count() % 2 else 0)
+    ports = routing['ports']
+    assert len(set(ports)) == v and set(map(tau, word['ports'])) == set(ports)
+    mapping = {i: ports.index(tau(p)) for i, p in enumerate(word['ports'])}
+    mapping.update({v+i: v+mapping[i] for i in range(v)})
+    mapping.update({r: r for r in range(2*v, n)})
+    full = tuple(1 << i for i in range(h-1, -1, -1))
+    frames, frame_ids = [(), full], {(): 0, full: 1}
+
+    def fid(vectors):
+        frame = basis(vectors)
+        if frame not in frame_ids:
+            frame_ids[frame] = len(frames)
+            frames.append(frame)
+        return frame_ids[frame]
+
+    def transform(e):
+        e = copy.deepcopy(e)
+        e[1] = mapping[e[1]]
+        if e[0] == 'add':
+            e[2] = mapping[e[2]]
+        if e[-1] is not None:
+            e[-1] = fid([tau(x) for x in e[-1]])
+        return e
+
+    canonical = {key: [transform(e) for e in word[key]]
+                 for key in ('A', 'B', 'cut', 'cleanup', 'precondition')}
+    canonical['compensation'] = [transform(e) for e in compensation]
+    canonical['start'] = [fid([p]) for p in ports] + [0]*(v+helpers)
+    for r, frame in word.get('start_extra', {}).items():
+        assert 2*v <= int(r) < n
+        canonical['start'][int(r)] = fid([tau(x) for x in frame])
+    canonical['final'] = ([1]*v +
+        [fid(x for x in range(1, 1 << h) if (x & p).bit_count() % 2 == 0) for p in ports] +
+        [1]*helpers)
+    canonical.update(h=h, v=v, R=helpers, ports=ports, frames=frames,
+                     centers=[mapping[r] for r in word['centers']],
+                     center_frames=[fid(tau(x) for x in frame) for frame in word['center_frames']])
+    levels = {mapping[v+int(t)]-v: fid(tau(x) for x in frame)
+              for t, frame in word.get('target_levels', {}).items()}
+    canonical['target_levels'] = {str(t): f for t, f in levels.items()}
+    current, paid, edges = canonical['start'].copy(), Counter(), set()
+
+    def climb(r, f):
+        old = current[r]
+        assert basis(frames[old] + frames[f]) == frames[f], ('nonmonotone', r, old, f)
+        if old != f:
+            degree = len(frames[f]) - len(frames[old])
+            assert degree > 0
+            paid[degree] += 1
+            edges.add((old, f))
+            current[r] = f
+
+    for part in ('A', 'B'):
+        if part == 'B':
+            assert all(current[r] == f for r, f in zip(canonical['centers'], canonical['center_frames']))
+            assert all(current[v+t] == levels.get(t, 0) for t in range(v))
+            for r, frame in zip(canonical['centers'], canonical['center_frames']):
+                served = {levels.get(e[1]-v, 0) for e in canonical['cut'] if e[2] == r}
+                old = frame
+                for f in sorted(served, key=lambda f: -len(frames[f])):
+                    assert basis(frames[old] + frames[f]) == frames[old]
+                    if old != f:
+                        paid[len(frames[old])-len(frames[f])] += 1
+                        edges.add((old, f))
+                        edges.add((f, old))
+                        old = f
+        for e in canonical[part]:
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []):
+                climb(r, e[-1])
+    for r, f in enumerate(canonical['final']):
+        climb(r, f)
+    assert dict(paid) == {int(r): count for r, count in word['report']['local_profile'].items()}
+    canonical['local_profile'] = dict(sorted(paid.items()))
+    canonical['edges'] = sorted(edges)
+    out.mkdir(parents=True, exist_ok=False)
+    payload = json.dumps(canonical, sort_keys=True, separators=(',', ':')).encode()
+    (out/'CANONICAL-WORD.json.gz').write_bytes(gzip.compress(payload, mtime=0))
+    (out/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word, sort_keys=True, separators=(',', ':')).encode(), mtime=0))
+    receipt = dict(status='PASS_CHANGED_WORD_ALL_COLUMNS_AND_NATIVE_FRAMES',
+                   input_content_sha256=content_hash(raw_path), routing_content_sha256=content_hash(routing_path),
+                   canonical_content_sha256=hashlib.sha256(payload).hexdigest(),
+                   live_columns_each_orientation=n, helpers=helpers,
+                   compensation_additions=len(compensation), scalar_operations=len(program),
+                   center_rank_sum=sum(map(len, word['center_frames'])),
+                   local_profile=dict(sorted(paid.items())), local_rank_mass=sum(r*z for r, z in paid.items()),
+                   widths=[h-len(frames[f]) for f in canonical['start'][2*v:]],
+                   frames=len(frames), directed_edges=len(edges),
+                   tau=43, target_port_order_matches_baseline=True,
+                   seconds=time.monotonic()-start_time,
+                   scope='Fresh exact forward and inverse-transpose scalar replay on every arbitrary input; all native frame chains and dyadic primitives. Phase lowering, wrappers, global owners and global assembly are separate.')
+    (out/'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(json.dumps({k: value for k, value in receipt.items() if k != 'widths'}, indent=2), flush=True)
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--raw', type=Path, required=True)
+    parser.add_argument('--routing', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    run(args.raw, args.routing, args.out)
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/code/audit_local.py b/research/contextual-provider-pooling/complex-global/vendor531/code/audit_local.py
new file mode 100644
index 0000000000..a09611844a
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/code/audit_local.py
@@ -0,0 +1,144 @@
+# Local-only extraction of the attributed PR514 / PR433 independent replay.
+# Prepared for icekylinx with OpenAI Codex assistance. Apache-2.0.
+# The complete local checker and its negative controls are retained verbatim.
+# Global hosting is verified separately for the changed 112-port geometry.
+import copy,gzip,hashlib,json,sys
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+OUT=Path(sys.argv[1])
+c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'))
+ir={'local_programs':json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'))}
+v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames']
+levels={int(t):f for t,f in c.get('target_levels',{}).items()}
+entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+plain={r for r in range(n) if r not in set(entering)}
+def contains(a,b):
+    for x in a:
+        for y in b:
+            if x>>(y.bit_length()-1)&1:x^=y
+        if x:return False
+    return True
+def local(events,back):
+    rows={('L',r):{r:Q(1)} for r in range(n)}
+    norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={}
+    hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256();chain={};wrappers=[]
+    allowed=['zero_frame_precondition','entry_adapters','A','centers','B','final','exit_adapters','full_frame_cleanup','done']
+    for event in events:
+        tag=event[0]
+        if tag=='phase':
+            phases.append(event[1]);assert phases==allowed[:len(phases)]
+            if event[1]=='A':assert entry==[(r,f) for r,f in enumerate(c['start']) if r in plain] and sorted(r for k_,r,f_ in wrappers if k_=='pre')==entering   # GK
+            if event[1]=='centers':assert all(cur[r]==levels.get(r-v,0) for r in range(v,2*v))   # GK
+            if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==list(enumerate(c['final']))
+            assert not private
+        elif tag=='residual_adapter':   # GK: paid wrappers of entering helpers: R_E^-1 before the invocation, L_E^-1 after the full-frame cleanup
+            _,kind,r,f=event;assert r in entering and f==c['start'][r] and kind in ('pre','post')
+            assert (kind=='pre' and phases[-1]=='entry_adapters') or (kind=='post' and phases[-1]=='full_frame_cleanup')
+            assert (kind,r) not in {(k,x) for k,x,_ in wrappers};wrappers.append((kind,r,f))
+        elif tag=='adapter':
+            assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]]
+            (entry if event[1]=='old_to_new' else exit).append((event[2],event[3]))
+        elif tag=='climb':
+            _,part,r,a,b,rank=event
+            assert not private and phases[-1]==part and cur[r]==a
+            assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0
+            hist[rank]+=1;cur[r]=b
+        elif tag=='center':
+            _,k,a,b,rank=event
+            assert phases[-1]=='centers' and private=={('C',k):a}
+            cf=c['center_frames'][k];cr=len(frames[cf])
+            # GK: stepwise descent cf -> served levels -> lowest (forward), reversed ascent (backward); each step is a nested child
+            assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a])
+            assert rank==abs(len(frames[a])-len(frames[b]))>0
+            chain.setdefault(k,[]).append((a,b))
+            private['C',k]=b;hist[rank]+=1;centers.append(k)
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None
+            if target[0]=='C' and op=='clear':
+                assert private.get(target,f)==f
+                private.pop(target,None)
+            else:
+                for r in (target,source):
+                    if r is None:continue
+                    if r[0]=='L':assert cur[r[1]]==f,('common frame',r,cur[r[1]],f)
+                    else:
+                        if r==target and r not in private:private[r]=f
+                        assert private[r]==f
+            if op=='clear':rows[target]={};norm[target]=Q(0)
+            elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source]
+            elif op=='scale':
+                q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator
+                assert a&(a-1)==0 and b&(b-1)==0
+                rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q)
+            else:
+                q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator
+                assert source!=target and b&(b-1)==0
+                # Independent symbolic replay of the cleared coefficient work.
+                w=0
+                for bit in bin(a)[2:]:w=2*w+int(bit)
+                assert Q(w,b)*(1 if q>0 else -1)==q
+                prefix=max(prefix,Q(a)*norm[source])
+                norm[target]=norm.get(target,Q(0))+abs(q)*norm[source]
+                row=rows.setdefault(target,{})
+                for j,x in list(rows[source].items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+            prefix=max(prefix,norm[target])
+        else:raise AssertionError(tag)
+    assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private
+    assert sorted(r for k,r,_ in wrappers if k=='pre')==entering and sorted(r for k,r,_ in wrappers if k=='post')==entering   # GK
+    for k,st in chain.items():   # GK: the steps of each centre chain link up and end at the centre frame
+        cf=c['center_frames'][k]
+        if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+        else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+    assert all(not row for reg,row in rows.items() if reg[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert rows['L',r]==expected
+    # A 192-bit local payload allowance vastly dominates even coefficient work.
+    assert prefix<2**192
+    return hist,{'all_exact_columns':n,'prefix_l1_upper':str(prefix),
+                 'prefix_bits_upper':prefix.numerator.bit_length()-prefix.denominator.bit_length()+1,
+                 'charged_payload_bits':192,'private_work_erased':True}
+
+profiles={};checks={}
+for name in ('forward','backward'):
+    profiles[name],checks[name]=local(ir['local_programs'][name],name=='backward')
+    assert dict(profiles[name])=={int(r):z for r,z in c['local_profile'].items()}
+    print('independent emitted replay PASS',name,flush=True)
+controls=[]
+for name,mut in [
+    ('wrong_scale',lambda es:next(e for e in es if e[0]=='scalar' and e[1][0]=='scale')[1].__setitem__(2,3)),
+    ('missing_center',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center'))),
+    ('wrong_common_frame',lambda es:next(e for e in es if e[0]=='scalar' and e[2]!=0).__setitem__(2,0)),
+    ('wrong_child_rank',lambda es:next(e for e in es if e[0]=='climb').__setitem__(5,99)),
+]+([
+    ('missing_pre_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre'))),
+    ('missing_post_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post'))),
+    ('wrapper_with_wrong_frame',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(3,0)),
+    ('wrapper_in_wrong_phase',lambda es:es.insert(es.index(['phase','A']),es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post')))),
+    ('wrapper_on_a_data_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,3)),
+    ('wrapper_on_a_target_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,v+3)),
+    ('wrapper_on_a_centre_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,['C',0])),
+] if entering else [])+([
+    ('centre_step_not_nested',lambda es:next(e for e in es if e[0]=='center').__setitem__(3,next(f for f in range(len(frames)) if not contains(frames[f],frames[next(e for e in es if e[0]=='center')[2]]) and not contains(frames[next(e for e in es if e[0]=='center')[2]],frames[f])))),
+    ('centre_descent_step_skipped',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center' and e[3]!=0))),
+] if levels else []):
+    es=copy.deepcopy(ir['local_programs']['forward']);mut(es)
+    try:local(es,False)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('mutation accepted: '+name)
+
+
+result={'status':'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY',
+'canonical_word_sha256':hashlib.sha256((OUT/'CANONICAL-WORD.json.gz').read_bytes()).hexdigest(),
+'local_programs_sha256':hashlib.sha256((OUT/'LOCAL-PROGRAMS.json.gz').read_bytes()).hexdigest(),
+'v':v,'helpers':R,'local':checks,'paid_profiles':{name:dict(H) for name,H in profiles.items()},
+'entering_helpers':len(entering),'negative_controls_rejected':controls,
+'scope':'Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate.'}
+(OUT/'INDEPENDENT-LOCAL-REPLAY.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],len(controls),'controls rejected',flush=True)
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/code/audit_supplier_hosted.py b/research/contextual-provider-pooling/complex-global/vendor531/code/audit_supplier_hosted.py
new file mode 100644
index 0000000000..62b721b6e6
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/code/audit_supplier_hosted.py
@@ -0,0 +1,155 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: VERIFIED_VARIANT POOLED_HOSTED OUT.json [--mutation-controls]
+The local provider is read from VERIFIED_VARIANT, never from a baseline width histogram.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json');V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers']);assert V==112 and canon['h']==9; width=[9-len(canon['frames'][canon['start'][2*V+h]])for h in range(R)];prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(V)]
+# Bind the selected provider's actual normalization recipes, including newly
+# selected entrance frames; a baseline recipe registry cannot silently survive.
+required_artifacts={'split-centres/CANONICAL-WORD.json.gz','split-centres/LOCAL-PROGRAMS.json.gz','split-centres/LOCAL-CHECKS.json','split-centres/RESIDUAL-ADAPTERS.json','work/complex-nine-native/DATA-PHASES.json'}
+assert required_artifacts <= set(summary['source_artifacts'])
+adapter_path=BASE/'split-centres/RESIDUAL-ADAPTERS.json'
+assert hashlib.sha256(adapter_path.read_bytes()).hexdigest()==parent['residual_adapter_sha256']
+adapters=read(adapter_path)['recipes']
+for h,w in enumerate(width):
+ if w<9:
+  f=canon['start'][(2*V)+h];a=adapters[str(f)]
+  assert a['frame']==f and a['vectors']==canon['frames'][f] and a['rank']==w and a['entrance_rank']==9-w
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_programs']==parent['local_programs']and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert len(t['calls'])==72 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','exact_local_clifford_recipe_sha256','residual_adapter_sha256','adapter_policy'):assert t[key]==parent[key]
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==72
+ all_local=[];perrep={r:[]for r in range(8)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<8 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   assert e==expected
+   assert 0<=e['time']<72 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[DATA,DATA]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,DATA],charged_calls_per_cover=DATA)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[],children=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,DATA],charged_calls_per_cover=DATA)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time')}=={k:v for k,v in old.items()if k!='owners'}
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:(2*V)]==old['owners'][:(2*V)]
+  for h,(family,route)in enumerate(own[(2*V):]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,(8*V));fampair,sub=divmod(sub,(2*V));side,port=divmod(sub,V)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*V+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(8)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*(8*V)+(2*pairs[i]+sides[i])*V+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==2560 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ if '--mutation-controls' not in sys.argv[4:]:return
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA))
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],widths=dict(sorted(Counter(width).items())),scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses the new selected local program bound by fresh scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
+# Literal residual frames are a compact export of the already checked offsets,
+# not another global replay. Every row names its actual inherited axes.
+frames=[]
+for z in ct['idle_children']:
+ axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes']))
+ tail=axes[z['pending_offset']:]
+ assert len(tail)==z['rank']
+ frames.append(dict(z,orthogonal_axes=tail))
+frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode()
+(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(gzip.compress(frame_raw,mtime=0))
+frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'],
+ uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames),
+ rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())),
+ source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(),
+ scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.')
+(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n')
+
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/code/emit_local.py b/research/contextual-provider-pooling/complex-global/vendor531/code/emit_local.py
new file mode 100644
index 0000000000..a54170b002
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/code/emit_local.py
@@ -0,0 +1,156 @@
+# GK: modified copy of PR #433's complex_emit.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted from PR425 by icekylinx with Codex assistance.
+"""Emit both local programs, integrate the fixed nine-stage geometry, and bill.
+
+The expanded scalar interface is justified in PROOF.txt. This script does not
+claim a Lean proof or discharge the inherited all-size/analytic interfaces.
+"""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path(_sys.argv[1]);cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp))
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def basis(vs):
+    b={}
+    for x in vs:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def dual(e):
+    e=list(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def scalar(e,back):
+    e=dual(e) if back else list(e)
+    if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]]
+    return ['scale',['L',e[1]],e[2],e[3]]
+def primitive_bound(e):
+    if e[0] in ('clear','copy'):return 1
+    q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])
+    a,b=abs(q.numerator),q.denominator
+    assert b&(b-1)==0
+    if e[0]=='scale':
+        assert a&(a-1)==0
+        return abs(a.bit_length()-b.bit_length())+int(q<0)
+    # Exact binary Horner multiplication on a cleared private stream, repeated
+    # halving, signed accumulation into the target, then clear the private stream.
+    return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1)
+
+def emit(back):
+    out=[];cur=c['start'].copy()
+    def event(e):out.append(e)
+    def scal(e,f):event(['scalar',e,f])
+    event(['phase','zero_frame_precondition'])
+    for e in c['precondition']+c['compensation']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['start'][r]==0 for r in regs)
+        scal(scalar(e,back),0)
+    event(['phase','entry_adapters'])
+    # GK: a helper that starts at a nonzero entrance frame has NO entry adapter; its paid wrapper R_E^-1 (Lemma A) precedes every gate
+    # that touches it and L_E^-1 follows the full-frame cleanup.  Words without entrances emit PR #433's events.
+    entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+    for r,f in enumerate(c['start']):
+        if r in entering:event(['residual_adapter','pre',r,f])
+        else:event(['adapter','old_to_new',r,f])
+    def climb(r,f,part):
+        old=cur[r]
+        if old==f:return
+        assert basis(frames[old]+frames[f])==tuple(frames[f])
+        rank=len(frames[f])-len(frames[old]);assert rank>0
+        event(['climb',part,r,old,f,rank]);cur[r]=f
+    for part in ('A','centers','B','final'):
+        event(['phase',part])
+        if part in ('A','B'):
+            for e in c[part]:
+                regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+                for r in regs:climb(r,e[-1],part)
+                scal(scalar(e,back),e[-1])
+        elif part=='centers':
+            # GK: targets sit at their nonzero-frame-compensation level (0 at the defaults); a centre copy descends
+            # cf -> served levels (descending chain) -> lowest served level and scatters into each target at its level
+            lv=lambda r:c.get('target_levels',{}).get(str(r-v),0)
+            assert all(cur[r]==lv(r) for r in range(v,2*v))
+            for k,r in enumerate(c['centers']):
+                cf=c['center_frames'][k];assert cur[r]==cf
+                terms=[e for e in c['cut'] if e[2]==r]
+                path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x]))
+                C=['C',k]
+                if not back:
+                    scal(['clear',C],cf);scal(['copy',C,['L',r]],cf)
+                    for a in range(len(path)):
+                        if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])])
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a])
+                    scal(['clear',C],path[-1])
+                else:
+                    scal(['clear',C],path[-1])
+                    for a in range(len(path)-1,-1,-1):
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a])
+                        if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])])
+                    scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf)
+        else:
+            for r,f in enumerate(c['final']):climb(r,f,part)
+    event(['phase','exit_adapters'])
+    for r,f in enumerate(c['final']):event(['adapter','new_to_old',r,f])
+    event(['phase','full_frame_cleanup'])
+    for e in c['cleanup']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['final'][r]==1 for r in regs)
+        scal(scalar(e,back),1)
+    for r in entering:event(['residual_adapter','post',r,c['start'][r]])   # GK: L_E^-1 after the full-frame cleanup
+    event(['phase','done'])
+    return out
+
+def check_local(events,back):
+    # Literal scalar replay of the emitted stream, including center lifetimes.
+    state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0
+    for e in events:
+        if e[0]=='climb':assert not live;paid[e[5]]+=1
+        elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1
+        elif e[0]=='scalar':
+            op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op)
+            if tag=='clear':
+                state[t]={}
+                if t[0]=='C' and t[1] in live:live.remove(t[1])
+            elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1])
+            elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()}
+            else:
+                s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{})
+                if t[0]=='C' and t[1] not in live:live.append(t[1])
+                for j,x in list(state.get(s,{}).items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+    assert not live and all(not row for r,row in state.items() if r[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert state['L',r]==expected,('emitted column mismatch',back,r)
+    assert dict(paid)=={int(r):z for r,z in c['local_profile'].items()}
+    return {'sha256':digest(events),'events':len(events),'scalar_macros':macros,
+            'real_component_primitive_bound':prims,'paid_profile':dict(sorted(paid.items())),
+            'all_columns':n,'private_centers_cleared':True,'private_coefficient_stream_cleared_after_each_macro':True}
+
+programs={};checks={}
+for name,back in [('forward',False),('backward',True)]:
+    programs[name]=emit(back);checks[name]=check_local(programs[name],back)
+    print('PASS emitted',name,checks[name]['events'],'events',flush=True)
+
+
+(OUT/'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(json.dumps(programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'LOCAL-CHECKS.json').write_text(json.dumps(checks,indent=2)+'\n')
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/code/emit_supplier_hosted.py b/research/contextual-provider-pooling/complex-global/vendor531/code/emit_supplier_hosted.py
new file mode 100644
index 0000000000..41c46015c7
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/code/emit_supplier_hosted.py
@@ -0,0 +1,100 @@
+"""Punctured 112-port whole-owner derivative, adapted for icekylinx with GPT-6 Astra.
+Based on PR514 and its credited PR484/507 lineage.
+CLI: --base VERIFIED_VARIANT --owners ASYNC-OWNERS.json.gz --plan ASYNC-PLAN.json --out OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy,argparse
+from pathlib import Path
+from collections import Counter,defaultdict
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--base',type=Path,required=True);parser.add_argument('--owners',type=Path,required=True);parser.add_argument('--plan',type=Path,required=True);parser.add_argument('--out',type=Path,required=True)
+a=parser.parse_args();BASE,MAP,PLAN,OUT=(p.resolve()for p in(a.base,a.owners,a.plan,a.out));assert not OUT.exists();OUT.mkdir(parents=True)
+class OH:
+ @staticmethod
+ def idle_basis(q):
+  z=next(i for i in range(9)if not(q>>i)&1);u=q^(1<<z);order=list(range(9));order[0],order[z]=order[z],order[0]
+  return[(1<<i)^(u if u>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ @staticmethod
+ def spectators(q,pending,off,w):
+  B=OH.idle_basis(q);occ=[B.index(v)for v in pending[off:off+w]]
+  return[j for j in range(73)if j not in occ][:9-w]
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+plan=read(PLAN);call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==72;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);T=8;V=canon['v'];M=73;R=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)
+assert(len(roles),len(canon['start']),len(ph['recipes']))==(72*R,2*V+R,V)
+widths=[9-len(canon['frames'][canon['start'][(2*V)+h]])for h in range(R)];assert widths==plan['baseline_widths'], 'source-bound selected provider widths'
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==widths[h] and 0<=orp<T
+ assert f==orp*(8*V)+(2*pairs[i]+side[i])*V+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f<DATA for f,r in c['owners'])
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in checks[c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*(8*V)+(2*pairs[i]+side[i])*V+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==2560
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='round20-R504-asynchronous-whole-owner-v1',live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['bank_padding']['children']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert t['local_programs']==parent['local_programs']
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',template_sha256=hashlib.sha256(raw).hexdigest(),parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),rank_mass=sum(r*n for r,n in paid.items()),deficit=2560,maxchild=max(paid),hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),source_artifacts={p.relative_to(BASE).as_posix():hashlib.sha256(p.read_bytes()).hexdigest()for p in [BASE/'split-centres/CANONICAL-WORD.json.gz',BASE/'split-centres/LOCAL-PROGRAMS.json.gz',BASE/'split-centres/LOCAL-CHECKS.json',BASE/'split-centres/RESIDUAL-ADAPTERS.json',BASE/'split-centres/CLIFFORD-RECIPES.json',BASE/'split-centres/CLIFFORD-REVIEW.json',BASE/'split-centres/INDEPENDENT-LOCAL-REPLAY.json',BASE/'work/complex-nine-native/DATA-PHASES.json']},scope='New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/code/invoice_final.py b/research/contextual-provider-pooling/complex-global/vendor531/code/invoice_final.py
new file mode 100644
index 0000000000..abefcee47b
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/code/invoice_final.py
@@ -0,0 +1,299 @@
+"""Recount a changed local word and its actual asynchronous finite invoice.
+
+Prepared for icekylinx with OpenAI Codex assistance. Apache-2.0.
+Adapted from the attributed Round19 audit_async_invoice.py and its PR484/514
+ancestry. Uses the fresh hash-bound independent local replay for exact scalar
+endpoints; independently recounts emitted Horner work, prefix envelopes,
+paid local calls, wrappers and finite charges. Does not rerun the old baseline
+or read an old INTEGRATION.json as evidence for the changed word.
+"""
+import argparse
+import gzip
+import hashlib
+import json
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def filehash(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def contenthash(path):
+    data = path.read_bytes()
+    return hashlib.sha256(gzip.decompress(data) if path.suffix == '.gz' else data).hexdigest()
+
+
+def run(base, hosted, audit, out, retained_invoice=None):
+    local_dir = base / 'split-centres'
+    cp = local_dir / 'CANONICAL-WORD.json.gz'
+    pp = local_dir / 'LOCAL-PROGRAMS.json.gz'
+    rp = local_dir / 'INDEPENDENT-LOCAL-REPLAY.json'
+    w, programs, replay = read(cp), read(pp), read(rp)
+    checks = read(local_dir / 'LOCAL-CHECKS.json')
+    parent = read(local_dir / 'GLOBAL-TEMPLATE.json.gz')
+    template_path = hosted / 'GLOBAL-TEMPLATE.json.gz'
+    template = read(template_path)
+    owners = read(audit / 'OWNERS-AND-PROFILE.json')
+    control = read(audit / 'ASYNC-AUDIT.json')
+    template_hash = contenthash(template_path)
+    assert template_hash == control['complex_template_sha256'] == owners['template_sha256']
+    assert owners['status'] == 'PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+    assert replay['status'] == 'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+    assert replay['canonical_word_sha256'] == filehash(cp)
+    assert replay['local_programs_sha256'] == filehash(pp)
+    assert template['local_programs'] == parent['local_programs'] == programs
+    assert template['recipe'] == parent['recipe']
+    assert Counter(c['orientation'] for c in template['calls']) == Counter(c['orientation'] for c in parent['calls'])
+
+    v, helpers, h, m = w['v'], w['R'], w['h'], template['m']
+    assert v == 112 and h == 9 and m == 73
+    assert replay['v'] == v and replay['helpers'] == helpers
+    n = 2*v + helpers
+    stages, replicas, blocks_per_stream = 9, 8, 4
+    call_count = len(template['calls'])
+    assert call_count == stages*replicas == control['complete_invocations']
+    assert control['one_owner_per_complete_invocation']
+    payload = 512
+
+    widths = [h-len(w['frames'][f]) for f in w['start'][2*v:]]
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    assert entering == replay['entering_helpers']
+    local = {}
+    for orientation, events in programs.items():
+        # Endpoint equality and native frames were already independently
+        # replayed on all n columns in the hash-bound receipt above.
+        env = {('L', r): Q(1) for r in range(n)}
+        peak = Q(1)
+        real = macros = workops = 0
+        paid = Counter()
+        wrappers = {'pre': set(), 'post': set()}
+        for event in events:
+            tag = event[0]
+            if tag == 'climb':
+                paid[event[5]] += 1
+            elif tag == 'center':
+                paid[event[4]] += 1
+            elif tag == 'residual_adapter':
+                _, kind, register, frame = event
+                assert kind in wrappers and entrances.get(register) == frame
+                assert register not in wrappers[kind]
+                wrappers[kind].add(register)
+            elif tag == 'scalar':
+                macros += 1
+                scalar = event[1]
+                op, target = scalar[0], tuple(scalar[1])
+                if op == 'clear':
+                    env[target] = Q(0)
+                    count = 1
+                elif op == 'copy':
+                    env[target] = env[tuple(scalar[2])]
+                    count = 1
+                elif op == 'scale':
+                    q = Q(scalar[2], scalar[3])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert numerator and numerator & (numerator-1) == 0
+                    assert denominator & (denominator-1) == 0
+                    env[target] *= abs(q)
+                    count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0)
+                elif op == 'add':
+                    source = tuple(scalar[2])
+                    q = Q(scalar[3], scalar[4])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert source != target and numerator > 0
+                    assert denominator & (denominator-1) == 0
+                    acc, count = 0, 1  # clear coefficient work
+                    for i, bit in enumerate(bin(numerator)[2:]):
+                        if i:
+                            acc *= 2
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                        if bit == '1':
+                            acc += 1
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                    value = Q(acc)
+                    for _ in range(denominator.bit_length()-1):
+                        value /= 2
+                        count += 1
+                        peak = max(peak, value*env[source])
+                    assert value == abs(q)
+                    count += 2  # signed accumulation and work clear
+                    env[target] = env.get(target, Q(0)) + abs(q)*env[source]
+                    workops += count
+                else:
+                    raise AssertionError(op)
+                real += 2*count
+                peak = max(peak, env[target])
+            else:
+                assert tag in ('adapter', 'phase')
+        assert wrappers['pre'] == wrappers['post'] == set(entrances)
+        assert all(value == 0 for register, value in env.items() if register[0] == 'C')
+        prior = replay['local'][orientation]
+        assert prior['all_exact_columns'] == n and prior['private_work_erased']
+        assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits']
+        bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1
+        assert bits == prior['prefix_bits_upper']
+        assert real == checks[orientation]['real_component_primitive_bound']
+        assert macros == checks[orientation]['scalar_macros']
+        assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()}
+        assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}
+        local[orientation] = dict(
+            events=len(events), macros=macros, real_component_primitives=real,
+            prefix_l1=str(peak), prefix_bits=bits,
+            coefficient_work_primitive_count=workops, all_exact_columns=n,
+            dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True,
+            private_centres_and_coefficient_work_cleared=True,
+            pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']),
+            endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json')
+
+    centres = len(w['centers'])
+    children = sum(checks['forward']['paid_profile'].values())
+    assert checks['forward']['paid_profile'] == checks['backward']['paid_profile']
+    macro_bound = max(row['macros'] for row in local.values())
+    compiler = 64*(m+1)**3
+    adapters = 16*(macro_bound+children+n+centres)+64*m
+    primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler
+
+    bridge_steps = sum(event['kind'] == 'bridge' for event in parent['recipe'])
+    bridge_sweeps = sum(event['kind'] == 'bridge' for event in template['execution_schedule'])
+    assert bridge_sweeps == replicas*bridge_steps
+    bridge_additions = 2*v*bridge_sweeps
+    shifts = blocks_per_stream*v*replicas
+    moves = 2*shifts
+    parent_live, parent_physical = parent['live'], parent['physical']
+    data_stock = 2*v*blocks_per_stream*replicas
+    assert (parent_live-data_stock) % stages == 0
+    parent_banks = (parent_live-data_stock)//stages
+    assert parent_banks >= 0
+    assert parent_physical == parent_live+helpers+centres+2
+    scalar = sum(local[call['orientation']]['real_component_primitives'] for call in template['calls'])
+    factors_per_wrapper = 2*(m-1)
+    wrapper_factors = 2*call_count*entering*factors_per_wrapper
+    nonlocal_items = (
+        4*v*replicas*stages + 2*v*replicas*stages
+        + 2*call_count*helpers
+        + sum(child['replicas'] for child in parent['idle_children'])
+        + stages*parent_banks + bridge_additions + shifts + moves
+        + parent_live + parent_physical + wrapper_factors)
+    outside = 8*nonlocal_items+64*m
+    parent_pervertex = (
+        scalar+bridge_additions+shifts+moves+parent_live
+        +(call_count*adapters+outside)*compiler+64*parent_physical)
+
+    live, physical = template['live'], template['physical']
+    mass, profile = owners['rank_mass'], owners['paid_profile']
+    assert m*live-mass == owners['deficit'] == 2560
+    assert mass == sum(int(r)*count for r, count in profile.items())
+    assert physical == live+helpers+centres+2
+    assert live == owners['live'] and physical == owners['physical']
+    assert live <= parent_live and physical <= parent_physical
+    assert not template['bank_padding']['families']
+    assert owners['explicit_idle_remainder_children'] <= owners['source_idle_children_charged']
+    rebased = parent_pervertex+65*(physical-parent_physical)+(live-parent_live)
+    used = max(rebased, parent_pervertex)
+    retained = None
+    if retained_invoice is not None:
+        previous = read(retained_invoice)
+        assert previous['compiler'] == compiler
+        assert previous['charged_prefix_bits'] == payload
+        previous_bound = previous['conservative_pervertex_used']
+        # The entire newly reconstructed charge is added to the retained old
+        # allowance. This is intentionally stronger than only paying positive
+        # deltas and makes no claim that the old integration certifies this word.
+        used = max(used, previous_bound+parent_pervertex)
+        retained = dict(sha256=filehash(retained_invoice),
+                        previous_pervertex_allowance=previous_bound,
+                        added_complete_new_pervertex=parent_pervertex,
+                        policy='Retain old allowance and add the entire fresh recount.')
+
+    half = m//2
+    group = 2**(half*half)
+    for i in range(1, half+1):
+        group *= 2**(2*i)-1
+    stock, streamed_mass = group*physical, group*mass
+    logical = group*used+64
+    router = compiler*(logical+1)*(stock+1)**2
+    g_bound, e_bound, c0 = 2**30000, 2**100000, 2**210000
+    total_mass = streamed_mass+e_bound
+    literal = 2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m
+    row = 2*stock.bit_length()+9909+252+2*payload
+    maxchild = max(map(int, profile))
+    inequalities = dict(
+        local_primitive_bound=primitive_bound < 2**48,
+        logical=logical < 2**6050, router=router < g_bound,
+        literal=literal < e_bound, mass=total_mass < 2**100001,
+        precision=32*m*total_mass*total_mass < c0,
+        tape=2*total_mass+18 < c0, row=row < 20161,
+        halving=m*m > 2*maxchild*maxchild)
+    assert all(inequalities.values())
+    localbits = max(row['prefix_bits'] for row in local.values())
+    input_l2_bits = (m+1)//2
+    required_prefix = localbits+input_l2_bits+call_count+bridge_sweeps+4
+    assert required_prefix < payload
+
+    receipt = dict(
+        status='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',
+        template_sha256=template_hash,
+        parent_template_sha256=contenthash(local_dir/'GLOBAL-TEMPLATE.json.gz'),
+        owner_audit_sha256=filehash(audit/'OWNERS-AND-PROFILE.json'),
+        controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        independent_local_replay_sha256=filehash(rp),
+        canonical_word_sha256=filehash(cp), local_programs_sha256=filehash(pp),
+        local_checks_sha256=filehash(local_dir/'LOCAL-CHECKS.json'),
+        global_prefix_bits=required_prefix, charged_prefix_bits=payload,
+        complete_invocation_sweeps=call_count, bridge_sweeps=bridge_sweeps,
+        row_prefix_extra=2*payload, local=local, helpers=helpers,
+        centres=centres, live=live, physical=physical,
+        physical_stock_identity=dict(data_and_owner_families=live,
+                                     local_helpers=helpers, private_centres=centres,
+                                     coefficient_work=2),
+        entering_helpers=entering, entrance_rank=sum(h-width for width in widths),
+        width_inventory=dict(sorted(Counter(widths).items())),
+        local_adapters=adapters, local_primitive_bound=primitive_bound,
+        wrapper_elementary_factors_charged=wrapper_factors,
+        factors_per_wrapper=factors_per_wrapper, compiler=compiler,
+        unhosted_pervertex=parent_pervertex, hosted_rebased_pervertex=rebased,
+        conservative_pervertex_used=used, retained_prior_overcharge=retained,
+        finite=dict(physical_stock_bits=stock.bit_length(), router_bits=router.bit_length(),
+                    literal_bits=literal.bit_length(), physical_row_coefficient=row,
+                    retained_row_coefficient=20161,
+                    required_C0_bits=(32*m*total_mass*total_mass).bit_length(),
+                    halving_integer_inequality=[m*m, 2*maxchild*maxchild],
+                    G_exponent=30000, E_exponent=100000, C0_exponent=210000),
+        strict_checks=inequalities,
+        scope='Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged.')
+    prefix = dict(
+        status='PASS_ASYNC_GLOBAL_PREFIX', template_sha256=template_hash,
+        global_prefix_bits=required_prefix, retained_payload_bits=payload,
+        complete_invocation_cover_sweeps=call_count,
+        bridge_factor_two_sweeps=bridge_sweeps,
+        local_scalar_coefficient_work_prefix_bits=localbits,
+        stream_input_sup_to_l2_bits=input_l2_bits,
+        primitive_arithmetic_margin_bits=4,
+        controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        independent_local_replay_sha256=filehash(rp),
+        proof=f'Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Actual full orthogonal owner charts act by right-translation bijections on the retained cover group. Count all {call_count} complete local sweeps and {bridge_sweeps} individual bridge sweeps. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently recounted scalar/Horner envelope uses {localbits} bits; input sup-to-L2 uses {input_l2_bits}; arithmetic margin is 4. Total {required_prefix} < {payload}. All-size child/compiler and precision/tape interfaces remain inherited.')
+    out.mkdir(parents=True, exist_ok=True)
+    (out/'PREFIX-AND-INVOICE.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    (out/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix, indent=2)+'\n')
+    print(json.dumps(receipt, indent=2), flush=True)
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--base', type=Path, required=True)
+    parser.add_argument('--hosted', type=Path, required=True)
+    parser.add_argument('--audit', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    parser.add_argument('--retained-invoice', type=Path)
+    args = parser.parse_args()
+    run(args.base, args.hosted, args.audit, args.out, args.retained_invoice)
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/code/phases_delta.py b/research/contextual-provider-pooling/complex-global/vendor531/code/phases_delta.py
new file mode 100644
index 0000000000..8d78d26b3b
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/code/phases_delta.py
@@ -0,0 +1,158 @@
+"""Reuse the pinned PR523 phase certificates and lower only changed edges.
+
+The inherited Gaussian-dyadic compiler still checks every fresh tableau and
+global phase. Its zero-state interpreter is accelerated with cached exact
+integer permutations and Z4 phases. Overflow is checked before every sum;
+there is no floating-point arithmetic in a phase equality.
+
+Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0.
+Compiler and certificate format: PR425/433, icekylinx with Codex assistance.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import sys
+import time
+from collections import Counter
+from functools import lru_cache
+from pathlib import Path
+
+import numpy as np
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def frozen(x):
+    return tuple(map(frozen, x)) if isinstance(x, (list, tuple)) else x
+
+
+def main():
+    p = argparse.ArgumentParser()
+    p.add_argument('--local', type=Path, required=True)
+    p.add_argument('--baseline', type=Path, required=True)
+    p.add_argument('--compiler', type=Path, required=True)
+    a = p.parse_args()
+    sys.path.insert(0, str(a.compiler.resolve()))
+    import clifford_exact as ce
+    started = time.monotonic()
+    assert sha(a.compiler/'clifford_exact.py') == '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962', 'baseline canonical-frame and phase convention must remain pinned'
+    c = json.load(gzip.open(a.local/'CANONICAL-WORD.json.gz'))
+    b = json.load(gzip.open(a.baseline/'CANONICAL-WORD.json.gz'))
+    old = json.loads((a.baseline/'CLIFFORD-RECIPES.json').read_text())
+    prior = json.loads((a.baseline/'CLIFFORD-REVIEW.json').read_text())
+    assert prior['all_child_equalities_include_global_phase']
+    assert prior['recipe_sha256'] == sha(a.baseline/'CLIFFORD-RECIPES.json')
+    assert prior['canonical_word_sha256'] == sha(a.baseline/'CANONICAL-WORD.json.gz')
+    assert c['h'] == b['h'] == 9 and c['ports'] == b['ports']
+    n = c['h']; N = 1 << n
+    xs = np.arange(N, dtype=np.int64)
+    parity = np.array([x.bit_count() & 1 for x in range(N)], dtype=np.int64)
+
+    @lru_cache(None)
+    def action(e):
+        if e[0] == 'P':
+            return sum(parity[xs & row] << i for i, row in enumerate(e[1]))
+        if e[0] == 'D':
+            Q, alpha = e[1:]
+            phase = np.zeros(N, dtype=np.int64)
+            for i in range(n):
+                phase += ((xs >> i) & 1) * alpha[i]
+                for j in range(i+1, n):
+                    if (Q[i] >> j) & 1:
+                        phase += 2*((xs >> i) & (xs >> j) & 1)
+            return phase % 4
+        if e[0] in ('C', 'X'):
+            return xs ^ e[1]
+        return e[1]
+
+    @lru_cache(maxsize=4096)
+    def state(circuit, basis):
+        re = np.zeros(N, dtype=np.int64); im = np.zeros(N, dtype=np.int64)
+        re[basis] = 1; den = 0
+        for e in circuit:
+            z = action(e)
+            if e[0] == 'P':
+                rr = np.empty_like(re); ii = np.empty_like(im)
+                rr[z] = re; ii[z] = im; re, im = rr, ii
+            elif e[0] == 'X':
+                re, im = re[z], im[z]
+            elif e[0] in ('D', 'phase'):
+                sign = 1 - 2*(z//2)
+                odd = z % 2
+                re, im = sign*np.where(odd, -im, re), sign*np.where(odd, re, im)
+            elif e[0] == 'C':
+                assert max(int(np.max(np.abs(re))), int(np.max(np.abs(im)))) < 2**60
+                s = e[2]; rr, ii = re[z], im[z]
+                re, im = re-s*im+rr+s*ii, im+s*re+ii-s*rr
+                den += 1
+            else:
+                raise AssertionError(e)
+            while den and not bool(np.any((re & 1) | (im & 1))):
+                re //= 2; im //= 2; den -= 1
+        return tuple(zip(map(int, re), map(int, im))), den
+
+    original = ce.Op.zero_state
+    # Check the independent vectorized interpreter against the inherited
+    # literal one on one nontrivial changed edge and its adjoint, once.
+    probe = ce.canonical_frame(n, c['frames'][c['center_frames'][0]])
+    probes = (probe, probe.adjoint().then(ce.fourier(n)))
+    for op in probes:
+        expected, den = original(op)
+        got, d = state(frozen(op.circuit), 0)
+        assert tuple(expected) == got and den == d
+    ce.Op.zero_state = lambda self, basis=0: state(frozen(self.circuit), basis)
+
+    @lru_cache(None)
+    def frame(U):
+        op = ce.canonical_frame(n, U)
+        L = [u | (u << n) for u in U] + [v << n for v in ce.nullspace(U, n)]
+        pre = [x | (z << n) for x, z, _ in ce.inverse(op.tab)[n:]]
+        assert ce.rank(L) == ce.rank(L+pre) == n
+        assert ce.rank([x for x, _, _ in op.tab[n:]]) == len(U)
+        return op
+
+    key = lambda frames, x, y: (tuple(frames[x]), tuple(frames[y]))
+    known = {key(b['frames'], r['old'], r['new']): r for r in old['children']}
+    edges = set(map(tuple, c['edges'])) | {(x,y) for f in c['center_frames'] for x,y in ((f,0),(0,f))}
+    recipes = []; hist = Counter(); fresh = []; reused = []
+    for i, (x, y) in enumerate(sorted(edges)):
+        U, V = key(c['frames'], x, y)
+        if (U,V) in known:
+            rec = copy.deepcopy(known[U,V]); rec.update(old=x, new=y); reused.append([x,y])
+        else:
+            rec, _ = ce.lower_child(frame(U).adjoint().then(frame(V)))
+            rec = dict(old=x, new=y, **rec); fresh.append([x,y])
+        assert rec['rank'] == abs(len(U)-len(V))
+        hist[rec['rank']] += 1; recipes.append(rec)
+        if i and i % 600 == 0:
+            print('delta phases', i, '/', len(edges), 'fresh', len(fresh), 'seconds', round(time.monotonic()-started, 2), flush=True)
+    adapters = []
+    for r in old['endpoint_adapters']:
+        rec = copy.deepcopy(r); port = r['port']
+        f = c['start'][port] if r['role'] == 'source' else c['final'][c['v']+port]
+        assert tuple(c['frames'][f]) == tuple(b['frames'][r['frame']]) and rec['rank'] == 0
+        rec['frame'] = f; adapters.append(rec)
+    assert len(adapters) == 2*c['v']
+    assert {(r['role'], r['port']) for r in adapters} == {(role, port) for role in ('source', 'target') for port in range(c['v'])}
+    payload = json.dumps(dict(children=recipes, endpoint_adapters=adapters), sort_keys=True, separators=(',',':')).encode()
+    (a.local/'CLIFFORD-RECIPES.json').write_bytes(payload)
+    report = dict(status='PASS_REUSED_AND_FRESH_EXACT_LOCAL_PHASE_RECIPES',
+        canonical_word_sha256=sha(a.local/'CANONICAL-WORD.json.gz'), frames=len(c['frames']),
+        directed_edges=len(edges), reused_edges=len(reused), fresh_edges=len(fresh),
+        ranks=dict(hist), endpoint_adapters=len(adapters), reused_endpoint_adapters=len(adapters),
+        all_child_equalities_include_global_phase=True, recipe_sha256=hashlib.sha256(payload).hexdigest(),
+        baseline_recipe_sha256=prior['recipe_sha256'], baseline_review_sha256=sha(a.baseline/'CLIFFORD-REVIEW.json'),
+        compiler_sha256=sha(a.compiler/'clifford_exact.py'), seconds=time.monotonic()-started,
+        vector_arithmetic='Exact checked int64 Gaussian dyadics; cached permutations and Z4 phase actions. No floating-point equality.',
+        fresh_edge_ids=fresh,
+        scope='Only previously unseen ordered pairs of actual canonical subspaces were freshly lowered. Identical baseline pairs and all endpoint adapters reuse the pinned phase certificates; no full cold replay was performed.')
+    (a.local/'CLIFFORD-REVIEW.json').write_text(json.dumps(report,indent=2)+'\n')
+    print(json.dumps({k:report[k] for k in ('status','directed_edges','reused_edges','fresh_edges','seconds')},sort_keys=True),flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/code/prepare_supplier_base.py b/research/contextual-provider-pooling/complex-global/vendor531/code/prepare_supplier_base.py
new file mode 100644
index 0000000000..650fc9fd77
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/code/prepare_supplier_base.py
@@ -0,0 +1,95 @@
+"""Bind the new supplier to the unchanged verified 112-port data controller.
+
+The parent uses one dedicated bank per helper and stage. Each of its eight
+complete invocations uses a disjoint width-w block; the residual bank frame is
+listed literally. The final whole-owner derivative removes every such bank.
+All inherited data routes and exact data phase recipes remain byte-identical.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import shutil
+from collections import Counter
+from pathlib import Path
+
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--data-base',type=Path,required=True)
+ap.add_argument('--local',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args()
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def dump(p,obj):
+ b=json.dumps(obj,sort_keys=True,separators=(',',':')).encode();p.parent.mkdir(parents=True,exist_ok=True)
+ p.write_bytes(gzip.compress(b,mtime=0)if p.suffix=='.gz'else b+b'\n')
+ return hashlib.sha256(b).hexdigest()
+assert not a.out.exists(),'Output must be new'
+old=read(a.data_base/'split-centres/GLOBAL-TEMPLATE.json.gz')
+oldcan=read(a.data_base/'split-centres/CANONICAL-WORD.json.gz')
+can=read(a.local/'CANONICAL-WORD.json.gz');checks=read(a.local/'LOCAL-CHECKS.json');programs=read(a.local/'LOCAL-PROGRAMS.json.gz')
+V,H,R=can['v'],can['h'],can['R'];C=len(can['centers']);M,T,L,K=73,8,9,4
+assert(V,H,C)==(112,9,8)and can['ports']==oldcan['ports']
+widths=[H-len(can['frames'][f])for f in can['start'][2*V:]];assert len(widths)==R
+local_H={int(r):n for r,n in checks['forward']['paid_profile'].items()}
+assert all({int(r):n for r,n in z['paid_profile'].items()}==local_H for z in checks.values())
+assert sum(r*n for r,n in local_H.items())==2*V*(H-1)+64+sum(widths)
+D=a.out/'split-centres';D.mkdir(parents=True)
+required=('CANONICAL-WORD.json.gz','FULL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json','INDEPENDENT-LOCAL-REPLAY.json')
+for name in required:assert(a.local/name).is_file()
+for p in a.local.iterdir():
+ if p.is_file():shutil.copyfile(p,D/p.name)
+shutil.copyfile(a.local/'INDEPENDENT-LOCAL-REPLAY.json',D/'INDEPENDENT-REPLAY.json')
+for rel in('work/complex-nine-native/DATA-PHASES.json',*[f'work/pr361/code/engines/{n}'for n in('moment.py','base_two_moment.py','outer.py')]):
+ dst=a.out/rel;dst.parent.mkdir(parents=True,exist_ok=True);shutil.copyfile(a.data_base/rel,dst)
+DATA=2*K*T*V;W=DATA+L*R;P=W+R+C+2
+t=copy.deepcopy(old);t.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=W,physical=P,local_programs=programs)
+t['private_namespace']={'centers':[W,W+C],'reserved_tableau':[W+C,W+C+R],'coefficient':[P-2,P]}
+for c in t['calls']:
+ s,rep=c['stage'],c['replica'];owners=copy.deepcopy(c['owners'][:2*V])
+ for helper,w in enumerate(widths):
+  family=DATA+s*R+helper
+  route=[2,rep]if w==9 else[2,rep*w,w,list(range(T*w,T*w+9-w))]
+  owners.append([family,route])
+ assert len(owners)==len({f for f,_ in owners})==2*V+R
+ c['owners']=owners;c['local_program_sha256']=checks[c['orientation']]['sha256']
+bank_children=[];pad=Counter()
+for s in range(L):
+ for helper,w in enumerate(widths):
+  f=DATA+s*R+helper;axes=list(range(T*w,M));rank=len(axes)
+  assert 0<rank<52
+  bank_children.append(dict(family=f,rank=rank,axis_indices=axes,orthogonal_axes=[1<<j for j in axes]))
+  pad[rank]+=1
+t['bank_padding']={'families':list(range(DATA,W)),'children':bank_children,
+ 'semantics':'Each listed complement frame is applied once after the eight disjoint residual blocks of that dedicated bank. The final hosted derivative has empty families and children.'}
+t['cover_final_correction'].update(families=[0,W],charged_calls_per_cover=W)
+for i,e in enumerate(t['execution_schedule']):
+ if e['kind']=='bank_padding_cover_sweep':
+  t['execution_schedule'][i]={'kind':'bank_padding_cover_sweep','families':[DATA,W],'children_source':'bank_padding.children'}
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+t['exact_data_phase_recipe_sha256']=sha(a.out/'work/complex-nine-native/DATA-PHASES.json')
+t['exact_local_clifford_recipe_sha256']=sha(D/'CLIFFORD-RECIPES.json')
+t['residual_adapter_sha256']=sha(D/'RESIDUAL-ADAPTERS.json')
+t['supplier_substitution']={'parent_template_sha256':sha(a.data_base/'split-centres/GLOBAL-TEMPLATE.json.gz'),
+ 'old_canonical_word_sha256':sha(a.data_base/'split-centres/CANONICAL-WORD.json.gz'),
+ 'new_canonical_word_sha256':sha(D/'CANONICAL-WORD.json.gz'),
+ 'exact_same_ports':True,'data_contract':'The same ordered 112 data ports and both complete-invocation identity-shear orientations feed the unchanged nine-stage controller. No old local program or helper profile is reused.'}
+t['route_semantics']['helper']='Dedicated family DATA+stage*R+helper; one helper per bank per complete invocation. Width-nine route[2,replica] uses axes9*replica..9*replica+8. Width-w entering route[2,w*replica,w,spectators] uses the disjoint residual block and paid normalization wrappers; spectator axes start at8*w, beyond all residual blocks.'
+paid=Counter(pad)
+for c in t['calls']:
+ for r,n in checks[c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for z in t['idle_children']:paid[z['rank']]+=z['replicas']
+mass=sum(r*n for r,n in paid.items());assert M*W-mass==2560 and M*M>2*max(paid)**2
+assert t['recipe']==old['recipe'] and t['idle_children']==old['idle_children']
+assert t['execution_schedule'][:30]==old['execution_schedule'][:30]
+assert all(c['owners'][:2*V]==oc['owners'][:2*V]for c,oc in zip(t['calls'],old['calls']))
+th=dump(D/'GLOBAL-TEMPLATE.json.gz',t)
+report=dict(status='BOUND_NEW_LOCAL_SUPPLIER_TO_UNCHANGED_DATA_CONTROLLER',R=R,v=V,m=M,
+ live=W,physical=P,rank_mass=mass,deficit=2560,global_profile=dict(sorted(paid.items())),
+ bank_remainder_profile=dict(sorted(pad.items())),bank_assignments=L*T*R,
+ global_template_sha256=th,local_program_checks=checks,
+ canonical_word_sha256=sha(D/'CANONICAL-WORD.json.gz'),exact_phase_receipt_sha256=sha(D/'CLIFFORD-REVIEW.json'),
+ scope='The new local programs and phase/normalization artifacts are hash-bound to the unchanged data controller. Every dedicated bank and complement frame is explicit. The final whole-owner placement and independent scalar/finite recount are supplied separately; this file does not assert an old finite invoice.')
+dump(D/'INTEGRATION.json',report)
+print(json.dumps({k:report[k]for k in('status','R','live','physical','global_profile','bank_remainder_profile')},indent=2),flush=True)
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json b/research/contextual-provider-pooling/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..a16bf40bcc
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json
@@ -0,0 +1,105 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "ed47b5454779f7ad6b32ae492a13f8b5172b11c94c3877cbc5cc5d7a4c357738",
+  "parent_template_sha256": "9bebafae2c7e21a8a134cc9f2d4709c075b1641abafc33825d116b2508253ceb",
+  "owner_audit_sha256": "e5f11e7b920f9985f085546c641dbac5b8d98231d562e1e030ab2566ccea4bd6",
+  "controller_audit_sha256": "01ea0015d4e08170ac65f1cdd051be64e07f622eba62eadbf39524317388cba7",
+  "independent_local_replay_sha256": "4149f3d2ec3041965c5d72869748090d9aeed422f36d753550c543bb7808b30b",
+  "canonical_word_sha256": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667",
+  "local_programs_sha256": "755a5c4ebe958fd9f7b5d4a6e7a506d2c802e31c4d9da46b63db1994c4d8ffa6",
+  "local_checks_sha256": "c6807681d40cb46c21a50edc1058044ddc758f2dd3e6b0bab16d7cb28d41732f",
+  "global_prefix_bits": 225,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "local": {
+    "backward": {
+      "events": 22937,
+      "macros": 17872,
+      "real_component_primitives": 177740,
+      "prefix_l1": "1014379823310",
+      "prefix_bits": 40,
+      "coefficient_work_primitive_count": 88098,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 152,
+      "post_wrappers": 152,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "forward": {
+      "events": 22937,
+      "macros": 17872,
+      "real_component_primitives": 177692,
+      "prefix_l1": "86491024246",
+      "prefix_bits": 37,
+      "coefficient_work_primitive_count": 88066,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 152,
+      "post_wrappers": 152,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    }
+  },
+  "helpers": 504,
+  "centres": 8,
+  "live": 7168,
+  "physical": 7682,
+  "physical_stock_identity": {
+    "data_and_owner_families": 7168,
+    "local_helpers": 504,
+    "private_centres": 8,
+    "coefficient_work": 2
+  },
+  "entering_helpers": 152,
+  "entrance_rank": 152,
+  "width_inventory": {
+    "8": 152,
+    "9": 352
+  },
+  "local_adapters": 357568,
+  "local_primitive_bound": 9273288832588,
+  "wrapper_elementary_factors_charged": 3151872,
+  "factors_per_wrapper": 144,
+  "compiler": 25934336,
+  "unhosted_pervertex": 1361655146111768,
+  "hosted_rebased_pervertex": 1361655145812392,
+  "conservative_pervertex_used": 2877946989724568,
+  "retained_prior_overcharge": {
+    "sha256": "bb43ef04791037a37d2596c395e81191991fde6581326118995cf4318ee472a3",
+    "previous_pervertex_allowance": 1516291843612800,
+    "added_complete_new_pervertex": 1361655146111768,
+    "policy": "Retain old allowance and add the entire fresh recount."
+  },
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7985,
+    "literal_bits": 35282,
+    "physical_row_coefficient": 16467,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged."
+}
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/evidence/local/CANONICAL-WORD.json.gz b/research/contextual-provider-pooling/complex-global/vendor531/evidence/local/CANONICAL-WORD.json.gz
new file mode 100644
index 0000000000..3b0a475178
Binary files /dev/null and b/research/contextual-provider-pooling/complex-global/vendor531/evidence/local/CANONICAL-WORD.json.gz differ
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/inputs/PR523-ANCESTRY.json b/research/contextual-provider-pooling/complex-global/vendor531/inputs/PR523-ANCESTRY.json
new file mode 100644
index 0000000000..4af8dd0d34
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/inputs/PR523-ANCESTRY.json
@@ -0,0 +1,118 @@
+{
+  "prepared_at_utc": "2026-10-12T00:00:25Z",
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "new_contribution": "Exact 112-port direct-sum restriction, new complete physical whole-owner allocation, independent raw geometric/chronological audit and exact global assembly.",
+  "baseline": {
+    "pr": 514,
+    "author": "contributor (handle omitted)",
+    "head_repository": "contributor (handle omitted)/integer-mult-bounds",
+    "head": "246bfacd4cb4072836ae3147099f548bb728229f",
+    "source_path": "research/partial-kernel92-async",
+    "local_path": "vendor/pr514",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/514",
+    "kappa": "1391523459591829/1000000000000000000",
+    "manifest_sha256": "4e6ffc149df6515f330d984e99b86e7d1deef01ed2bbac24bba3f19708f36c02"
+  },
+  "pinned_bit_supplier": {
+    "pr": 493,
+    "author": "eumemic",
+    "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/493",
+    "scope": "Published profile repriced; unchanged operator cited, not freshly rebuilt."
+  },
+  "comparison_only": [
+    {
+      "pr": 518,
+      "author": "contributor (handle omitted)",
+      "head": "e0a071dce251eeca96d446f73147048cfebbd5c7",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/518",
+      "kappa": "1393662920776407/1000000000000000000",
+      "created_at": "2026-10-11T23:50:50Z",
+      "role": "Newer comparable numerical report observed during packaging; no added pair choices, 99-pivot word, or owner transport copied."
+    },
+    {
+      "pr": 519,
+      "head": "ffd3c48a80ba8b579dc300e785e387fe8acddfef",
+      "role": "Automatic-width binary counting formalization; public context only."
+    },
+    {
+      "pr": 517,
+      "head": "65518fcff5a7bd490365273ae5469a82aac14853",
+      "kappa": "0.001389125582984265",
+      "role": "Smaller asynchronous result and fixed-word packing ceiling; no code adopted."
+    },
+    {
+      "pr": 516,
+      "head": "1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814",
+      "role": "Lemma A Lean realization, updated during work; formal context only, not recompiled or used as a newly discharged interface.",
+      "first_observed_head": "871b1c51e53918c5e6c945dfe8ef45546c17da56"
+    },
+    {
+      "pr": 510,
+      "head": "64edee18af02aab0c1696b677a0287dd0146381b",
+      "role": "Larger nonbinding bit rate; not adopted."
+    },
+    {
+      "pr": 520,
+      "head": "6077fa76950facbce11ec2f04dfbc93493114a44",
+      "author": "higherbeing",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/520",
+      "role": "Open asynchronous allocator and delivery map. Viewed only during the final comparison refresh; no code or claimed gain adopted. No larger global kappa stated."
+    }
+  ],
+  "retained_ancestry": [
+    {
+      "pr": 496,
+      "head": "00cf70efd6a8637531deafef698157ca83e249ee",
+      "role": "whole-owner parent, invoice and assembly ancestry"
+    },
+    {
+      "pr": 484,
+      "head": "035845ce95f31d0a2dcfb42b8c8e13411271fa5f",
+      "role": "PR496 pinned gauge80-kernel42 parent, not newer moving head"
+    },
+    {
+      "pr": 493,
+      "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7",
+      "role": "unchanged cited R489 bit supplier"
+    },
+    {
+      "pr": 502,
+      "head": "4d30b8322184598e65e90a92389e17e1baedd9eb",
+      "role": "retiming transfer constructor and PR495 schedule fixture"
+    },
+    {
+      "pr": 501,
+      "head": "1dc056496fdbbc74073ed26d948a2dc235dbf356",
+      "role": "parallel retiming integration; credited, no duplicated gain"
+    },
+    {
+      "pr": 473,
+      "head": "628b454d3df00367d2d4f78de7d4eb9cbcbd47ca",
+      "role": "single-helper gauge withdrawal inspiration"
+    },
+    {
+      "pr": 507,
+      "head": "8d4444cf8a16d500cbb94add6e4fa8bcfb9c7d5e",
+      "role": "partial-own factory, 84-pivot reference and retiming map"
+    },
+    {
+      "pr": 505,
+      "head": "4ee769c8e28837482272b5f4742497da8e2fc9d4",
+      "role": "Complete-invocation asynchronous scheduling",
+      "author": "contributor (handle omitted)"
+    },
+    {
+      "pr": 506,
+      "head": "a4948baee6c7ea35323db74ff636620c6af2925a",
+      "role": "public asynchronous retiming comparison and portability feedback"
+    }
+  ],
+  "original_additional_credits_file": "vendor/pr514/NOTICE.md",
+  "excluded_interfaces": {
+    "494": "Disputed residual splitting is not used.",
+    "499": "Larger claimed number using the disputed split-residual interface is not a proof ingredient."
+  },
+  "last_public_comparison_utc": "2026-10-12T00:09:14Z",
+  "public_snapshot": "evidence/PUBLIC-SNAPSHOT.json"
+}
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/complex-nine-native/DATA-PHASES.json b/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/complex-nine-native/DATA-PHASES.json
new file mode 100644
index 0000000000..d9a4f84211
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/complex-nine-native/DATA-PHASES.json
@@ -0,0 +1 @@
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complete recipe is unchanged except its port index; the retained parent polynomial checks establish every selected equality.","scope":"All compressed data boundary operators, idle children, terminal X_q and all-live cover correction. Internal arbitrary-subspace canonical labels are checked separately.","source_parent_sha256":"f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a","status":"PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES","terminal_omission_controls_rejected":112}
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/base_two_moment.py b/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/moment.py b/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/outer.py b/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/contextual-provider-pooling/complex-global/vendor531/vendor/clifford/clifford_exact.py b/research/contextual-provider-pooling/complex-global/vendor531/vendor/clifford/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor531/vendor/clifford/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/contextual-provider-pooling/complex-global/vendor535/LICENSE b/research/contextual-provider-pooling/complex-global/vendor535/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor535/LICENSE
@@ -0,0 +1,201 @@
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+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
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+      the terms of any separate license agreement you may have executed
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+
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+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
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+      incidental, or consequential damages of any character arising as a
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+      Work (including but not limited to damages for loss of goodwill,
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+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
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diff --git a/research/contextual-provider-pooling/complex-global/vendor535/NOTICE.md b/research/contextual-provider-pooling/complex-global/vendor535/NOTICE.md
new file mode 100644
index 0000000000..f42e0eed85
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor535/NOTICE.md
@@ -0,0 +1,70 @@
+# Attribution and dependency notice
+
+Package: **`integer_mult_round21_rank4_delta`**.
+
+Copyright 2026 icekylinx. Local review and packaging used OpenAI Codex.
+
+## New work
+
+Prepared by **icekylinx with GPT-6 Astra assistance**. The new contribution is
+the post-center timing and ordered composition of dirty gauges with rank-four
+response kernels, including the 14 disjoint M-helper groups, explicit scalar
+word, frame and cleanup treatment, independent local argument, physical global
+integration, paid accounting, and combined conditional κ assembly.
+
+The same helper can first serve its own gauge and then donate to a larger
+kernel because compensation occurs before the new pivot dirt is injected.
+This ordering, its actual frame nesting, and its global use are the substantive
+delta. Earlier gauge/kernel primitives and the SAME504 scalar construction
+retain their original authorship.
+
+## Baseline
+
+[PR531](https://github.com/CrocSwap/integer-mult-bounds/pull/531), by icekylinx
+with the disclosed GPT-6 Astra assistance, supplies the SAME504 construction
+and the baseline package `research/direct-delivery504-global`. The final
+baseline head is `e07a8a3f9f79c22113398a0c5dbbc7601f489b3e`; the scientific
+files used here match the original Round20 pins.
+
+**The original PR531 NOTICE is retained separately and remains applicable.**
+That notice records the scalar, geometry, controller, phase, wrapper, hosting,
+and analytic ancestry. This short incremental notice does not replace it.
+
+In particular, DreamingOfClouds's PR484 response/kernel implementation and its
+predecessors retain their source notices. Zhihao Chen's PR425 mutable-basis
+lemma, the PR425/433/514 scalar lineage, and the previously credited source
+and delivery contributions remain attributed through PR531's notice.
+
+## Adopted bit supplier
+
+[PR510](https://github.com/CrocSwap/integer-mult-bounds/pull/510), pinned to
+`64edee18af02aab0c1696b677a0287dd0146381b`, is by **DreamingOfClouds with
+Claude Opus 5.5 assistance via Claude Code**, as disclosed by that package.
+Its R480 nine-stage bit endpoint is adopted as a cited conditional dependency.
+It is not a new bit-side research result of this delta, and no cold replay
+of that full bit pipeline was performed here.
+
+**The original PR510 NOTICE is retained separately and remains applicable.**
+Its ancestry includes eumemic's PR493 carrier-skeleton word; PR503's R480
+dead-total change; chafreaky's PR443/444 replication pipeline; DaysSky's PR442
+whole-residual hosting and PR381 column checker; Zhihao Chen's PR386 geometry;
+DreamingOfClouds's PR315 moment engines and pipeline adaptations; and Dylan
+Crow's PR370 framework, with the assistance disclosures in those sources.
+
+The present PR510 mutable-source carryover exposition is by icekylinx with
+GPT-6 Astra assistance. It expands the role-independent common-label argument
+already present in PR472 and the mutable-basis lemma of PR425; it does not
+claim those underlying ideas as new.
+
+## Comparison, evidence, and licenses
+
+PR493 is also retained as the former-bit-supplier control. PR533 is used only
+for numerical comparison. A cited rate, reused certificate, or prior notice
+does not imply a fresh replay in this package; the README states the completed
+validation scope.
+
+Original source headers, notices, licenses, and pinned provenance remain in
+force. This incremental notice does not relicense upstream material. New
+Python research/audit files carry the Apache-2.0 notice stated in their source
+headers. All reported bounds remain conditional on the listed inherited
+interfaces.
diff --git a/research/contextual-provider-pooling/complex-global/vendor535/code/assemble_combined.py b/research/contextual-provider-pooling/complex-global/vendor535/code/assemble_combined.py
new file mode 100644
index 0000000000..ea740f367e
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor535/code/assemble_combined.py
@@ -0,0 +1,178 @@
+"""Exact composition of the new complex supplier and pinned PR510 bit supplier.
+
+Prepared for icekylinx with GPT-6 Astra assistance, Apache-2.0.
+Adapted from the attributed PR531 assembly. Both rational moment engines and
+the 47-constraint outer engine remain pinned inherited implementations.
+The bit operator is a cited conditional dependency, not freshly reconstructed.
+Usage: assemble_combined.py AUDIT BASE HOSTED PR510_EXPECTED
+"""
+import hashlib
+import importlib.util
+import json
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+
+if not __debug__:
+    raise SystemExit('Run with assertions enabled.')
+assert __debug__, 'Run with assertions enabled.'
+O, V, H, B = map(Path, sys.argv[1:5])
+BIT_COMMIT = '64edee18af02aab0c1696b677a0287dd0146381b'
+BIT_EXPECTED_SHA256 = '19b861f69f7602e47b390d472b487d044bff4230b250520807537c213ad0249f'
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def load(name):
+    path = V / 'work/pr361/code/engines' / (name + '.py')
+    spec = importlib.util.spec_from_file_location('combined_' + name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def decimal(value, places):
+    scaled = value * 10 ** places
+    assert scaled.denominator == 1
+    digits = str(scaled.numerator).zfill(places + 1)
+    return digits[:-places] + '.' + digits[-places:]
+
+
+M, Other, Outer = [load(name) for name in ['moment', 'base_two_moment', 'outer']]
+owner = json.loads((O / 'OWNERS-AND-PROFILE.json').read_text())
+inv = json.loads((O / 'PREFIX-AND-INVOICE.json').read_text())
+host = json.loads((H / 'HOSTED.json').read_text())
+assert owner['template_sha256'] == inv['template_sha256'] == host['template_sha256']
+assert inv['owner_audit_sha256'] == sha(O / 'OWNERS-AND-PROFILE.json')
+assert all(inv['strict_checks'].values())
+P = {int(rank): count for rank, count in owner['paid_profile'].items()}
+m, W = 73, owner['live']
+assert m * W - sum(rank * count for rank, count in P.items()) == 2560
+
+
+def two_moments(profile, dimension, live, lower):
+    """Keep the full rational sign intervals for both independent engines."""
+    fallback = 32 * dimension * dimension * sum(profile.values())
+    receipts = []
+    for endpoint, accept in [(lower, True), (lower + Q(1, 10**24), False)]:
+        lo, hi = M.moment(profile, dimension, live, endpoint, True)
+        a, b = Other.moment(dimension, live, list(profile.items()), endpoint)
+        f, g = Other.moment(dimension, live, [(1, fallback)], endpoint)
+        a += f / 10**16
+        b += g / 10**16
+        assert (hi < 1 and b < 1) if accept else (lo > 1 and a > 1)
+        receipts.append(dict(endpoint=str(endpoint), accept=accept,
+                             mercator=[str(lo - 1), str(hi - 1)],
+                             base_two=[str(a - 1), str(b - 1)]))
+    return receipts
+
+
+cert = M.certify(P, m, W, True)
+b, bp = Q(cert['lower']), Q(cert['upper'])
+assert bp - b == Q(1, 10**24)
+complex_receipts = two_moments(P, m, W, b)
+
+# These checks bind and reprice published bit data. They do not stand in for
+# the physical-operator and mutable-source realization dependency.
+assert sha(B) == BIT_EXPECTED_SHA256
+bit = json.loads(B.read_text())['nine']
+bitP = {int(rank): count for rank, count in bit['profile'].items()}
+bit_inv = bit['bit']
+bm, bW = bit['m'], bit_inv['live']
+assert (bm, bW, bit['stages'], bit['replicas']) == (64, 30720, 9, 32)
+assert sum(rank * count for rank, count in bitP.items()) == bit_inv['rank_mass']
+assert bm * bW - bit_inv['rank_mass'] == 9984
+assert max(bitP) == bit_inv['maxchild'] == 8
+assert bm * bm > 2 * 64 * max(bitP)
+assert bit_inv['physical'] == bW + 9 == 30729
+assert bit_inv['hosted_residuals'] == 480 * 9 * 32
+assert bit_inv['bank_assignments'] == 0
+assert bit['nine_stage_payload_bits'] < 104
+assert bit_inv['prefix_bits'] < bit_inv['charged_prefix_bits'] == 256
+assert bit_inv['two_level_coefficient_bits'] < bit_inv['charged_two_level_coefficient_bits'] == 512
+assert bit_inv['row_coefficient'] < 20161
+c = Q(bit['bit_lower'])
+assert c == Q(bit['bit_lower_decimal'])
+bit_receipts = two_moments(bitP, bm, bW, c)
+
+eta = beta = grid = Q(1, 10**18)
+s = min(c, (1 - beta) * b) - Q(1, 10**24)
+assert 0 < s < c and s < (1 - beta) * b
+coeff = bit_inv['charged_two_level_coefficient_bits']
+row = max(20161, bit_inv['row_coefficient'], inv['finite']['physical_row_coefficient'])
+chain, cuts = [Q(384599, 10**10)], []
+
+
+def ceil(value):
+    return -(-value.numerator // value.denominator)
+
+
+for _ in range(6):
+    old = chain[-1]
+    a = (1 - s) * s + s * old
+    gap = min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s)
+    assert old < a < s < 1 - a and gap > 0
+    cut = max(ceil(36 / gap**2), ceil(2 * (4 + coeff) / gap))
+    assert cut * gap**2 >= 36 and cut * gap >= 2 * (4 + coeff)
+    cuts.append(dict(gap=str(gap), cutoff_log2=str(cut)))
+    chain.append(a)
+q = chain[-1] * (1 - 2 * eta)
+margin = (1 - eta) * q / (1 + q)
+ticks = margin / grid
+kap = grid * ((ticks.numerator - 1) // ticks.denominator)
+bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1},
+          'rows': {'degree_gap': Q(10**6) - Q(51 * row, 25)}}
+assembly = Outer.assembly(chain[-1], b, bridge, kap, eta=eta, beta=beta)
+assert len(assembly['strict_constraints']) == 47
+assert all(value > 0 for value in assembly['strict_constraints'].values())
+controls = []
+for name, k, e, be in [('next_grid', kap + grid, eta, beta),
+                       ('zero_eta', kap, Q(0), beta),
+                       ('zero_beta', kap, eta, Q(0)),
+                       ('unit_beta', kap, eta, Q(1))]:
+    try:
+        Outer.assembly(chain[-1], b, bridge, k, eta=e, beta=be)
+    except AssertionError:
+        controls.append(name)
+    else:
+        raise AssertionError(name)
+
+baselines = {'PR531': Q('0.001517760977820331'),
+             'rejected_POST208_checkpoint': Q('0.001543640781718742'),
+             'PR533': Q('0.001524207950793244')}
+res = dict(
+    status='PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY',
+    complex_lower=str(b), complex_decimal=decimal(b, 24),
+    next_b_rejected=str(bp), exact_moment_receipts=complex_receipts,
+    bit_lower=str(c), bit_decimal=decimal(c, 24),
+    bit_exact_moment_receipts=bit_receipts,
+    bit_result_sha256=sha(B),
+    bit_dependency={'pull_request': 510, 'commit': BIT_COMMIT,
+                    'path': 'research/e8-r480-nine-stage',
+                    'expected_sha256': BIT_EXPECTED_SHA256},
+    bit_prefix_bits=bit_inv['charged_prefix_bits'],
+    bit_charged_two_level_coefficient_bits=coeff,
+    external_row_allowance=row,
+    kappa=str(kap), kappa_decimal=decimal(kap, 18),
+    binding_component='bit' if c < (1 - beta) * b else 'complex',
+    improvements={name: {'baseline': str(value),
+                         'relative_gain': str(kap / value - 1),
+                         'percent_display': f'{float(100 * (kap / value - 1)):.8f}'}
+                  for name, value in baselines.items()},
+    strict_outer_constraints={k: str(v) for k, v in assembly['strict_constraints'].items()},
+    outer_controls=controls, bootstrap=cuts,
+    complex_template_sha256=host['template_sha256'],
+    owner_audit_sha256=sha(O / 'OWNERS-AND-PROFILE.json'),
+    invoice_sha256=sha(O / 'PREFIX-AND-INVOICE.json'),
+    bit_scope='Pinned PR510 published profile and operator are cited dependencies. '
+              'Both exact moments are freshly repriced here; the unchanged physical '
+              'bit operator is not cold-reconstructed. See PR510-MUTABLE-SOURCE-CARRYOVER.md.',
+    scope='Conditional finite witness under the retained all-size compiler, '
+          'common-label/mutable-basis, whole-call hosting, restored-work, '
+          'precision/tape and analytic-transfer contracts. Fresh complex admission '
+          'and finite invoice are separately hash-bound; no unconditional theorem is claimed.')
+(O / 'EXACT-ASSEMBLY.json').write_text(json.dumps(res, indent=2) + '\n')
+print(res['status'], 'b', res['complex_decimal'], 'kappa', res['kappa_decimal'])
+print(json.dumps(res['improvements'], sort_keys=True))
diff --git a/research/contextual-provider-pooling/complex-global/vendor535/inputs/PR510-EXPECTED.json b/research/contextual-provider-pooling/complex-global/vendor535/inputs/PR510-EXPECTED.json
new file mode 100644
index 0000000000..9e5d366963
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-global/vendor535/inputs/PR510-EXPECTED.json
@@ -0,0 +1,102 @@
+{
+ "nine": {
+  "bit_lower": "396861776523137034277/250000000000000000000000",
+  "bit_lower_decimal": "0.001587447106092548137108",
+  "profile": {
+   "1": 345600,
+   "2": 430080,
+   "4": 67200,
+   "6": 49920,
+   "7": 23040,
+   "8": 2592
+  },
+  "bit": {
+   "live": 30720,
+   "physical": 30729,
+   "maxchild": 8,
+   "rank_mass": 1956096,
+   "hosted_residuals": 138240,
+   "bank_assignments": 0,
+   "prefix_bits": 193,
+   "charged_prefix_bits": 256,
+   "coefficient_bits": 193,
+   "two_level_coefficient_bits": 425,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr484": {
+    "kappa": "662515748707749/500000000000000000",
+    "kappa_decimal": "0.001325031497415498",
+    "binding_component": "complex",
+    "complex_lower": "663394767670133/500000000000000000"
+   },
+   "pr471": {
+    "kappa": "260706019542937/200000000000000000",
+    "kappa_decimal": "0.001303530097714685",
+    "binding_component": "complex",
+    "complex_lower": "1305231506267591/1000000000000000000"
+   },
+   "pr458": {
+    "kappa": "323880830669511/250000000000000000",
+    "kappa_decimal": "0.001295523322678044",
+    "binding_component": "complex",
+    "complex_lower": "1297203880559577927527/1000000000000000000000000"
+   }
+  },
+  "nine_stage_payload_bits": 102,
+  "stages": 9,
+  "replicas": 32,
+  "m": 64
+ },
+ "parent_r480": {
+  "pr": 503,
+  "bit_lower": "393688338238452162729/250000000000000000000000",
+  "bit_lower_decimal": "0.001574753352953808650916",
+  "stages": 11
+ },
+ "parent_r489": {
+  "pr": 493,
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "bit_lower_decimal": "0.001565442026981656908596",
+  "stages": 11
+ },
+ "findings": {
+  "lp_helpers_per_4frame": 16,
+  "lp_total": 480,
+  "levels": {
+   "1": {
+    "frames": 120,
+    "helper_visits": 240
+   },
+   "2": {
+    "frames": 180,
+    "helper_visits": 480
+   },
+   "4": {
+    "frames": 60,
+    "helper_visits": 360
+   },
+   "6": {
+    "frames": 180,
+    "helper_visits": 480
+   },
+   "7": {
+    "frames": 120,
+    "helper_visits": 240
+   }
+  },
+  "cells": {
+   "2,2,0": 60,
+   "3,0,0": 120
+  },
+  "d6": {
+   "2,1,2": 60,
+   "3,0,0": 120
+  },
+  "pivots_max": 0,
+  "line_classes": 120,
+  "class_nullity": 0
+ }
+}
diff --git a/research/contextual-provider-pooling/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz b/research/contextual-provider-pooling/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz
new file mode 100644
index 0000000000..3e28a9b59f
Binary files /dev/null and b/research/contextual-provider-pooling/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz differ
diff --git a/research/contextual-provider-pooling/complex-local/README.md b/research/contextual-provider-pooling/complex-local/README.md
new file mode 100644
index 0000000000..840555bd17
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/README.md
@@ -0,0 +1 @@
+Run python -B run_local.py --out NEW_DIRECTORY --vendor PATH_TO_COMPLEX_GLOBAL_VENDOR531. This rebuilds primitive inputs, static44, PR534 frame lifts, the earlier syndrome substitution, eight collective hyperplane waves and twelve weighted coset rewrites, then checks the full emitted local program. Final canonical SHA-256:371638c4f444515caa0586fa7bac838fc7a7c01c4f6110caccf1d4c4f90453b1. Use the enclosing top-level verifier for the complete global and numerical result.
diff --git a/research/contextual-provider-pooling/complex-local/SOURCE-MANIFEST.json b/research/contextual-provider-pooling/complex-local/SOURCE-MANIFEST.json
new file mode 100644
index 0000000000..0f3ff6125b
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/SOURCE-MANIFEST.json
@@ -0,0 +1,29 @@
+{
+  "README.md": "1018ca8cbd77cb7b2bd52b77859613724d9ddedb61908e9f103db23c203aa65e",
+  "run_local.py": "607d144221726b69d8e9da8a1438c83264154bba0fc4a010281962143f40bd35",
+  "code/apply_syndrome.py": "e2e88b38f6b0a087814c54f65cdf8439fc10e6377ca13e356eb39fdbca6ef99c",
+  "code/port_frames.py": "7f86660cfbf7a9123347587f467a5775118f5842ccf03bf9837daf8cb0bbd376",
+  "code/run_portable.py": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955",
+  "docs/OPENAI-SOURCES.json": "46c3a475a4c58f4137373fdf0705690b7f085536671d7be75cc3863895190062",
+  "docs/SEARCH-RECORD.md": "7b09479215c407e4258ef6af64c34dc865e3b9a60c845040258413a2a960f5b8",
+  "docs/TWO-SOURCE-PROOF.md": "4d6423f773ec47d2eea984e02f11f2d636e02ad3e6f3eb3e640a3768fa04fe75",
+  "inputs/PR534-WORD.json.gz": "a275792cb9f5729fac295cb04c556afbaa4513945c517190219fd0e44ab90095",
+  "inputs/phase-baseline/CANONICAL-WORD.json.gz": "e070ae2c78b4a1b644b418774af62b40d8d16e6ba89602f0474afb557d507c37",
+  "inputs/phase-baseline/CLIFFORD-RECIPES.json": "577a1be13f5140d9c3997637784b2f812f46b24c61877699430b02de4f662102",
+  "inputs/phase-baseline/CLIFFORD-REVIEW.json": "cd48fe6882a39c57021c4614747cc5c2c88ec07e806cebb914cf533997b73d9b",
+  "static44/audit_scalar.py": "d22159087c1d0df0edf452aae3a1a7a45bf2cde4ce6e177850e415f9620151e1",
+  "static44/build.py": "31d68795916985e2abb3207b07c1d3e39ed3560f1b46f18ade0a509278c710dc",
+  "static44/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "static44/META-SOURCES.json": "b30c82ad1d707b68e84af85e90b1bab0e41e49ccacda3069b952c790092be920",
+  "static44/NOTICE-upstream.md": "1547136e6d269fdcef2b68c10a97a786a79a4732a12738363f679bfb282430cd",
+  "static44/PROOF.md": "d1dafe41a1698d6df575ec86f796bcba08c54fe14b6d69e78f5f6cff8b55de4a",
+  "static44/README.md": "c4b3ce02012fe97598e76a77877541a8f3387ba4305cee600ee557a48b3493e8",
+  "static44/RECIPE.json": "973f1975213398f2b711e8ce4eddece181d4cbea83be5b6b650115b9bc43f2eb",
+  "static44/replay.py": "5b12ea184b3afde41b1028d1926a0d158f2f05585dae6d9024e31424c290bccf",
+  "static44/SOURCE-MANIFEST.json": "9c64b98a2c7771e77eccc476910a91c17eefc0ee95fb638b058c598c96bbdaf3",
+  "static44/gk/gk_common.py": "e68d190fd436b2f3955decb590adb53344d5d4ea0a19d62d86df1e4b55ecd198",
+  "static44/gk/gk_word.py": "f027a9273bcf4e0971258c160b7d3b3c196366b32a529cff6e6a0e666b03826b",
+  "static44/inputs/BASE535.json.gz": "edfffb8e8735e0d1f07c81d818022b705ef0889c2bccc193a2f7a661b9f7d390",
+  "static44/inputs/OLD-RECIPE.json": "7e5c179246261edd9e1019e81e6e979537f02559da773b993a318f771cb7d763",
+  "static44/inputs/RAW504.json.gz": "1c6144791dbedf6427e3ee7b4c24fb05b5bf407f6346592f50f8dd8d9638108d"
+}
diff --git a/research/contextual-provider-pooling/complex-local/code/apply_syndrome.py b/research/contextual-provider-pooling/complex-local/code/apply_syndrome.py
new file mode 100644
index 0000000000..6fd085c5ed
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/code/apply_syndrome.py
@@ -0,0 +1,23 @@
+from pathlib import Path
+from fractions import Fraction as Q
+import json,gzip,sys,copy,hashlib,argparse
+ap=argparse.ArgumentParser();ap.add_argument('--input',type=Path,required=True);ap.add_argument('--gk',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);args=ap.parse_args();sys.path.insert(0,str(args.gk))
+import gk_word as g,gk_common as c
+g.V=c.V=112;g.DATA=c.DATA=7168
+p=Path(__file__).resolve().parent;w=json.load(gzip.open(args.input));old=copy.deepcopy(w)
+N=728;V=112;protected=set(range(V))|set(map(int,w['start_extra']))
+rows=[{i:Q(1)}for i in range(N)]
+e=w['A'][33];assert e[1:3]==[513,523]
+for op in w['A'][:33]:g.apply_op(op,rows)
+a=Q(-1);err=rows[523].copy()
+for j,x in rows[512].items():
+ err[j]=err.get(j,Q(0))-a*x
+ if not err[j]:err.pop(j)
+assert err and not protected&set(err) and all(j>=224 for j in err)
+e[2]=512;e[3]*=-1
+w['cleanup']=[g.inverse(e,g.FULL)for e in reversed(w['A']+w['B'])if not V<=e[1]<2*V]
+before=g.profile(old);after=g.profile(w);assert before==after
+out=args.out;out.mkdir(exist_ok=False)
+raw=json.dumps(w,sort_keys=True,separators=(',',':')).encode();(out/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+r=dict(status='PASS_EXACT_COLD_DIRT_QUOTIENT_SUBSTITUTION',section='A',index=33,old_operation=old['A'][33],new_operation=e,source_relation_multiplier=str(a),cold_initial_error={str(j):str(x)for j,x in err.items()},protected_columns=len(protected),source_rows_computed_by_finite_triangular_forward_elimination=True,local_profile=dict(after),profile_unchanged=True,requires_regenerated_frame_zero_compensation=True,source_content_sha256=hashlib.sha256(json.dumps(old,sort_keys=True,separators=(',',':')).encode()).hexdigest(),output_content_sha256=hashlib.sha256(raw).hexdigest())
+(out/'SYNDROME-CERTIFICATE.json').write_text(json.dumps(r,indent=2)+'\n');print(json.dumps(r))
diff --git a/research/contextual-provider-pooling/complex-local/code/port_frames.py b/research/contextual-provider-pooling/complex-local/code/port_frames.py
new file mode 100644
index 0000000000..bd9187bd06
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/code/port_frames.py
@@ -0,0 +1,50 @@
+from pathlib import Path
+from collections import defaultdict,Counter,deque
+import json,gzip,sys,copy,math,argparse
+ap=argparse.ArgumentParser();ap.add_argument('--input',type=Path,required=True);ap.add_argument('--source',type=Path,required=True);ap.add_argument('--gk',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);args=ap.parse_args();sys.path.insert(0,str(args.gk))
+import gk_word as g, gk_common as c
+g.V=c.V=112;g.DATA=c.DATA=7168
+p=Path(__file__).resolve().parent
+src=args.input
+a=json.load(gzip.open(src));b=json.load(gzip.open(args.source))
+old=copy.deepcopy(a);before=g.profile(a);sp={}
+def span(E):
+ E=g.basis(E)
+ if E not in sp:sp[E]=g.span(E)
+ return sp[E]
+def meet(A,B):return g.basis(span(A)&span(B))
+def join(A,B):return g.basis(tuple(A)+tuple(B))
+N=728;V=112
+changes=[]
+for sec in ('B','A'):
+ mapping=defaultdict(deque)
+ for e in b[sec]:mapping[tuple(e[:-1])].append(e[-1])
+ desired=[]
+ for e in a[sec]:
+  d=mapping[tuple(e[:-1])];desired.append(d.popleft()if d else e[-1])
+ nxt=[g.FULL]*N
+ for r in range(V,2*V):nxt[r]=g.perp(a['ports'][r-V])
+ if sec=='A':
+  for e in reversed(a['B']):
+   for r in (e[1:3]if e[0]=='add'else e[1:2]):nxt[r]=g.basis(e[-1])
+  for r,F in zip(a['centers'],a['center_frames']):nxt[r]=g.basis(F)
+  for r in range(V,2*V):nxt[r]=g.basis(a.get('target_levels',{}).get(str(r-V),[]))
+ for i in reversed(range(len(a[sec]))):
+  e=a[sec][i];rs=e[1:3]if e[0]=='add'else e[1:2]
+  upper=nxt[rs[0]]
+  for r in rs[1:]:upper=meet(upper,nxt[r])
+  E=join(e[-1],meet(desired[i],upper))
+  assert span(E)<=span(upper)
+  if E!=g.basis(e[-1]):changes.append([sec,i,e[-1],list(E)]);e[-1]=list(E)
+  for r in rs:nxt[r]=E
+prof=g.profile(a);gain=sum((prof[r]-before[r])*r*math.log(r)for r in set(prof)|set(before))
+a['report']['local_profile']={str(k):v for k,v in sorted(prof.items())}
+a['cleanup']=[g.inverse(e,g.FULL)for e in reversed(a['A']+a['B'])if not V<=e[1]<2*V]
+out=args.out;out.mkdir(exist_ok=False);(out/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(a,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+r=dict(before=dict(before),after=dict(prof),delta={r:prof[r]-before[r]for r in set(prof)|set(before)if prof[r]!=before[r]},changes=changes,entropy_gain=gain)
+(out/'PORT.json').write_text(json.dumps(r,indent=2)+'\n');print(json.dumps({k:v for k,v in r.items()if k!='changes'}));print('changes',len(changes))
+
+assert len(changes)==477 and dict(prof)=={1:2284,2:456,3:488,4:168,5:56,6:56,8:8}
+assert all(old[k]==a[k] for k in ('cut','precondition','centers','center_frames','start_extra','target_levels'))
+assert all(x[:-1]==y[:-1] for sec in ('A','B') for x,y in zip(old[sec],a[sec]))
+assert all(span(x[-1])<=span(y[-1]) for sec in ('A','B') for x,y in zip(old[sec],a[sec]))
diff --git a/research/contextual-provider-pooling/complex-local/code/run_portable.py b/research/contextual-provider-pooling/complex-local/code/run_portable.py
new file mode 100644
index 0000000000..2fed13f432
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/code/run_portable.py
@@ -0,0 +1,24 @@
+"""Run one retained verifier with UTF-8/LF text outputs on every platform.
+This changes output serialization only; no mathematical operation is replaced.
+"""
+from pathlib import Path
+import runpy,sys,gzip
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+original_write_text=Path.write_text
+def write_text_lf(self,data,encoding=None,errors=None,newline=None):
+    return original_write_text(self,data,encoding=encoding or 'utf-8',errors=errors,newline='\n')
+Path.write_text=write_text_lf
+# Pin generated gzip serialization. Python3.11 may expose zlib's platform OS
+# byte, Python3.13 normalizes it, and Python3.15 changes the default level.
+# Immutable input files are never rewritten by this wrapper.
+original_gzip_compress=gzip.compress
+def compress_portable(data,compresslevel=9,*,mtime=0):
+    raw=original_gzip_compress(data,compresslevel=compresslevel,mtime=mtime)
+    assert raw[:3]==b'\x1f\x8b\x08' and len(raw)>=18
+    return raw[:9]+b'\xff'+raw[10:]
+gzip.compress=compress_portable
+script=Path(sys.argv[1]).resolve()
+sys.argv=sys.argv[1:]
+sys.path.insert(0,str(script.parent))
+runpy.run_path(str(script),run_name='__main__')
diff --git a/research/contextual-provider-pooling/complex-local/docs/OPENAI-SOURCES.json b/research/contextual-provider-pooling/complex-local/docs/OPENAI-SOURCES.json
new file mode 100644
index 0000000000..9d480f5d1c
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/docs/OPENAI-SOURCES.json
@@ -0,0 +1,22 @@
+[
+  {
+    "technique": "finite_inverse",
+    "path": "lean/OAI/Algebra/OddKaplansky/FiniteInverse.lean",
+    "sha256": "451f40d08deec33d91ceb4e3f03b1366933c48220bce5d230ca2fe395ea78118",
+    "declarations": [
+      "series_mul",
+      "inverse_formula"
+    ],
+    "scope": "Source inspected; no Lean compilation in this campaign"
+  },
+  {
+    "technique": "dual_syndrome",
+    "path": "lean/OAI/Algebra/AuslanderReiten/Duality/LinearHomologyDuality.lean",
+    "sha256": "842a26ea92d7687bb607b331dd4f8e9fb4a47f024b9def1c2c48a7767d3e6459",
+    "declarations": [
+      "dualCyclesToDualHomology_kernel",
+      "dualHomologyEquiv"
+    ],
+    "scope": "Source inspected; no Lean compilation in this campaign"
+  }
+]
diff --git a/research/contextual-provider-pooling/complex-local/docs/SEARCH-RECORD.md b/research/contextual-provider-pooling/complex-local/docs/SEARCH-RECORD.md
new file mode 100644
index 0000000000..5fd16a03a4
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/docs/SEARCH-RECORD.md
@@ -0,0 +1,9 @@
+# Bounded discovery record
+
+1. Bit finite-inverse prefix expansion: 480 first-helper packets screened. 300 replacements passed the fixed frame-chain gate; all were neutral direct loads. The remaining 180 were blocked by this specific early-source frame schedule. This is not a general impossibility result.
+2. Complex protected-syndrome screen: 324 protected columns, modulus 1000000007, 130 legal proportional-source nominations; none had strict immediate paid-profile gain. These modular results are discovery filters, not rational certificates.
+3. Zero-incremental-frame-cost basis factoring and greedy frame-fee weighted factoring found no positive nomination in the bounded scan. No optimality claim follows.
+4. One modular nomination was reconstructed over the rationals and passed the full native pipeline: A[33] source523 becomes minus source512. This changes the cold-dirt response and removes four compensation operations, while preserving all paid ranks.
+5. PR534 frame assignment transfers constructively to static44 through exact successor intersections and frame joins. The resulting positive paid-profile change was fully replayed. It is public-mechanism composition, not a newly invented numerical technique.
+
+Native discovery sources and complete negative results remain in the research lane. Shipping replay uses only frozen constructors; it does not perform search.
diff --git a/research/contextual-provider-pooling/complex-local/docs/TWO-SOURCE-PROOF.md b/research/contextual-provider-pooling/complex-local/docs/TWO-SOURCE-PROOF.md
new file mode 100644
index 0000000000..7ab57778a1
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/docs/TWO-SOURCE-PROOF.md
@@ -0,0 +1,64 @@
+# Finite inverse and cold-dirt syndrome substitution
+
+The two OpenAI sources are listed with exact source hashes in OPENAI-SOURCES.json. They were inspected as mathematical sources. No Lean execution or new Lean certificate is claimed.
+
+## 1. Finite version-DAG expansion
+
+Let v be the vector of all assigned register versions in a finite linear straight-line program, ordered chronologically. Every version has an equation using earlier versions and initial registers x. Thus v = N v + B x with N strictly triangular. If there are n versions then N^n = 0, and
+
+v = (I + N + ... + N^(n-1)) B x.
+
+Multiplying by I-N proves this identity; the two products telescope to I-N^n = I. Conversely these equations have a unique solution, by forward substitution. This remains true when mutable physical registers are reused: distinct versions, rather than register names, are the vertices. Every scalar coefficient remains exact.
+
+This is the constructive specialization of OAI.OddKaplansky.FiniteMatrixInverse.series_mul and inverse_formula in Algebra/OddKaplansky/FiniteInverse.lean. We use the identity to derive actual register functionals at a chosen cut. It does not itself permit moving a gate or changing its frame.
+
+## 2. Exact syndrome factorization
+
+Let S: X -> Z be a linear map over a field and f: X -> K a linear functional. Then the following are equivalent:
+
+- f vanishes on ker S;
+- there is a functional a on Z with f = a S.
+
+For sufficiency of the first condition, define a on im S by a(Sx)=f(x). This is well defined because two preimages differ by ker S. Extend a from a basis of im S to a basis of Z. Necessity follows by evaluation on ker S. Finite Gaussian elimination constructs the extension and checks the complete identity.
+
+The relevant OpenAI source is Algebra/AuslanderReiten/Duality/LinearHomologyDuality.lean, particularly dualCyclesToDualHomology_kernel and its use of LinearMap.range_dualMap_eq_dualAnnihilator_ker. The present finite matrix statement is proved above independently; the larger homology theorem is not assumed as a circuit compiler.
+
+## 3. Sufficient circuit replacement theorem
+
+Partition initial coordinates into protected coordinates P and cold helper dirt D. Cold helpers have entrance frame zero. At a program cut let f be the current source value and g_j other available register values. Suppose exact version expansion proves
+
+f - sum_j a_j g_j = q(D),
+
+where q is an explicitly known linear functional of cold initial dirt only. Replace a background shear t += c f by the sequence t += c a_j g_j. The destination is excluded from all g_j. Every replacement coefficient is admitted by the native dyadic primitive contract, and its actual register-frame chains must be legal.
+
+For every initial vector with D=0 the programs agree at this cut and therefore at every later point. Their full output difference is a linear function of D only. In particular the data map, action on initial targets, and responses to every warm helper are identical. This argument applies to any number of subsequent target deliveries.
+
+Assume, as in the emitted program, that the background subsystem never reads target registers, that all changed background operations are invertible elementary gates, and that cleanup is regenerated as their literal reverse inverse. Background registers then return to their arbitrary initial values. Write the target action of the main program as A y + B x + C D after separating the protected coordinates. Its fixed initial target preconditioner is L=A^-1. Insert the explicit frame-zero target compensation -L C D after that preconditioner. Then the final target map is y+B x, with all cold dirt canceled. This compensation is sufficient only after checking its coefficients and that every referenced helper is indeed cold. The independent native auditor computes C from the entire changed main program; it does not trust a supplied compensation table.
+
+The theorem has no free storage or routing assumption. The replacement gate sequence, changed cleanup, compensations, frame edges, exact Clifford phases, wrappers, full owner program and finite toll are separately charged by the enclosing verifier.
+
+## Concrete application
+
+On the pinned static44 plus PR534 frame-lift word, immediately before A[33], exact rational version expansion proves
+
+value(z523) + value(z512) = initial(z512).
+
+Register 512 is cold. The 324 protected columns are 112 original data columns and 212 warm helper columns. Therefore the operation z513 -= z523 at frame [480] can be replaced by z513 += z512 at the same frame. The difference is exactly one known cold initial coordinate, not an approximate or clean-only equality.
+
+The frozen constructor checks this exact identity and all frame chains. Regenerated compensation has 9,756 additions instead of 9,760. Both oriented emitted programs have 22,107 events instead of 22,111. All 728 formal columns pass in both orientations, including arbitrary dirty helpers; 11 independent local mutation controls are rejected. All 2,929 directed phase edges and 23 residual adapter recipes are checked. The paid child profile is unchanged by this substitution, so it contributes a scalar-program simplification, not a new paid-rank saving.
+
+## Positive paid-rank composition and attribution
+
+The numerical paid-rank improvement in this lane comes from composing the previously proved static44 response presentation with PR534's supplied frame assignment. Matching unchanged scalar operations, the constructor transports desired frames and clips each lift to the exact common successor frame while processing events in reverse dependency order. Each chosen frame contains the old frame and lies below every next use. The existing coalescing realization therefore applies gate by gate; all register chains stay nested.
+
+There are 477 changed frames. The local profile changes from
+
+{1:2204, 2:728, 3:184, 4:280, 5:56, 6:56, 8:8}
+
+to
+
+{1:2284, 2:456, 3:488, 4:168, 5:56, 6:56, 8:8}.
+
+The exact delta is 80 e1 - 272 e2 + 304 e3 - 112 e4. Rank mass and ordered helper widths remain unchanged. Its entropy gain is approximately 3.802467258994966 per invocation; the enclosing package uses exact moment bounds, not this approximation, for its final claim. PR534 supplies the new frame assignment, PR535 supplies the post-center rank-four construction, and the retained PR531/PR484 code supplies transport, response compilation and native audits. Earlier attribution and licenses are preserved in static44/NOTICE-upstream.md and the shared vendor tree.
+
+The OpenAI-inspired syndrome rewrite is composed after these frame lifts. We do not attribute PR534's numerical gain to the two OpenAI lemmas.
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+    "8": 16,
+    "3": 142,
+    "4": 280,
+    "5": 14,
+    "6": 56
+  },
+  "endpoint_adapters": 224,
+  "reused_endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "577a1be13f5140d9c3997637784b2f812f46b24c61877699430b02de4f662102",
+  "baseline_recipe_sha256": "69b97e89376eaaeed3cc4c9257168164dde509f288c0cb47aa93e99b6634e0c0",
+  "baseline_review_sha256": "b5ede34038f2e5006d4bd3bfcf328f792de29f33decde1b2af88f79dfa876145",
+  "compiler_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+  "seconds": 2.2902056210004957,
+  "vector_arithmetic": "Exact checked int64 Gaussian dyadics; cached permutations and Z4 phase actions. No floating-point equality.",
+  "fresh_edge_ids": [
+    [
+      420,
+      424
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+    [
+      420,
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+    [
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+    [
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+    [
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+    [
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+    [
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+    [
+      434,
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+    [
+      434,
+      619
+    ],
+    [
+      434,
+      620
+    ],
+    [
+      435,
+      621
+    ],
+    [
+      435,
+      622
+    ],
+    [
+      435,
+      623
+    ],
+    [
+      435,
+      624
+    ],
+    [
+      435,
+      625
+    ],
+    [
+      435,
+      626
+    ],
+    [
+      435,
+      627
+    ],
+    [
+      435,
+      628
+    ],
+    [
+      436,
+      605
+    ],
+    [
+      436,
+      606
+    ],
+    [
+      436,
+      607
+    ],
+    [
+      436,
+      608
+    ],
+    [
+      436,
+      609
+    ],
+    [
+      436,
+      610
+    ],
+    [
+      436,
+      611
+    ],
+    [
+      436,
+      612
+    ]
+  ],
+  "scope": "Only previously unseen ordered pairs of actual canonical subspaces were freshly lowered. Identical baseline pairs and all endpoint adapters reuse the pinned phase certificates; no full cold replay was performed."
+}
diff --git a/research/contextual-provider-pooling/complex-local/run_local.py b/research/contextual-provider-pooling/complex-local/run_local.py
new file mode 100644
index 0000000000..ed94d6c21b
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/run_local.py
@@ -0,0 +1,27 @@
+"""Rebuild the chosen complex word from primitive inputs and independently audit it."""
+from pathlib import Path
+import argparse,subprocess,sys,json,gzip,hashlib
+if not __debug__:raise SystemExit('Assertions must remain enabled.')
+p=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser();ap.add_argument('--out',type=Path,required=True);ap.add_argument('--vendor',type=Path,required=True);a=ap.parse_args()
+out=a.out.resolve();assert not out.exists();out.mkdir(parents=True)
+v=a.vendor.resolve();launcher=p/'code/run_portable.py'
+def run(script,*args):
+ subprocess.run([sys.executable,'-B',str(launcher),str(script),*map(str,args)],check=True)
+s=p/'static44';g=s/'gk'
+run(s/'build.py','--raw',s/'inputs/RAW504.json.gz','--base',s/'inputs/BASE535.json.gz','--old-recipe',s/'inputs/OLD-RECIPE.json','--recipe',s/'RECIPE.json','--gk-dir',g,'--out',out/'static44')
+run(s/'audit_scalar.py',out/'static44/FULL-WORD.json.gz',out/'static44/SELECTION.json',out/'static44/SCALAR-AUDIT.json')
+run(p/'code/port_frames.py','--input',out/'static44/FULL-WORD.json.gz','--source',p/'inputs/PR534-WORD.json.gz','--gk',g,'--out',out/'lifted')
+run(p/'code/apply_syndrome.py','--input',out/'lifted/FULL-WORD.json.gz','--gk',g,'--out',out/'syndrome')
+run(p.parent/'code/build_wave.py','--input',out/'syndrome/FULL-WORD.json.gz','--recipe',p.parent/'inputs/WAVES.json','--gk',g,'--out',out/'wave')
+run(p.parent/'response/build_weighted_coset.py','--input',out/'wave/FULL-WORD.json.gz','--selection',p.parent/'response/WEIGHTED-COSET-SELECTION.json','--gk-dir',g,'--out',out/'weighted')
+run(p.parent/'epoch/build_epoch14.py','--input',out/'weighted/FULL-WORD.json.gz','--gk-dir',g,'--out',out/'epoch')
+local=out/'local';base=p/'inputs/phase-baseline'
+run(v/'code/audit_and_transport.py','--raw',out/'epoch/FULL-WORD.json.gz','--routing',base/'CANONICAL-WORD.json.gz','--out',local)
+run(v/'code/phases_delta.py','--local',local,'--baseline',base,'--compiler',v/'vendor/clifford')
+run(v/'code/adapters_local.py',local/'CANONICAL-WORD.json.gz',local/'RESIDUAL-ADAPTERS.json',local/'WRAPPER-CHECKS.json')
+run(v/'code/emit_local.py',local)
+run(v/'code/audit_local.py',local)
+actual=hashlib.sha256(gzip.decompress((local/'CANONICAL-WORD.json.gz').read_bytes())).hexdigest()
+assert actual=='970a0761d1a707ef2b2dc263b8fcc1800b401f35ae022094c6b98a007bfcf42d',actual
+print('PASS complete local reconstruction, all columns and controls, final canonical hash',actual)
diff --git a/research/contextual-provider-pooling/complex-local/static44/LICENSE b/research/contextual-provider-pooling/complex-local/static44/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
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+      "Licensor" shall mean the copyright owner or entity authorized by
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+      "Legal Entity" shall mean the union of the acting entity and all
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+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
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+      "Work" shall mean the work of authorship, whether in Source or
+      Object form, made available under the License, as indicated by a
+      copyright notice that is included in or attached to the work
+      (an example is provided in the Appendix below).
+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
+      excluding communication that is conspicuously marked or otherwise
+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
+      publicly display, publicly perform, sublicense, and distribute the
+      Work and such Derivative Works in Source or Object form.
+
+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
+      and charge a fee for, acceptance of support, warranty, indemnity,
+      or other liability obligations and/or rights consistent with this
+      License. However, in accepting such obligations, You may act only
+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
+      defend, and hold each Contributor harmless for any liability
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+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
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+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
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+   limitations under the License.
diff --git a/research/contextual-provider-pooling/complex-local/static44/META-SOURCES.json b/research/contextual-provider-pooling/complex-local/static44/META-SOURCES.json
new file mode 100644
index 0000000000..8cbd32f8bd
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/META-SOURCES.json
@@ -0,0 +1,24 @@
+{
+  "scope": "Actual source statements inspected as structural analogues; no Lean compilation or source theorem directly certifies the new circuit.",
+  "sources": [
+    {
+      "relative_source": "Mathlib/LinearAlgebra/Matrix/Transvection.lean",
+      "sha256": "c8c60dfbda7a09877a884aa2c7ce385f24f5370bb2a456cc20aae872c7dd41ef",
+      "statements": [
+        "mul_transvection_apply_same",
+        "mul_transvection_apply_of_ne",
+        "TransvectionStruct.reverse_inv_prod_mul_prod",
+        "TransvectionStruct.prod_mul_reverse_inv_prod"
+      ]
+    },
+    {
+      "relative_source": "OAI/GroupTheory/Congruence/Elementary.lean",
+      "sha256": "dde2c70e97566d678e96c126476314c994ce4b68858b9aa6c484b9820e950bd8",
+      "statements": [
+        "OAI.CoboundaryExpanders.Elementary.E_mul_apply",
+        "OAI.CoboundaryExpanders.Elementary.upper_E_mul",
+        "OAI.CoboundaryExpanders.Elementary.clear_step"
+      ]
+    }
+  ]
+}
diff --git a/research/contextual-provider-pooling/complex-local/static44/NOTICE-upstream.md b/research/contextual-provider-pooling/complex-local/static44/NOTICE-upstream.md
new file mode 100644
index 0000000000..f42e0eed85
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/NOTICE-upstream.md
@@ -0,0 +1,70 @@
+# Attribution and dependency notice
+
+Package: **`integer_mult_round21_rank4_delta`**.
+
+Copyright 2026 icekylinx. Local review and packaging used OpenAI Codex.
+
+## New work
+
+Prepared by **icekylinx with GPT-6 Astra assistance**. The new contribution is
+the post-center timing and ordered composition of dirty gauges with rank-four
+response kernels, including the 14 disjoint M-helper groups, explicit scalar
+word, frame and cleanup treatment, independent local argument, physical global
+integration, paid accounting, and combined conditional κ assembly.
+
+The same helper can first serve its own gauge and then donate to a larger
+kernel because compensation occurs before the new pivot dirt is injected.
+This ordering, its actual frame nesting, and its global use are the substantive
+delta. Earlier gauge/kernel primitives and the SAME504 scalar construction
+retain their original authorship.
+
+## Baseline
+
+[PR531](https://github.com/CrocSwap/integer-mult-bounds/pull/531), by icekylinx
+with the disclosed GPT-6 Astra assistance, supplies the SAME504 construction
+and the baseline package `research/direct-delivery504-global`. The final
+baseline head is `e07a8a3f9f79c22113398a0c5dbbc7601f489b3e`; the scientific
+files used here match the original Round20 pins.
+
+**The original PR531 NOTICE is retained separately and remains applicable.**
+That notice records the scalar, geometry, controller, phase, wrapper, hosting,
+and analytic ancestry. This short incremental notice does not replace it.
+
+In particular, DreamingOfClouds's PR484 response/kernel implementation and its
+predecessors retain their source notices. Zhihao Chen's PR425 mutable-basis
+lemma, the PR425/433/514 scalar lineage, and the previously credited source
+and delivery contributions remain attributed through PR531's notice.
+
+## Adopted bit supplier
+
+[PR510](https://github.com/CrocSwap/integer-mult-bounds/pull/510), pinned to
+`64edee18af02aab0c1696b677a0287dd0146381b`, is by **DreamingOfClouds with
+Claude Opus 5.5 assistance via Claude Code**, as disclosed by that package.
+Its R480 nine-stage bit endpoint is adopted as a cited conditional dependency.
+It is not a new bit-side research result of this delta, and no cold replay
+of that full bit pipeline was performed here.
+
+**The original PR510 NOTICE is retained separately and remains applicable.**
+Its ancestry includes eumemic's PR493 carrier-skeleton word; PR503's R480
+dead-total change; chafreaky's PR443/444 replication pipeline; DaysSky's PR442
+whole-residual hosting and PR381 column checker; Zhihao Chen's PR386 geometry;
+DreamingOfClouds's PR315 moment engines and pipeline adaptations; and Dylan
+Crow's PR370 framework, with the assistance disclosures in those sources.
+
+The present PR510 mutable-source carryover exposition is by icekylinx with
+GPT-6 Astra assistance. It expands the role-independent common-label argument
+already present in PR472 and the mutable-basis lemma of PR425; it does not
+claim those underlying ideas as new.
+
+## Comparison, evidence, and licenses
+
+PR493 is also retained as the former-bit-supplier control. PR533 is used only
+for numerical comparison. A cited rate, reused certificate, or prior notice
+does not imply a fresh replay in this package; the README states the completed
+validation scope.
+
+Original source headers, notices, licenses, and pinned provenance remain in
+force. This incremental notice does not relicense upstream material. New
+Python research/audit files carry the Apache-2.0 notice stated in their source
+headers. All reported bounds remain conditional on the listed inherited
+interfaces.
diff --git a/research/contextual-provider-pooling/complex-local/static44/PROOF.md b/research/contextual-provider-pooling/complex-local/static44/PROOF.md
new file mode 100644
index 0000000000..1d43cf78f4
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/PROOF.md
@@ -0,0 +1,61 @@
+# Filtered elimination and state-version transport
+
+These are sufficient compilation theorems. They do not assert that a desired low-cost factorization exists, that the searched family is complete, or that scalar rank alone determines the recurrence exponent. Every elementary operation and changed frame transition remains part of the actual invoice.
+
+## Theorem 1: elimination with reusable donors and reversed execution
+
+Let C be the observed target-response matrix on helper coordinates over a field. Suppose we have stages j=1,...,k. At stage j choose new pivots P_j, donor indices D_j disjoint from P_j, and relations between the current response columns
+
+    C_j[:,p] = sum_{d in D_j} q[d,p] C_j[:,d].
+
+No previously eliminated pivot may be used again as a new pivot or a donor. A donor may become a pivot at a later stage. Form U_j from the commuting shears d <- d-q[d,p]p. Then right multiplication by U_j changes only the pivot columns, setting them to zero, and leaves all other columns unchanged. Thus, by induction, C U_1 ... U_k has zero columns at every selected pivot, including pivots which previously served as donors. The products are invertible, with explicit inverse obtained by reversing the elementary operations and their signs.
+
+The actual physical prefix must execute the stage blocks in order k,...,1, since column states are multiplied on the left while the response map is on the right. This reversal is essential: merely concatenating algebraic discovery order is generally wrong. The numerical relations at later stages can be evaluated on the original remaining columns because only already-eliminated columns changed.
+
+For each helper, collect the frames of every stage touching it in physical execution order, followed by its original first-touch frame. Require this list to be nested. A pivot starts at its own elimination frame; other helpers start at their specified old entrance. Require all initial frames to be contained in their first physical touch. These are finite sufficient geometric tests. Regenerate the inverse background cleanup. If the background subsystem never reads output target registers, this cleanup restores every background coordinate for arbitrary initial dirt. Zero response of every warm pivot ensures its dirt never needs a forbidden zero-frame output compensation. Existing gauges may be retained only under explicitly checked separation or a proved read-before-injection order, not by ignoring overlap.
+
+The exact local resource signature is obtained register by register from the successive dimension differences in this list. Repeated equal frames cost zero; every positive difference contributes one child of that rank. A pivot's residual width decreases by its entrance dimension. This chain invoice is valid even when supports overlap and the simple sum of disjoint component invoices is not. Full wrapper and physical owner costs remain separate.
+
+Proof of the response assertion is the elementary column-update identity above and induction. Proof of geometric legality is exactly the nested-chain test at every instruction. Proof of restoration is inversion of the explicitly changed background product. There is no existential oracle in the construction.
+
+## Concrete application: the PR535 static quotient presentation
+
+The frozen PR535 construction has 40 static rank-one pivots, 112 post-center gauges and 56 rank-four post-center pivots. We leave its post-center construction unchanged and replace only the static response presentation. The new selection uses six line classes:
+
+| Frame | Pivots | Active donor list size |
+| --- | ---: | ---: |
+| 96 | 8 | 8 |
+| 102 | 8 | 8 |
+| 120 | 8 | 8 |
+| 126 | 8 | 8 |
+| 480 | 10 | 14 |
+| 486 | 2 | 6 |
+
+This gives 44 static pivots. The actual scalar word loses exactly four rank-one children; all other local rank multiplicities remain identical. Residual inventory changes from 56 width-five, 152 width-eight, 296 width-nine to 56 width-five, 156 width-eight, 292 width-nine.
+
+This witness is a depth-one special case of the staged theorem: its selected supports do not need donor-to-pivot reuse. The broader nested search generated it, but we do not attribute its numerical change to deeper nesting. The gain here comes from choosing a different joint response presentation across line classes, rather than maximizing each public component in isolation.
+
+`build_static44_portable.py` recomputes every selected rational relation, retains the original downstream scalar operations and frame labels, regenerates cleanup, and checks source/result semantic hashes. It checks the actual nested frames, complete local histogram and dyadic scalar contract. `STATIC44-SCALAR-AUDIT.json` independently checks every one of the 728 formal columns in both orientations and rejects all 44 omitted-static-correction controls with the correct compensation held fixed. Arbitrary helper dirt is included among these columns. This is a checked local construction, not a claimed globally hosted bound. The final package may continue to use unchanged PR535 if the bit supplier still binds.
+
+## Theorem 2: compensation transport along exact register versions
+
+Split state into background X and outputs Y. Let an invertible background prefix act by X -> A X and leave Y unchanged. The old compensation is Y -> Y+D X. Then the exact identity
+
+    [A on X] after [add D X to Y]
+      = [add (D A^{-1}) X to Y] after [A on X]
+
+holds on every input, including arbitrary helper dirt. Therefore compensation may be moved to another program cut by computing the inverse-version response D A^{-1}. One must factor the transported map into actual allowed scalar gates and check that every source and target frame can reach the chosen common frame and still reach their next uses. If those finite checks pass, the transformed program has precisely the same full scalar endpoint. It is not enough to compare clean-input columns or to reuse D without the inverse-version factor.
+
+For a sequence of elementary background gates, D A^{-1} is computed by the opposite column update, in the original prefix order. Thus this theorem supplies a constructive compiler pass with an exact rejection test. The untouched-register case gives a useful safe normal form: each dirty compensation read can be delayed up to the first instruction that touches its helper, while the target remains at frame zero. This special case needs no extra storage and preserves the frame-chain invoice. It is not claimed as an exponent improvement. `transport_compensation.py` implements this normal form on R480: all 480 helper dirt reads move to their last untouched versions, all 720 scalar columns agree exactly, and every deduplicated register frame chain is unchanged. The exact receipt is `transport-bit510/TRANSPORT.json`. This appendix does not claim a new native phase or global-program replay.
+
+## Bounded screens and scope
+
+On the original filtered504 source, 100 native nested-elimination trials were preserved; they reached up to 92 pivots and rank188, but became secondary when PR535 moved the frontier. No whole-profile gain is inferred from those counts.
+
+On the new binding R480 bit source, the exact post-center compensation screen rejected every individual helper under its specified first-B-frame schedule: 448 failed because a transported source frame was already above the target frame, and 23 failed the next-use containment test. The full transported compensator had 1273 incompatible support entries in that schedule. A separate exact screen of 120 additional non-root sum/difference lines, together with all 120 root lines, found no entry response circuit. These are bounded family failures, not a theorem excluding other cuts, joint cancellation, general frames, or other schedules.
+
+On PR535, all 112 post-center gauges already attain rank one in the intersection of their actual first frames, target first-use caps and donor-kernel caps. The remaining static census examined 27195 first-frame subspaces and found 12 nonzero-nullity line classes and no higher-rank candidate in that restricted interface. A bounded 100-seed presentation search yielded the checked 44-pivot witness above. No optimality claim follows.
+
+## Structural source references
+
+Mathlib's matrix transvection file supplies explicit left/right elementary update identities and reverse-inverse product identities. OpenAI's congruence elementary-matrix development supplies `clear_step`: an elementary update clears another entry while preserving an already-cleared prefix. We inspected these actual statements as structural models for the inductive invariant and product order. The new geometric compilation theorem and its changed provider were proved and checked here; they are not asserted to be direct imports or newly Lean-certified theorems. Exact source hashes are in META-SOURCES.json.
diff --git a/research/contextual-provider-pooling/complex-local/static44/README.md b/research/contextual-provider-pooling/complex-local/static44/README.md
new file mode 100644
index 0000000000..6aed83ec92
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/README.md
@@ -0,0 +1,7 @@
+# Static44 local construction appendix
+
+Run `python -B replay.py --out NEW_DIRECTORY` from any working directory. This reconstructs the exact new static response presentation and checks all 728 scalar columns in both orientations, including arbitrary helper dirt, plus44 omitted-correction controls. Python standard library only. The output directory must not exist.
+
+The local profile changes by -4 rank-one children relative to PR535. The residual inventory becomes56 width-five,156 width-eight,292 width-nine. The global controller, owner charts, phase recipes and outer assembly are NOT replayed here. This appendix does not contribute a claimed final kappa gain.
+
+The attributed raw and baseline words and old recipe come from PR535 post-center-rank4-global. The gauge/kernel primitives come from PR531's attributed PR484 lineage; their original copyright/assistance notices are preserved. The new selection, replacement proof and constructor are our contribution. No new all-size or analytic interfaces are claimed discharged.
diff --git a/research/contextual-provider-pooling/complex-local/static44/RECIPE.json b/research/contextual-provider-pooling/complex-local/static44/RECIPE.json
new file mode 100644
index 0000000000..68c751bb56
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/RECIPE.json
@@ -0,0 +1,168 @@
+{
+  "selection": {
+    "kernel": [
+      {
+        "E": [
+          96
+        ],
+        "donors": [
+          250,
+          251,
+          256,
+          257,
+          266,
+          267,
+          302,
+          303
+        ],
+        "pivots": [
+          264,
+          265,
+          312,
+          313,
+          314,
+          315,
+          350,
+          351
+        ]
+      },
+      {
+        "E": [
+          102
+        ],
+        "donors": [
+          252,
+          253,
+          254,
+          255,
+          278,
+          279,
+          290,
+          291
+        ],
+        "pivots": [
+          276,
+          277,
+          324,
+          325,
+          326,
+          327,
+          338,
+          339
+        ]
+      },
+      {
+        "E": [
+          120
+        ],
+        "donors": [
+          238,
+          239,
+          244,
+          245,
+          268,
+          269,
+          292,
+          293
+        ],
+        "pivots": [
+          262,
+          263,
+          322,
+          323,
+          328,
+          329,
+          352,
+          353
+        ]
+      },
+      {
+        "E": [
+          126
+        ],
+        "donors": [
+          240,
+          241,
+          242,
+          243,
+          280,
+          281,
+          304,
+          305
+        ],
+        "pivots": [
+          274,
+          275,
+          310,
+          311,
+          316,
+          317,
+          340,
+          341
+        ]
+      },
+      {
+        "E": [
+          480
+        ],
+        "donors": [
+          286,
+          287,
+          288,
+          289,
+          298,
+          300,
+          334,
+          335,
+          336,
+          337,
+          346,
+          348,
+          358,
+          360
+        ],
+        "pivots": [
+          299,
+          301,
+          347,
+          349,
+          359,
+          361,
+          370,
+          371,
+          372,
+          373
+        ]
+      },
+      {
+        "E": [
+          486
+        ],
+        "donors": [
+          362,
+          363,
+          364,
+          365,
+          374,
+          376
+        ],
+        "pivots": [
+          375,
+          377
+        ]
+      }
+    ]
+  },
+  "raw_semantic": "e00e571c80795516eff434392fe48f64ff430a866afd42608808e2f302064275",
+  "base_semantic": "39a1b5a6b237f52f59ebf55f39b22dc06292bc43403c04aa1f086a0277128b33",
+  "output_semantic": "f6183f32b354e0feec39170ee29bfad577af23e4697e9f25a0ad9dc2d5c2d9d4",
+  "profile": {
+    "1": 2204,
+    "4": 280,
+    "8": 8,
+    "3": 184,
+    "2": 728,
+    "6": 56,
+    "5": 56
+  }
+}
diff --git a/research/contextual-provider-pooling/complex-local/static44/SOURCE-MANIFEST.json b/research/contextual-provider-pooling/complex-local/static44/SOURCE-MANIFEST.json
new file mode 100644
index 0000000000..468918ea58
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/SOURCE-MANIFEST.json
@@ -0,0 +1,16 @@
+{
+  "audit_scalar.py": "d22159087c1d0df0edf452aae3a1a7a45bf2cde4ce6e177850e415f9620151e1",
+  "build.py": "31d68795916985e2abb3207b07c1d3e39ed3560f1b46f18ade0a509278c710dc",
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "META-SOURCES.json": "b30c82ad1d707b68e84af85e90b1bab0e41e49ccacda3069b952c790092be920",
+  "NOTICE-upstream.md": "1547136e6d269fdcef2b68c10a97a786a79a4732a12738363f679bfb282430cd",
+  "PROOF.md": "d1dafe41a1698d6df575ec86f796bcba08c54fe14b6d69e78f5f6cff8b55de4a",
+  "README.md": "c4b3ce02012fe97598e76a77877541a8f3387ba4305cee600ee557a48b3493e8",
+  "RECIPE.json": "973f1975213398f2b711e8ce4eddece181d4cbea83be5b6b650115b9bc43f2eb",
+  "replay.py": "5b12ea184b3afde41b1028d1926a0d158f2f05585dae6d9024e31424c290bccf",
+  "gk/gk_common.py": "e68d190fd436b2f3955decb590adb53344d5d4ea0a19d62d86df1e4b55ecd198",
+  "gk/gk_word.py": "f027a9273bcf4e0971258c160b7d3b3c196366b32a529cff6e6a0e666b03826b",
+  "inputs/BASE535.json.gz": "edfffb8e8735e0d1f07c81d818022b705ef0889c2bccc193a2f7a661b9f7d390",
+  "inputs/OLD-RECIPE.json": "7e5c179246261edd9e1019e81e6e979537f02559da773b993a318f771cb7d763",
+  "inputs/RAW504.json.gz": "1c6144791dbedf6427e3ee7b4c24fb05b5bf407f6346592f50f8dd8d9638108d"
+}
diff --git a/research/contextual-provider-pooling/complex-local/static44/audit_scalar.py b/research/contextual-provider-pooling/complex-local/static44/audit_scalar.py
new file mode 100644
index 0000000000..834e8b5103
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/audit_scalar.py
@@ -0,0 +1,55 @@
+"""Independent exact scalar witness for a selected complex kernel word.
+Uses immutable correct-word compensation for omission controls; no repaired
+compensation is silently supplied to a mutant. No physical-hosting claim.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+p=Path(__file__).resolve().parent
+path=Path(sys.argv[1]);selection=Path(sys.argv[2]);out=Path(sys.argv[3]);w=json.loads(gzip.decompress(path.read_bytes()));sel=json.loads(selection.read_text());v=len(w['ports']);n=2*v+w['report']['R']
+def ident():return[{r:Q(1)}for r in range(n)]
+def apply(e,rows):
+ if e[0]=='scale':
+  _,t,a,b,*_=e;q=Q(a,b);rows[t]={j:q*x for j,x in rows[t].items()};return
+ _,t,s,a,b,*_=e;q=Q(a,b)
+ for j,x in list(rows[s].items()):
+  z=rows[t].get(j,Q(0))+q*x
+  if z:rows[t][j]=z
+  else:rows[t].pop(j,None)
+def inv(e,dual=False):
+ e=copy.deepcopy(e)
+ if e[0]=='add':
+  e[3]*=-1
+  if dual:e[1],e[2]=e[2],e[1]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def replay(es):
+ rows=ident()
+ for e in es:apply(e,rows)
+ return rows
+main=w['A']+w['cut']+w['B'];mx=replay(main);dirty=[{}for _ in range(n)]
+for r in range(v,2*v):dirty[r]={j:x for j,x in mx[r].items()if j>=2*v}
+for e in w['precondition']:apply(e,dirty)
+comp=[]
+for r in range(v,2*v):
+ for j,x in sorted(dirty[r].items()):
+  assert not w.get('start_extra',{}).get(str(j)),('nonzero-frame compensation',j)
+  comp.append(['add',r,j,-x.numerator,x.denominator,[]])
+cleanup=[inv(e)for e in reversed(w['A']+w['B'])if not v<=e[1]<2*v]
+assert[e[:-1]for e in cleanup]==[e[:-1]for e in w['cleanup']]
+program=w['precondition']+comp+main+cleanup;expected=ident()
+for t in range(v):expected[v+t][t]=Q(1)
+assert replay(program)==expected
+back=ident()
+for t in range(v):back[t][v+t]=Q(-1)
+assert replay([inv(e,True)for e in program])==back
+controls={}
+for cl in sel['kernel']:
+ for h in cl['pivots']:
+  aa=[e for e in w['A']if not(e[0]=='add'and e[2]==2*v+h and e[1]>=2*v and e[-1]==cl['E'])]
+  assert len(aa)<len(w['A']);cc=[inv(e)for e in reversed(aa+w['B'])if not v<=e[1]<2*v]
+  assert replay(w['precondition']+comp+aa+w['cut']+w['B']+cc)!=expected
+  controls[str(h)]='REJECTED_OMITTED_KERNEL_CORRECTION'
+r=dict(status='PASS_EXACT_RATIONAL_FORWARD_AND_INVERSE_TRANSPOSE',word_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),selection_sha256=hashlib.sha256(selection.read_bytes()).hexdigest(),columns_each_orientation=n,compensations=len(comp),program_operations=len(program),kernel_pivots=len(controls),controls=controls,scope='Exact local scalar identity and preserved frame-zero compensation; physical owner routing, complete invoice and outer kappa separate.')
+out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],n,len(controls))
diff --git a/research/contextual-provider-pooling/complex-local/static44/build.py b/research/contextual-provider-pooling/complex-local/static44/build.py
new file mode 100644
index 0000000000..de64849739
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/build.py
@@ -0,0 +1,30 @@
+"""Source-bound static response-presentation replacement on PR535. No search."""
+import argparse,copy,gzip,hashlib,json,sys
+from pathlib import Path
+from fractions import Fraction as Q
+
+def main():
+ if not __debug__:raise SystemExit('Assertions must remain enabled.')
+ a=argparse.ArgumentParser();a.add_argument('--raw',type=Path,required=True);a.add_argument('--base',type=Path,required=True);a.add_argument('--old-recipe',type=Path,required=True);a.add_argument('--recipe',type=Path,required=True);a.add_argument('--gk-dir',type=Path,required=True);a.add_argument('--out',type=Path,required=True);a=a.parse_args()
+ sys.path.insert(0,str(a.gk_dir));import gk_word as g,gk_common as co;g.V=co.V=112;g.DATA=co.DATA=7168
+ load=lambda f:json.loads(gzip.decompress(f.read_bytes())if f.suffix=='.gz'else f.read_bytes())
+ semantic=lambda w:hashlib.sha256(json.dumps({k:v for k,v in w.items()if k!='report'},sort_keys=True,separators=(',',':')).encode()).hexdigest()
+ raw,base,old,r=map(load,[a.raw,a.base,a.old_recipe,a.recipe]);assert semantic(raw)==r['raw_semantic']and semantic(base)==r['base_semantic']
+ sel=r['selection'];seed=g.build(raw,sel,check=True);assert all(len(c['E'])==1 for c in sel['kernel']);assert sum(len(c['pivots'])for c in sel['kernel'])==44
+ prefix=seed['A'][:-len(raw['A'])];w=copy.deepcopy(base)
+ assert[e[:-1]for e in base['A'][-len(raw['A']):]]==[e[:-1]for e in raw['A']]
+ w['A']=prefix+base['A'][-len(raw['A']):]
+ for cl in old['selection']['kernel']:
+  for h in cl['pivots']:del w['start_extra'][str(224+h)]
+ w['start_extra'].update(seed['start_extra'])
+ w['cleanup']=[g.inverse(e,g.FULL)for e in reversed(w['A']+w['B'])if not 112<=e[1]<224]
+ for sec in ('A','B','cut','cleanup','precondition'):
+  for e in w.get(sec,[]):
+   if e[0]=='add':assert e[1]!=e[2];q=Q(e[3],e[4])
+   else:q=Q(e[2],e[3]);assert q and abs(q.numerator)&(abs(q.numerator)-1)==0
+   assert q.denominator&(q.denominator-1)==0
+ H=g.profile(w);assert dict(H)=={int(k):v for k,v in r['profile'].items()};assert semantic(w)==r['output_semantic']
+ widths=g.widths_of(w);w['report']['local_profile']=dict(H);w['report']['local_rank_mass']=sum(k*v for k,v in H.items());w['report']['static_pivots']=44;w['report']['entrance_rank']=sum(9-x for x in widths);w['report']['entering_helpers']=sum(x<9 for x in widths);w['report']['width_inventory']={x:widths.count(x)for x in sorted(set(widths))};w['report']['status']='EXACT_STATIC44_RESPONSE_PRESENTATION_PENDING_INDEPENDENT_AUDIT'
+ a.out.mkdir(parents=True,exist_ok=False);(a.out/'FULL-WORD.json.gz').write_bytes(g.dump(w));(a.out/'SELECTION.json').write_text(json.dumps(sel,indent=2)+'\n');(a.out/'REPLAY.json').write_text(json.dumps({'status':'PASS_EXACT_STATIC44_CONSTRUCTOR','semantic_sha256':semantic(w),'profile':dict(H),'widths':g.widths_of(w)},indent=2)+'\n')
+ print('PASS exact static44 constructor')
+if __name__=='__main__':main()
diff --git a/research/contextual-provider-pooling/complex-local/static44/gk/gk_common.py b/research/contextual-provider-pooling/complex-local/static44/gk/gk_common.py
new file mode 100644
index 0000000000..0e5fde920d
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/gk/gk_common.py
@@ -0,0 +1,94 @@
+"""Shared helpers for the complex shared-donor-kernel / entrance-gauge word.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+
+A "gk word" is PR #433's FULL-WORD.json.gz with optional extension keys (absent in #433's word, so every default is
+#433's behaviour):
+  start_extra   {register: entrance frame (list of F2^9 vectors)}  helpers that start at a nonzero frame (width 9 - dim)
+  target_levels {target: frame}                                    frame a target reaches through nonzero-frame compensation
+Entrance gauges are ordinary gates at the head of A (target += c * helper at the entrance frame); kernel updates are
+ordinary gates at the head of A (donor += q * pivot at the entrance frame).
+"""
+import math
+from collections import Counter
+
+V, K, T, L, M = 120, 4, 8, 9, 73
+DATA = 2 * K * V * T          # 7680
+FULL = tuple(1 << i for i in range(8, -1, -1))
+
+
+def basis(vs):
+    b = {}
+    for x in vs:
+        for p in sorted(b, reverse=True):
+            if x >> p & 1: x ^= b[p]
+        if x:
+            p = x.bit_length() - 1
+            for q in b:
+                if b[q] >> p & 1: b[q] ^= x
+            b[p] = x
+    return tuple(b[p] for p in sorted(b, reverse=True))
+
+
+def widths_of(word):
+    """residual width of every helper: 9 - dim(entrance frame); 9 when the word has no extension"""
+    R = word['report']['R'] if 'R' not in word else word['R']
+    w = [L] * R
+    for r, E in word.get('start_extra', {}).items():
+        assert 2 * V <= int(r) < 2 * V + R
+        w[int(r) - 2 * V] = L - len(basis(E))
+    return w
+
+
+def split_pad(p):
+    """a pad of rank p is paid as nested commuting children of rank <= 51 (so that 73^2 > 2*child^2); rank 1 stays 1"""
+    if p == 0: return []
+    n = -(-p // 51); return [p // n + (1 if i < p % n else 0) for i in range(n)]
+
+
+def tile(items):
+    """Bank tiling of unhosted residuals.  items: list of (rep, helper, width); a bank has M = 73 cells.
+    * width-9 residuals (no wrapper acts on them): first fit in the given order, packed from offset 0, eight per bank, pad rank 1
+      (PR #433/#442's tiling and routes [2, slot]);
+    * ENTERING residuals (width w < 9, paid wrappers, e = 9 - w spectators): banks of their own in which every entering helper is the ONLY
+      owner of its bank family in its invocation (the one-helper rule of PR #458 extended to banks): bank j holds the j-th entering
+      helper of each replica, residuals packed from offset 0 in replica order (at most one helper per replica, hence per invocation).
+      The spectators of an entering helper are the first e cells of the bank beyond every residual cell of the bank (the pad, which no call
+      uses for a residual, is paid as before: rank 73 - sum of widths; the spectators are borrowed inside it and not deducted).
+    Returns (assign, banks, pads): assign[(rep, helper)] = (bank, offset, width, pure, spectators) with pure = the bank holds only width-9
+    residuals and spectators = () for width 9; pads = Counter of pad ranks (split into children of rank <= 51)."""
+    assign = {}; pads = Counter(); fill = []
+    for z, (rep, h, w) in enumerate(items):             # width 9: first fit, as PR #433 (all widths 9 reproduces it exactly)
+        if w != L: continue
+        for b, f in enumerate(fill):
+            if f + w <= M: break
+        else:
+            b = len(fill); fill.append(0)
+        assign[(rep, h)] = (b, fill[b], w, True, ()); fill[b] += w
+    nwide = len(fill); byrep = {}
+    for rep, h, w in items:
+        if w < L: byrep.setdefault(rep, []).append((h, w))
+    cells = [0] * max((len(v) for v in byrep.values()), default=0); emax = [0] * len(cells); place = {}
+    for rep in sorted(byrep):                           # the j-th entering helper of every replica goes to entering bank j
+        for j, (h, w) in enumerate(byrep[rep]):
+            place[(rep, h)] = (nwide + j, cells[j], w); cells[j] += w; emax[j] = max(emax[j], L - w)
+    for j in range(len(cells)): assert cells[j] + emax[j] <= M, ('entering bank without room for its spectators', j)
+    for (rep, h), (b, off, w) in place.items():
+        assign[(rep, h)] = (b, off, w, False, tuple(range(cells[b - nwide], cells[b - nwide] + L - w)))
+    fill += cells
+    for f in fill:
+        for part in split_pad(M - f): pads[part] += 1
+    return assign, len(fill), pads
+
+
+def route(off, w, pure, sp=()):
+    """owner route of a banked helper residual: PR #433's [2, slot] for width 9 (pure width-9 bank); an entering helper (w < 9) is
+    [2, offset, width, [spectator cells]] with e = 9 - w spectators"""
+    if w == L: assert pure and not sp; return [2, off // L]
+    assert not pure and len(sp) == L - w; return [2, off, w, list(sp)]
+
+
+def unhosted_stock(widths):
+    """live stock and padding histogram of the unhosted (parent) template, per stage x nine"""
+    R = len(widths)
+    _, nb, pads = tile([(rep, h, widths[h]) for rep in range(T) for h in range(R)])
+    return DATA + L * nb, Counter({r: z * L for r, z in pads.items()})
diff --git a/research/contextual-provider-pooling/complex-local/static44/gk/gk_word.py b/research/contextual-provider-pooling/complex-local/static44/gk/gk_word.py
new file mode 100644
index 0000000000..15782ba625
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/gk/gk_word.py
@@ -0,0 +1,194 @@
+"""Apply a frozen selection (shared-donor kernel + entrance gauges) to PR #433's complex word.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+usage: gk_word.py BASE_FULL-WORD.json.gz SELECTION.json OUT_FULL-WORD.json.gz
+An empty selection ({}) copies the input byte for byte (regression anchor).
+
+selection = {"kernel": [{"E": [x], "donors": [h..], "pivots": [h..]}..], "gauge": {"h": [x..]}}   (h = helper index 0..R-1)
+Kernel (PR #417/#435/#434/#440): a pivot starts at E; every donor receives  donor += -q * pivot  at frame E before the main
+word, where col(pivot) = sum q_d col(d) are the exact dirty-response columns; the pivot's frame-zero compensation vanishes.
+Gauge (#401/#408-#416): the compensation  target += -C[t,h] * helper  of helper h is executed at frame E_h as the first gates
+of the main word; h starts at E_h and its targets climb to the level L_t = largest E over their entering helpers.
+The exact verification is the arbitrary-dirt replay of audit_gk.py; this module also checks the structural conditions."""
+import copy, gzip, hashlib, json, sys
+from collections import Counter, defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from gk_common import *
+
+
+def apply_op(e, rows):
+    if e[0] == 'scale':
+        _, t, a, b, *_ = e; q = Q(a, b); rows[t] = {j: q * x for j, x in rows[t].items()}
+    else:
+        _, t, s, a, b, *_ = e; q = Q(a, b)
+        for j, x in list(rows[s].items()):
+            z = rows[t].get(j, Q(0)) + q * x
+            if z: rows[t][j] = z
+            else: rows[t].pop(j, None)
+
+
+def inverse(e, F):
+    e = copy.deepcopy(e)
+    if e[0] == 'add': e[3] *= -1
+    else: e[2], e[3] = e[3], e[2]
+    e[-1] = list(F); return e
+
+
+def responses(word):
+    """dirty-response columns col[h] = {target: coefficient} of the unmodified word (after the frame-zero preconditioner)"""
+    R = word['report']['R']; n = 2 * V + R
+    rows = [{r: Q(1)} for r in range(n)]
+    for e in word['A'] + word['cut'] + word['B']: apply_op(e, rows)
+    dirty = [{} for _ in range(n)]
+    for r in range(V, 2 * V): dirty[r] = {j: x for j, x in rows[r].items() if j >= 2 * V}
+    for e in word['precondition']: apply_op(e, dirty)
+    col = [{} for _ in range(R)]
+    for r in range(V, 2 * V):
+        for j, x in dirty[r].items(): col[j - 2 * V][r - V] = x
+    return col
+
+
+def first_frames(word):
+    first = {}
+    for seq in (word['A'], word['B']):
+        for e in seq:
+            F = basis(e[-1])
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []):
+                if r >= 2 * V: first.setdefault(r - 2 * V, F)
+    return first
+
+
+def solve_relation(col, donors, p):
+    """exact rational c with col[p] = sum_d c_d col[d]; None if p is not in the span"""
+    ts = sorted({t for d in donors for t in col[d]} | set(col[p]))
+    idx = {t: i for i, t in enumerate(ts)}
+    Mx = [[Q(0)] * (len(donors) + 1) for _ in ts]
+    for ci, d in enumerate(donors):
+        for t, x in col[d].items(): Mx[idx[t]][ci] = x
+    for t, x in col[p].items(): Mx[idx[t]][-1] = x
+    piv = []; r = 0
+    for c in range(len(donors)):
+        pr = next((i for i in range(r, len(Mx)) if Mx[i][c]), None)
+        if pr is None: continue
+        Mx[r], Mx[pr] = Mx[pr], Mx[r]; q = Mx[r][c]; Mx[r] = [x / q for x in Mx[r]]
+        for i in range(len(Mx)):
+            if i != r and Mx[i][c]:
+                f = Mx[i][c]; Mx[i] = [a - f * b for a, b in zip(Mx[i], Mx[r])]
+        piv.append(c); r += 1
+    if any(Mx[i][-1] for i in range(r, len(Mx))): return None
+    assert r == len(donors), 'donors must have independent response columns'
+    return {donors[c]: Mx[i][-1] for i, c in enumerate(piv) if Mx[i][-1]}
+
+
+def span(U):
+    s = {0}
+    for b in U: s |= {x ^ b for x in s}
+    return s
+
+
+def perp(x): return basis([z for z in range(1, 512) if not (x & z).bit_count() % 2])
+
+
+def profile(word):
+    """local paid profile of a gk word by direct simulation of the frame chains (second implementation: audit_gk.py)"""
+    R = word['report']['R']; n = 2 * V + R; P = word['ports']
+    cur = {}
+    for r in range(n):
+        cur[r] = (P[r],) if r < V else ((basis(word['start_extra'][str(r)]) if str(r) in word.get('start_extra', {}) else ()) if r >= 2 * V else ())
+    paid = Counter()
+    def climb(r, F):
+        F = basis(F); o = cur[r]
+        assert basis(list(o) + list(F)) == F, ('frame violation', r, o, F)
+        if o != F: paid[len(F) - len(o)] += 1; cur[r] = F
+    lev = {int(t): basis(E) for t, E in word.get('target_levels', {}).items()}
+    for seq, part in ((word['A'], 'A'), (word['B'], 'B')):
+        if part == 'B':
+            for r, f in zip(word['centers'], word['center_frames']):
+                assert cur[r] == basis(f), 'centre frame'
+                served = sorted({lev.get(e[1] - V, ()) for e in word['cut'] if e[2] == r}, key=lambda E: -len(E))
+                o = basis(f)
+                for Lv in served:
+                    assert span(Lv) <= span(o), 'served levels must descend inside the centre frame'
+                    if Lv != o: paid[len(o) - len(Lv)] += 1; o = Lv
+            for t in range(V): assert cur[V + t] == lev.get(t, ()), 'target level at the centre scatter'
+        for e in seq:
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): climb(r, e[-1])
+    for r in range(n): climb(r, FULL if (r < V or r >= 2 * V) else perp(P[r - V]))
+    return paid
+
+
+def global_profile(local, widths):
+    """unhosted nine-stage profile: local x (stages*replicas) + the 240*8 idle children per rank + bank pads"""
+    live, pads = unhosted_stock(widths)
+    g = Counter({r: z * L * T for r, z in local.items()})
+    for r in (16, 8, 32, 8, 48, 8, 48, 32, 16): g[r] += 240 * T
+    g.update(pads)
+    return live, g
+
+
+def build(word, sel, check=True):    # check=False only for the mutation controls that must be caught by the certifying scripts
+    if not sel: return word
+    w = copy.deepcopy(word); R = w['report']['R']
+    col = responses(word); first = first_frames(word)
+    gauge = {int(h): basis(E) for h, E in sel.get('gauge', {}).items()}
+    classes = sel.get('kernel', [])
+    pivots = {p for c in classes for p in c['pivots']}; donors = {d for c in classes for d in c['donors']}
+    assert not (pivots & donors) and not (pivots | donors) & set(gauge) and len(pivots) == sum(len(c['pivots']) for c in classes)
+    # --- structural conditions -------------------------------------------------------------------------------------
+    for h, E in gauge.items():
+        assert not check or span(E) <= span(first[h]), ('gauge entrance outside the first frame', h)
+    levels = defaultdict(list)
+    for h, E in gauge.items():
+        for t in col[h]: levels[t].append(E)
+    for t, Es in levels.items():                                   # pairwise nested comps per target
+        for a in Es:
+            for b in Es: assert not check or span(a) <= span(b) or span(b) <= span(a), ('non-nested gauges at target', t)
+    lev = {t: max(Es, key=len) for t, Es in levels.items()}
+    for k, r in enumerate(w['centers']):                              # chain per centre, inside the centre frame
+        served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == r}
+        for a in served:
+            for b in served: assert not check or span(a) <= span(b) or span(b) <= span(a), ('centre chain', k)
+        top = max(served, key=len)
+        assert not check or span(top) <= span(basis(w['center_frames'][k])), ('level outside centre frame', k)
+    # --- gates ----------------------------------------------------------------------------------------------------------
+    gates = []
+    for h, E in sorted(gauge.items(), key=lambda kv: (len(kv[1]), kv[0])):
+        for t, x in sorted(col[h].items()):
+            c = -x; gates.append(['add', V + t, 2 * V + h, c.numerator, c.denominator, list(E)])
+    pre = []
+    start = {2 * V + h: list(E) for h, E in gauge.items()}
+    for cl in sorted(classes, key=lambda c: (len(c['E']), c['E'])):
+        E = basis(cl['E'])
+        for x in [*cl['donors'], *cl['pivots']]: assert span(E) <= span(first[x]), ('kernel entrance outside the first frame', x)
+        for p in cl['pivots']:
+            rel = solve_relation(col, cl['donors'], p)
+            assert rel is not None, ('pivot response not in the donor span', p)
+            start[2 * V + p] = list(E)
+            for d, c in rel.items():
+                q = -c; pre.append(['add', 2 * V + d, 2 * V + p, q.numerator, q.denominator, list(E)])
+    w['A'] = gates + pre + w['A']
+    w['cleanup'] = [inverse(e, FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V]
+    w['start_extra'] = {str(r): list(E) for r, E in sorted(start.items())}
+    w['target_levels'] = {str(t): list(E) for t, E in sorted(lev.items()) if E}
+    if not check: return w
+    prof = profile(w); widths = widths_of(w)
+    live, g = global_profile(prof, widths)
+    w['report']['local_profile'] = {str(k): z for k, z in sorted(prof.items())}
+    w['report']['global_profile'] = {str(k): z for k, z in sorted(g.items())}
+    w['report']['live'] = live
+    w['report']['entrance_rank'] = sum(L - x for x in widths); w['report']['entering_helpers'] = sum(1 for x in widths if x < L)
+    w['report']['selection_sha256'] = hashlib.sha256(json.dumps(sel, sort_keys=True).encode()).hexdigest()
+    return w
+
+
+def dump(w): return gzip.compress(json.dumps(w, sort_keys=True, separators=(',', ':')).encode(), mtime=0)
+
+
+if __name__ == '__main__':
+    src, selp, out = map(Path, sys.argv[1:4])
+    sel = json.loads(selp.read_text())
+    if not sel: out.write_bytes(src.read_bytes()); print('empty selection: copied byte for byte'); sys.exit(0)
+    word = json.load(gzip.open(src)); w = build(word, sel); out.write_bytes(dump(w))
+    print('gk word: entering helpers', w['report']['entering_helpers'], 'entrance rank', w['report']['entrance_rank'],
+          'local profile', w['report']['local_profile'], 'unhosted live', w['report']['live'])
diff --git a/research/contextual-provider-pooling/complex-local/static44/inputs/BASE535.json.gz b/research/contextual-provider-pooling/complex-local/static44/inputs/BASE535.json.gz
new file mode 100644
index 0000000000..bcc1647b7d
Binary files /dev/null and b/research/contextual-provider-pooling/complex-local/static44/inputs/BASE535.json.gz differ
diff --git a/research/contextual-provider-pooling/complex-local/static44/inputs/OLD-RECIPE.json b/research/contextual-provider-pooling/complex-local/static44/inputs/OLD-RECIPE.json
new file mode 100644
index 0000000000..52d4b5f382
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/inputs/OLD-RECIPE.json
@@ -0,0 +1,1163 @@
+{
+  "source_sha256": "1c6144791dbedf6427e3ee7b4c24fb05b5bf407f6346592f50f8dd8d9638108d",
+  "selection": {
+    "kernel": [
+      {
+        "E": [
+          510
+        ],
+        "donors": [
+          242,
+          243,
+          244,
+          245,
+          254,
+          256,
+          266,
+          267,
+          268,
+          269,
+          270,
+          271,
+          278,
+          280,
+          282,
+          283,
+          290,
+          292,
+          294,
+          295,
+          306,
+          307
+        ],
+        "pivots": [
+          255,
+          257,
+          279,
+          281,
+          291,
+          293,
+          302,
+          303,
+          304,
+          305
+        ]
+      },
+      {
+        "E": [
+          504
+        ],
+        "donors": [
+          238,
+          239,
+          240,
+          241,
+          250,
+          252,
+          314,
+          315,
+          316,
+          317,
+          318,
+          319,
+          326,
+          328,
+          330,
+          331,
+          338,
+          340,
+          342,
+          343,
+          354,
+          355
+        ],
+        "pivots": [
+          251,
+          253,
+          327,
+          329,
+          339,
+          341,
+          350,
+          351,
+          352,
+          353
+        ]
+      },
+      {
+        "E": [
+          486
+        ],
+        "donors": [
+          262,
+          263,
+          264,
+          265,
+          274,
+          276,
+          310,
+          311,
+          312,
+          313,
+          322,
+          324,
+          362,
+          364
+        ],
+        "pivots": [
+          275,
+          277,
+          323,
+          325,
+          363,
+          365,
+          374,
+          375,
+          376,
+          377
+        ]
+      },
+      {
+        "E": [
+          480
+        ],
+        "donors": [
+          286,
+          287,
+          288,
+          289,
+          298,
+          300,
+          334,
+          335,
+          336,
+          337,
+          346,
+          348,
+          358,
+          360
+        ],
+        "pivots": [
+          299,
+          301,
+          347,
+          349,
+          359,
+          361,
+          370,
+          371,
+          372,
+          373
+        ]
+      }
+    ],
+    "gauge": {
+      "224": [
+        6
+      ],
+      "225": [
+        6
+      ],
+      "226": [
+        24
+      ],
+      "227": [
+        24
+      ],
+      "228": [
+        30
+      ],
+      "229": [
+        30
+      ],
+      "230": [
+        30
+      ],
+      "231": [
+        30
+      ],
+      "232": [
+        24
+      ],
+      "233": [
+        24
+      ],
+      "234": [
+        6
+      ],
+      "235": [
+        6
+      ],
+      "236": [
+        6
+      ],
+      "237": [
+        6
+      ],
+      "246": [
+        6
+      ],
+      "247": [
+        6
+      ],
+      "248": [
+        6
+      ],
+      "249": [
+        6
+      ],
+      "258": [
+        6
+      ],
+      "259": [
+        6
+      ],
+      "260": [
+        24
+      ],
+      "261": [
+        24
+      ],
+      "272": [
+        24
+      ],
+      "273": [
+        24
+      ],
+      "284": [
+        30
+      ],
+      "285": [
+        30
+      ],
+      "296": [
+        30
+      ],
+      "297": [
+        30
+      ],
+      "308": [
+        30
+      ],
+      "309": [
+        30
+      ],
+      "320": [
+        30
+      ],
+      "321": [
+        30
+      ],
+      "332": [
+        24
+      ],
+      "333": [
+        24
+      ],
+      "344": [
+        24
+      ],
+      "345": [
+        24
+      ],
+      "356": [
+        6
+      ],
+      "357": [
+        6
+      ],
+      "366": [
+        6
+      ],
+      "367": [
+        6
+      ],
+      "368": [
+        6
+      ],
+      "369": [
+        6
+      ],
+      "378": [
+        6
+      ],
+      "379": [
+        6
+      ],
+      "380": [
+        6
+      ],
+      "381": [
+        6
+      ],
+      "382": [
+        24
+      ],
+      "383": [
+        24
+      ],
+      "384": [
+        30
+      ],
+      "385": [
+        30
+      ],
+      "386": [
+        30
+      ],
+      "387": [
+        30
+      ],
+      "388": [
+        24
+      ],
+      "389": [
+        24
+      ],
+      "390": [
+        6
+      ],
+      "391": [
+        6
+      ],
+      "392": [
+        6
+      ],
+      "393": [
+        6
+      ],
+      "394": [
+        6
+      ],
+      "396": [
+        6
+      ],
+      "400": [
+        6
+      ],
+      "401": [
+        6
+      ],
+      "402": [
+        6
+      ],
+      "404": [
+        6
+      ],
+      "408": [
+        6
+      ],
+      "409": [
+        6
+      ],
+      "410": [
+        6
+      ],
+      "412": [
+        6
+      ],
+      "416": [
+        24
+      ],
+      "417": [
+        24
+      ],
+      "418": [
+        24
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+  ],
+  "rank4_anchor_after_post_gauge_additions": 320,
+  "operation_order": [
+    "A with original static40 kernels",
+    "center cut",
+    "112 post-center gauge compensations",
+    "56 rank-four pivot injections",
+    "native B",
+    "inverse source/helper cleanup"
+  ],
+  "report": {
+    "R": 504,
+    "borrowed_output_pairs": 56,
+    "centre_ranks": [
+      8,
+      8,
+      8,
+      8,
+      8,
+      8,
+      8,
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+    "first_load_join_counts": {
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+    },
+    "h": 9,
+    "local_profile": {
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+      "2": 888,
+      "3": 216,
+      "4": 168,
+      "5": 56,
+      "6": 56,
+      "8": 8
+    },
+    "local_rank_mass": 6016,
+    "m": 73,
+    "scope": "Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.",
+    "selected_load_join_counts": {
+      "6": 112
+    },
+    "selected_partitions": [
+      0,
+      0
+    ],
+    "source_and_helper_cleanup_exact_on_clean_columns": true,
+    "source_columns_exact": 112,
+    "status": "EXACT_RELATIONS_AND_FRAMES_PENDING_INDEPENDENT_REPLAY",
+    "v": 112,
+    "width_inventory": {
+      "5": 56,
+      "8": 152,
+      "9": 296
+    },
+    "post_center_gauges": 112,
+    "post_center_compensation_additions": 320,
+    "entrance_rank": 376,
+    "entering_helpers": 208,
+    "rank4_kernel_groups": 14,
+    "rank4_kernel_pivots": 56,
+    "rank4_kernel_additions": 168,
+    "post_gauge_kernel_anchor": 320
+  },
+  "output_sha256": "5d510cf5588450b520cd6481d328b3849a31d56dfb250b7c542a5edf9f06052f",
+  "output_uncompressed_sha256": "66ce5aab59b0469229ab4cf1d7e01a92b06170472618ff6256c9f1f15a367f68"
+}
diff --git a/research/contextual-provider-pooling/complex-local/static44/inputs/RAW504.json.gz b/research/contextual-provider-pooling/complex-local/static44/inputs/RAW504.json.gz
new file mode 100644
index 0000000000..903eeb2161
Binary files /dev/null and b/research/contextual-provider-pooling/complex-local/static44/inputs/RAW504.json.gz differ
diff --git a/research/contextual-provider-pooling/complex-local/static44/replay.py b/research/contextual-provider-pooling/complex-local/static44/replay.py
new file mode 100644
index 0000000000..ef5642ccfd
--- /dev/null
+++ b/research/contextual-provider-pooling/complex-local/static44/replay.py
@@ -0,0 +1,9 @@
+"""Standalone exact local-only static44 reconstruction and scalar audit."""
+from pathlib import Path
+import argparse,subprocess,sys
+if not __debug__:raise SystemExit('Assertions must remain enabled.')
+p=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser();ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();assert not a.out.exists()
+subprocess.run([sys.executable,'-B',str(p/'build.py'),'--raw',str(p/'inputs/RAW504.json.gz'),'--base',str(p/'inputs/BASE535.json.gz'),'--old-recipe',str(p/'inputs/OLD-RECIPE.json'),'--recipe',str(p/'RECIPE.json'),'--gk-dir',str(p/'gk'),'--out',str(a.out)],check=True)
+subprocess.run([sys.executable,'-B',str(p/'audit_scalar.py'),str(a.out/'FULL-WORD.json.gz'),str(a.out/'SELECTION.json'),str(a.out/'SCALAR-AUDIT.json')],check=True)
+print('PASS standalone local-only appendix')
diff --git a/research/contextual-provider-pooling/docs/CURRENT-SOURCE-PINS.json b/research/contextual-provider-pooling/docs/CURRENT-SOURCE-PINS.json
new file mode 100644
index 0000000000..c3a0337d34
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/CURRENT-SOURCE-PINS.json
@@ -0,0 +1,17 @@
+{
+  "frozen_through_pr": 559,
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "heads": {
+    "559": "d858c0b2edcc704ef370b3c96dc51a75439b77b0",
+    "558": "060b137c8a6f9d73fd7864c7f8cf2736d6441774",
+    "557": "a1e805c528884818ddf7d730024c1d8de9660f81",
+    "556": "24321d9347828751adabd86de4a4a7807207afac",
+    "555": "65a6bc19f820c8b1873f65a517bcf70cd6887223",
+    "554": "c1c252e2838918f3de866b228f5a3f21cb9f4b2d",
+    "553": "a03dc4a87b6fc5d365ba07644d7a621000931dda",
+    "552": "33c33af0b7697155be1ea708e08cbd3f0707d94c",
+    "551": "e7faafc4fec401d24080e5b2df12f964f1cfe123"
+  },
+  "PR558_owners_sha256": "c72892f5b3b36e75ec4db7742b046bd9194f638ff32be9cc8843914af950e6dc",
+  "PR555_expected_sha256": "7c2675fd49afd7e328606399a4421fd49c43fe8a6c5b57154cc908c00588abe2"
+}
diff --git a/research/contextual-provider-pooling/docs/DAG-STRUCTURES.json b/research/contextual-provider-pooling/docs/DAG-STRUCTURES.json
new file mode 100644
index 0000000000..699b69e691
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/DAG-STRUCTURES.json
@@ -0,0 +1,208 @@
+{
+  "\"Submodule\" \"inf\" \"le\"": [
+    [
+      "Mathproof.CrossCombine100.finrank_inf_le_of_invariantsAdditive",
+      "project::Mathproof.CrossCombine100",
+      "theorem finrank_inf_le_of_invariantsAdditive [FiniteDimensional K V]\n    {U U' inv : Submodule K V} (h : InvariantsAdditive U U' inv) :\n    Module.finrank K \u21a5((U \u2294 U') \u2293 inv)\n      \u2264 Module.finrank K \u21a5(U \u2293 inv) + Module.finrank K \u21a5(U' \u2293 inv)"
+    ],
+    [
+      "Mathproof.CrossCombine100.finrank_inf_le_trivial",
+      "project::Mathproof.CrossCombine100",
+      "theorem finrank_inf_le_trivial [FiniteDimensional K V] (U inv : Submodule K V) :\n    Module.finrank K \u21a5(U \u2293 inv) \u2264 Module.finrank K \u21a5U"
+    ],
+    [
+      "map_inf_le",
+      "package:mathlib::Mathlib.Algebra.Lie.Submodule",
+      "theorem map_inf_le : (N \u2293 N\u2082).map f \u2264 N.map f \u2293 N\u2082.map f"
+    ],
+    [
+      "invtSubmodule_inf_invtSubmodule_le_invtSubmodule_add",
+      "package:mathlib::Mathlib.Algebra.Module.Submodule.Invariant",
+      "lemma invtSubmodule_inf_invtSubmodule_le_invtSubmodule_add :\r\n    f.invtSubmodule \u2293 g.invtSubmodule \u2264 (f + g).invtSubmodule"
+    ],
+    [
+      "map_inf_le",
+      "package:mathlib::Mathlib.Algebra.Module.Submodule.Map",
+      "theorem map_inf_le (f : M \u2192\u209b\u2097[\u03c3\u2081\u2082] M\u2082) {p q : Submodule R M} :\r\n    (p \u2293 q).map f \u2264 p.map f \u2293 q.map f"
+    ],
+    [
+      "inf_comap_le_comap_add",
+      "package:mathlib::Mathlib.Algebra.Module.Submodule.Map",
+      "theorem inf_comap_le_comap_add (f\u2081 f\u2082 : M \u2192\u209b\u2097[\u03c4\u2081\u2082] M\u2082) :\r\n    comap f\u2081 q \u2293 comap f\u2082 q \u2264 comap (f\u2081 + f\u2082) q"
+    ]
+  ],
+  "\"GaloisConnection\" \"map\" \"comap\"": [
+    [
+      "gc_map_comap",
+      "package:mathlib::Mathlib.Algebra.Algebra.NonUnitalSubalgebra",
+      "theorem gc_map_comap (f : F) :\r\n    GaloisConnection (map f : NonUnitalSubalgebra R A \u2192 NonUnitalSubalgebra R B) (comap f)"
+    ],
+    [
+      "gc_map_comap",
+      "package:mathlib::Mathlib.Algebra.Algebra.Subalgebra.Basic",
+      "theorem gc_map_comap (f : A \u2192\u2090[R] B) : GaloisConnection (map f) (comap f)"
+    ],
+    [
+      "gc_map_comap",
+      "package:mathlib::Mathlib.Algebra.Field.Subfield.Basic",
+      "theorem gc_map_comap (f : K \u2192+* L) : GaloisConnection (map f) (comap f)"
+    ],
+    [
+      "gc_map_comap",
+      "package:mathlib::Mathlib.Algebra.Group.Subgroup.Map",
+      "theorem gc_map_comap (f : G \u2192* N) : GaloisConnection (map f) (comap f)"
+    ],
+    [
+      "gc_map_comap",
+      "package:mathlib::Mathlib.Algebra.Group.Submonoid.Operations",
+      "theorem gc_map_comap (f : F) : GaloisConnection (map f) (comap f)"
+    ],
+    [
+      "gc_map_comap",
+      "package:mathlib::Mathlib.Algebra.Group.Subsemigroup.Operations",
+      "theorem gc_map_comap (f : M \u2192\u2099* N) : GaloisConnection (map f) (comap f)"
+    ]
+  ],
+  "\"Filtration\" \"monotone\"": [
+    [
+      "filtration_monotone",
+      "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex",
+      "lemma filtration_monotone : Monotone f.filtration"
+    ],
+    [
+      "w",
+      "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex",
+      "lemma w (j : \u03b9) :\r\n    f.t j \u226b homOfLE (f.filtration_monotone (Order.le_succ j)) = f.m j \u226b f.b j"
+    ],
+    [
+      "isPullback",
+      "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex",
+      "lemma isPullback (j : \u03b9) :\r\n    IsPullback (f.t j) (f.m j) (homOfLE (f.filtration_monotone (Order.le_succ j))) (f.b j) where\r\n  w"
+    ],
+    [
+      "range_homOfLE_app_union_range_b_app",
+      "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex",
+      "lemma range_homOfLE_app_union_range_b_app (j : \u03b9) (d : SimplexCategory\u1d52\u1d56) :\r\n    Set.range ((homOfLE (f.filtration_monotone (Order.le_succ j))).app d) \u2294\r\n      Set.range ((f.b j).app d) = Set.univ"
+    ],
+    [
+      "isPushout",
+      "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex",
+      "lemma isPushout (j : \u03b9) :\r\n    IsPushout (f.t j) (f.m j) (homOfLE (f.filtration_monotone (Order.le_succ j))) (f.b j) where\r\n  w"
+    ],
+    [
+      "succEquiv_coherence",
+      "package:mathlib::Mathlib.FieldTheory.CardinalEmb",
+      "theorem succEquiv_coherence (i : \u03b9) (f) : (succEquiv i f).1 =\r\n    f.comp (Subalgebra.inclusion <| strictMono_filtration.monotone <| le_succ i)"
+    ]
+  ],
+  "\"finrank\" \"ker\"": [
+    [
+      "MathproofImported",
+      "project::MathproofImported",
+      "/-\n# MathproofImported \u2014 root for the audited ChatGPT-archive formalizations (2026-08-30)\n\nThe 23 modules under Mathproof/Imported/ were produced by five auditing agents from\nVPVNP_CHAT_RESULTS_ALL_SO_FAR_2026-08-30.zip, each verified twice (agent + independent sweep)\nat 0 errors / 0 sorry / 0 axiom. They import Mathproof, so this SEPARATE root avoids a cycle;\nnot in defaultTargets. Every theorem gets #print axioms; acceptable dependencies are exactly\nthe classical trio. Findings: D:/Proof/grind/notes/ARCHIVE_G*_FINDINGS_2026-08-30.md.\n-/\nimport Mathproof.Imported.G1Coherence\nimport Mathproof.Imported.G1Fca\nimport Mathproof.Imported.G1FirstLoss\nimport Mathproof.Imported.G2BalancedSplit\nimport Mathproof.Imported.G2ContextIdentity\nimport Mathproof.Imported.G2Homogenization\nimport Mathproof.Imported.G2ParseCount\nimport Mathproof.Imported.G2Recurrences\nimport Mathproof.Imported.G3CompletionFibers\nimport Mathproof.Imported.G3GeneratorAllocation\nimport Mathproof.Imported.G3InnovationRank\nimport Mathproof.Imported.G3RefinementTelescope\nimport Mathproof.Imported.G3RowDescent\nimport Mathproof.Imported.G4CrossThreshold\nimport Mathproof.Imported.G4OneShotSaving\nimport Mathproof.Imported.G4SavingParameter\nimport Mathproof.Imported.G4VerifierAudit\nimport Mathproof.Imported.G5BottomFanin\nimport Mathproof.Imported.G5BottomSupport\nimport Mathproof.Imported.G5Multilinearity\nimport Mathproof.Imported.G5RestrictionAudit\nimport Mathproof.Imported.G5TopFanin\nimport Mathproof.Imported.G5UniqueParse\n\n#print axioms Mathproof.Imported.G1.exists_independent_subset\n#print axioms Mathproof.Imported.G1.rows_linearIndependent_of_diagonal_on\n#print axioms Mathproof.Imported.G1.coherence_capacity\n#print axioms Mathproof.Imported.G1.coherence_dichotomy\n#print axioms Mathproof.Imported.G1.anchorId_diag\n#print axioms Mathproof.Imported.G1.anchorId_rowFan\n#print axioms Mathproof.Imported.G1.anchorId_colFan\n#print axioms Mathproof.Imported.G1.anchorId_rank\n#print axioms Mathproof.Imported.G1.anchorId_bound\n#print axioms Mathproof.Imported.G1.anchorId_tight\n#print axioms Mathproof.Imported.G1.anchorOnes_diag\n#print axioms Mathproof.Imported.G1.anchorOnes_rowFan\n#print axioms Mathproof.Imported.G1.anchorOnes_colFan\n#print axioms Mathproof.Imported.G1.anchorOnes_rank\n#print axioms Mathproof.Imported.G1.anchorOnes_bound\n#print axioms Mathproof.Imported.G1.anchorOnes_slack\n#print axioms Mathproof.Imported.G1.finrank_ker_comp_of_comp\n#print axioms Mathproof.Imported.G1.finrank_prod_submodule\n#print axioms Mathproof.Imported.G1.finrank_ker_prodMap\n#print axioms Mathproof.Imported.G1.fca_one_step\n#print axioms Mathproof.Imported.G1.mem_ker_addGate\n#print axioms Mathproof.Imported.G1.crossResp_ne_zero\n#print axioms Mathproof.Imported.G1.crossResp_injective\n#print axioms Mathproof.Imported.G1.crossResp_cancels\n#print axioms Mathproof.Imported.G1.crossResp_not_linearIndependent\n#print axioms Mathproof.Imported.G1.not_distinctContextsIndependent\n#print axioms Mathproof.Imported.G1.FTree\n#print axioms Mathproof.Imported.G1.FTree\n#print axioms Mathproof.Imported.G1.FTree\n#print axioms Mathproof.Imported.G1.FTree\n#print axioms Mathproof.Imported.G1.finrank_ker_addGate_rat\n#print axioms Mathproof.Imported.G1.anchorTree_leafKerSum\n#print axioms Mathproof.Imported.G1.anchorTree_size\n#print axioms Mathproof.Imported.G1.anchorTree_collisionSum\n#print axioms Mathproof.Imported.G1.anchorTree_fca\n#print axioms Mathproof.Imported.G1.firstLossMap_apply\n#print axioms Mathproof.Imported.G1.firstLossMap_surjective\n#print axioms Mathproof.Imported.G1.firstLossMap_ker\n#print axioms Mathproof.Imported.G1.finrank_ker_comp\n#print axioms Mathproof.Imported.G1.cumul_succ\n#print axioms Mathproof.Imported.G1.ker_cumul_finrank\n#print axioms Mathproof.Imported.G1.ssfl\n#print axioms Mathproof.Imported.G1.ssfl_total_kill\n#print axioms Mathproof.Imported.G1.ssfl_detector\n#print axioms Mathproof.Imported.G1.exists_stage_first_loss\n#print axioms Mathproof.Imported.G1.collision_stack_ssfl\n#print axioms Math"
+    ],
+    [
+      "probe_qv",
+      "project::probe_qv",
+      "import Mathproof.Meta.BipartiteCancellation20260902\nimport Mathlib\n\nopen Mathproof.Meta.BipartiteCancellation20260902 in\n#check @BRep\n#check @Mathproof.Meta.BipartiteCancellation20260902.BRep.SimEquiv\n#check @Mathproof.Meta.BipartiteCancellation20260902.BRep.dsum\n#check @Mathproof.Meta.BipartiteCancellation20260902.bipartite_cancel\n#check @Mathproof.Meta.KrullSchmidtCancellation20260902.Indecomposable\n#check @Mathproof.Meta.KrullSchmidtCancellation20260902.isUnit_or_isNilpotent\n#check @Mathproof.Meta.KrullSchmidtCancellation20260902.cancel_of_finiteDimensional\n\n#check @Submodule.prodEquivOfIsCompl\n#check @Submodule.coe_prodEquivOfIsCompl\n#check @Submodule.exists_isCompl\n#check @LinearEquiv.ofBijective\n#check @LinearMap.rangeRestrict\n#check @LinearMap.finrank_range_add_finrank_ker\n#check @LinearEquiv.ofFinrankEq\n#check @Module.finrank_prod\n#check @Fintype.sum_bool\n#check @Finset.sum_const\n#check @Submodule.mem_sup\n#check @LinearEquiv.prodCongr\n#check @LinearEquiv.ofEq\n#check @Submodule.disjoint_def\n#check @LinearMap.ker_eq_bot\n#check @Quiver\n#check @Quiver.Path\n"
+    ],
+    [
+      "codim_iInf_ker_le_fintypeCard",
+      "project::APAP.Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality",
+      "lemma codim_iInf_ker_le_fintypeCard [Fintype \u03b9] :\r\n    Module.finrank (ZMod q) G - (\u2a05 i, (\u03b3 i).toAddMonoidHom.ker.toZModSubmodule q).finrank\r\n      \u2264 Fintype.card \u03b9"
+    ],
+    [
+      "codim_iInf_ker_le_finsetCard",
+      "project::APAP.Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality",
+      "lemma codim_iInf_ker_le_finsetCard :\r\n    Module.finrank (ZMod q) G - ((\u2a05 i \u2208 s, (\u03b3 i).toAddMonoidHom.ker).toZModSubmodule q).finrank\r\n      \u2264 #s"
+    ],
+    [
+      "codim_iInf_ker_le_fintypeCard",
+      "project::APAP.Mathlib.LinearAlgebra.FiniteDimensional.Lemmas",
+      "lemma codim_iInf_ker_le_fintypeCard [Fintype \u03b9] :\r\n    finrank K V - (\u2a05 i, (f i).ker).finrank \u2264 Fintype.card \u03b9"
+    ],
+    [
+      "codim_biInf_ker_le_finsetCard",
+      "project::APAP.Mathlib.LinearAlgebra.FiniteDimensional.Lemmas",
+      "lemma codim_biInf_ker_le_finsetCard : finrank K V - (\u2a05 i \u2208 s, (f i).ker).finrank \u2264 #s"
+    ]
+  ],
+  "typed:\"Submodule\" \"inf_le_left\"": [
+    [
+      "AlgebraicGeometry.SmallExtension.naturality_pair_comp_eq_and_quotient_comp_eq_of_local_lifts_hom",
+      "theorem AlgebraicGeometry.SmallExtension.naturality_pair_comp_eq_and_quotient_comp_eq_of_local_lifts_hom\n    (T' T : Type u) [CommRing T'] [IsLocalRing T'] [IsArtinianRing T']\n    [CommRing T] (\u03c0 : T' \u2192+* T) (h\u03c0 : Function.Surjective \u03c0) (hker : IsNilpotent (RingHom.ker \u03c0))\n    (hsmall : RingHom.ker \u03c0 * maximalIdeal T' = \u22a5)\n\n    (hI : RingHom.ker \u03c0 \u2264 maximalIdeal T')\n    (\u03c1 : T \u2192+* ResidueField T') (h\u03c1 : \u03c1.comp \u03c0 = residue T')\n    (V : Type u) [AddCommGroup V] [Module (ResidueField T') V] [Module.Finite (ResidueField T') V]\n    [Module T' V] [IsScalarTower T' (ResidueField T') V]\n    [Module (ResidueField T')\u1d50\u1d52\u1d56 V] [IsCentralScalar (ResidueField T') V]\n    (\u03b9 : V \u2192\u2097[T'] T') (h\u03b9 : Function.Injective \u03b9)\n    (h\u03b9I : LinearMap.range \u03b9 = Submodule.restrictScalars T' (RingHom.ker \u03c0))\n\n    {A\u2080 : Scheme.{u}} (f\u2080 : A\u2080 \u27f6 Spec (CommRingCat.of T)) [IsSeparated f\u2080] [Smooth f\u2080]\n\n    (\ud835\udcb0 : A\u2080.OrderedAffineCover)\n    (Y : \ud835\udcb0.\u03b9 \u2192 Scheme.{u}) (q : \u2200 a, Y a \u27f6 Spec (CommRingCat.of T')) (hq : \u2200 a, Smooth (q a))\n    (g : \u2200 a, (\u2191(\ud835\udcb0.U a) : Scheme.{u}) \u27f6 Y a)\n    (hg : \u2200 a, IsPullback (g a) ((\ud835\udcb0.U a).\u03b9 \u226b f\u2080) (q a) (Spec.map (CommRingCat.ofHom \u03c0)))\n\n    {Ak : Scheme.{u}} (fk : Ak \u27f6 Spec (CommRingCat.of (ResidueField T'))) [IsSeparated fk]\n    (Lk : RelativeGroupLaw (ResidueField T') fk)\n    (i\u2080 : Ak \u27f6 A\u2080) [IsAffineHom i\u2080] (hi\u2080 : IsPullback i\u2080 fk f\u2080 (Spec.map (CommRingCat.ofHom \u03c1)))\n    (Ue : Ak.Opens) (hUe : IsAffineOpen Ue)\n    (e\u2081 : Spec (CommRingCat.of (ResidueField T')) \u27f6 (Ue : Scheme.{u})) (he\u2081 : e\u2081 \u226b Ue.\u03b9 = (Lk.one (\ud835\udfd9 _)).1)\n\n    (O : \u2200 a, A\u2080.Opens \u2192 (Y a).Opens)\n    (hO : \u2200 (a : \ud835\udcb0.\u03b9) (W : A\u2080.Opens), g a \u207b\u00b9\u1d41 O a W = (\ud835\udcb0.U a).\u03b9 \u207b\u00b9\u1d41 W)\n    (hOm : \u2200 a, Monotone (O a))\n    (hOtop : \u2200 a, O a (\ud835\udcb0.U a) = \u22a4)\n    (hOinf : \u2200 (a : \ud835\udcb0.\u03b9) (W W' : A\u2080.Opens), O a W \u2293 O a W' \u2264 O a (W \u2293 W'))\n    (hOaff : \u2200 (a : \ud835\udcb0.\u03b9) (W : A\u2080.Opens), IsAffineOpen W \u2192 W \u2264 \ud835\udcb0.U a \u2192 IsAffineOpen (O a W))\n\n    (\u03c3 : \u2200 {n : \u2115} (s : \ud835\udcb0.Idx n),\n      letI := algebraOfHom (q (s.1 0)) (O (s.1 0) (\ud835\udcb0.inter s))\n      ((ResidueField T') \u2297[T'] \u0393(Y (s.1 0), O (s.1 0) (\ud835\udcb0.inter s))) \u2243+* \u0393(Ak, (\ud835\udcb0.comap i\u2080).inter s))\n    (h\u03c3\u2081 : \u2200 {n : \u2115} (s : \ud835\udcb0.Idx n),\n      letI := algebraOfHom (q (s.1 0)) (O (s.1 0) (\ud835\udcb0.inter s))\n      (Scheme.OrderedAffineCover.isAffineOpen_inter fk (\ud835\udcb0.comap i\u2080) s).isoSpec.hom \u226b\n          Spec.map (CommRingCat.ofHom (\u03c3 s).toRingHom) \u226b\n          Spec.map (CommRingCat.ofHom\n            (Algebra.TensorProduct.includeRight : \u0393(Y (s.1 0), O (s.1 0) (\ud835\udcb0.inter s)) \u2192\u2090[T']\n              (ResidueField T') \u2297[T'] \u0393(Y (s.1 0), O (s.1 0) (\ud835\udcb0.inter s))).toRingHom) \u226b\n          (hOaff (s.1 0) (\ud835\udcb0.inter s) (Scheme.OrderedAffineCover.isAffineOpen_inter f\u2080 \ud835\udcb0 s) (\ud835\udcb0.inter_le s 0)).fromSpec =\n        Ak.homOfLE (\ud835\udcb0.comap_inter_le i\u2080 s) \u226b (i\u2080 \u2223_ \ud835\udcb0.inter s) \u226b A\u2080.homOfLE (\ud835\udcb0.inter_le s 0) \u226b g (s.1 0))\n    (h\u03c3\u2082 : \u2200 {n : \u2115} (s : \ud835\udcb0.Idx n) (x : ResidueField T'),\n      letI := algebraOfHom (q (s.1 0)) (O (s.1 0) (\ud835\udcb0.inter s))\n      letI := algebraOfHom fk ((\ud835\udcb0.comap i\u2080).inter s)\n      \u03c3 s (x \u2297\u209c[T'] (1 : \u0393(Y (s.1 0), O (s.1 0) (\ud835\udcb0.inter s)))) = algebraMap (ResidueField T') \u0393(Ak, (\ud835\udcb0.comap i\u2080).inter s) x)\n\n    (\u03c6 : \u2200 (a b : \ud835\udcb0.\u03b9), a < b \u2192 ((\u2191(O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)) : Scheme.{u}) \u2245 \u2191(O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b))))\n    (h\u03c6q : \u2200 (a b : \ud835\udcb0.\u03b9) (h : a < b),\n      (\u03c6 a b h).hom \u226b (O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 \u226b q b = (O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 \u226b q a)\n    (h\u03c6g : \u2200 (a b : \ud835\udcb0.\u03b9) (h : a < b),\n      \u2203 (\u03b3 : (\u2191(\ud835\udcb0.U a \u2293 \ud835\udcb0.U b) : Scheme.{u}) \u27f6 \u2191(O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)))\n        (\u03b3' : (\u2191(\ud835\udcb0.U a \u2293 \ud835\udcb0.U b) : Scheme.{u}) \u27f6 \u2191(O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b))),\n        \u03b3 \u226b (O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 = A\u2080.homOfLE inf_le_left \u226b g a \u2227\n        \u03b3' \u226b (O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 = A\u2080.homOfLE inf_le_right \u226b g b \u2227\n        \u03b3 \u226b (\u03c6 a b h).hom = \u03b3')\n    (h\u03c6O : \u2200 (a b : \ud835\udcb0.\u03b9) (h : a < b) (W : A\u2080.Opens),\n      (\u03c6 a b h).hom \u207b\u00b9\u1d41 ((O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 \u207b\u00b9\u1d41 O b W) = (O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 \u207b\u00b9\u1d41 O a W)\n\n    (\u03c1ab : \u2200 r : \ud835\udcb0.Idx 2, ((\u2191(O (r.1 0) (\ud835\udcb0.inter r)) : Scheme.{u}) \u2245 \u2191(O (r.1 1) (\ud835\udcb0.inter r))))\n    (\u03c1bc : \u2200 r : \ud835\udcb0.Idx 2, ((\u2191(O (r.1 1) (\ud835\udcb0.inter r)) : Scheme.{u}) \u2245 \u2191(O (r.1 2) (\ud835\udcb0.inter r))))\n    (\u03c1ac : \u2200 r : \ud835\udcb0.Idx 2, ((\u2191(O (r.1 0) (\ud835\udcb0.inter r)) : Scheme.{u}) \u2245 \u2191(O (r.1 2) (\ud835\udcb0.inter r))))\n    (h\u03c1ab : \u2200 r : \ud835\udcb0.Idx 2,\n      (\u03c1ab r).hom \u226b (Y (r.1 1)).homOfLE (hOm (r.1 1) (le_inf (\ud835\udcb0.inter_le r 0) (\ud835\udcb0.inter_le r 1))) =\n        (Y (r.1 0)).homOfLE (hOm (r.1 0) (le_inf (\ud835\udcb0.inter_le r 0) (\ud835\udcb0.inter_le r 1))) \u226b\n          (\u03c6 (r.1 0) (r.1 1) (r.2 (by decide))).hom)\n    (h\u03c1bc : \u2200 r : \ud835\udcb0.Idx 2,\n      (\u03c1bc r).hom \u226b (Y (r.1 2)).homOfLE (hOm (r.1 2) (le_inf (\ud835\udcb0.inter_le r 1) (\ud835\udcb0.inter_le r 2))) =\n        (Y (r.1 1)).homOfLE (hOm (r.1 1) (le_inf (\ud835\udcb0.inter_le r 1) (\ud835\udcb0.inter_le r 2))) \u226b\n          (\u03c6 (r.1 1) (r.1 2) (r.2 (by decide))).hom)\n    (h\u03c1ac : \u2200 r : \ud835\udcb0.Idx 2,\n      (\u03c1ac r).hom \u226b (Y (r.1 2)).homOfLE (hOm (r.1 2) (le_inf (\ud835\udcb0.inter_le r 0) (\ud835\udcb0.inter_le r 2))) =\n        (Y (r.1 0)).homOfLE (hOm (r.1 0) (le_inf (\ud835\udcb0.inter_le r 0) (\ud835\udcb0.inter_le r 2))) \u226b\n          (\u03c6 (r.1 0) (r.1 2) (r.2 (by decide))).hom)\n\n    (\u03c9 : letI := algebraOfHom fk Ue\n      \u21a5(Algebra.PointDerivations (ResidueField T') \u0393(Ak, Ue)\n          ((Ue.topIso.inv \u226b e\u2081.appTop \u226b (Scheme.\u0393SpecIso (CommRingCat.of (ResidueField T'))).hom).hom)\n          (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T'] (OModulePresheaf.unit fk).cochain (\ud835\udcb0.comap i\u2080) 2)))\n    (h\u03c9 : \u2200 r : \ud835\udcb0.Idx 2,\n      letI := algebraOfHom (q (r.1 0)) (O (r.1 0) (\ud835\udcb0.inter r))\n      letI := algebraOfHom fk Ue\n      \u2203 cs : \u0393(Ak, Ue) \u2192 (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T']\n                ((ResidueField T') \u2297[T'] \u0393(Y (r.1 0), O (r.1 0) (\ud835\udcb0.inter r)))),\n        IsTangentCoordsOfPairAtVia (RingHom.ker \u03c0) V \u03b9 \u0393(Y (r.1 0), O (r.1 0) (\ud835\udcb0.inter r))\n          ((hOaff (r.1 0) (\ud835\udcb0.inter r) (Scheme.OrderedAffineCover.isAffineOpen_inter f\u2080 \ud835\udcb0 r) (\ud835\udcb0.inter_le r 0)).isoSpec.inv \u226b\n              (\u03c1ac r).hom \u226b (O (r.1 2) (\ud835\udcb0.inter r)).\u03b9)\n          ((hOaff (r.1 0) (\ud835\udcb0.inter r) (Scheme.OrderedAffineCover.isAffineOpen_inter f\u2080 \ud835\udcb0 r) (\ud835\udcb0.inter_le r 0)).isoSpec.inv \u226b\n              (\u03c1ab r).hom \u226b (\u03c1bc r).hom \u226b (O (r.1 2) (\ud835\udcb0.inter r)).\u03b9)\n          fk Lk (i\u2080 \u207b\u00b9\u1d41 \ud835\udcb0.U (r.1 2)) ((i\u2080 \u2223_ \ud835\udcb0.U (r.1 2)) \u226b g (r.1 2)) Ue cs \u2227\n        \u2200 (a : \u0393(Ak, Ue)) (\u03be : Module.Dual (ResidueField T') V), \u03c3 r (cs a \u03be) = \u03c9.1 a \u03be r)\n    (h\u03c9Z : letI := algebraOfHom fk Ue\n      \u2200 (a : \u0393(Ak, Ue)) (\u03be : Module.Dual (ResidueField T') V),\n        (OModulePresheaf.unit fk).d (\ud835\udcb0.comap i\u2080) 2 (\u03c9.1 a \u03be) = 0)\n    {X\u2080 : Scheme.{u}} (fX\u2080 : X\u2080 \u27f6 Spec (CommRingCat.of T)) [IsSeparated fX\u2080] [Smooth fX\u2080]\n\n    (\ud835\udcb1 : X\u2080.OrderedAffineCover)\n    (Z : \ud835\udcb1.\u03b9 \u2192 Scheme.{u}) (qZ : \u2200 a, Z a \u27f6 Spec (CommRingCat.of T')) (hqZ : \u2200 a, Smooth (qZ a))\n    (gZ : \u2200 a, (\u2191(\ud835\udcb1.U a) : Scheme.{u}) \u27f6 Z a)\n    (hgZ : \u2200 a, IsPullback (gZ a) ((\ud835\udcb1.U a).\u03b9 \u226b fX\u2080) (qZ a) (Spec.map (CommRingCat.ofHom \u03c0)))\n\n    {Xk : Scheme.{u}} (fXk : Xk \u27f6 Spec (CommRingCat.of (ResidueField T'))) [IsSeparated fXk]\n    (LX : RelativeGroupLaw (ResidueField T') fXk)\n    (j\u2080 : Xk \u27f6 X\u2080) [IsAffineHom j\u2080] (hj\u2080 : IsPullback j\u2080 fXk fX\u2080 (Spec.map (CommRingCat.ofHom \u03c1)))\n    (UXe : Xk.Opens) (hUXe : IsAffineOpen UXe)\n    (eX\u2081 : Spec (CommRingCat.of (ResidueField T')) \u27f6 (UXe : Scheme.{u})) (heX\u2081 : eX\u2081 \u226b UXe.\u03b9 = (LX.one (\ud835\udfd9 _)).1)\n\n    (OX : \u2200 a, X\u2080.Opens \u2192 (Z a).Opens)\n    (hOX : \u2200 (a : \ud835\udcb1.\u03b9) (W : X\u2080.Opens), gZ a \u207b\u00b9\u1d41 OX a W = (\ud835\udcb1.U a).\u03b9 \u207b\u00b9\u1d41 W)\n    (hOXm : \u2200 a, Monotone (OX a))\n    (hOXtop : \u2200 a, OX a (\ud835\udcb1.U a) = \u22a4)\n    (hOXinf : \u2200 (a : \ud835\udcb1.\u03b9) (W W' : X\u2080.Opens), OX a W \u2293 OX a W' \u2264 OX a (W \u2293 W'))\n    (hOXaff : \u2200 (a : \ud835\udcb1.\u03b9) (W : X\u2080.Opens), IsAffineOpen W \u2192 W \u2264 \ud835\udcb1.U a \u2192 IsAffineOpen (OX a W))\n\n    (\u03c3X : \u2200 {n : \u2115} (s : \ud835\udcb1.Idx n),\n      letI := algebraOfHom (qZ (s.1 0)) (OX (s.1 0) (\ud835\udcb1.inter s))\n      ((ResidueField T') \u2297[T'] \u0393(Z (s.1 0), OX (s.1 0) (\ud835\udcb1.inter s))) \u2243+* \u0393(Xk, (\ud835\udcb1.comap j\u2080).inter s))\n    (h\u03c3X\u2081 : \u2200 {n : \u2115} (s : \ud835\udcb1.Idx n),\n      letI := algebraOfHom (qZ (s.1 0)) (OX (s.1 0) (\ud835\udcb1.inter s))\n      (Scheme.OrderedAffineCover.isAffineOpen_inter fXk (\ud835\udcb1.comap j\u2080) s).isoSpec.hom \u226b\n          Spec.map (CommRingCat.ofHom (\u03c3X s).toRingHom) \u226b\n          Spec.map (CommRingCat.ofHom\n            (Algebra.TensorProduct.includeRight : \u0393(Z (s.1 0), OX (s.1 0) (\ud835\udcb1.inter s)) \u2192\u2090[T']\n              (ResidueField T') \u2297[T'] \u0393(Z (s.1 0), OX (s.1 0) (\ud835\udcb1.inter s))).toRingHom) \u226b\n          (hOXaff (s.1 0) (\ud835\udcb1.inter s) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 s) (\ud835\udcb1.inter_le s 0)).fromSpec =\n        Xk.homOfLE (\ud835\udcb1.comap_inter_le j\u2080 s) \u226b (j\u2080 \u2223_ \ud835\udcb1.inter s) \u226b X\u2080.homOfLE (\ud835\udcb1.inter_le s 0) \u226b gZ (s.1 0))\n    (h\u03c3X\u2082 : \u2200 {n : \u2115} (s : \ud835\udcb1.Idx n) (x : ResidueField T'),\n      letI := algebraOfHom (qZ (s.1 0)) (OX (s.1 0) (\ud835\udcb1.inter s))\n      letI := algebraOfHom fXk ((\ud835\udcb1.comap j\u2080).inter s)\n      \u03c3X s (x \u2297\u209c[T'] (1 : \u0393(Z (s.1 0), OX (s.1 0) (\ud835\udcb1.inter s)))) = algebraMap (ResidueField T') \u0393(Xk, (\ud835\udcb1.comap j\u2080).inter s) x)\n\n    (\u03c6X : \u2200 (a b : \ud835\udcb1.\u03b9), a < b \u2192 ((\u2191(OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)) : Scheme.{u}) \u2245 \u2191(OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b))))\n    (h\u03c6Xq : \u2200 (a b : \ud835\udcb1.\u03b9) (h : a < b),\n      (\u03c6X a b h).hom \u226b (OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 \u226b qZ b = (OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 \u226b qZ a)\n    (h\u03c6Xg : \u2200 (a b : \ud835\udcb1.\u03b9) (h : a < b),\n      \u2203 (\u03b3 : (\u2191(\ud835\udcb1.U a \u2293 \ud835\udcb1.U b) : Scheme.{u}) \u27f6 \u2191(OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)))\n        (\u03b3' : (\u2191(\ud835\udcb1.U a \u2293 \ud835\udcb1.U b) : Scheme.{u}) \u27f6 \u2191(OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b))),\n        \u03b3 \u226b (OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 = X\u2080.homOfLE inf_le_left \u226b gZ a \u2227\n        \u03b3' \u226b (OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 = X\u2080.homOfLE inf_le_right \u226b gZ b \u2227\n        \u03b3 \u226b (\u03c6X a b h).hom = \u03b3')\n    (h\u03c6XO : \u2200 (a b : \ud835\udcb1.\u03b9) (h : a < b) (W : X\u2080.Opens),\n      (\u03c6X a b h).hom \u207b\u00b9\u1d41 ((OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 \u207b\u00b9\u1d41 OX b W) = (OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 \u207b\u00b9\u1d41 OX a W)\n\n    (\u03c1Xab : \u2200 r : \ud835\udcb1.Idx 2, ((\u2191(OX (r.1 0) (\ud835\udcb1.inter r)) : Scheme.{u}) \u2245 \u2191(OX (r.1 1) (\ud835\udcb1.inter r))))\n    (\u03c1Xbc : \u2200 r : \ud835\udcb1.Idx 2, ((\u2191(OX (r.1 1) (\ud835\udcb1.inter r)) : Scheme.{u}) \u2245 \u2191(OX (r.1 2) (\ud835\udcb1.inter r))))\n    (\u03c1Xac : \u2200 r : \ud835\udcb1.Idx 2, ((\u2191(OX (r.1 0) (\ud835\udcb1.inter r)) : Scheme.{u}) \u2245 \u2191(OX (r.1 2) (\ud835\udcb1.inter r))))\n    (h\u03c1Xab : \u2200 r : \ud835\udcb1.Idx 2,\n      (\u03c1Xab r).hom \u226b (Z (r.1 1)).homOfLE (hOXm (r.1 1) (le_inf (\ud835\udcb1.inter_le r 0) (\ud835\udcb1.inter_le r 1))) =\n        (Z (r.1 0)).homOfLE (hOXm (r.1 0) (le_inf (\ud835\udcb1.inter_le r 0) (\ud835\udcb1.inter_le r 1))) \u226b\n          (\u03c6X (r.1 0) (r.1 1) (r.2 (by decide))).hom)\n    (h\u03c1Xbc : \u2200 r : \ud835\udcb1.Idx 2,\n      (\u03c1Xbc r).hom \u226b (Z (r.1 2)).homOfLE (hOXm (r.1 2) (le_inf (\ud835\udcb1.inter_le r 1) (\ud835\udcb1.inter_le r 2))) =\n        (Z (r.1 1)).homOfLE (hOXm (r.1 1) (le_inf (\ud835\udcb1.inter_le r 1) (\ud835\udcb1.inter_le r 2))) \u226b\n          (\u03c6X (r.1 1) (r.1 2) (r.2 (by decide))).hom)\n    (h\u03c1Xac : \u2200 r : \ud835\udcb1.Idx 2,\n      (\u03c1Xac r).hom \u226b (Z (r.1 2)).homOfLE (hOXm (r.1 2) (le_inf (\ud835\udcb1.inter_le r 0) (\ud835\udcb1.inter_le r 2))) =\n        (Z (r.1 0)).homOfLE (hOXm (r.1 0) (le_inf (\ud835\udcb1.inter_le r 0) (\ud835\udcb1.inter_le r 2))) \u226b\n          (\u03c6X (r.1 0) (r.1 2) (r.2 (by decide))).hom)\n\n    (\u03c9X : letI := algebraOfHom fXk UXe\n      \u21a5(Algebra.PointDerivations (ResidueField T') \u0393(Xk, UXe)\n          ((UXe.topIso.inv \u226b eX\u2081.appTop \u226b (Scheme.\u0393SpecIso (CommRingCat.of (ResidueField T'))).hom).hom)\n          (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T'] (OModulePresheaf.unit fXk).cochain (\ud835\udcb1.comap j\u2080) 2)))\n    (h\u03c9X : \u2200 r : \ud835\udcb1.Idx 2,\n      letI := algebraOfHom (qZ (r.1 0)) (OX (r.1 0) (\ud835\udcb1.inter r))\n      letI := algebraOfHom fXk UXe\n      \u2203 cs : \u0393(Xk, UXe) \u2192 (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T']\n                ((ResidueField T') \u2297[T'] \u0393(Z (r.1 0), OX (r.1 0) (\ud835\udcb1.inter r)))),\n        IsTangentCoordsOfPairAtVia (RingHom.ker \u03c0) V \u03b9 \u0393(Z (r.1 0), OX (r.1 0) (\ud835\udcb1.inter r))\n          ((hOXaff (r.1 0) (\ud835\udcb1.inter r) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 r) (\ud835\udcb1.inter_le r 0)).isoSpec.inv \u226b\n              (\u03c1Xac r).hom \u226b (OX (r.1 2) (\ud835\udcb1.inter r)).\u03b9)\n          ((hOXaff (r.1 0) (\ud835\udcb1.inter r) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 r) (\ud835\udcb1.inter_le r 0)).isoSpec.inv \u226b\n              (\u03c1Xab r).hom \u226b (\u03c1Xbc r).hom \u226b (OX (r.1 2) (\ud835\udcb1.inter r)).\u03b9)\n          fXk LX (j\u2080 \u207b\u00b9\u1d41 \ud835\udcb1.U (r.1 2)) ((j\u2080 \u2223_ \ud835\udcb1.U (r.1 2)) \u226b gZ (r.1 2)) UXe cs \u2227\n        \u2200 (a : \u0393(Xk, UXe)) (\u03be : Module.Dual (ResidueField T') V), \u03c3X r (cs a \u03be) = \u03c9X.1 a \u03be r)\n    (h\u03c9XZ : letI := algebraOfHom fXk UXe\n      \u2200 (a : \u0393(Xk, UXe)) (\u03be : Module.Dual (ResidueField T') V),\n        (OModulePresheaf.unit fXk).d (\ud835\udcb1.comap j\u2080) 2 (\u03c9X.1 a \u03be) = 0)\n\n    (h\u2080 : X\u2080 \u27f6 A\u2080) (hh\u2080 : h\u2080 \u226b f\u2080 = fX\u2080)\n    (lam : \ud835\udcb1.\u03b9 \u2192 \ud835\udcb0.\u03b9) (hlam\u2080 : \u2200 w, \ud835\udcb1.U w \u2264 h\u2080 \u207b\u00b9\u1d41 \ud835\udcb0.U (lam w))\n    (hk : Xk \u27f6 Ak) (hhk : hk \u226b i\u2080 = j\u2080 \u226b h\u2080) (hhkf : hk \u226b fk = fXk)\n    (hhom : \u2200 {S : Scheme.{u}} (t : S \u27f6 Spec (CommRingCat.of (ResidueField T'))) (P Q : SchemeHomOver t fXk),\n      (LX.mul t P Q).1 \u226b hk =\n        (Lk.mul t \u27e8P.1 \u226b hk, by rw [Category.assoc, hhkf, P.2]\u27e9 \u27e8Q.1 \u226b hk, by rw [Category.assoc, hhkf, Q.2]\u27e9).1)\n    (hUX : UXe \u2264 hk \u207b\u00b9\u1d41 Ue)\n    (hlamk : \u2200 w, (\ud835\udcb1.comap j\u2080).U w \u2264 hk \u207b\u00b9\u1d41 (\ud835\udcb0.comap i\u2080).U (lam w))\n    (hZ : \u2200 w, Z w \u27f6 Y (lam w)) (hhZq : \u2200 w, hZ w \u226b q (lam w) = qZ w)\n    (hhZg : \u2200 w, gZ w \u226b hZ w = X\u2080.homOfLE (hlam\u2080 w) \u226b (h\u2080 \u2223_ \ud835\udcb0.U (lam w)) \u226b g (lam w))\n\n    (\u03a6 : \u2200 (a b : \ud835\udcb0.\u03b9) (W : A\u2080.Opens), W \u2264 \ud835\udcb0.U a \u2192 W \u2264 \ud835\udcb0.U b \u2192 ((\u2191(O a W) : Scheme.{u}) \u2245 \u2191(O b W)))\n    (h\u03a6q : \u2200 (a b : \ud835\udcb0.\u03b9) (W : A\u2080.Opens) (ha : W \u2264 \ud835\udcb0.U a) (hb : W \u2264 \ud835\udcb0.U b),\n      (\u03a6 a b W ha hb).hom \u226b (O b W).\u03b9 \u226b q b = (O a W).\u03b9 \u226b q a)\n    (h\u03a6g : \u2200 (a b : \ud835\udcb0.\u03b9) (W : A\u2080.Opens) (ha : W \u2264 \ud835\udcb0.U a) (hb : W \u2264 \ud835\udcb0.U b)\n      (\u03b3 : (\u2191W : Scheme.{u}) \u27f6 \u2191(O a W)) (\u03b3' : (\u2191W : Scheme.{u}) \u27f6 \u2191(O b W)),\n      \u03b3 \u226b (O a W).\u03b9 = A\u2080.homOfLE ha \u226b g a \u2192 \u03b3' \u226b (O b W).\u03b9 = A\u2080.homOfLE hb \u226b g b \u2192 \u03b3 \u226b (\u03a6 a b W ha hb).hom = \u03b3')\n    (h\u03a6res : \u2200 (a b : \ud835\udcb0.\u03b9) (W W' : A\u2080.Opens) (ha : W \u2264 \ud835\udcb0.U a) (hb : W \u2264 \ud835\udcb0.U b) (ha' : W' \u2264 \ud835\udcb0.U a) (hb' : W' \u2264 \ud835\udcb0.U b)\n      (hWW : W' \u2264 W),\n      (\u03a6 a b W' ha' hb').hom \u226b (Y b).homOfLE (hOm b hWW) = (Y a).homOfLE (hOm a hWW) \u226b (\u03a6 a b W ha hb).hom)\n    (h\u03a6refl : \u2200 (a : \ud835\udcb0.\u03b9) (W : A\u2080.Opens) (ha ha' : W \u2264 \ud835\udcb0.U a), (\u03a6 a a W ha ha').hom = \ud835\udfd9 _)\n    (h\u03a6symm : \u2200 (a b : \ud835\udcb0.\u03b9) (W : A\u2080.Opens) (ha : W \u2264 \ud835\udcb0.U a) (hb : W \u2264 \ud835\udcb0.U b),\n      (\u03a6 a b W ha hb).hom \u226b (\u03a6 b a W hb ha).hom = \ud835\udfd9 _)\n    (h\u03a6\u03c6 : \u2200 (a b : \ud835\udcb0.\u03b9) (h : a < b), (\u03a6 a b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b) inf_le_left inf_le_right).hom = (\u03c6 a b h).hom)\n\n    (\u03a6X : \u2200 (x y : \ud835\udcb1.\u03b9), x < y \u2192 \u2200 (W : X\u2080.Opens), W \u2264 \ud835\udcb1.U x \u2293 \ud835\udcb1.U y \u2192 ((\u2191(OX x W) : Scheme.{u}) \u2245 \u2191(OX y W)))\n    (h\u03a6X : \u2200 (x y : \ud835\udcb1.\u03b9) (h : x < y) (W : X\u2080.Opens) (hW : W \u2264 \ud835\udcb1.U x \u2293 \ud835\udcb1.U y),\n      (\u03a6X x y h W hW).hom \u226b (Z y).homOfLE (hOXm y hW) = (Z x).homOfLE (hOXm x hW) \u226b (\u03c6X x y h).hom)\n\n    (\u2113 : \u2200 (x : \ud835\udcb1.\u03b9) (WX : X\u2080.Opens) (WA : A\u2080.Opens), WX \u2264 h\u2080 \u207b\u00b9\u1d41 WA \u2192 ((\u2191(OX x WX) : Scheme.{u}) \u27f6 \u2191(O (lam x) WA)))\n    (h\u2113 : \u2200 (x : \ud835\udcb1.\u03b9) (WX : X\u2080.Opens) (WA : A\u2080.Opens) (h : WX \u2264 h\u2080 \u207b\u00b9\u1d41 WA),\n      \u2113 x WX WA h \u226b (O (lam x) WA).\u03b9 = (OX x WX).\u03b9 \u226b hZ x)\n    :\n    (\u2200 t : \ud835\udcb1.Idx 1,\n      letI := algebraOfHom (qZ (t.1 0)) (OX (t.1 0) (\ud835\udcb1.inter t))\n      (((hOXaff (t.1 0) (\ud835\udcb1.inter t) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 t) (\ud835\udcb1.inter_le t 0)).isoSpec.inv \u226b\n                (\u03a6X (t.1 0) (t.1 1) (t.2 (by decide)) (\ud835\udcb1.inter t) (le_inf (\ud835\udcb1.inter_le t 0) (\ud835\udcb1.inter_le t 1))).hom \u226b\n                \u2113 (t.1 1) (\ud835\udcb1.inter t) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) (by rw [Scheme.Hom.preimage_inf]; exact le_inf ((\ud835\udcb1.inter_le t 0).trans (hlam\u2080 (t.1 0))) ((\ud835\udcb1.inter_le t 1).trans (hlam\u2080 (t.1 1)))) \u226b (O (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1)))).\u03b9)) \u226b q (lam (t.1 1)) = Spec.map (CommRingCat.ofHom (algebraMap T' \u0393(Z (t.1 0), OX (t.1 0) (\ud835\udcb1.inter t)))) \u2227\n      (((hOXaff (t.1 0) (\ud835\udcb1.inter t) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 t) (\ud835\udcb1.inter_le t 0)).isoSpec.inv \u226b\n                \u2113 (t.1 0) (\ud835\udcb1.inter t) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) (by rw [Scheme.Hom.preimage_inf]; exact le_inf ((\ud835\udcb1.inter_le t 0).trans (hlam\u2080 (t.1 0))) ((\ud835\udcb1.inter_le t 1).trans (hlam\u2080 (t.1 1)))) \u226b\n                (\u03a6 (lam (t.1 0)) (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) inf_le_left inf_le_right).hom \u226b (O (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1)))).\u03b9)) \u226b q (lam (t.1 1)) = Spec.map (CommRingCat.ofHom (algebraMap T' \u0393(Z (t.1 0), OX (t.1 0) (\ud835\udcb1.inter t))))) \u2227\n    (\u2200 t : \ud835\udcb1.Idx 1,\n      letI := algebraOfHom (qZ (t.1 0)) (OX (t.1 0) (\ud835\udcb1.inter t))\n      Spec.map (CommRingCat.ofHom (Ideal.Quotient.mk ((RingHom.ker \u03c0).map (algebraMap T' \u0393(Z (t.1 0), OX (t.1 0) (\ud835\udcb1.inter t)))))) \u226b\n        (((hOXaff (t.1 0) (\ud835\udcb1.inter t) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 t) (\ud835\udcb1.inter_le t 0)).isoSpec.inv \u226b\n                (\u03a6X (t.1 0) (t.1 1) (t.2 (by decide)) (\ud835\udcb1.inter t) (le_inf (\ud835\udcb1.inter_le t 0) (\ud835\udcb1.inter_le t 1))).hom \u226b\n                \u2113 (t.1 1) (\ud835\udcb1.inter t) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) (by rw [Scheme.Hom.preimage_inf]; exact le_inf ((\ud835\udcb1.inter_le t 0).trans (hlam\u2080 (t.1 0))) ((\ud835\udcb1.inter_le t 1).trans (hlam\u2080 (t.1 1)))) \u226b (O (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1)))).\u03b9)) =\n      Spec.map (CommRingCat.ofHom (Ideal.Quotient.mk ((RingHom.ker \u03c0).map (algebraMap T' \u0393(Z (t.1 0), OX (t.1 0) (\ud835\udcb1.inter t)))))) \u226b\n        (((hOXaff (t.1 0) (\ud835\udcb1.inter t) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 t) (\ud835\udcb1.inter_le t 0)).isoSpec.inv \u226b\n                \u2113 (t.1 0) (\ud835\udcb1.inter t) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) (by rw [Scheme.Hom.preimage_inf]; exact le_inf ((\ud835\udcb1.inter_le t 0).trans (hlam\u2080 (t.1 0))) ((\ud835\udcb1.inter_le t 1).trans (hlam\u2080 (t.1 1)))) \u226b\n                (\u03a6 (lam (t.1 0)) (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) inf_le_left inf_le_right).hom \u226b (O (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1)))).\u03b9)))"
+    ],
+    [
+      "AlgebraicGeometry.OModulePresheaf.unitPullback_prodCover_cup_sub_cup_unitPullback_mem",
+      "theorem AlgebraicGeometry.OModulePresheaf.unitPullback_prodCover_cup_sub_cup_unitPullback_mem\n    {k : Type u} [Field k] {X Y : Scheme.{u}}\n    (\u03c0X : X \u27f6 Spec (CommRingCat.of k)) (\u03c0Y : Y \u27f6 Spec (CommRingCat.of k)) [IsSeparated \u03c0X] [IsSeparated \u03c0Y]\n    (\ud835\udd18 : X.OrderedAffineCover) (\ud835\udd19 : Y.OrderedAffineCover)\n    (haff : \u2200 i j, IsAffineOpen ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).U i \u2293 (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)).U j))\n    (hcov : \u2a06 ij : \ud835\udd18.\u03b9 \u00d7 \ud835\udd19.\u03b9,\n      (\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).U ij.1 \u2293 (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)).U ij.2 = \u22a4)\n\n    (\ud835\udcb2 : (pullback \u03c0X \u03c0Y).OrderedAffineCover) (lam\u2081 : \ud835\udcb2.\u03b9 \u2192 \ud835\udd18.\u03b9) (lam\u2082 : \ud835\udcb2.\u03b9 \u2192 \ud835\udd19.\u03b9)\n    (h\u2081 : \u2200 w, \ud835\udcb2.U w \u2264 pullback.fst \u03c0X \u03c0Y \u207b\u00b9\u1d41 \ud835\udd18.U (lam\u2081 w))\n    (h\u2082 : \u2200 w, \ud835\udcb2.U w \u2264 pullback.snd \u03c0X \u03c0Y \u207b\u00b9\u1d41 \ud835\udd19.U (lam\u2082 w))\n    (h\u03bc : \u2200 w, \ud835\udcb2.U w \u2264 (\ud835\udfd9 (pullback \u03c0X \u03c0Y)) \u207b\u00b9\u1d41\n      ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov).U\n        (toLex (lam\u2081 w, lam\u2082 w)))\n    (p q n : \u2115) (hn : p + q = n)\n    (\u03b1 : \u21a5(LinearMap.ker ((OModulePresheaf.unit \u03c0X).d \ud835\udd18 p))) (\u03b2 : \u21a5(LinearMap.ker ((OModulePresheaf.unit \u03c0Y).d \ud835\udd19 q))) :\n    (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (\ud835\udfd9 (pullback \u03c0X \u03c0Y)) \ud835\udcb2\n        ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov)\n        (fun w => toLex (lam\u2081 w, lam\u2082 w)) h\u03bc n\n        ((OModulePresheaf.unit (pullback.fst \u03c0X \u03c0Y \u226b \u03c0X)).cup\n          ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov) p q n hn\n          (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (pullback.fst \u03c0X \u03c0Y)\n            ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov) \ud835\udd18\n            (fun ij => (ofLex ij).1) (fun ij => inf_le_left) p \u03b1.1)\n          (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (pullback.snd \u03c0X \u03c0Y)\n            ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov) \ud835\udd19\n            (fun ij => (ofLex ij).2) (fun ij => inf_le_right) q \u03b2.1)) -\n      (OModulePresheaf.unit (pullback.fst \u03c0X \u03c0Y \u226b \u03c0X)).cup \ud835\udcb2 p q n hn\n        (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (pullback.fst \u03c0X \u03c0Y) \ud835\udcb2 \ud835\udd18 lam\u2081 h\u2081 p \u03b1.1)\n        (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (pullback.snd \u03c0X \u03c0Y) \ud835\udcb2 \ud835\udd19 lam\u2082 h\u2082 q \u03b2.1))\n      \u2208 (show Submodule k ((OModulePresheaf.unit (pullback.fst \u03c0X \u03c0Y \u226b \u03c0X)).cochain \ud835\udcb2 n) from\n          match n with\n          | 0 => \u22a5\n          | m + 1 => LinearMap.range ((OModulePresheaf.unit (pullback.fst \u03c0X \u03c0Y \u226b \u03c0X)).d \ud835\udcb2 m))"
+    ],
+    [
+      "AlgebraicGeometry.RelPicard.IsDeformationClassMap.exists_crossSections",
+      "theorem IsDeformationClassMap.exists_crossSections\n    {R : Type u} [CommRing R] {C : Scheme.{u}}\n    (c : C \u27f6 Spec (.of R)) (\u03b5 : SchemeHomOver (\ud835\udfd9 (Spec (.of R))) c)\n    (A : Type u) [CommRing A] [Algebra R A]\n    [IsSeparated (pullback.snd c (Scheme.TwoAffineOpenCover.specMap R A))]\n    (\ud835\udcb2 \ud835\udcb2' : C.TwoAffineOpenCover)\n    {\u03b4  : RigKerDualNumber c \u03b5 A \u2192 H1StructureSheaf c A \ud835\udcb2}\n    {\u03b4' : RigKerDualNumber c \u03b5 A \u2192 H1StructureSheaf c A \ud835\udcb2'}\n    (h\u03b4 : IsDeformationClassMap c \u03b5 A \ud835\udcb2 \u03b4) (h\u03b4' : IsDeformationClassMap c \u03b5 A \ud835\udcb2' \u03b4')\n    (x : RigKerDualNumber c \u03b5 A)\n    (s  : ((\ud835\udcb2.pullback c A).cover  (pullback.snd c (Scheme.TwoAffineOpenCover.specMap R A))).A01)\n    (s' : ((\ud835\udcb2'.pullback c A).cover (pullback.snd c (Scheme.TwoAffineOpenCover.specMap R A))).A01)\n    (hs : \u03b4 x = Submodule.Quotient.mk s) (hs' : \u03b4' x = Submodule.Quotient.mk s') :\n    let X' := Limits.pullback c (Scheme.TwoAffineOpenCover.specMap R A)\n    let W0 := (\ud835\udcb2.pullback c A).U0;  let W1 := (\ud835\udcb2.pullback c A).U1\n    let V0 := (\ud835\udcb2'.pullback c A).U0; let V1 := (\ud835\udcb2'.pullback c A).U1\n    \u2203 (g00 : \u0393(X', W0 \u2293 V0)) (g01 : \u0393(X', W0 \u2293 V1)) (g10 : \u0393(X', W1 \u2293 V0)) (g11 : \u0393(X', W1 \u2293 V1)),\n      (X'.presheaf.map (homOfLE (inf_le_inf_right V0 inf_le_left  : (W0 \u2293 W1) \u2293 V0 \u2264 W0 \u2293 V0)).op).hom g00\n        = (X'.presheaf.map (homOfLE (inf_le_inf_right V0 inf_le_right : (W0 \u2293 W1) \u2293 V0 \u2264 W1 \u2293 V0)).op).hom g10\n          + (X'.presheaf.map (homOfLE (inf_le_left : (W0 \u2293 W1) \u2293 V0 \u2264 W0 \u2293 W1)).op).hom s \u2227\n      (X'.presheaf.map (homOfLE (inf_le_inf_right V1 inf_le_left  : (W0 \u2293 W1) \u2293 V1 \u2264 W0 \u2293 V1)).op).hom g01\n        = (X'.presheaf.map (homOfLE (inf_le_inf_right V1 inf_le_right : (W0 \u2293 W1) \u2293 V1 \u2264 W1 \u2293 V1)).op).hom g11\n          + (X'.presheaf.map (homOfLE (inf_le_left : (W0 \u2293 W1) \u2293 V1 \u2264 W0 \u2293 W1)).op).hom s \u2227\n      (X'.presheaf.map (homOfLE (inf_le_inf_left W0 inf_le_right : W0 \u2293 (V0 \u2293 V1) \u2264 W0 \u2293 V1)).op).hom g01\n        = (X'.presheaf.map (homOfLE (inf_le_inf_left W0 inf_le_left  : W0 \u2293 (V0 \u2293 V1) \u2264 W0 \u2293 V0)).op).hom g00\n          + (X'.presheaf.map (homOfLE (inf_le_right : W0 \u2293 (V0 \u2293 V1) \u2264 V0 \u2293 V1)).op).hom s' \u2227\n      (X'.presheaf.map (homOfLE (inf_le_inf_left W1 inf_le_right : W1 \u2293 (V0 \u2293 V1) \u2264 W1 \u2293 V1)).op).hom g11\n        = (X'.presheaf.map (homOfLE (inf_le_inf_left W1 inf_le_left  : W1 \u2293 (V0 \u2293 V1) \u2264 W1 \u2293 V0)).op).hom g10\n          + (X'.presheaf.map (homOfLE (inf_le_right : W1 \u2293 (V0 \u2293 V1) \u2264 V0 \u2293 V1)).op).hom s'"
+    ],
+    [
+      "AlgebraicGeometry.SmallExtension.exists_overlap_iso_isTangentCoordsOfPairAtVia_of_pointDerivations",
+      "theorem AlgebraicGeometry.SmallExtension.exists_overlap_iso_isTangentCoordsOfPairAtVia_of_pointDerivations\n    (T' T : Type u) [CommRing T'] [IsLocalRing T'] [IsArtinianRing T']\n    [CommRing T] (\u03c0 : T' \u2192+* T) (h\u03c0 : Function.Surjective \u03c0) (hker : IsNilpotent (RingHom.ker \u03c0))\n    (hsmall : RingHom.ker \u03c0 * maximalIdeal T' = \u22a5)\n    (hI : RingHom.ker \u03c0 \u2264 maximalIdeal T')\n    (V : Type u) [AddCommGroup V] [Module (ResidueField T') V] [Module.Finite (ResidueField T') V]\n    [Module T' V] [IsScalarTower T' (ResidueField T') V]\n    [Module (ResidueField T')\u1d50\u1d52\u1d56 V] [IsCentralScalar (ResidueField T') V]\n    (\u03b9 : V \u2192\u2097[T'] T') (h\u03b9 : Function.Injective \u03b9)\n    (h\u03b9I : LinearMap.range \u03b9 = Submodule.restrictScalars T' (RingHom.ker \u03c0))\n    {A\u2080 : Scheme.{u}} (f\u2080 : A\u2080 \u27f6 Spec (CommRingCat.of T))\n    (Ua Ub : A\u2080.Opens)\n    {Ya Yb : Scheme.{u}} (qa : Ya \u27f6 Spec (CommRingCat.of T')) (qb : Yb \u27f6 Spec (CommRingCat.of T')) (hqa : Smooth qa)\n    (ga : (\u2191Ua : Scheme.{u}) \u27f6 Ya) (gb : (\u2191Ub : Scheme.{u}) \u27f6 Yb)\n    (hgb : IsPullback gb (Ub.\u03b9 \u226b f\u2080) qb (Spec.map (CommRingCat.ofHom \u03c0)))\n    (Oa : A\u2080.Opens \u2192 Ya.Opens) (Ob : A\u2080.Opens \u2192 Yb.Opens)\n    (hOb : \u2200 W : A\u2080.Opens, gb \u207b\u00b9\u1d41 Ob W = Ub.\u03b9 \u207b\u00b9\u1d41 W)\n    (hOaffa : IsAffineOpen (Oa (Ua \u2293 Ub))) (hOaffb : IsAffineOpen (Ob (Ua \u2293 Ub)))\n\n    {Ak : Scheme.{u}} (fk : Ak \u27f6 Spec (CommRingCat.of (ResidueField T'))) (Lk : RelativeGroupLaw (ResidueField T') fk)\n    (W : Ak.Opens) (aW : (W : Scheme.{u}) \u27f6 Yb)\n    (haW : IsPullback aW (W.\u03b9 \u226b fk) qb (Spec.map (CommRingCat.ofHom (residue T'))))\n    (Ue : Ak.Opens) (hUe : IsAffineOpen Ue)\n    (e\u2081 : Spec (CommRingCat.of (ResidueField T')) \u27f6 (Ue : Scheme.{u})) (he\u2081 : e\u2081 \u226b Ue.\u03b9 = (Lk.one (\ud835\udfd9 _)).1)\n\n    (\u03c6 : (\u2191(Oa (Ua \u2293 Ub)) : Scheme.{u}) \u2245 \u2191(Ob (Ua \u2293 Ub)))\n    (h\u03c6q : \u03c6.hom \u226b (Ob (Ua \u2293 Ub)).\u03b9 \u226b qb = (Oa (Ua \u2293 Ub)).\u03b9 \u226b qa)\n    (h\u03c6g : \u2203 (\u03b3 : (\u2191(Ua \u2293 Ub) : Scheme.{u}) \u27f6 \u2191(Oa (Ua \u2293 Ub))) (\u03b3' : (\u2191(Ua \u2293 Ub) : Scheme.{u}) \u27f6 \u2191(Ob (Ua \u2293 Ub))),\n        \u03b3 \u226b (Oa (Ua \u2293 Ub)).\u03b9 = A\u2080.homOfLE inf_le_left \u226b ga \u2227\n        \u03b3' \u226b (Ob (Ua \u2293 Ub)).\u03b9 = A\u2080.homOfLE inf_le_right \u226b gb \u2227\n        \u03b3 \u226b \u03c6.hom = \u03b3')\n    (h\u03c6O : \u2200 W' : A\u2080.Opens, \u03c6.hom \u207b\u00b9\u1d41 ((Ob (Ua \u2293 Ub)).\u03b9 \u207b\u00b9\u1d41 Ob W') = (Oa (Ua \u2293 Ub)).\u03b9 \u207b\u00b9\u1d41 Oa W')\n\n    (\u03b4 : letI := algebraOfHom qa (Oa (Ua \u2293 Ub)); letI := algebraOfHom fk Ue\n      \u21a5(Algebra.PointDerivations (ResidueField T') \u0393(Ak, Ue)\n          ((Ue.topIso.inv \u226b e\u2081.appTop \u226b (Scheme.\u0393SpecIso (CommRingCat.of (ResidueField T'))).hom).hom)\n          (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T'] (ResidueField T' \u2297[T'] \u0393(Ya, Oa (Ua \u2293 Ub)))))) :\n    letI := algebraOfHom qa (Oa (Ua \u2293 Ub)); letI := algebraOfHom fk Ue\n    \u2203 \u03c6' : (\u2191(Oa (Ua \u2293 Ub)) : Scheme.{u}) \u2245 \u2191(Ob (Ua \u2293 Ub)),\n      \u03c6'.hom \u226b (Ob (Ua \u2293 Ub)).\u03b9 \u226b qb = (Oa (Ua \u2293 Ub)).\u03b9 \u226b qa \u2227\n      (\u2203 (\u03b3 : (\u2191(Ua \u2293 Ub) : Scheme.{u}) \u27f6 \u2191(Oa (Ua \u2293 Ub))) (\u03b3' : (\u2191(Ua \u2293 Ub) : Scheme.{u}) \u27f6 \u2191(Ob (Ua \u2293 Ub))),\n        \u03b3 \u226b (Oa (Ua \u2293 Ub)).\u03b9 = A\u2080.homOfLE inf_le_left \u226b ga \u2227\n        \u03b3' \u226b (Ob (Ua \u2293 Ub)).\u03b9 = A\u2080.homOfLE inf_le_right \u226b gb \u2227\n        \u03b3 \u226b \u03c6'.hom = \u03b3') \u2227\n      (\u2200 W' : A\u2080.Opens, \u03c6'.hom \u207b\u00b9\u1d41 ((Ob (Ua \u2293 Ub)).\u03b9 \u207b\u00b9\u1d41 Ob W') = (Oa (Ua \u2293 Ub)).\u03b9 \u207b\u00b9\u1d41 Oa W') \u2227\n      IsTangentCoordsOfPairAtVia (RingHom.ker \u03c0) V \u03b9 \u0393(Ya, Oa (Ua \u2293 Ub))\n        (hOaffa.isoSpec.inv \u226b \u03c6.hom \u226b (Ob (Ua \u2293 Ub)).\u03b9)\n        (hOaffa.isoSpec.inv \u226b \u03c6'.hom \u226b (Ob (Ua \u2293 Ub)).\u03b9)\n        fk Lk W aW Ue\n        (fun x => (\u03b4 : \u0393(Ak, Ue) \u2192\u2097[ResidueField T']\n          (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T'] (ResidueField T' \u2297[T'] \u0393(Ya, Oa (Ua \u2293 Ub))))) x)"
+    ],
+    [
+      "M4aHerbrand.exists_unit_forall_exists_localFundamentalClass_eq_smul_res_and_pow_dvd_of_forall_map_inclusion_eq",
+      "theorem M4aHerbrand.exists_unit_forall_exists_localFundamentalClass_eq_smul_res_and_pow_dvd_of_forall_map_inclusion_eq\n    (p : \u2115) [Fact p.Prime] (hp2 : p \u2260 2)\n    (E F : Type) [Field E] [NumberField E] [Field F] [NumberField F] [Algebra E F] [IsGalois E F]\n    (D : IdeleGaloisDescent (\ud835\udcde F) E F)\n    [MulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)]\n    (hact : \u2200 (g : F \u2243\u2090[E] F) (c : IdeleClassGroup (\ud835\udcde F) F), g \u2022 c = D.classAct g c)\n    (\u03b9 : \u2200 w : HeightOneSpectrum (\ud835\udcde F), (w.adicCompletion F)\u02e3 \u2192* (AdeleRing (\ud835\udcde F) F)\u02e3)\n    (h\u03b9 : \u2200 (w : HeightOneSpectrum (\ud835\udcde F)) (x : (w.adicCompletion F)\u02e3),\n      finPart w (\u03b9 w x) = x \u2227 (\u2200 w' : HeightOneSpectrum (\ud835\udcde F), w' \u2260 w \u2192 finPart w' (\u03b9 w x) = 1) \u2227 infPart (\u03b9 w x) = 1)\n    (lam : \u2200 w : HeightOneSpectrum (\ud835\udcde F),\n      Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (w.adicCompletion F)\u02e3 \u27f6\n        Rep.res (NumberField.PlaceDecomp.decomp E F w).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)))\n    (hlam : \u2200 (w : HeightOneSpectrum (\ud835\udcde F)) (x : (w.adicCompletion F)\u02e3),\n      (lam w).hom (Additive.ofMul x) = Additive.ofMul (QuotientGroup.mk (\u03b9 w x) : IdeleClassGroup (\ud835\udcde F) F))\n    (u\u2080 : groupCohomology (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)) 2)\n    (h2 : \u2200 (S : Subgroup (F \u2243\u2090[E] F)) [Fintype S], Nat.card\n        (groupCohomology (Rep.res S.subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))) 2) = Fintype.card S)\n    (h3 : \u2200 S : Subgroup (F \u2243\u2090[E] F), Submodule.span \u2124\n        {(groupCohomology.map S.subtype (\ud835\udfd9 (Rep.res S.subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)))) 2).hom u\u2080} = \u22a4)\n    (P : Subgroup (F \u2243\u2090[E] F)) (hP : IsPGroup p P) (hPidx : \u00ac p \u2223 P.index)\n    (uP : groupCohomology (Rep.res P.subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))) 2) (hspan : Submodule.span \u2124 {uP} = \u22a4)\n    (hloc :\n      \u2200 (w : HeightOneSpectrum (\ud835\udcde F))\n        (q : \u2115) [Fact q.Prime] (L' : IntermediateField \u211a_[q] (PadicAlgCl q)) [FiniteDimensional \u211a_[q] L']\n        [MulSemiringAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) L'] [MulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3]\n        (\u03a6 : w.adicCompletion F \u2243+* L')\n        (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (x : \u211a_[q]), g \u2022 algebraMap \u211a_[q] L' x = algebraMap \u211a_[q] L' x)\n        (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (v : (\u21a5L')\u02e3), ((g \u2022 v : (\u21a5L')\u02e3) : L') = g \u2022 (v : L'))\n        (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (x : w.adicCompletion F), \u03a6 (g \u2022 x) = g \u2022 \u03a6 x)\n        (K\u2080 : IntermediateField \u211a_[q] (PadicAlgCl q)) [FiniteDimensional \u211a_[q] K\u2080]\n        (_ : ExtCitation.LocalLevel.IsBase q L' (\u21a5(NumberField.PlaceDecomp.decomp E F w)) K\u2080)\n        (\u03b8 : Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3 \u27f6\n          Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (w.adicCompletion F)\u02e3)\n        (_ : \u2200 v : (\u21a5L')\u02e3, ((Additive.toMul (\u03b8.hom (Additive.ofMul v)) : (w.adicCompletion F)\u02e3) : w.adicCompletion F) = \u03a6.symm (v : L'))\n        (u' : groupCohomology.H2 (Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3))\n        (_ : ExtCitation.LocalLevel.IsLocalFundamentalClass q L' (\u21a5(NumberField.PlaceDecomp.decomp E F w)) K\u2080 u'),\n        ((groupCohomology.map (Subgroup.inclusion (inf_le_left : (NumberField.PlaceDecomp.decomp E F w) \u2293 P \u2264 (NumberField.PlaceDecomp.decomp E F w)))\n            (\ud835\udfd9 (Rep.res (Subgroup.inclusion (inf_le_left : (NumberField.PlaceDecomp.decomp E F w) \u2293 P \u2264 (NumberField.PlaceDecomp.decomp E F w))) (Rep.res (NumberField.PlaceDecomp.decomp E F w).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))))) 2).hom\n          ((groupCohomology.map (MonoidHom.id \u21a5(NumberField.PlaceDecomp.decomp E F w)) (lam w) 2).hom ((groupCohomology.map (MonoidHom.id \u21a5(NumberField.PlaceDecomp.decomp E F w)) \u03b8 2).hom u')) : groupCohomology (Rep.res ((NumberField.PlaceDecomp.decomp E F w) \u2293 P).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))) 2) =\n        ((groupCohomology.map (Subgroup.inclusion (inf_le_right : (NumberField.PlaceDecomp.decomp E F w) \u2293 P \u2264 P))\n            (\ud835\udfd9 (Rep.res (Subgroup.inclusion (inf_le_right : (NumberField.PlaceDecomp.decomp E F w) \u2293 P \u2264 P)) (Rep.res P.subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))))) 2).hom\n          uP : groupCohomology (Rep.res ((NumberField.PlaceDecomp.decomp E F w) \u2293 P).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))) 2)) :\n    \u2203 a : \u2124, \u00ac (p : \u2124) \u2223 a \u2227\n      \u2200 (w : HeightOneSpectrum (\ud835\udcde F))\n        (q : \u2115) [Fact q.Prime] (L' : IntermediateField \u211a_[q] (PadicAlgCl q)) [FiniteDimensional \u211a_[q] L']\n        [MulSemiringAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) L'] [MulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3]\n        (\u03a6 : w.adicCompletion F \u2243+* L')\n        (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (x : \u211a_[q]), g \u2022 algebraMap \u211a_[q] L' x = algebraMap \u211a_[q] L' x)\n        (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (v : (\u21a5L')\u02e3), ((g \u2022 v : (\u21a5L')\u02e3) : L') = g \u2022 (v : L'))\n        (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (x : w.adicCompletion F), \u03a6 (g \u2022 x) = g \u2022 \u03a6 x)\n        (K\u2080 : IntermediateField \u211a_[q] (PadicAlgCl q)) [FiniteDimensional \u211a_[q] K\u2080]\n        (_ : ExtCitation.LocalLevel.IsBase q L' (\u21a5(NumberField.PlaceDecomp.decomp E F w)) K\u2080)\n        (\u03b8 : Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3 \u27f6\n          Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (w.adicCompletion F)\u02e3)\n        (_ : \u2200 v : (\u21a5L')\u02e3, ((Additive.toMul (\u03b8.hom (Additive.ofMul v)) : (w.adicCompletion F)\u02e3) : w.adicCompletion F) = \u03a6.symm (v : L'))\n        (u' : groupCohomology.H2 (Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3))\n        (_ : ExtCitation.LocalLevel.IsLocalFundamentalClass q L' (\u21a5(NumberField.PlaceDecomp.decomp E F w)) K\u2080 u'),\n        \u2203 c : \u2124, ((groupCohomology.map (MonoidHom.id \u21a5(NumberField.PlaceDecomp.decomp E F w)) (lam w) 2).hom ((groupCohomology.map (MonoidHom.id \u21a5(NumberField.PlaceDecomp.decomp E F w)) \u03b8 2).hom u')) = c \u2022 ((groupCohomology.map (NumberField.PlaceDecomp.decomp E F w).subtype (\ud835\udfd9 (Rep.res (NumberField.PlaceDecomp.decomp E F w).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)))) 2).hom u\u2080) \u2227\n          \u2200 n : \u2115, p ^ n \u2223 Nat.card \u21a5(NumberField.PlaceDecomp.decomp E F w) \u2192 (p : \u2124) ^ n \u2223 c * a - 1"
+    ],
+    [
+      "AlgebraicGeometry.OModulePresheaf.exists_forall_eq_thread_and_eq_zero_of_forall_eq_zero_of_isAdicComplete_of_isProper",
+      "theorem AlgebraicGeometry.OModulePresheaf.exists_forall_eq_thread_and_eq_zero_of_forall_eq_zero_of_isAdicComplete_of_isProper\n    {A : Type u} [CommRing A] [IsNoetherianRing A] (I : Ideal A)\n    {P : Scheme.{u}} (q : P \u27f6 Spec (CommRingCat.of A)) [IsProper q]\n    {Z : Scheme.{u}} (i : Z \u27f6 P) [IsClosedImmersion i]\n    {V' : Scheme.{u}} (g : V' \u27f6 Z) [IsProper g] (K' : V'.OrderedAffineCover)\n    (U : Z.Opens) (hU : IsIso (CategoryTheory.Limits.pullback.snd g U.\u03b9))\n    (T' : Closeds P) (hT' : \u2200 z : Z, z \u2209 U \u2192 i.base z \u2208 T')\n\n    (F : \u2115 \u2192 OModulePresheaf q) (hFc : \u2200 k, (F k).IsCoherent) (hFq : \u2200 k, (F k).IsQuasicoherent)\n    (\u03c6 : \u2200 k, OModulePresheaf.AffHom (F (k + 1)) (F k))\n    (h\u03c6s : \u2200 (k : \u2115) (U : P.affineOpens), Function.Surjective ((\u03c6 k).app U))\n    (h\u03c6k : \u2200 (k : \u2115) (U : P.affineOpens),\n      LinearMap.ker ((\u03c6 k).app U) = I ^ (k + 1) \u2022 (\u22a4 : Submodule A ((F (k + 1)).obj U.1)))\n    (hFZ : \u2200 k, OModulePresheaf.IdealAnnihilates q i.ker (F k))\n\n    (F' : \u2115 \u2192 OModulePresheaf ((g \u226b i) \u226b q)) (\u03c6' : \u2200 k, OModulePresheaf.AffHom (F' (k + 1)) (F' k))\n    (\u03b7 : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V : V'.affineOpens), V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1 \u2192\n      ((F k).obj U\u2080.1 \u2192\u2097[A] (F' k).obj V.1))\n    (h\u03b7s : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1) (a : \u0393(P, U\u2080.1))\n      (x : (F k).obj U\u2080.1), \u03b7 k U\u2080 V h (a \u2022 x) = ((g \u226b i).appLE U\u2080.1 V.1 h).hom a \u2022 \u03b7 k U\u2080 V h x)\n    (h\u03b7V : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V\u2081 V\u2082 : V'.affineOpens) (h\u2081 : V\u2081.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1)\n      (h\u2082 : V\u2082.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1) (hV : V\u2081.1 \u2264 V\u2082.1) (x : (F k).obj U\u2080.1),\n      (F' k).res hV (\u03b7 k U\u2080 V\u2082 h\u2082 x) = \u03b7 k U\u2080 V\u2081 h\u2081 x)\n    (h\u03b7U : \u2200 (k : \u2115) (U\u2081 U\u2082 : P.affineOpens) (V : V'.affineOpens) (h\u2081 : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2081.1)\n      (h\u2082 : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2082.1) (hU\u2081\u2082 : U\u2081.1 \u2264 U\u2082.1) (x : (F k).obj U\u2082.1),\n      \u03b7 k U\u2082 V h\u2082 x = \u03b7 k U\u2081 V h\u2081 ((F k).res hU\u2081\u2082 x))\n    (h\u03b7\u03c6 : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1)\n      (x : (F (k + 1)).obj U\u2080.1), (\u03c6' k).app V (\u03b7 (k + 1) U\u2080 V h x) = \u03b7 k U\u2080 V h ((\u03c6 k).app U\u2080 x))\n    (h\u03b2 : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1),\n      letI := ((g \u226b i).appLE U\u2080.1 V.1 h).hom.toAlgebra\n      \u2203 \u03b2 : \u0393(V', V.1) \u2297[\u0393(P, U\u2080.1)] (F k).obj U\u2080.1 \u2243\u2097[\u0393(V', V.1)] (F' k).obj V.1,\n        \u2200 x : (F k).obj U\u2080.1, \u03b2 (1 \u2297\u209c x) = \u03b7 k U\u2080 V h x)\n\n    (v : \u2200 k, OModulePresheaf.AffHom (F k) (OModulePresheaf.cechPushforward (g \u226b i) q K' (F' k)))\n    (hv\u03b7 : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (x : (F k).obj U\u2080.1) (j : K'.\u03b9),\n      ((v k).app U\u2080 x).1 j\n        = \u03b7 k U\u2080 (OModulePresheaf.AffHom.affineChart (g \u226b i) q K' U\u2080 j)\n            (OModulePresheaf.cechPushforward.chart_le_preimage (g \u226b i) K' U\u2080.1 j) x)\n\n    (W : P.affineOpens)\n    (R : Type u) [CommRing R] [Algebra \u0393(P, W.1) R]\n    (L : Type u) [AddCommGroup L] [Module \u0393(P, W.1) L] [Module R L] [IsScalarTower \u0393(P, W.1) R L]\n    [Module.Finite R L]\n    (pr : \u2200 n : \u2115, L \u2192\u2097[\u0393(P, W.1)] (F n).obj W.1)\n    (hprc : \u2200 (n : \u2115) (x : L), (\u03c6 n).app W (pr (n + 1) x) = pr n x)\n    (hpri : \u2200 x : L, (\u2200 n : \u2115, pr n x = 0) \u2192 x = 0)\n    (hprs : \u2200 n : \u2115, Function.Surjective (pr n))\n    (hprk : \u2200 n : \u2115, LinearMap.ker (pr n) = (I.map ((Scheme.\u0393SpecIso (CommRingCat.of A)).inv \u226b q.appLE \u22a4 W.1 le_top).hom) ^ (n + 1) \u2022 (\u22a4 : Submodule \u0393(P, W.1) L))\n    [IsNoetherianRing R] (hRc : IsAdicComplete (I.map ((algebraMap \u0393(P, W.1) R).comp ((Scheme.\u0393SpecIso (CommRingCat.of A)).inv \u226b q.appLE \u22a4 W.1 le_top).hom)) R)\n\n    {Y : Scheme.{u}} (sY : Y \u27f6 Spec (CommRingCat.of R)) [IsProper sY] (t : Y \u27f6 V')\n    (hY : IsPullback t sY (g \u226b i) (Spec.map (CommRingCat.ofHom (algebraMap \u0393(P, W.1) R)) \u226b W.2.fromSpec))\n    (hta : \u2200 V : V'.affineOpens, V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1 \u2192 IsAffineOpen (t \u207b\u00b9\u1d41 V.1))\n\n    (G : OModulePresheaf sY) (hGc : G.IsCoherent) (hGq : G.IsQuasicoherent)\n    (\u03b5 : \u2200 U : Y.Opens, L \u2192\u2097[R] G.obj U)\n    (h\u03b5r : \u2200 (U U' : Y.Opens) (h : U \u2264 U') (x : L), G.res h (\u03b5 U' x) = \u03b5 U x)\n    (h\u03b5\u03b2 : \u2200 U : Y.affineOpens,\n      letI := Scheme.TwoAffineOpenCover.algebraOfHom sY U.1\n      \u2203 \u03b2 : \u0393(Y, U.1) \u2297[R] L \u2243\u2097[\u0393(Y, U.1)] G.obj U.1, \u2200 x : L, \u03b2 (1 \u2297\u209c x) = \u03b5 U.1 x)\n\n    (\u03b8 : \u2200 (n : \u2115) (V : V'.affineOpens), V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1 \u2192 (G.obj (t \u207b\u00b9\u1d41 V.1) \u2192+ (F' n).obj V.1))\n    (h\u03b8s : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (c : \u0393(V', V.1))\n      (y : G.obj (t \u207b\u00b9\u1d41 V.1)), \u03b8 n V h ((t.app V.1).hom c \u2022 y) = c \u2022 \u03b8 n V h y)\n    (h\u03b8r : \u2200 (n : \u2115) (V\u2081 V\u2082 : V'.affineOpens) (h\u2081 : V\u2081.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (h\u2082 : V\u2082.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1)\n      (hV : V\u2081.1 \u2264 V\u2082.1) (y : G.obj (t \u207b\u00b9\u1d41 V\u2082.1)),\n      (F' n).res hV (\u03b8 n V\u2082 h\u2082 y) = \u03b8 n V\u2081 h\u2081 (G.res ((Opens.map t.base).monotone hV) y))\n    (h\u03b8\u03c6 : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (y : G.obj (t \u207b\u00b9\u1d41 V.1)),\n      (\u03c6' n).app V (\u03b8 (n + 1) V h y) = \u03b8 n V h y)\n    (h\u03b8\u03b5 : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (x : L),\n      \u03b8 n V h (\u03b5 (t \u207b\u00b9\u1d41 V.1) x) = \u03b7 n W V h (pr n x))\n    (h\u03b8o : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1), Function.Surjective (\u03b8 n V h))\n    (h\u03b8k : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (y : G.obj (t \u207b\u00b9\u1d41 V.1)),\n      \u03b8 n V h y = 0 \u2194 y \u2208 (I.map ((algebraMap \u0393(P, W.1) R).comp ((Scheme.\u0393SpecIso (CommRingCat.of A)).inv \u226b q.appLE \u22a4 W.1 le_top).hom)) ^ (n + 1) \u2022 (\u22a4 : Submodule R (G.obj (t \u207b\u00b9\u1d41 V.1)))) :\n    (\u2200 (\u2113 : \u2200 n, (OModulePresheaf.cechPushforward (g \u226b i) q K' (F' n)).obj W.1),\n        (\u2200 n, ((\u03c6' n).cechPushforward (g \u226b i) q K').app W (\u2113 (n + 1)) = \u2113 n) \u2192\n        \u2203 c : \u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j)),\n          (\u2200 j j' : K'.\u03b9,\n          G.res ((Opens.map t.base).monotone (inf_le_left : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j)\n            = G.res ((Opens.map t.base).monotone (inf_le_right : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j')) \u2227\n          \u2200 (n : \u2115) (j : K'.\u03b9),\n            \u03b8 n (OModulePresheaf.AffHom.affineChart (g \u226b i) q K' W j)\n              (OModulePresheaf.cechPushforward.chart_le_preimage (g \u226b i) K' W.1 j) (c j) = (\u2113 n).1 j) \u2227\n    (\u2200 c : \u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j)),\n        (\u2200 j j' : K'.\u03b9,\n          G.res ((Opens.map t.base).monotone (inf_le_left : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j)\n            = G.res ((Opens.map t.base).monotone (inf_le_right : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j')) \u2192\n        (\u2200 (n : \u2115) (j : K'.\u03b9),\n            \u03b8 n (OModulePresheaf.AffHom.affineChart (g \u226b i) q K' W j)\n              (OModulePresheaf.cechPushforward.chart_le_preimage (g \u226b i) K' W.1 j) (c j) = 0) \u2192\n        c = 0) \u2227\n    (\u2203 s : Finset (\u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j))),\n        (\u2200 c \u2208 s, (\u2200 j j' : K'.\u03b9,\n          G.res ((Opens.map t.base).monotone (inf_le_left : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j)\n            = G.res ((Opens.map t.base).monotone (inf_le_right : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j'))) \u2227\n        \u2200 c : \u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j)),\n          (\u2200 j j' : K'.\u03b9,\n          G.res ((Opens.map t.base).monotone (inf_le_left : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j)\n            = G.res ((Opens.map t.base).monotone (inf_le_right : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j')) \u2192 c \u2208 Submodule.span R (s : Set (\u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j)))))"
+    ]
+  ],
+  "typed:\"GaloisConnection\"": [
+    [
+      "segment_galois_connection",
+      "theorem segment_galois_connection (hm : StrictMono f) (h0 : f 0 = 0) :\r\n    GaloisConnection f (segment f)"
+    ],
+    [
+      "gc_map_comap",
+      "theorem gc_map_comap (f : F) :\r\n    GaloisConnection (map f : NonUnitalSubalgebra R A \u2192 NonUnitalSubalgebra R B) (comap f)"
+    ],
+    [
+      "gc",
+      "protected theorem gc : GaloisConnection (adjoin R : Set A \u2192 NonUnitalSubalgebra R A) (\u2191)"
+    ],
+    [
+      "gc_map_comap",
+      "theorem gc_map_comap (f : A \u2192\u2090[R] B) : GaloisConnection (map f) (comap f)"
+    ],
+    [
+      "gc",
+      "protected theorem gc : GaloisConnection (adjoin R : Set A \u2192 Subalgebra R A) (\u2191)"
+    ],
+    [
+      "gc_map_comap",
+      "theorem gc_map_comap (f : K \u2192+* L) : GaloisConnection (map f) (comap f)"
+    ]
+  ],
+  "typed:\"finrank\" \"ker\"": [
+    [
+      "parentHamiltonianGroundSpaceES_finrank_eq_ker",
+      "theorem parentHamiltonianGroundSpaceES_finrank_eq_ker\r\n    (A : MPSTensor d D) (L N : \u2115) :\r\n    Module.finrank \u2102 (parentHamiltonianGroundSpaceES A L N) =\r\n      Module.finrank \u2102 (LinearMap.ker (parentHamiltonian A L N))"
+    ],
+    [
+      "HasBNTSectorData.eventually_parentHamiltonian_groundSpace_finrank_eq",
+      "theorem HasBNTSectorData.eventually_parentHamiltonian_groundSpace_finrank_eq\r\n    {d : \u2115} {P : SectorDecomposition d}\r\n    (hBNT : HasBNTSectorData P)\r\n    (hNNCPH : HasNNCPHGroundSpaces P.toTensor P.basis) :\r\n    \u2203 N\u2080 : \u2115, \u2200 N : \u2115, N\u2080 < N \u2192\r\n      Module.finrank \u2102 (LinearMap.ker (parentHamiltonian P.toTensor 2 N)) =\r\n        P.basisCount"
+    ],
+    [
+      "codim_iInf_ker_le_fintypeCard",
+      "lemma codim_iInf_ker_le_fintypeCard [Fintype \u03b9] :\r\n    Module.finrank (ZMod q) G - (\u2a05 i, (\u03b3 i).toAddMonoidHom.ker.toZModSubmodule q).finrank\r\n      \u2264 Fintype.card \u03b9"
+    ],
+    [
+      "codim_iInf_ker_le_finsetCard",
+      "lemma codim_iInf_ker_le_finsetCard :\r\n    Module.finrank (ZMod q) G - ((\u2a05 i \u2208 s, (\u03b3 i).toAddMonoidHom.ker).toZModSubmodule q).finrank\r\n      \u2264 #s"
+    ],
+    [
+      "codim_iInf_ker_le_fintypeCard",
+      "lemma codim_iInf_ker_le_fintypeCard [Fintype \u03b9] :\r\n    finrank K V - (\u2a05 i, (f i).ker).finrank \u2264 Fintype.card \u03b9"
+    ],
+    [
+      "codim_biInf_ker_le_finsetCard",
+      "lemma codim_biInf_ker_le_finsetCard : finrank K V - (\u2a05 i \u2208 s, (f i).ker).finrank \u2264 #s"
+    ]
+  ]
+}
diff --git a/research/contextual-provider-pooling/docs/ELIMINATION-AVALANCHE-INDEPENDENT-REVIEW.json b/research/contextual-provider-pooling/docs/ELIMINATION-AVALANCHE-INDEPENDENT-REVIEW.json
new file mode 100644
index 0000000000..37deca7fcb
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/ELIMINATION-AVALANCHE-INDEPENDENT-REVIEW.json
@@ -0,0 +1,112 @@
+{
+  "status": "PASS_INDEPENDENT_EIGHT_HYPERPLANE_WAVE_REVIEW",
+  "source_sha256": "29b11448963546b959bda379d82711c25f768d5579dcd6bc004887de808e8ae6",
+  "word_sha256": "931fa9d365eabacacbed055f00ce589ce29647ea904270dfe8943dd5d4ea609d",
+  "nodes": 5471,
+  "register_edges": 8372,
+  "waves": [
+    {
+      "functional": 33,
+      "node_count": 9,
+      "delta": {
+        "1": 2,
+        "2": -2,
+        "3": -2,
+        "4": 2
+      }
+    },
+    {
+      "functional": 33,
+      "node_count": 10,
+      "delta": {
+        "1": 2,
+        "2": -2,
+        "3": -2,
+        "4": 2
+      }
+    },
+    {
+      "functional": 39,
+      "node_count": 8,
+      "delta": {
+        "1": 2,
+        "2": -2,
+        "3": -2,
+        "4": 2
+      }
+    },
+    {
+      "functional": 39,
+      "node_count": 10,
+      "delta": {
+        "1": 2,
+        "2": -2,
+        "3": -2,
+        "4": 2
+      }
+    },
+    {
+      "functional": 192,
+      "node_count": 10,
+      "delta": {
+        "1": 2,
+        "2": -2,
+        "3": -2,
+        "4": 2
+      }
+    },
+    {
+      "functional": 192,
+      "node_count": 10,
+      "delta": {
+        "1": 2,
+        "2": -2,
+        "3": -2,
+        "4": 2
+      }
+    },
+    {
+      "functional": 198,
+      "node_count": 10,
+      "delta": {
+        "1": 2,
+        "2": -2,
+        "3": -2,
+        "4": 2
+      }
+    },
+    {
+      "functional": 198,
+      "node_count": 10,
+      "delta": {
+        "1": 2,
+        "2": -2,
+        "3": -2,
+        "4": 2
+      }
+    }
+  ],
+  "exact_paid_delta": {
+    "1": 16,
+    "2": -16,
+    "3": -16,
+    "4": 16
+  },
+  "all_edges_nested": true,
+  "fixed_boundary_nodes_unchanged": true,
+  "scalar_coefficients_destinations_sources_unchanged": true,
+  "retained_cut_cleanup_and_dirt_interfaces_unchanged": true,
+  "strict_moment_proof": "For 0<a<1, f(r)=r^a is strictly concave, so f(4)-f(3)<f(2)-f(1). Thus16[f(1)-f(2)-f(3)+f(4)]<0. Rank mass and childcount remain equal.",
+  "codim2_review": {
+    "passes": [],
+    "best_delta": -1e-13,
+    "lambda": 0,
+    "mu": 0,
+    "nodes": [],
+    "losses": [],
+    "screened": 7381812,
+    "feasible": 1920,
+    "charged_edges": 7968
+  },
+  "scope": "Independent exact span/incidence/profile and source-identity review. Physical phase realization, global owner billing and outer assembly are separately checked by the main pipeline. No numerical claim from the neutral codim2 screen."
+}
diff --git a/research/contextual-provider-pooling/docs/ELIMINATION-CODIM2.json b/research/contextual-provider-pooling/docs/ELIMINATION-CODIM2.json
new file mode 100644
index 0000000000..f495a8d1e3
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/ELIMINATION-CODIM2.json
@@ -0,0 +1 @@
+{"passes":[],"best_delta":-1.000000000000000030374e-13,"lambda":0,"mu":0,"nodes":[],"losses":[],"screened":7381812,"feasible":1920,"charged_edges":7968}
diff --git a/research/contextual-provider-pooling/docs/ELIMINATION-ELIMINATION-AND-PATH-TRANSFER.md b/research/contextual-provider-pooling/docs/ELIMINATION-ELIMINATION-AND-PATH-TRANSFER.md
new file mode 100644
index 0000000000..847fc9e4b0
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/ELIMINATION-ELIMINATION-AND-PATH-TRANSFER.md
@@ -0,0 +1,41 @@
+# Exact circuit reductions from elimination and path algebra
+
+These are sufficient constructive transformations. No new global originality claim or Lean certificate is made. Sources actually read and hashed are in SOURCES.json. The electrical analogy is exact Schur elimination of an internal linear variable; no positivity, passive-network or electrical complexity bound is imported into the circuit model.
+
+## A. Eliminate a cold internal register while retaining reversible semantics
+
+Let a linear straight-line program over a field use background registers z, targets y and one designated cold internal register h. No target feeds a background register. The raw program may interleave background and target updates. Its compensated endpoint is (z,h,y)->(z,h,y+Jz) after literal inverse cleanup of its background updates. Initial h is arbitrary dirt and its target contribution is cancelled by the explicit input preconditioner.
+
+The following algorithm is a sufficient elimination procedure, provided every emitted nonzero coefficient and inverse is allowed and every emitted frame passes the ordinary incidence checks. Simulate the old program with initial h=0. Maintain an exact expression h=sum_j g_j z_j in the CURRENT surviving registers, rather than in stale inputs.
+
+* At h+=a*z_s set g_s+=a. At h*=a multiply all g by a. Emit neither old update.
+* At a surviving z_t+=a*z_s not reading h, emit the update and change g_s to g_s-a*g_t. At z_t*=a, divide g_t by a.
+* At a read z_t+=a*h, put lambda=1+a*g_t. Require lambda!=0. Emit z_t*=lambda followed by z_t+=a*g_s*z_s for every s!=t with nonzero g_s. Then divide every g coefficient by lambda. These formulas are precisely one-coordinate Schur elimination and its reconstruction map. When t is a target, g_t=0 by the no-feedback assumption, hence lambda=1.
+
+Proof of the invariant: after an ordinary surviving addition, substitute old z_t=new z_t-a*z_s into the maintained expression. For a read of h, new z_t=lambda*old z_t+a*sum_(s!=t)g_s*z_s. Solving this equation and substituting into h divides every coefficient by lambda. The required nonzero pivot is explicitly checked; it is not an assumed oracle. Induction now proves equality with the old h=0 execution on every surviving input column. Restrict the old initial dirt preconditioner by removing its h term, or recompute the exact response preconditioner. Regenerate inverse cleanup from the actually emitted background sequence. Every emitted update is invertible by its checked lambda or elementary transvection, so surviving background dirt is restored. The target map is the same J on all surviving inputs. The deleted register has no physical initial value to restore.
+
+For the framed compiler, each added read/write must climb monotonically to its actual gate frame. Every fill-in addition, scale, inverse scale, cleanup gate, copy and normalization wrapper is charged. Deleting a helper does not itself establish a kappa gain: it changes local rank mass and the required residual inventory together; the new complete global assignment and invoice are compulsory. For dyadic circuits, exact denominator/pivot checks are additional sufficient hypotheses, tested on a constructed witness rather than replaced by arbitrary-field division.
+
+A one-variable example is h=a*x+b*z, y+=c*h with h initially zero. Eliminating h emits y+=ca*x and y+=cb*z. For arbitrary initial h, the old preconditioner contributes -c*h_initial; the new program has no such coordinate. This example demonstrates correctness, not an uncharged saving: the two products and both cleanup implications must be billed.
+
+## B. Whole-region path transfer and triangular factorization
+
+Time-expand every linear assignment: each register version becomes a vertex, carry edges have weight1, and an addition creates an edge with its actual scalar coefficient. The resulting graph is acyclic in time. The coefficient from a boundary input to a boundary output equals the sum of products of weights over directed paths. Proof is induction on the destination time: updating a coordinate adds exactly the paths whose final edge is that update. Thus two finite regions with equal exact boundary path matrices can replace each other on arbitrary input/dirt columns.
+
+A useful special case is a unitriangular region. Its strict-upper matrix N is nilpotent, so (I-N)^-1=I+N+...+N^(d-1). Every entry of N^k is the sum of k-edge path weights. Schur elimination removes an internal vertex by adding each incoming-weight times outgoing-weight to the corresponding boundary edge. Repeated elimination therefore computes the same finite path sum, including all length-three and longer cross terms. The construction terminates after the finite vertex set is eliminated; it never assumes an unknown circuit synthesis oracle.
+
+For three ordered vertices, the exact source theorem gives
+
+  U = T12(U12) T13(U13-U12*U23) T23(U23).
+
+The correction U13-U12*U23 subtracts the length-two path already created by the outer factors. In larger regions one may eliminate coordinates in a fixed order, reading the residual coefficients after each step. Equality follows inductively from elementary row identities, not from matching an approximate objective. This is a region-level procedure, rather than the last round's fixed seven three-gate cells.
+
+A replacement becomes a sufficient compiler optimization only after: exact boundary matrix equality; legal actual frame labels for every new gate; unchanged or explicitly reconstructed retained-copy interfaces; regenerated background inverse; full paid profile and coefficient-prefix recount; and any changed whole-owner inventory allocation. No equality of unframed transfer matrices alone makes an illegal physical frame move admissible.
+
+## Bounded application record
+
+Current target was the tn24 complex syndrome word, the binding supplier after public PR543/545 improved the bit side. Native C++ gates tested284 cold helper eliminations with explicit current-expression substitution: all were rejected by the prescribed fixed-frame incidence gate. Another screen multiplied1,669 maximal equal-frame regions and found no coordinate whose boundary row AND column both became identity, so that narrow coordinate-removal resynthesis had no nominee. Exact signed critical-pair comparisons found235 legal candidates with no paid improvement. The same bounded screens were rerun on root's avalanche8 frame rewrite, with the same counts and outcomes.
+
+The helper-elimination nominator uses a prime-field support image only; no successful exact characteristic-zero witness or impossibility statement is claimed from it. Likewise, the equal-frame gate is merely a cheap nomination filter for one restricted reduction. These are not barriers to other Schur decompositions, alternate frames, new source words or larger path regions. The universal sufficient transformations above remain applicable when their explicit checks pass.
+
+A preliminary old-bit screen also found seven further rank1+rank1->rank2 merges unlocked by the preceding Steinberg word. That smaller bit route became nonbinding when PR543/545 arrived and was not represented as a new numerical contribution. No native or final kappa claim is attached to these two routes in this round. Root's independently constructed frame avalanche, if fully admitted, is the numerical candidate.
diff --git a/research/contextual-provider-pooling/docs/ELIMINATION-SCREEN-REVIEW.json b/research/contextual-provider-pooling/docs/ELIMINATION-SCREEN-REVIEW.json
new file mode 100644
index 0000000000..720db44ac3
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/ELIMINATION-SCREEN-REVIEW.json
@@ -0,0 +1,15 @@
+{
+  "status": "BOUNDED_CONSTRUCTIVE_ROUTE_SCREENS_COMPLETE",
+  "complex_source_sha256": "a8adc158c7253c2e89783df0b874418b1eeecde3bbfc86da0cad5fbfe4d3a54c",
+  "base": {
+    "cold_elimination_candidates": 284,
+    "cold_frame_passes": 0,
+    "signed_critical_candidates": 235,
+    "paid_critical_wins": 0,
+    "equal_frame_regions": 1669,
+    "inactive_coordinates": 0
+  },
+  "avalanche8_same_counts": true,
+  "claimed_new_numerical_gain": false,
+  "scope": "Sufficient transformations proved in companion note; restricted screens are nominations only, not global impossibility results."
+}
diff --git a/research/contextual-provider-pooling/docs/ELIMINATION-SOURCES.json b/research/contextual-provider-pooling/docs/ELIMINATION-SOURCES.json
new file mode 100644
index 0000000000..33f50caa28
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/ELIMINATION-SOURCES.json
@@ -0,0 +1,34 @@
+[
+  {
+    "connection": "schur",
+    "path": "D:/proof/lean/mathproof/.lake/packages/mathlib/Mathlib/LinearAlgebra/Matrix/SchurComplement.lean",
+    "sha256": "1db6e549ad08177da0ed454199b62ddbb162fd821be159b76a81526ccd5ff219",
+    "declarations": [
+      "Matrix.fromBlocks_eq_of_invertible\u2081\u2081",
+      "Matrix.fromBlocks_eq_of_invertible\u2082\u2082",
+      "Matrix.invOf_fromBlocks_zero\u2082\u2081_eq"
+    ],
+    "source_only": true
+  },
+  {
+    "connection": "quiver",
+    "path": "D:/proof/external/openai-math/lean/OAI/Topology/CoarseAssembly/CongruenceElementary.lean",
+    "sha256": "9b1839abca1a2b02440e1221dc7d2ef365eb6e2285b2ad9e460c69051b3e5552",
+    "declarations": [
+      "elementary_row_same",
+      "elementary_row_other",
+      "upperUnitriangular_mem_elementaryReduction"
+    ],
+    "source_only": true
+  },
+  {
+    "connection": "filtered_pattern",
+    "path": "D:/proof/external/openai-math/lean/OAI/GroupTheory/Congruence/Patterns.lean",
+    "sha256": "65dbc74c8e955c8aa314fb4f56059fd463d0048dbaa049ff287c9c8c5de35d65",
+    "declarations": [
+      "reindexSL_E",
+      "upper_prime_power"
+    ],
+    "source_only": true
+  }
+]
diff --git a/research/contextual-provider-pooling/docs/FIVEFOLD-DIRECT-SUM-REVIEW.md b/research/contextual-provider-pooling/docs/FIVEFOLD-DIRECT-SUM-REVIEW.md
new file mode 100644
index 0000000000..daa4694e3f
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/FIVEFOLD-DIRECT-SUM-REVIEW.md
@@ -0,0 +1,59 @@
+# Independent sufficient proof for five-fold controller pooling at fixed m=73
+
+Verdict: the five-fold construction is admissible under the same retained whole-family normalized-call and all-size compiler interfaces, provided the actual new owner schedule and finite invoice pass. There is no mathematical requirement W=7168 in the generic moment or outer assembly engines. The current physical audit has T=8,72 calls and W=7168 as explicit fixture assertions; it must be generalized and rerun for the new literal program. This note does not claim that those old receipts certify a larger allocation automatically.
+
+## Source contracts actually inspected
+
+The emitted template fixes the cover to all d in O(73,2), and gives each family a full array with73 binary axes. Its helper route contract permits a whole family from another replica, with an orthogonal port basis and residual/spectator permutation, at most one helper per family per complete invocation, no simultaneous active data ownership, and paid entrance wrappers. Work streams must be erased before reuse. The data contract specifies the same112 ordered ports and both complete identity-shear orientations. The retained port restriction explicitly describes the data route as a portwise direct sum after each completed invocation.
+
+The independent owner audit decodes a family as replica, pair, side, port; checks actual touch windows including bridges; checks whole-family uniqueness; checks all73 columns of every orthogonal chart; accounts for each residual-axis cell at most once; and explicitly emits every remaining pending child. Its constants DATA=8*T*V, T=8, CALLS=72, deficit2560 are fixed-instance checks, not a theorem that no other finite family count is legal.
+
+The finite invoice uses stock=|O(73,2)|*physical, streamed_mass=|O(73,2)|*rank_mass, and recomputes routing, literal, precision and tape bounds from these numbers. The exact moment engine receives H,m,W as arguments and normalizes by m*W. The47-inequality outer engine receives supplier savings and the finite bridge; it does not mention W, T or7168. Hashes of the inspected sources accompany this note.
+
+## Construction and operator proof
+
+Take five disjoint copies of every data family in the old controller. A family is tagged (block,old_family), with block in {0,...,4}. Keep m=73, all73-column charts, the local112-port scalar word, the old orientation choices, and each old per-replica recipe unchanged. Rename all literal family references injectively. Private work may be separately allocated per block; sharing private work instead requires its already-checked erasure at each complete call. A conservative construction can retain all five private namespaces.
+
+Before pooling, this is the literal direct sum of five programs. Renaming preserves each elementary operator, and operations on disjoint families commute, so the endpoint is the direct sum of the five original data endpoints and restored private work. This establishes every copied data identity without changing the73-axis cover or inventing a larger local operator.
+
+Now choose a new finite whole-owner allocation among pending idle children of any block. Retain all of the following checks:
+
+1. Each complete local cover call is indivisible and retains the original local program, exact phases and both entrance wrappers. Its data roles lie in its own controller block.
+2. Every helper occupies a different whole family from every other helper and active data role of that call. Its residual axes are an explicitly charted subset of one pending child of its owner family; the rest of that same full family supplies the normalized spectators.
+3. The actual global serialized order places the entire call strictly inside that owner's pending window, including all bridge touches and remainder deadlines. Checking only a stage label is insufficient.
+4. Across all calls, no pending axis is consumed twice. All unused axes execute as a literal remaining child before the owner's next conflicting operation. Every terminal translation is performed exactly once per final live family.
+5. The new complete profile, global namespace and actual73-column maps are independently recounted; no fractional role or split-family invocation is permitted.
+
+By the retained normalized-call theorem, arbitrary helper dirt does not survive as a coupling into the call's data output. At the complete endpoint, the call has its prescribed data shear and the prescribed residual transform on each selected whole helper family, with its spectators restored. Therefore a helper may belong to another controller block: temporary cross-block scalar interactions have disappeared at the complete boundary, and the only remaining action on the owner is the intended piece of its pending operator.
+
+On each owner, the assigned residual axes and the remaining axes partition the original pending child. Their transforms compose to that child within its no-touch window. Replacing each such partition by the original pending operator gives the disjoint five-controller program already proved above. This proves the pooled data endpoint. It does not assume the endpoint is identity on helper families; the residual operator is essential to the argument.
+
+For arbitrary sizes admitted by the retained compiler, the block tag is a finite family-name tag, not a new vector-space coordinate or a change in the cover group. Every existing local chart and complete-call identity is reused at the same m and same size, and the above finite composition is uniform in that size. The only enlarged quantities are the finite number of families, calls, elementary operations and recursive children, all explicitly represented in the new program and invoice. Thus this uses the existing uniform primitive/compiler contract, rather than requiring an unproved conversion between different m values. The inherited all-size/compiler and analytic assumptions remain conditional exactly as before.
+
+## Rank and moment accounting
+
+The live count becomes W'=5*7168=35840. With unchanged local calls, the unpooled profile is5H and its rank deficit is5*2560=12800. If the actual integer owner map realizes the proposed repacking, five rank39 remainder children are replaced by four rank48 children and one rank3 child. The total rank is unchanged:5*39=4*48+3=195. Hence the deficit remains12800 and the maximum child rank remains48; the existing73^2>2*48^2 halving condition is unchanged.
+
+For any exponent alpha in (0,1), strict concavity gives
+
+    4*48^alpha + 3^alpha < 5*39^alpha.
+
+Indeed the five entries on the left have average39 and are not equal. Thus the full normalized paid moment is strictly smaller than that of five unchanged copies, once the literal assignment is established. The number of remainder calls stays five, so the retained per-child bad-class envelope is unchanged by this replacement. The new supplier saving and outer kappa must still be computed by the exact engines; savings are not added.
+
+## Conservative finite invoice
+
+Use the complete-call count360 and complete bridge count360, rather than assuming cross-block hosting leaves a blockwise prefix estimate unchanged. The retained local envelope40 plus input conversion37 plus360+360 plus margin4 gives801 bits. Charging1024 is sufficient under this same retained envelope rule.
+
+The row formula actually read is
+
+    row=2*bit_length(|O(73,2)|*physical)+9909+252+2*payload.
+
+Even reserving five copies of all7682 physical families increases the stock bit length by at most3. Relative to the old row16467, increasing the payload from512 to1024 gives row at most16467+6+1024=17497, below the retained20161 allowance. The logical/router/literal/precision/tape inequalities must still be evaluated on the larger actual counts. No claim is made that multiplying the old row bound by five is necessary, or that old finite receipts can simply be reused.
+
+The generalized checker must bind the fivefold source projection, all360 complete calls and bridges, every global family/window, every chart, every remainder and the new namespace. If it merely changes W in the moment while leaving the old72-call program or old ownership receipt, the construction is not certified.
+
+## Final source-lift implementation check
+
+The final construction uses the subsequently selected epoch14 local provider. The standalone audit_clone_lift.py was run against its actual source parent and the fivefold parent. It compares every metadata field outside an explicit eight-field structural whitelist, then compares the entire expected clone dictionary. It checks262,080 owner entries,360 source calls, every copied bank family/complement, replica schedule, final correction and shared514-family private reserve. Its source artifacts are byte-bound to the independent local replay proving private work erased in both orientations. Each dedicated bank is used by eight replicas, never forty. Eight explicitly changed negative controls are rejected. FINAL-CLONE-LIFT.json records the actual final source hashes.
+
+The40-bit local prefix used above illustrates the previous provider's invoice; the final invoice must use the freshly measured epoch14 prefix. Even the conservative admitted local bound192 would give192+37+360+360+4=953<1024. The final physical owner/chart audit is separate from the lift audit, as is the exact assembly. This review does not replace either.
diff --git a/research/contextual-provider-pooling/docs/FRAME-SOURCES.json b/research/contextual-provider-pooling/docs/FRAME-SOURCES.json
new file mode 100644
index 0000000000..c6cbc8f794
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/FRAME-SOURCES.json
@@ -0,0 +1,12 @@
+[
+  {
+    "path": "Algebra/Module/Submodule/Map.lean",
+    "sha256": "ac82f62923e5f25850b6e6977c6f88924be3401869d331c9c98ebbc84ed6ea22",
+    "source_only": true
+  },
+  {
+    "path": "LinearAlgebra/FiniteDimensional/Lemmas.lean",
+    "sha256": "c5374ea73d4011cb0cddafac24ed494f4f43c563b2ab5676601de7b7ec442157",
+    "source_only": true
+  }
+]
diff --git a/research/contextual-provider-pooling/docs/FRAME-TRANSFERS.md b/research/contextual-provider-pooling/docs/FRAME-TRANSFERS.md
new file mode 100644
index 0000000000..f078183102
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/FRAME-TRANSFERS.md
@@ -0,0 +1,66 @@
+# Two exact cross-field transfers behind the frame improvement
+
+The useful connection is structural, not a claim that disparate fields were historically unrelated. A frame history is literally a finite diagram of vector spaces with injective maps. Its admissible edits are order-preserving edits of that diagram. We use that identification to discover a construction that isolated gate edits miss.
+
+## 1. Persistence diagrams of inclusions become frame histories
+
+Let an acyclic event graph have a vertex for each scalar gate and immutable vertices for every register entrance, exit, retained-copy observation and target cut. Every register supplies directed edges between its successive occurrences. A vertex e carries a subspace F_e of a finite-dimensional vector space. The legal frame condition is exactly F_e <= F_f on every edge e -> f. A two-register gate is a shared vertex; its two histories must agree there.
+
+Restricted to a register chain, this is a persistence module with injective structure maps. A basis adapted to its flag decomposes it into coordinates with birth times. A jump of rank r means r births at that point. The compiler's paid histogram counts these jumps. Its recurrence moment charges a concave function of the number born together. Delaying births so they occur in a larger group can therefore improve cost, provided all shared-event constraints are respected.
+
+This is an identification of the finite linear objects, not an application of persistent-homology stability estimates. We do not assume that the entire branching diagram has an interval decomposition or that one common coordinate basis works for all frames. The explicit subspace updates below avoid both assumptions.
+
+Fix a nonzero linear functional lambda and H=ker(lambda). On a chain, F -> F intersect H is a sub-persistence module, and the exact sequence
+
+    0 -> F intersect H -> F -> lambda(F) -> 0
+
+shows that each affected space loses exactly one dimension. The quotient is either zero or the one-dimensional field. Thus intersecting a chosen time region with H modifies a concrete birth history by a rank-one change. The algorithm uses the actual spaces, not just their dimensions or a guessed barcode.
+
+## 2. Galois adjunction becomes a legality-closure algorithm
+
+For the inclusion j:H -> V, image and preimage of subspaces form an adjunction:
+
+    j(S) <= F  iff  S <= j^-1(F).
+
+The counit in the ambient space is F intersect H. This is the same meet operation that appears in the modular subspace lattice underlying type-A flag geometry. It is monotone and deflationary. Its dual operation is adding a fixed line, a monotone inflationary operation. These order properties give a concrete compiler transformation.
+
+Sufficient contraction theorem. Start from any legal frame diagram with its immutable vertices. Choose a set S of mutable vertices satisfying, for every edge e -> f with f in S and e outside S, F_e <= H. Replace F_e by F_e intersect H for e in S and leave all other vertices unchanged. The resulting diagram is legal and has identical immutable boundaries.
+
+Proof, edge by edge. If both vertices are changed, intersection is monotone. If neither changes, use the original inclusion. If only the source changes, it only shrinks, so inclusion survives. If only the destination changes, the stated boundary condition gives F_e <= F_f intersect H. These are all cases. No unknown extension, common apartment or unproved gadget appears.
+
+Construct S from a seed by following predecessor edges. Whenever a predecessor's frame is not contained in H, include it as well. Stop with failure if this would change an immutable vertex. Otherwise the resulting finite closure satisfies the theorem. It is the smallest predecessor closure for this prescribed uniform-intersection action after vertices already inside H are ignored. Minimal closure does not imply optimal cost. A cost bound is computed from every affected register edge, including internal edges when codimension exceeds one.
+
+The dual sufficient theorem adds a fixed line L on a successor closure, stopping when a successor already contains L. The same four-edge-case proof applies. This gives a second family of checked moves, even though the selected witness uses only contractions.
+
+## Operator correctness is a separate obligation
+
+Only frames change; the full scalar instructions, order, cuts, preconditioner, compensation and literal inverse cleanup are held fixed. The scalar endpoint therefore stays the same on arbitrary inputs. Changing frames changes the physical lifted word and its phases, however. The old phase receipt cannot be reused wholesale. The actual construction rebuilds changed Clifford phases, wrappers and local programs, audits all728 columns in both orientations, then rebuilds every global owner chart and the complete finite invoice. This is the necessary bridge from the order-theoretic theorem to the retained compiler interface.
+
+## Concrete witness and universal moment improvement
+
+The frozen input is the prior static44/PR534/syndrome word. Single-event frame changes over999 present frames, followed by whole equal-frame-plateau changes, found no improvement. The closure search instead selected eight hyperplane waves, using functionals33,33,39,39,192,192,198,198 on F2^9. Each wave changes8 to10 scalar-event frames together; no scalar instruction is deleted or reordered.
+
+Every wave changes the complete local paid histogram by
+
+    2 e1 - 2 e2 - 2 e3 + 2 e4.
+
+All eight give16 copies of the same replacement. Rank mass, helper widths and complete-call signatures remain unchanged. The pair (2,3) is a doubly stochastic averaging of (1,4): use the matrix with diagonal2/3 and off-diagonal1/3. Strict concavity therefore proves
+
+    1^a + 4^a < 2^a + 3^a  for every 0<a<1.
+
+This proves a strict paid-moment gain for every relevant recurrence exponent, not just at the optimizer's floating score. Child count is unchanged, so the count-proportional fallback term is unchanged too. Each complete call uses this improved local word; the actual owner map is then reconstructed with the new frames. The global delta is72 times the local delta.
+
+The constructor checks every actual finite subspace chain and unchanged boundary. Eight omission controls restore one necessary frame change in each wave and are rejected by the chain checker. An independent worker reconstructs the edge model and verifies every wave's exact histogram delta. Final physical verification remains essential and is performed by the package's replay.
+
+## Bounded searches and sources
+
+The single-functional search examined31,627,350 seed/direction candidates across the improvement sequence, including the final pass with no further gain. The extension with two simultaneous functionals examined7,381,812 seed cases, of which1,920 closures were feasible; it found no further paid gain. These are finite neighborhood results, not an impossibility theorem or a global optimum.
+
+Source structures inspected:
+
+- Mathlib Algebra/Module/Submodule/Map.lean, gc_map_comap: the exact image/preimage adjunction.
+- Mathlib LinearAlgebra/FiniteDimensional/Lemmas.lean, finrank_sup_add_finrank_inf_eq: the dimension arithmetic of the subspace lattice.
+- [Parallel computation of interval bases for persistence module decomposition](https://arxiv.org/abs/2106.11884): persistence modules as type-A quiver representations, and flag-based computation. Our application only uses the elementary finite injective-chain specialization proved above.
+- The registered source catalog and typed DAG were queried for submodule meets, map/comap adjunctions, filtrations and kernels. Results and source hashes are retained. No fresh Lean compilation is claimed.
+
+OpenAI's coarse-assembly Persistence.lean was inspected, but its direct-limit nonvanishing theorem is not the needed finite flag theorem and is not used as a spurious citation. The source search led to the actual order/subspace structures instead of forcing a semantic filename match.
diff --git a/research/contextual-provider-pooling/docs/MIXTURE-SOURCE-PINS.json b/research/contextual-provider-pooling/docs/MIXTURE-SOURCE-PINS.json
new file mode 100644
index 0000000000..45d6cd835f
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/MIXTURE-SOURCE-PINS.json
@@ -0,0 +1,14 @@
+[
+  {
+    "path": "D:\\proof\\external\\openai-math\\lean\\OAI\\InformationTheory\\AmplitudeDamping\\BlockFactors.lean",
+    "sha256": "387bc9814014e15722aff05e772003725af068d08567547ff93181be8335509c"
+  },
+  {
+    "path": "D:\\proof\\external\\openai-math\\lean\\OAI\\Topology\\CoarseAssembly\\ProjectionBlocks.lean",
+    "sha256": "7cac1e035c22b0fbee15564f71daf60204f60ff7d42d3fb4ee865582102dd84b"
+  },
+  {
+    "path": "D:\\proof\\external\\openai-math\\lean\\OAI\\Algebra\\Determinantal\\RankTransfer.lean",
+    "sha256": "d4f57cdb1280f933d60ae3b40ed5a215172d82b28916e66de1e5e821186f2713"
+  }
+]
diff --git a/research/contextual-provider-pooling/docs/NESTED-PROMOTION-AND-MIXTURE.md b/research/contextual-provider-pooling/docs/NESTED-PROMOTION-AND-MIXTURE.md
new file mode 100644
index 0000000000..cfbde5fc65
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/NESTED-PROMOTION-AND-MIXTURE.md
@@ -0,0 +1,33 @@
+# Nested prefix promotion and supplier substitution
+
+## Exact prefix transformation
+Let the commuting correction prefix consist of gates D_d <- D_d + a_dp P_p, with donor and pivot register sets disjoint. Give each pivot p an entrance frame F_p containing its old entrance E_p. Require F_p to lie in the first downstream frame of p and of every donor with a_dp != 0. For each donor, require the frames of its incoming gates to form a containment chain above its previous frame. Order these gates by that chain (a global increasing-dimension order works when all the requirements hold), and regenerate literal background cleanup.
+
+The scalar prefix is unchanged: the product is I+sum a_dp e_d e_p^T because every cross product vanishes. Hence its entire arbitrary-dirt transfer is unchanged, not merely its clean response. The only changed paid edges are the actually reconstructed donor and pivot frame chains. Exact phase/normalization and physical owner compatibility still require the ordinary finite pipeline. This is a sufficient compiler transformation, not an assertion that every promotion is profitable.
+
+## Complete bounded census on epoch14
+The frozen input is recorded in NESTED-PIVOT-CENSUS.json. For each of 56 pivots we intersected its first downstream frame with the first frames of all donors that it writes. We enumerated every extension of its original rank-four entrance within that intersection. Twelve four-pivot groups each have exactly one rank-five extension per pivot; two groups have none. There is no rank-six option. Because each available quotient has dimension at most one, this enumeration is complete for this fixed prefix and downstream word. All 194 legal group assignments were enumerated; no claim extends this census to changed donor bases or changed downstream gates.
+
+For j=0,1,2,3,4 promotions within an eligible group the local histogram changes are respectively
+  0;
+  7[r1]-4[r2];
+  10[r1]-6[r2];
+  10[r1]-7[r2]-[r3]+[r4];
+  8[r1]-8[r2]-4[r3]+4[r4].
+Each promotion changes one width-five helper to width four. These signatures are identical in all twelve eligible groups.
+
+At any paid exponent 0<p<1, every partial group has strictly larger moment than the mixture j/4 of the fully promoted group and 1-j/4 of the original group, at the same mean width inventory. To prove this, subtract that mixture. For j=1, the positive ranks are (3,1,1,1,1,1), the negative ranks are (4,2,2,0,0,0). For j=2 they are (3,3,1,1,1,1,1,1) and (4,4,2,2,0,0,0,0). For j=3 they are (3,3,1,1,1,1) and (4,4,2,0,0,0). In every case the negative list majorizes the positive list, with equal total rank. Strict concavity of x^p proves the claim. This supports whole-group mixtures in the fractional stock problem; it does not replace an actual timed integer owner construction.
+
+## Complete-call mixture theorem
+Take any sequence of full normalized supplier calls, selected from a finite registry. Suppose all variants implement the same required data transformation in each orientation. Each selected variant must independently satisfy the arbitrary-dirt local identity and have its exact phase recipes, entrance normalization, output adapters, and scalar ledger bound to its immutable source.
+
+A helper endpoint on a borrowed owner is the prescribed residual C_[w] on its selected subspace, tensor identity on the restored spectator coordinates; it is not the identity on the whole owner. For each call require distinct whole owners for distinct roles, actual per-role width and chart matching that selected variant, and every borrowed owner idle for the complete call. Across calls require an exact disjoint decomposition of each owner's pending coordinate axes into the hosted residual subspaces and its explicitly executed remainder. Require all private work erased at the end of every complete call.
+
+Under these conditions the registry may vary call by call. Each call's arbitrary-dirt identity applies to the actual state left by previous calls. Its data endpoint is the required data gate. Every spectator is restored, while the selected residual acts only on the admitted pending subspace. Owner-wise these disjoint factors commute and multiply with the explicit remainder to the original pending operator. Induction in actual execution order therefore proves the full global data and owner endpoint. The proof applies separately to both required orientations. If the inverse program of the total composition is needed, call order reverses as well as local inversion; one may not simply invert each call in the same order.
+
+The paid profile is the sum of actual selected local profiles plus actual owner remainders. Row and prefix invoices must bound both variants, every invocation, every bridge, and all routing/normalization primitives. No gains are added numerically. The ordinary exact moment and outer assembly compute the resulting kappa.
+
+## Source connections, novelty and scope
+We read OAI.InformationTheory.AmplitudeDamping.BlockFactors.blockProjection_range and blockInjection_isometry: a proved projection-range condition gives an actual reconstructing injection, and the injection has an exact left adjoint inverse. This motivates demanding full owner charts and spectator identities rather than matching dimensions alone. We also read OAI.Topology.CoarseAssembly.ProjectionBlocks.blockOperator_adjoint and flattenOperator_eq_conjugation: blockwise adjoints and explicit flattening preserve actual operators. Their finite-dimensional specialization motivates the independent orientation and disjoint-copy bookkeeping above. These statements are structural analogues; the present circuit lemma is proved explicitly here and does not import these Lean files as a formal certificate.
+
+OAI.Algebra.Determinantal.RankTransfer.exists_matrix_right_inverse was also examined. Its surjectivity hypothesis supplies an actual right-inverse matrix, but no new such coordinate transformation with a profitable paid bill was found. We do not count it as an achieved numerical technique. Likewise, this lane's complete promotion census found no improvement beyond whole-group mixtures; the positive mixture is the resource lane's construction, extending PR558 and the prior finite-copy pooling work.
diff --git a/research/contextual-provider-pooling/docs/OAI-BLOCK-NORM.md b/research/contextual-provider-pooling/docs/OAI-BLOCK-NORM.md
new file mode 100644
index 0000000000..5b01bb8e5f
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/OAI-BLOCK-NORM.md
@@ -0,0 +1,9 @@
+# OpenAI block-operator transfer and scope
+
+Read source: OAI/Topology/CoarseAssembly/BlockOperators.lean, SHA256 0cc11714ca746be1e1bba6925731221d8f81138d48445714a50f7676675a6d52. Theorems blockLinear_norm_le and blockOperator_norm_le prove that an orthogonal direct sum of operators each bounded byC is bounded byC, independently of the number of blocks. partitionCompression_norm_le in the adjacent PartitionCompression file proves a related partition-of-unity compression estimate; it does not supply free recursive work.
+
+Sufficient transfer: fix a finite partition of live data families into copied original controllers. At each complete local-call boundary, suppose the exact normalized endpoint has its data shear entirely inside the active copy, and acts on every borrowed family separately by its exact unitary residual/spectator map; shared private work is zero. Then each boundary operator is block diagonal in the copy partition. Products remain block diagonal even when the scalar interior used another copy as temporary helper. If each copy has at mostK data shears andJ factor-two bridges, with all other boundary factors unitary, every complete boundary prefix has norm at most2^(K+J), not2^(q*(K+J)). This follows by submultiplicativity within each block and the cited block-sum norm bound. A partial active call is additionally bounded by the maximum actual local scalar-prefix envelope, with its own coefficient-work and input conversion charges. Boundary semantics must be proved first: zeroing dirty helper scalars alone is insufficient.
+
+This can avoid a prefix penalty linear in the copy count. It is not presently counted as extra kappa; the candidate may retain the more conservative full-call charge when that already fits. The actual current construction must still pay total operations, storage, tables, routing and every child. Approximation or operator-norm closeness cannot replace the exact column/phase identity.
+
+The block invariant is a reusable sufficient theorem, not a claim that the external source already proves this multiplication controller. No fresh Lean certification is claimed. We will not use the stronger bound in the final invoice without auditing its boundary partition conditions.
diff --git a/research/contextual-provider-pooling/docs/PR-LINEAGE.md b/research/contextual-provider-pooling/docs/PR-LINEAGE.md
new file mode 100644
index 0000000000..48a59836b2
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/PR-LINEAGE.md
@@ -0,0 +1,17 @@
+# Pinned upstream lineage
+
+Snapshot through PR547. Exact changed heads and read scope are in PUBLIC-PINS.json. The refreshed conversations cover89 recently created/updated PRs with zero fetch errors; every changed source package in that snapshot was acquired, with no cold revalidation of unchanged external operators.
+
+Direct numerical and source dependencies:
+
+- [PR543](https://github.com/CrocSwap/integer-mult-bounds/pull/543), head2065fe4f72a914d907f1046603f5a36f17018535: R420 bit supplier, its actual paid profile, finite invoice and H1-H5 interleaved source-write argument. The original word's content hash and source file hash are retained in inputs/PR543-EXPECTED.json. Physical operator admission is cited, not rerun here.
+- [PR547](https://github.com/CrocSwap/integer-mult-bounds/pull/547), head4e25588aac914732bde23ab0bd6628d25a3df0db: exact two-supplier assembly pattern and comparison kappa. This package replaces its complex operand with a freshly reconstructed improved supplier.
+- [PR534](https://github.com/CrocSwap/integer-mult-bounds/pull/534): source of the477 previously accepted frame lifts, preserved in the construction chain.
+- [PR535](https://github.com/CrocSwap/integer-mult-bounds/pull/535) and [PR531](https://github.com/CrocSwap/integer-mult-bounds/pull/531): source complex word,parent controller,phase/local verification,complete-owner admission and invoice implementations.
+- [PR541](https://github.com/CrocSwap/integer-mult-bounds/pull/541): predecessor preload/curvature and static44 work. The prior delivered wave input includes its subsequent frame/syndrome/owner composition; we do not attribute those new collective contractions to PR541.
+- [PR510](https://github.com/CrocSwap/integer-mult-bounds/pull/510), [PR503](https://github.com/CrocSwap/integer-mult-bounds/pull/503), [PR493](https://github.com/CrocSwap/integer-mult-bounds/pull/493): retained nine-stage bit and mutable-carrier ancestry.
+- [PR484](https://github.com/CrocSwap/integer-mult-bounds/pull/484), [PR463](https://github.com/CrocSwap/integer-mult-bounds/pull/463), [PR444](https://github.com/CrocSwap/integer-mult-bounds/pull/444), [PR442](https://github.com/CrocSwap/integer-mult-bounds/pull/442), [PR386](https://github.com/CrocSwap/integer-mult-bounds/pull/386): retained exact realization,Clifford/local and whole-owner interfaces.
+
+Read but not added as independent gains: PR542 sliced bit frames;PR544 selective/static44 composition;PR546 prior composition;PR545 punctured111 draft bit supplier;updated PR540 literal-invocation Lean scope. The stronger PR545 bit saving cannot move the minimum while this complex supplier binds, so the existing R420 conditional route is sufficient. PR539's sharper bad-class charge is not needed or used for this bound.
+
+OpenAI/math,Mathlib and the registered project DAG supplied structural research references. Each lane records the actual declarations/files or primary literature it used. Source-only inspection is labelled as such; no Lean-import or kernel-check claim is inferred from a matching theorem name.
diff --git a/research/contextual-provider-pooling/docs/PR552-PREVIOUS-README.md b/research/contextual-provider-pooling/docs/PR552-PREVIOUS-README.md
new file mode 100644
index 0000000000..f4c470edd1
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/PR552-PREVIOUS-README.md
@@ -0,0 +1,62 @@
+# Collective frame contraction and weighted response decoding
+
+Conditional **kappa = 0.001591968902833346** = 795984451416673 / 500000000000000000.
+This is **0.07906544% above PR547**, and improves the previous delivered0.001590591090759927. The public snapshot is frozen through PR547. The new contribution is a physically admitted collective frame transformation and a sparse-response rewrite family, composed with PR543's stronger bit supplier.
+
+## Concrete improvement
+
+The old construction was locally stuck under single-event frame choices and whole equal-frame plateaus. Interpret its frame histories as coupled persistence flags. Intersect a predecessor-closed collection of events with a hyperplane, leaving all observation and boundary frames fixed. Eight such collective waves change8 to10 event frames at a time. They preserve the scalar program but alter the paid rank distribution.
+
+Every wave replaces two copies of the pair of child ranks(2,3) by(1,4). Across all eight, the exact local delta is
+
+    16(e1 - e2 - e3 + e4).
+
+Strict concavity proves a better moment for every exponent in(0,1), with unchanged rank mass and child count. No floating optimization score is accepted as evidence. The new phases, local programs, global physical charts and scalar invoice are all reconstructed.
+
+Next, twelve exact weighted-coset source rewrites reduce the cold-dirt compensation table from9,756 to9,132 additions, saving624. The complete emitted local program shrinks from22,107 to21,483 events in each orientation. This second change preserves the paid histogram: its saving is scalar complexity, not an additional kappa increase.
+
+The exact final complex saving is b=0.001594507308884431019637. The cited PR543 bit saving is c=0.001653826988146798944268, so the complex side binds. Complete profiles, not separately estimated gains, enter both rational moment engines and all47 strict outer inequalities.
+
+## Eight cross-field structures, with their actual roles
+
+| Worker | Connection | What transfers here |
+|---|---|---|
+| Root | Persistent vector-space flags <-> register-frame histories | A birth-time picture exposes collective changes missed by isolated event edits; the selected eight waves improve the paid moment. |
+| Root | Galois adjunctions/subspace-lattice geometry <-> compiler legality closure | Meet with a hyperplane gives an exact predecessor-closure theorem with fixed boundaries; no global common-basis assumption. |
+| Elimination | Electrical Kron/Schur elimination <-> eliminating internal register versions | A sufficient paid-elimination theorem and independent exact boundary-transfer audit; direct helper-removal screens found no new gain. |
+| Elimination | Quiver path algebra <-> linear circuit transfer | Finite path sums verify the protected endpoint and all twelve source-error witnesses using an independent exact-dyadic C++ implementation. |
+| Response | State-space impulse response <-> prefix/suffix rank-one transfer updates | Supplies exact response updates for source changes; the separate minimal-realization search found no additional merge. |
+| Response | Coding-theory coset representatives <-> sparse cold-dirt compensation | Twelve checked rewrites save624 scalar additions, with all protected columns preserved. |
+| Resource | Integral space-time circulation <-> physical whole-owner schedules | Reuses the explicit feasible owner map and rebuilds its charts for the new provider; stage/mixed-provider searches yielded no extra gain. |
+| Resource | Majorization/thermomajorization <-> paid child-rank transport | An explicit doubly stochastic2x2 certificate proves the selected(2,3)->(1,4) change improves every relevant moment. |
+
+These are precise structural transfers with constructive hypotheses, not a claim that everything in one subject transfers automatically. The underlying mathematics is established; the new result is this compatible construction and application. Negative searches and their finite scope are retained. Detailed proofs and exact source hashes are in docs/, response/ and complex-global/.
+
+## Replay
+
+Requirements: Python3.11+ and NumPy. No network, Lean, optimizer, GPU or C++ compiler is needed for the mandatory replay. Run with assertions enabled:
+
+    python -B verify.py --work ../fresh-wavefront-run
+
+The output directory must be new and outside this package. The verifier validates the LF-aware manifest, normalizes a scratch copy, reconstructs the complex word from primitive inputs through the complete static44/frame/syndrome/wave/coset chain, runs the actual local phase and all-column checks, rebuilds the complete physical owner controller, recounts the invoice, and certifies both moment endpoints plus the outer assembly. EXPECTED.json pins the identities and result. The unchanged PR543 bit operator is a cited dependency; this package checks its numerical profile and invoice conditions without duplicating its cold physical replay.
+
+Checks include728 complex columns in both orientations,44 static-response omission controls,23 adapter recipes,all2,929 directed phase edges (199 fresh for the changed wave frames),11 local mutations,2,972 full73-column owner charts,seven controller mutations,eight new wave-omission controls and47 outer constraints with four invalid-parameter/grid controls. A separate independent exact-dyadic C++ path/Schur audit checks48,832 protected transfer entries and8,736 entries in the twelve source-error witnesses; its source, input and receipt are supplied as an optional audit artifact.
+
+Generated new word constructors and the complex launcher fix gzip level,timestamp and OS byte. Text files, including headers and hashes, are LF-normalized in the manifest. The release is tested from an all-text CRLF copy; the upload batches are checked by byte-for-byte reassembly.
+
+## Numerical and physical data
+
+- Local histogram: {1:2300,2:440,3:472,4:184,5:56,6:56,8:8}.
+- Global histogram: {1:165600,2:32128,3:35907,4:13248,5:4032,6:4032,7:208,8:576,39:1,48:1660}.
+- Complex live stock7168;physical7682;deficit2560;36,288 helper roles across72 calls.
+- Measured complex prefix225 is below charged512;row16467 is below retained20161.
+- Final canonical complex word hash371638c4f444515caa0586fa7bac838fc7a7c01c4f6110caccf1d4c4f90453b1.
+- Complete template hash1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0.
+
+## Scope and direct lineage
+
+This is a conditional finite witness under retained all-size realization,common-label/mutable-basis,complete-call hosting,precision/tape and analytic-transfer interfaces. PR543's interleaved phase-B source updates retain its explicit H1-H5 interface argument. No unconditional multiplication theorem, fresh Lean certification, global optimizer guarantee or measured end-to-end multiplication speedup is claimed. Restoring scalar helper dirt does not erase the complete helper's residual Q action.
+
+PR543 supplies the unchanged R420 bit supplier;PR547 supplies the latest two-supplier arithmetic composition pattern. PR544/546 supply current comparison compositions;PR545's larger draft bit bound was inspected but would not increase this complex-bound kappa. PR541 published the preceding preload/static44 work. PR534 supplies the earlier frame assignment;PR535 and531 supply the complex construction,transport,phase,owner and invoice machinery. The inherited bit lineage includes PR510/503/493, and the compiler/physical lineage includes PR484/463/444/442/386. Detailed attribution and source links are in docs/PR-LINEAGE.md; upstream notices and licenses are preserved.
+
+No files are published by these scripts. All submission actions remain manual.
diff --git a/research/contextual-provider-pooling/docs/PRIOR-TN27-README.md b/research/contextual-provider-pooling/docs/PRIOR-TN27-README.md
new file mode 100644
index 0000000000..71aaed09f4
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/PRIOR-TN27-README.md
@@ -0,0 +1,29 @@
+# Five-copy pooling and coherent epoch reduction
+
+Conditional kappa = **0.001591975256487475**, compared with the pinned PR551/552 value0.001591968902833346. The gain is0.0003991067 percent. This is a real but small numerical improvement, not a claimed large breakthrough.
+
+Five disjoint copies of the complete complex controller keep ambient dimension73 and pool five width9 helper roles into one pending rank48 region. Five rank39 remainders become four rank48 remainders and one rank3 remainder. All other costs are multiplied by five before this exact substitution. Strict concavity makes the normalized recurrence moment strictly smaller. These are five independent eight-replica data banks, not a40-replica within-block geometry.
+
+A separate coherent epoch basis rewrite removes14 forward scalar additions and14 cleanup additions while retaining the paid rank histogram. It is included in the physically rebuilt provider; its scalar saving is not counted as another kappa gain. The earlier eight collective frame waves and twelve weighted-coset rewrites are rebuilt from their primitive inputs.
+
+The complex saving is0.001594513682816650764990; the cited PR555 bit saving is0.001733052823330162099157. The complex side binds. PR555 supplies headroom, not the numerical gain over our previous result.
+
+## Replay
+
+Python3.11+ and NumPy, with assertions enabled:
+
+    python -B verify.py --work ../fresh-pooled-clone-run
+
+Use a new output directory outside this package. No network, optimizer, GPU, Lean or C++ compiler is required for the mandatory replay. The optional epoch/audit_epoch.cpp is an independent exact-dyadic endpoint auditor. The mandatory local physical replay checks the changed provider in both orientations including its dirty helpers and cleared private workspace.
+
+The replay validates the LF-aware manifest, reconstructs the complete changed complex provider, builds the five-copy parent, independently checks the literal parent lift and mutation controls, emits and independently audits181440 whole-helper ownership assignments across360 calls, recounts every invoice term, and certifies both supplier endpoints with two exact rational engines plus all47 strict assembly inequalities. The unchanged PR555 bit operator is cited rather than cold-reverified.
+
+The measured prefix801 is below charged1024; physical row17495 is below the retained20161 allowance. Live stock35840, physical36354, deficit12800. All514 private registers are charged; their reuse follows cleared-work receipts. Nothing relies on an uncharged extra controller or a free change of ambient dimension.
+
+## Scope and source history
+
+This remains a conditional finite-witness result under the inherited all-size realization, common-label/mutable-basis, complete-call hosting, precision/tape and analytic-transfer interfaces, including PR555's111-port and H1-H5 interfaces. No unconditional integer-multiplication theorem or new Lean certification is asserted.
+
+The files in docs/ and evidence/ inherited from PR552 describe earlier stages, with their original numerical values retained for provenance. EXPECTED.json and the fresh replay output determine this release's claim. Full current proof and experiment notes are in complex-global/RESOURCE-PROOF.md, complex-global/RESOURCE-RESEARCH.md, docs/FIVEFOLD-DIRECT-SUM-REVIEW.md and epoch/EPOCH-PROOF.md. Source attribution and notices remain intact. The frozen public snapshot ends at PR555.
+
+Nothing is published by any script. Submission is manual.
diff --git a/research/contextual-provider-pooling/docs/PUBLIC-PINS.json b/research/contextual-provider-pooling/docs/PUBLIC-PINS.json
new file mode 100644
index 0000000000..13fd4ac4bf
--- /dev/null
+++ b/research/contextual-provider-pooling/docs/PUBLIC-PINS.json
@@ -0,0 +1,447 @@
+[
+  {
+    "pr": 547,
+    "head": "4e25588aac914732bde23ab0bd6628d25a3df0db",
+    "changed_since_previous_round": true
+  },
+  {
+    "pr": 546,
+    "head": "77833ffa1110c6645f5d0866ebf41510ee3d27a3",
+    "changed_since_previous_round": true
+  },
+  {
+    "pr": 545,
+    "head": "376426f3b2b26ab430d10baf16bbd9ff42990a7c",
+    "changed_since_previous_round": true
+  },
+  {
+    "pr": 544,
+    "head": "4858bb38da10cd8a1cd25ef85e7c14f4e2b529dd",
+    "changed_since_previous_round": true
+  },
+  {
+    "pr": 543,
+    "head": "2065fe4f72a914d907f1046603f5a36f17018535",
+    "changed_since_previous_round": true
+  },
+  {
+    "pr": 542,
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+    "changed_since_previous_round": true
+  },
+  {
+    "pr": 541,
+    "head": "ec6a1eda73edd2e560d45c792264853921b96738",
+    "changed_since_previous_round": true
+  },
+  {
+    "pr": 540,
+    "head": "c4b1560a569f54064608bf88440f9e492c03fba3",
+    "changed_since_previous_round": true
+  },
+  {
+    "pr": 539,
+    "head": "915ca69db7f98c70b97ce96e1fcc96818517584c",
+    "changed_since_previous_round": false
+  },
+  {
+    "pr": 538,
+    "head": "a1460516226555dd375d9adb82a8e1dcbfe1ca79",
+    "changed_since_previous_round": false
+  },
+  {
+    "pr": 537,
+    "head": "39958faec4fd7e7958ca81f6cffcf70ce74c5e89",
+    "changed_since_previous_round": false
+  },
+  {
+    "pr": 536,
+    "head": "71a7ed7a95776810fede6f583885b7faf5d5ff2a",
+    "changed_since_previous_round": false
+  },
+  {
+    "pr": 535,
+    "head": "8b758a103915179322766bed5798f9b6e7198011",
+    "changed_since_previous_round": false
+  },
+  {
+    "pr": 534,
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+    "changed_since_previous_round": false
+  },
+  {
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+    "changed_since_previous_round": false
+  },
+  {
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+    "changed_since_previous_round": false
+  },
+  {
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+    "changed_since_previous_round": false
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+  {
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+  {
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+    "changed_since_previous_round": false
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+    "changed_since_previous_round": false
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+  {
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+  {
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+  {
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+  },
+  {
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+    "changed_since_previous_round": false
+  },
+  {
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+    "changed_since_previous_round": false
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+]
diff --git a/research/contextual-provider-pooling/engines/base_two_moment.py b/research/contextual-provider-pooling/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/contextual-provider-pooling/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/contextual-provider-pooling/engines/moment.py b/research/contextual-provider-pooling/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/contextual-provider-pooling/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/contextual-provider-pooling/engines/outer.py b/research/contextual-provider-pooling/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/contextual-provider-pooling/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/contextual-provider-pooling/epoch/EPOCH-PROOF.md b/research/contextual-provider-pooling/epoch/EPOCH-PROOF.md
new file mode 100644
index 0000000000..e4388f1722
--- /dev/null
+++ b/research/contextual-provider-pooling/epoch/EPOCH-PROOF.md
@@ -0,0 +1,67 @@
+# Exact carrier basis change across one read-only epoch
+
+This constructor replaces the A epoch using helpers r=571 and s=585 by an
+invertible change of carrier coordinates. Both helpers enter in frame [480].
+Neither is written during the original epoch. Set r' = r+s at frame [480],
+replace each read t += q*r by t += q*r' - q*s, combine only commuting shears at
+the identical frame, and finally restore r by r' -= s at frame [480].
+
+For each replaced read, q*(r+s)-q*s=q*r on arbitrary register values. Since
+neither carrier is written inside the epoch, this identity holds at every use.
+Shears on distinct destinations/sources commute precisely when neither writes
+the other's read source; equal-source/equal-destination shears then combine by
+coefficient addition. The constructor checks these dependencies. The final
+inverse restores both carrier values. Consequently the entire epoch has the
+same linear map on every input coordinate, including all arbitrary helper dirt.
+
+The changed A has 14 fewer gates, and its literal reverse background cleanup
+has 14 fewer gates. B, cut, precondition, target levels, centre interfaces,
+entrances and helper widths are unchanged. Both boundary basis operations are
+included; neither is treated as free. The paid rank histogram is exactly
+unchanged, so this change is a scalar-circuit simplification, not a separate
+recurrence-moment gain. Any numerical improvement in the combined submission
+must be attributed to its actual separately priced controller/resource change.
+
+The frozen source uses 728 registers (112 source ports, 112 target ports, 504
+helpers). The standalone C++ audit compares every one of the 529,984 endpoint
+coefficients after A+cut+B using arbitrary-precision dyadic rational arithmetic.
+It also checks two controls: omitting the terminal inverse changes 9 coefficients
+(4 target coefficients), and omitting one transformed reader changes 18
+coefficients (8 target coefficients). These controls are not vacuous. Fresh
+phase, adapter and full physical supplier admission belong to the enclosing
+submission's verifier.
+
+## Replay
+
+The constructor requires the checked tn25 weighted word and the inherited
+gk_word.py/gk_common.py directory. It accepts only the frozen canonical source
+hash and produces the frozen canonical output hash; compression bytes are
+recorded but are not a cross-version identity condition.
+
+    python -B build_epoch14.py --input WEIGHTED-WORD.json.gz --gk-dir GK_DIR --out NEW_DIRECTORY
+    c++ -O3 -std=c++20 -I BOOST_INCLUDE audit_epoch.cpp -o audit_epoch
+    audit_epoch NEW_DIRECTORY/AUDIT-INPUT.txt NEW_DIRECTORY/SCALAR-AUDIT.json
+
+Compile without NDEBUG. EPOCH-SELECTION.json resides beside the constructor;
+--selection can explicitly point to it. No discovery optimizer is used on replay.
+
+## Research scope
+
+Before selecting this exact rewrite, the lane screened 128 paid two-delivery
+windows, 1,052 coherent maximal read-only epochs (966 frame-legal), and 22,394
+bounded matched-producer/reader conjugations (14,520 legal). The last family
+also allowed omission of an inverse only when its destination had an exactly
+zero target suffix response. None gave a direct paid moment gain. Twelve
+alternating lower-join/upper-meet sweeps on the neutral epoch presentations also
+gave no paid gain. The broad generalized retiming variants were interrupted
+before completion and are not included in the completed census. A separate
+same-entrance full-lifetime warm-pair compatibility census was empty.
+
+The construction is an explicit finite holographic gauge identity: adjacent
+inverse basis maps cancel. It was motivated by the finite PEPS contraction
+representation in the inspected OpenAI TensorNetwork/VectorColumn source and
+the generalized Holant perspective, but no external source proves this
+register/frame/dirty-cleanup implementation automatically. The elementary proof
+above and exact supplier checks provide that transfer. Prior two-circuit
+representative screens are not claimed as new work or numerical ingredients.
+
diff --git a/research/contextual-provider-pooling/epoch/EPOCH-SELECTION.json b/research/contextual-provider-pooling/epoch/EPOCH-SELECTION.json
new file mode 100644
index 0000000000..c074b9af05
--- /dev/null
+++ b/research/contextual-provider-pooling/epoch/EPOCH-SELECTION.json
@@ -0,0 +1,22 @@
+{
+  "schema": "paid-epoch-shear-v1",
+  "source_semantic_sha256": "58e469f7f96dc1a79380d430f176a5d448f81643e5a639f5b447929cf36474be",
+  "section": "A",
+  "first": 0,
+  "last": 2006,
+  "destination": 571,
+  "source": 585,
+  "numerator": 1,
+  "denominator": 1,
+  "lower": [
+    480
+  ],
+  "upper": [
+    480
+  ],
+  "commutation_window": 200,
+  "expected_A_delta": -14,
+  "expected_cleanup_delta": -14,
+  "expected_word_semantic_sha256": "7d3b66098cf0b74cbbdc42993f4366f22f8e63302a2626628e2f753c68338e4e",
+  "reference_gzip_sha256": "a90d1194116a6daffc827df417baf684814ccd0d6fcd6bf14a664dc664d176bf"
+}
diff --git a/research/contextual-provider-pooling/epoch/MANIFEST.json b/research/contextual-provider-pooling/epoch/MANIFEST.json
new file mode 100644
index 0000000000..ddb2c0dc24
--- /dev/null
+++ b/research/contextual-provider-pooling/epoch/MANIFEST.json
@@ -0,0 +1,7 @@
+{
+  "build_epoch14.py": "b997ada563a932679e60b9b6ac2ff1856e1e7dd68145b12c98393106a9071db4",
+  "EPOCH-SELECTION.json": "59031dbb42920f751f9693bcd105e14654b7ce8dbc363153b3bdeb77e2ff6c95",
+  "audit_epoch.cpp": "7e151b3942b989b65c8e0b9ce6cdd9a6be615338e705719be8bbc27f1b9eddea",
+  "EPOCH-PROOF.md": "825f307aa95553c3e37b515a2509f94826c022b07146c5fe04b9fe5b0eb01cff",
+  "SOURCES.json": "07e21b5a817f72fe990980da5931f135ca17f768b7ced834b464bc95f05cb969"
+}
diff --git a/research/contextual-provider-pooling/epoch/SOURCES.json b/research/contextual-provider-pooling/epoch/SOURCES.json
new file mode 100644
index 0000000000..ebeb0aa04a
--- /dev/null
+++ b/research/contextual-provider-pooling/epoch/SOURCES.json
@@ -0,0 +1,15 @@
+[
+  {
+    "name": "OpenAI finite tensor contraction",
+    "source": "external/openai-math/lean/OAI/MathematicalPhysics/TensorNetwork/VectorColumn.lean",
+    "sha256": "4358a60f9de48a8a8e14e18645831e4adc0c37e2f2d6b96b5d25f51a85283073",
+    "use": "OAI.PolynomialPEPS.PEPS.contract; finite sum-of-products representation; no gauge theorem asserted",
+    "verification": "Source inspection only; no Lean invocation or new kernel verification."
+  },
+  {
+    "name": "Normal Factor Graphs and Holographic Transformations",
+    "url": "https://arxiv.org/abs/1004.3833v3",
+    "authors": "Ali Al-Bashabsheh and Yongyi Mao",
+    "use": "Generalized Holant transformation motivation. Our sequential dirty-register theorem below is proved directly, not imported from this paper."
+  }
+]
diff --git a/research/contextual-provider-pooling/epoch/audit_epoch.cpp b/research/contextual-provider-pooling/epoch/audit_epoch.cpp
new file mode 100644
index 0000000000..b62536e8b3
--- /dev/null
+++ b/research/contextual-provider-pooling/epoch/audit_epoch.cpp
@@ -0,0 +1,7 @@
+#include<bits/stdc++.h>
+#include<boost/multiprecision/cpp_int.hpp>
+using namespace std;using boost::multiprecision::cpp_int;
+struct D{cpp_int n=0;int e=0;D(){}D(int x):n(x){}void norm(){if(n==0){e=0;return;}cpp_int a=n<0?-n:n;int k=min(e,(int)boost::multiprecision::lsb(a));n>>=k;e-=k;}D mul(long long a,long long b)const{assert(b>0&&(b&(b-1))==0);D z=*this;z.n*=a;z.e+=countr_zero((unsigned long long)b);z.norm();return z;}D operator+(D const&b)const{D z;z.e=max(e,b.e);z.n=(n<<(z.e-e))+(b.n<<(z.e-b.e));z.norm();return z;}bool operator==(D const&b)const{return n==b.n&&e==b.e;}};
+int main(int ac,char**av){if(ac!=3)return 2;ifstream in(av[1]);int n,V,runs;in>>n>>V>>runs;assert(n==728&&V==112&&runs==4);vector<vector<D>>base;vector<long long>diffs,targetdiffs;
+for(int run=0;run<runs;run++){vector<vector<D>>A(n,vector<D>(n));for(int i=0;i<n;i++)A[i][i]=D(1);int m;in>>m;for(int k=0;k<m;k++){int kind,t,s;long long a,b;in>>kind>>t>>s>>a>>b;assert(t>=0&&t<n);for(int j=0;j<n;j++)if(kind)A[t][j]=A[t][j].mul(a,b);else if(A[s][j].n!=0)A[t][j]=A[t][j]+A[s][j].mul(a,b);}if(run==0){base=move(A);continue;}long long diff=0,tdiff=0;for(int i=0;i<n;i++)for(int j=0;j<n;j++)if(!(base[i][j]==A[i][j])){diff++;tdiff+=i>=V&&i<2*V;}diffs.push_back(diff);targetdiffs.push_back(tdiff);if(run==1)assert(diff==0);else assert(diff>0);}
+ofstream out(av[2]);out<<"{\"status\":\"PASS\",\"initial_columns\":"<<n<<",\"output_rows\":"<<n<<",\"exact_coefficients_checked\":"<<n*n<<",\"arithmetic\":\"cpp_int dyadic rational\",\"controls\":[{\"name\":\"omit terminal inverse\",\"differing_coefficients\":"<<diffs[1]<<",\"differing_target_coefficients\":"<<targetdiffs[1]<<"},{\"name\":\"omit transformed reader\",\"differing_coefficients\":"<<diffs[2]<<",\"differing_target_coefficients\":"<<targetdiffs[2]<<"}]}\n";cout<<"PASS full endpoint and two nonvacuous controls"<<endl;}
diff --git a/research/contextual-provider-pooling/epoch/build_epoch14.py b/research/contextual-provider-pooling/epoch/build_epoch14.py
new file mode 100644
index 0000000000..f6b6733c63
--- /dev/null
+++ b/research/contextual-provider-pooling/epoch/build_epoch14.py
@@ -0,0 +1,88 @@
+"""Construct a source-pinned exact interval shear; no optimizer or network access."""
+from pathlib import Path
+from fractions import Fraction as Q
+import argparse,copy,gzip,hashlib,json,sys
+def canon(w):return json.dumps(w,sort_keys=True,separators=(',',':')).encode()
+def main():
+ ap=argparse.ArgumentParser()
+ ap.add_argument('--input',required=True);ap.add_argument('--gk-dir',required=True)
+ ap.add_argument('--out',required=True)
+ ap.add_argument('--selection',default=str(Path(__file__).with_name('EPOCH-SELECTION.json')))
+ a=ap.parse_args();out=Path(a.out)
+ if out.exists() and any(out.iterdir()):raise SystemExit('Output must be absent or empty.')
+ out.mkdir(parents=True,exist_ok=True)
+ sys.path.insert(0,a.gk_dir)
+ import gk_word as g,gk_common as gc
+ g.V=gc.V=112;g.DATA=gc.DATA=7168
+ w=json.loads(gzip.decompress(Path(a.input).read_bytes()))
+ sel=json.loads(Path(a.selection).read_text())
+ assert hashlib.sha256(canon(w)).hexdigest()==sel['source_semantic_sha256'],'source pin mismatch'
+ sec=sel['section'];lo=sel['first'];hi=sel['last'];r=sel['destination'];s=sel['source']
+ q=Q(sel['numerator'],sel['denominator']);L=sel['lower'];U=sel['upper']
+ assert sec=='A'and lo==0 and hi==len(w['A'])-1
+ assert r!=s and r not in w['centers']and s not in w['centers']
+ assert g.basis(w['start_extra'][str(r)])==g.basis(L)
+ assert g.basis(w['start_extra'][str(s)])==g.basis(L)
+ assert not any(e[1]in(r,s)for e in w[sec][lo:hi+1]),'epoch is not read-only'
+ def add(t,src,v,F):return['add',t,src,v.numerator,v.denominator,list(F)]
+ def simplify(seq):
+  result=[]
+  for e in seq:
+   merged=False
+   if e[0]=='add':
+    assert e[1]!=e[2]
+    for j in range(len(result)-1,max(-1,len(result)-sel['commutation_window']),-1):
+     old=result[j]
+     if old[0]!='add':
+      if old[1]in(e[1],e[2]):break
+      continue
+     if e[1:3]==old[1:3]and e[-1]==old[-1]:
+      v=Q(e[3],e[4])+Q(old[3],old[4])
+      if v:result[j]=add(e[1],e[2],v,e[-1])
+      else:result.pop(j)
+      merged=True;break
+     if e[1]==old[2]or e[2]==old[1]:break
+   if not merged:result.append(e)
+  return result
+ body=[]
+ for e in w[sec][lo:hi+1]:
+  body.append(e)
+  if e[0]=='add'and e[2]==r:body.append(add(e[1],s,-q*Q(e[3],e[4]),e[-1]))
+ body=simplify(body)
+ z=copy.deepcopy(w)
+ z[sec]=w[sec][:lo]+[add(r,s,q,L)]+body+[add(r,s,-q,U)]+w[sec][hi+1:]
+ z['cleanup']=[g.inverse(e,g.FULL)for e in reversed(z['A']+z['B'])if not 112<=e[1]<224]
+ assert len(z['A'])-len(w['A'])==sel['expected_A_delta']
+ assert len(z['cleanup'])-len(w['cleanup'])==sel['expected_cleanup_delta']
+ assert g.profile(z)==g.profile(w),'paid profile changed'
+ assert z['start_extra']==w['start_extra'],'entrances changed'
+ for e in z['A']+z['B']+z['cleanup']:
+  den=(Q(e[3],e[4])if e[0]=='add'else Q(e[2],e[3])).denominator
+  assert den>0 and den&(den-1)==0,'nondyadic gate'
+ raw=g.dump(z)
+ assert hashlib.sha256(canon(z)).hexdigest()==sel['expected_word_semantic_sha256'],'semantic output pin mismatch'
+ (out/'FULL-WORD.json.gz').write_bytes(raw)
+ # A single retained reader inside the changed basis is a concrete mutation.
+ reader=next(i for i,e in enumerate(z['A'])if 0<i<len(z['A'])-1 and e[0]=='add'and e[2]==r)
+ controls=[]
+ c=copy.deepcopy(z);del c['A'][-1];controls.append(c)
+ c=copy.deepcopy(z);del c['A'][reader];controls.append(c)
+ def enc(e):
+  if e[0]=='add':return f"0 {e[1]} {e[2]} {e[3]} {e[4]}"
+  return f"1 {e[1]} -1 {e[2]} {e[3]}"
+ with(out/'AUDIT-INPUT.txt').open('w',newline='\n')as f:
+  f.write('728 112 4\n')
+  for word in[w,z,*controls]:
+   seq=word['A']+word['cut']+word['B']
+   f.write(str(len(seq))+'\n'+'\n'.join(map(enc,seq))+'\n')
+ receipt=dict(status='constructed; run audit_epoch for exact all-column evidence',
+  source_semantic_sha256=sel['source_semantic_sha256'],word_sha256=hashlib.sha256(raw).hexdigest(),
+  word_semantic_sha256=hashlib.sha256(canon(z)).hexdigest(),local_profile=dict(sorted(g.profile(z).items())),
+  A_delta=-14,cleanup_delta=-14,total_scalar_delta=-28,helper_count=504,
+  controls=['omit terminal inverse','omit transformed reader'],reader_control_index=reader,
+  widths_unchanged=True,paid_profile_unchanged=True)
+ (out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+ print(json.dumps(receipt))
+if __name__=='__main__':main()
+
+
diff --git a/research/contextual-provider-pooling/evidence/CLONE-ASSEMBLY.json b/research/contextual-provider-pooling/evidence/CLONE-ASSEMBLY.json
new file mode 100644
index 0000000000..1e1fb3760d
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/CLONE-ASSEMBLY.json
@@ -0,0 +1,168 @@
+{
+  "status": "PASS_FIVE_COPY_EPOCH_COMPLEX_AND_CITED_P111_COMPOSITION",
+  "kappa": "63679010259499/40000000000000000",
+  "kappa_decimal": "0.001591975256487475",
+  "complex_lower": "159451368281665076499/100000000000000000000000",
+  "complex_decimal": "0.00159451368281665076499",
+  "bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "bit_decimal": "0.001733052823330162099157",
+  "binding": "complex",
+  "gain_over_frozen551_552_percent": "0.000399106673358501352298015135516672472586856512389105370116450",
+  "gain_over_prior_delivery_percent": "0.000399106673358501352298015135516672472586856512389105370116450",
+  "complex_template_sha256": "bd6d43a8e4280fd38af2ce8486a7548f3f1208ecd6a329868d50bcd426501b57",
+  "complex_owner_audit_sha256": "6d22ec5aefd5df6bbcb846b6ffabef543bf32d535bc9656a2a038cdd6eece935",
+  "complex_invoice_sha256": "c4d508734659de70394fe784931862506751747ee9027f95f943e4b915b40894",
+  "complex_profile": {
+    "1": 828000,
+    "2": 160640,
+    "3": 179536,
+    "4": 66240,
+    "5": 20160,
+    "6": 20160,
+    "7": 1040,
+    "8": 2880,
+    "48": 8304
+  },
+  "moments": [
+    {
+      "side": "bit",
+      "endpoint": "1733052823330162099157/1000000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-9207823553958041733747765376010565755944111/13479973333575319897333507543509815336818572211270286240551805124608",
+        "-4603911776979020866873882688005282877972055/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "-1707686990214702474933/2500000000000000000000000000000000000000000000",
+        "-6830737960858809899617/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "bit",
+      "endpoint": "866526411665081049579/500000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "34854900798887949611269523362405257423109855/13479973333575319897333507543509815336818572211270286240551805124608",
+        "1089215649965248425352172605075164294472183/421249166674228746791672110734681729275580381602196445017243910144"
+      ],
+      "base_two": [
+        "25856802039414385003867/10000000000000000000000000000000000000000000000",
+        "12928406019707192501991/5000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "complex",
+      "endpoint": "159451368281665076499/100000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-5778767081990597938780972558851366869969995/13479973333575319897333507543509815336818572211270286240551805124608",
+        "-2889383540995298969390486279425683434984997/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "-4286931315981268700541/10000000000000000000000000000000000000000000000",
+        "-2143460657990634350203/5000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "complex",
+      "endpoint": "1594513682816650764991/1000000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "17850023206560616357850600117615517971374623/6739986666787659948666753771754907668409286105635143120275902562304",
+        "35700046413121232715701200235231035942749247/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "26483758684381095079063/10000000000000000000000000000000000000000000000",
+        "26483768684381095079199/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "bootstrap": [
+    {
+      "exponent": "15920325337687510047452179679260853935146309005035823523568186583416812477902999/10000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "24811490478997586492683492572638414953690994964176476431813416583187522097001/10000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "5847857653970"
+    },
+    {
+      "exponent": "1594509726590544779723691498120370243480884442655324763833715015153364366814709012673579222411926825307856082039563479499/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "3956226105983670794819062978991529115557344675236166284984846635633185290987326420777588073174692143917960436520501/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "2300065966924823682"
+    },
+    {
+      "exponent": "159451367650839410508708609664777791396440305035663757723429501452135560714240949289704044792696808499917942364563328482811753808452792377343739527970347546805999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "630825665830740022053557132104559694964336242276570498547864439285759050710295955207303191500082057635436671517188246191547207622656260472029652453194001/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "904656673476786807169712"
+    },
+    {
+      "exponent": "15945136828065921618380959259541603595552762107305719227999114861959032988304530100890699086473178257177864768238206396425554496740424471497658259161306143418038782457413329008354278237968639308552882499/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "100586015563903912291888754547237892694280772000885138040967011695469899109300913526821742822135231761793603574445503259575528502341740838693856581961217542586670991645721762031360691447117501/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "355817488991538437690491837171"
+    },
+    {
+      "exponent": "1594513682816634724816674651845361253369118068193316973596144084879530640178343987644689779247451030884794774425635478903102054971756491594152524882912647163089825453250685029534051571533761835286705545885694405213298239070735805253932206708999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "16038577811665337987981640881931806683026403855915120469359821656012355310220752548969115205225574364521096897945028243508405847475117087352836910174546749314970465948428466238164713294454114305594786701760929264194746067793291001/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "139949319099885297892330504876059236"
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+    "dimension_above_kappa": "1996810972634366698348176282042486655844059364793253845146666955571476106216364785542234156211509038822327020862856843339832304487709154470632565488788461048798069746890934348955413131215662911402926606504963792234658761152094378336299413565378275579473221999445736057167970478495919497293894748899608971726612597943705001/2003189027365633301469263454355860260637438089799003584832272767440414046439926966099490927446683780502117905558003681783234743639484791534835678663396844118719692287913782151483451090801811605911530814926487953739244005345635656157913734016067786820736462611090630997023559365426746999919355283374668580040000000000000000"
+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Exact composition of the freshly rebuilt epoch14 supplier and five-copy pooled complete controller with the pinned PR555 published bit receipt. The unchanged bit operator is cited, not rebuilt in this package. Inherited all-size compiler, common-label/mutable-source, hosting, precision/tape and analytic interfaces remain conditional. PR555 interleaved phase-B source writes and111 live ports retain its stated H1-H5 and punctured-supplier interface arguments."
+}
diff --git a/research/contextual-provider-pooling/evidence/CLONE-INVOICE.json b/research/contextual-provider-pooling/evidence/CLONE-INVOICE.json
new file mode 100644
index 0000000000..6fed03c303
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/CLONE-INVOICE.json
@@ -0,0 +1,106 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "bd6d43a8e4280fd38af2ce8486a7548f3f1208ecd6a329868d50bcd426501b57",
+  "parent_template_sha256": "b0671ac778e366abf27d9097dd2804637b41191cdeef4216895f79a46d1ed3df",
+  "owner_audit_sha256": "6d22ec5aefd5df6bbcb846b6ffabef543bf32d535bc9656a2a038cdd6eece935",
+  "controller_audit_sha256": "8a2eb1b5a2e335b2883bedc4da70c98b81c2a182ef1e9c621d361c42be71804b",
+  "independent_local_replay_sha256": "6bcb26454d545c16cd15f2a3058c0b9c38cbce27e3943a1f074f607ef0660725",
+  "canonical_word_sha256": "bdc28338d65fee98fbf00bb2b7dfe70da8def857187712a065ee2500fd13a5e3",
+  "local_programs_sha256": "8f17ffb28cd71d501fb437aecc113d29e30b6b8d7a7cc044475aaf169ed3d2b0",
+  "local_checks_sha256": "75fc20d2c9fce6348a3fdbef7c64c2ccddff9c9236120f3bf51be44daae9cde4",
+  "global_prefix_bits": 801,
+  "charged_prefix_bits": 1024,
+  "complete_invocation_sweeps": 360,
+  "bridge_sweeps": 360,
+  "row_prefix_extra": 2048,
+  "local": {
+    "backward": {
+      "events": 21455,
+      "macros": 16262,
+      "real_component_primitives": 161184,
+      "prefix_l1": "1044730572396",
+      "prefix_bits": 40,
+      "coefficient_work_primitive_count": 79820,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "forward": {
+      "events": 21455,
+      "macros": 16262,
+      "real_component_primitives": 161136,
+      "prefix_l1": "88876257700",
+      "prefix_bits": 37,
+      "coefficient_work_primitive_count": 79788,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    }
+  },
+  "helpers": 504,
+  "centres": 8,
+  "live": 35840,
+  "physical": 36354,
+  "physical_stock_identity": {
+    "data_and_owner_families": 35840,
+    "local_helpers": 504,
+    "private_centres": 8,
+    "coefficient_work": 2
+  },
+  "entering_helpers": 212,
+  "entrance_rank": 380,
+  "width_inventory": {
+    "5": 56,
+    "8": 156,
+    "9": 292
+  },
+  "local_adapters": 332896,
+  "local_primitive_bound": 8633436878240,
+  "wrapper_elementary_factors_charged": 21980160,
+  "factors_per_wrapper": 144,
+  "compiler": 25934336,
+  "unhosted_pervertex": 7867676337142680,
+  "hosted_rebased_pervertex": 7867676335645800,
+  "conservative_pervertex_used": 10745623326867248,
+  "retained_prior_overcharge": {
+    "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+    "previous_pervertex_allowance": 2877946989724568,
+    "added_complete_new_pervertex": 7867676337142680,
+    "policy": "Retain old allowance and add the entire fresh recount."
+  },
+  "finite": {
+    "physical_stock_bits": 2643,
+    "router_bits": 7991,
+    "literal_bits": 35287,
+    "physical_row_coefficient": 17495,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Payload1024 explicitly pays all360 invocation and360 bridge sweeps; physical row allowance20161 remains unchanged."
+}
diff --git a/research/contextual-provider-pooling/evidence/CLONE-LIFT.json b/research/contextual-provider-pooling/evidence/CLONE-LIFT.json
new file mode 100644
index 0000000000..0cf9d937c1
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/CLONE-LIFT.json
@@ -0,0 +1,54 @@
+{
+  "status": "PASS_INDEPENDENT_LITERAL_FIVEFOLD_SOURCE_LIFT",
+  "ambient_m": 73,
+  "clones": 5,
+  "replicas_per_clone": 8,
+  "replicas_total": 40,
+  "calls": 360,
+  "literal_owner_entries_checked": 262080,
+  "parent_live": 11704,
+  "cloned_parent_live": 58520,
+  "shared_private_reserve": 514,
+  "eight_replicas_per_dedicated_bank": true,
+  "private_work_erasure_bound_to_fresh_replay": true,
+  "immutable_metadata_keys": [
+    "adapter_policy",
+    "cover",
+    "exact_data_phase_recipe_sha256",
+    "exact_local_clifford_recipe_sha256",
+    "expanded_scalar_interface",
+    "local_programs",
+    "loop_order",
+    "m",
+    "port_restriction",
+    "recipe",
+    "residual_adapter_sha256",
+    "route_semantics",
+    "supplier_substitution",
+    "version"
+  ],
+  "source_template_sha256": "99711b0b784029b486f470e1250cdeff12c11dd31480e293e795b6ba2ffe2267",
+  "clone_template_sha256": "b0671ac778e366abf27d9097dd2804637b41191cdeef4216895f79a46d1ed3df",
+  "source_artifacts": {
+    "split-centres/CANONICAL-WORD.json.gz": "bdc28338d65fee98fbf00bb2b7dfe70da8def857187712a065ee2500fd13a5e3",
+    "split-centres/LOCAL-PROGRAMS.json.gz": "8f17ffb28cd71d501fb437aecc113d29e30b6b8d7a7cc044475aaf169ed3d2b0",
+    "split-centres/LOCAL-CHECKS.json": "75fc20d2c9fce6348a3fdbef7c64c2ccddff9c9236120f3bf51be44daae9cde4",
+    "split-centres/INDEPENDENT-LOCAL-REPLAY.json": "6bcb26454d545c16cd15f2a3058c0b9c38cbce27e3943a1f074f607ef0660725",
+    "split-centres/RESIDUAL-ADAPTERS.json": "a48b10e0dc3cc5d3bc3c1bd2ac33c3a5b898cb024984d77c0e562bc400249310",
+    "split-centres/CLIFFORD-RECIPES.json": "991a7ea839416fa6f6de304dabba850083c6a4256b2054961954c9bdf488a1aa",
+    "split-centres/CLIFFORD-REVIEW.json": "f5232da2c49bdb1bc2638d96da548d3d6aff4fb910707c15d70b7080a943dd03",
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"
+  },
+  "mutations_rejected": [
+    "collapse clone data namespace",
+    "share eight-replica bank across clones",
+    "change bank axis-copy route",
+    "omit cloned bank complement",
+    "understate shared private reserve",
+    "change immutable ambient rank",
+    "change source replica schedule",
+    "omit final family correction"
+  ],
+  "mutation_controls_run": true,
+  "scope": "Exact finite source lift with shared erased work, disjoint data and separate eight-replica banks. New hosted allocation, coefficient invoice and all-size compiler admission are separate; retained conditional interfaces are unchanged."
+}
diff --git a/research/contextual-provider-pooling/evidence/COMPLEX-INVOICE.json b/research/contextual-provider-pooling/evidence/COMPLEX-INVOICE.json
new file mode 100644
index 0000000000..2cd1365bdd
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/COMPLEX-INVOICE.json
@@ -0,0 +1,106 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0",
+  "parent_template_sha256": "7eddf21720ce26ff72069a0e94fa7f0e692cfe3bea2defb1a3769bea352cf471",
+  "owner_audit_sha256": "6572e69d9df9a72a600d7ee88404f96c525fea760b76cb6607273d85681579d1",
+  "controller_audit_sha256": "01d37b06d35ffb1995533cc618b0baaa093f55d288786153406fc46c94ab9926",
+  "independent_local_replay_sha256": "e871d8d56014146c19963430e4822714aadbf57367f783dc1dd42fa3f5b0a0ce",
+  "canonical_word_sha256": "995e46ed6dc8377f02bf05a3370171796364cedefdfeaeae47c2a207b5a8b173",
+  "local_programs_sha256": "7b191ec016ab99a0e1415206b898a8a6c5485fe9e8d91e59539e7c3710725563",
+  "local_checks_sha256": "2c51cdb9b282aadb99ea00d05b6c4bee140577111bdfd5c675b038373e309a17",
+  "global_prefix_bits": 225,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "local": {
+    "backward": {
+      "events": 21483,
+      "macros": 16290,
+      "real_component_primitives": 161356,
+      "prefix_l1": "1044730572396",
+      "prefix_bits": 40,
+      "coefficient_work_primitive_count": 79906,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "forward": {
+      "events": 21483,
+      "macros": 16290,
+      "real_component_primitives": 161308,
+      "prefix_l1": "88876257700",
+      "prefix_bits": 37,
+      "coefficient_work_primitive_count": 79874,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    }
+  },
+  "helpers": 504,
+  "centres": 8,
+  "live": 7168,
+  "physical": 7682,
+  "physical_stock_identity": {
+    "data_and_owner_families": 7168,
+    "local_helpers": 504,
+    "private_centres": 8,
+    "coefficient_work": 2
+  },
+  "entering_helpers": 212,
+  "entrance_rank": 380,
+  "width_inventory": {
+    "5": 56,
+    "8": 156,
+    "9": 292
+  },
+  "local_adapters": 333344,
+  "local_primitive_bound": 8645055460940,
+  "wrapper_elementary_factors_charged": 4396032,
+  "factors_per_wrapper": 144,
+  "compiler": 25934336,
+  "unhosted_pervertex": 1574554051175192,
+  "hosted_rebased_pervertex": 1574554050875816,
+  "conservative_pervertex_used": 4452501040899760,
+  "retained_prior_overcharge": {
+    "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+    "previous_pervertex_allowance": 2877946989724568,
+    "added_complete_new_pervertex": 1574554051175192,
+    "policy": "Retain old allowance and add the entire fresh recount."
+  },
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7985,
+    "literal_bits": 35282,
+    "physical_row_coefficient": 16467,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged."
+}
diff --git a/research/contextual-provider-pooling/evidence/EXACT-ASSEMBLY.json b/research/contextual-provider-pooling/evidence/EXACT-ASSEMBLY.json
new file mode 100644
index 0000000000..104ff571e6
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/EXACT-ASSEMBLY.json
@@ -0,0 +1,169 @@
+{
+  "status": "PASS_FRESH_WAVE_COMPLEX_AND_CITED_R420_COMPOSITION",
+  "kappa": "795984451416673/500000000000000000",
+  "kappa_decimal": "0.001591968902833346",
+  "complex_lower": "1594507308884431019637/1000000000000000000000000",
+  "complex_decimal": "0.001594507308884431019637",
+  "bit_lower": "413456747036699736067/250000000000000000000000",
+  "bit_decimal": "0.001653826988146798944268",
+  "binding": "complex",
+  "gain_over547_percent": "0.0790654379037971258366309784614671659549385616253931804131441",
+  "gain_over_prior_delivery_percent": "0.0866226449665785021331176315148894224195513542635131937074985",
+  "complex_template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0",
+  "complex_owner_audit_sha256": "6572e69d9df9a72a600d7ee88404f96c525fea760b76cb6607273d85681579d1",
+  "complex_invoice_sha256": "a21fd7e02d3001b1e8065e9eb6084d80e1f64c44035733ed1115a38675a01fd0",
+  "complex_profile": {
+    "1": 165600,
+    "2": 32128,
+    "3": 35907,
+    "4": 13248,
+    "5": 4032,
+    "6": 4032,
+    "7": 208,
+    "8": 576,
+    "39": 1,
+    "48": 1660
+  },
+  "moments": [
+    {
+      "side": "bit",
+      "endpoint": "413456747036699736067/250000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-6043813583626134311169770662156174867615397/13479973333575319897333507543509815336818572211270286240551805124608",
+        "-12087627167252268622339541324312349735230793/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
+        "-1120888283015460284783/2500000000000000000000000000000000000000000000",
+        "-4483543132061841139029/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "bit",
+      "endpoint": "1653826988146798944269/1000000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "70925594433828721229860776023154018035852861/26959946667150639794667015087019630673637144422540572481103610249216",
+        "70925594433828721229860776023154018035852863/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
+        "13153878434097279887307/5000000000000000000000000000000000000000000000",
+        "6576941717048639943679/2500000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "complex",
+      "endpoint": "1594507308884431019637/1000000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-40186902685703231311821970003273532124160065/13479973333575319897333507543509815336818572211270286240551805124608",
+        "-627920354464112989247218281301148939440001/210624583337114373395836055367340864637790190801098222508621955072"
+      ],
+      "base_two": [
+        "-1863269341316411144019/625000000000000000000000000000000000000000000",
+        "-3726537432632822288021/1250000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "complex",
+      "endpoint": "797253654442215509819/500000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "2584151432270445003531030214735456403866167/26959946667150639794667015087019630673637144422540572481103610249216",
+        "2584151432270445003531030214735456403866169/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
+        "958510539299785465391/10000000000000000000000000000000000000000000000",
+        "958520539299785465527/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "bootstrap": [
+    {
+      "exponent": "1592026179917994112061843167008221382040806512856772647783935869757111856520388231/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "2481128966436905979649524107347598322193487143227352216064130242888143479611769/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "5847952315725"
+    },
+    {
+      "exponent": "1594503352706159749520769553020794918467633927101230843448502982027906393689400212888299834336212396947794718841977575307853/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "3956178271268520723138094774061895366072898769156551497017972093606310599787111700165663787603052205281158022424692147/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "2300121588111717685"
+    },
+    {
+      "exponent": "1594507302576275849254063191710781752397707281524361062869067047330840668116515994507272067321340504427683664141040096311204708039395418994543535586903262617036690639/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "6308155168787429499404787227965292718475638937130932952669159331883484005492727932678659495572316335858959903688795291960604581005456464413096737382963309361/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "904685783068306507649493"
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+    "Gaussian_arithmetic_above_kappa": "3458192678974540530149830647114415416008814652724061025805738866911744975259976478655442505583939756800086116295165939599322872637304287618475900886439525006262771762099395245660488613692795836665190883890886833255876953150497410794098957754064599221633483857889187142132620292613089008455752040005440425846702209/4006378029235537723957117857677832346992435329311607599256670742628543812364673691126094004365381040405118485250945201349149077532363708351956042953184320178617662476674092888721000437884588038764818018050842082179014661957316778533032007117044763405730794020286752551673693673039287253988926783029544133986304536000000000000000000",
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+    "dimension_above_kappa": "249601373172778892125316318098057453789412123678215814601400999432204497686030274370530678351407280950258298316334856606508505752790186380661562696365455322489422828469102014323613148258507203896643491832488829919636717700959147255295569359798477123219573011370676487408846027970570014558734503452068713013282921462431594349258909/250398626827221107747319866104864521687027208081975474953541921414283988272792105695380875272836315025319905328184075084321817345772731771997252684574020011163603904792130805545062527367786752422801126128177630136188416372332298658314500444815297712858174626267922034479605854564955453374307923939346508374144033500000000000000000"
+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Exact composition of the freshly rebuilt and physically audited wave complex supplier with the pinned PR543 published bit receipt. The unchanged bit operator is cited, not rebuilt in this package. Inherited all-size compiler, common-label/mutable-source, hosting, precision/tape and analytic interfaces remain conditional. R420 interleaved phase-B source writes rely on its stated H1-H5 interface argument."
+}
diff --git a/research/contextual-provider-pooling/evidence/FINAL-MIXTURE-REVIEW.json b/research/contextual-provider-pooling/evidence/FINAL-MIXTURE-REVIEW.json
new file mode 100644
index 0000000000..48e293f63c
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/FINAL-MIXTURE-REVIEW.json
@@ -0,0 +1,97 @@
+{
+  "status": "PASS_INDEPENDENT_FINAL_MIXTURE_BINDING_AND_REVIEW",
+  "template_sha256": "94e14dfce4808c7f1c156b22a8bc0aec159a761b39946f030d485734331e0243",
+  "kappa": "318515327278119/200000000000000000",
+  "kappa_decimal": "0.001592576636390595",
+  "complex_lower": "7975584912145610089/5000000000000000000000",
+  "provider_counts": {
+    "n8": 275,
+    "n0": 75,
+    "n6": 5,
+    "n2": 5
+  },
+  "providers": {
+    "n0": {
+      "canonical_sha256": "bdc28338d65fee98fbf00bb2b7dfe70da8def857187712a065ee2500fd13a5e3",
+      "programs_sha256": "8f17ffb28cd71d501fb437aecc113d29e30b6b8d7a7cc044475aaf169ed3d2b0",
+      "replay_sha256": "6bcb26454d545c16cd15f2a3058c0b9c38cbce27e3943a1f074f607ef0660725",
+      "phase_review_sha256": "2ec2a424b551616c7d2d955c469b557f816a8ebd811d711b206d3fd1de72c1dc",
+      "phase_recipe_sha256": "991a7ea839416fa6f6de304dabba850083c6a4256b2054961954c9bdf488a1aa",
+      "widths": {
+        "9": 292,
+        "8": 156,
+        "5": 56
+      }
+    },
+    "n2": {
+      "canonical_sha256": "b25777f599727cd5d320ae23bd1198d97c2eb35a29ab90c0f7e3250b6540cdf3",
+      "programs_sha256": "8c0f306abc36b0bf3c5a63141a5c9b78794264fc51ab30b70775734d7783d45a",
+      "replay_sha256": "c4fe1c5c25ff5f5965577a4f12056c110eebc5f5a59ce17adcd0ce8996da8666",
+      "phase_review_sha256": "8e3e2f2919c2eb757b1f4efb3d5cac4e219316a51177fdbbf081e85045e37dce",
+      "phase_recipe_sha256": "f322d459e7bbe17bb83b758446a586373b4665c93fdc972b0f0f52ba2b682f33",
+      "widths": {
+        "9": 292,
+        "8": 156,
+        "5": 54,
+        "4": 2
+      }
+    },
+    "n6": {
+      "canonical_sha256": "79286d7f352f9e88e47ca4e616f97a99cea577a6868a5aed2998217d730d19ea",
+      "programs_sha256": "2a6b8a081b45b60470da99fc1306c08293dac92160815ec0d9540ab183967a48",
+      "replay_sha256": "be7a950a103471da3864362f8315e9e07cbde8d0a0eb0f8afff2407437ab82af",
+      "phase_review_sha256": "f87106907709aa3c03cc3fc87d5524b01a648428b9127d1ac333fe4be2ecde62",
+      "phase_recipe_sha256": "e2e80fcab55733f406e8eefd8a7bdda50321572e2c3128da77cde1ab9ebcf6e9",
+      "widths": {
+        "9": 292,
+        "8": 156,
+        "5": 50,
+        "4": 6
+      }
+    },
+    "n8": {
+      "canonical_sha256": "e58decc71478c1e5623776a1a0ce0a918fe778e47fb6a4d2656a330a6235d1af",
+      "programs_sha256": "c13c308504373160bf233e53a289e98a46a83b369f8f8e3133ea23b52e904a15",
+      "replay_sha256": "520be60830f40f6fc90ceaa35090f8ebb01b616dce39e8402f7633070b264cc3",
+      "phase_review_sha256": "aaa7776d7593f25f7cedd4ab55888ae4d21c00a34f547c0e109fae01399af4c5",
+      "phase_recipe_sha256": "3309965452129e58507b98aa31bc6b4a1238e1c0ae11fcf5304ab3fe019ffab8",
+      "widths": {
+        "9": 292,
+        "8": 156,
+        "5": 48,
+        "4": 8
+      }
+    }
+  },
+  "full_roles_checked": 181440,
+  "complete_calls_checked": 360,
+  "actual_orthogonal_charts": 3018,
+  "controls_rejected": [
+    "wrong selected provider",
+    "wrong provider program registry",
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve"
+  ],
+  "global_prefix_bits": 801,
+  "charged_prefix_bits": 1024,
+  "physical_row": 17495,
+  "all47_strict_outer_constraints_positive": true,
+  "source_and_evidence_sha256": {
+    "resource\\emit_mixed.py": "3dda361db82dbef4e9322855cedbf20e5d121a6775e8b63a06e7d2c87fc41e73",
+    "resource\\audit_mixed.py": "0c19cd9dfa1c06ef75e5c81973494e9a5d2b137802d499dc2a240a63297da191",
+    "resource\\build_mixed_clone.py": "8925ea3a4e1676b89e657f75424bfafafb0c88875894459153ba2a42732c80c7",
+    "lead\\invoice_mixed.py": "44d2a6b7f6ed907b355d0791a1af2913e545a958b341ffc26318eb39796388d2",
+    "response\\build_promoted_epoch.py": "36a47288ae281668b5d6512fe2f1661260854911418cb963ea3e28351c3ba47f",
+    "resource\\replay\\audit\\ASYNC-AUDIT.json": "e1ed47a87e9be101bdbca694c70fabdc340901f153bf39596ab0eec493a0cb2c",
+    "resource\\replay\\audit\\OWNERS-AND-PROFILE.json": "0918cdfb307dd9b89e7565eb86fcb0a961e1d0bb832efa5d793a6517ae9d9f82",
+    "resource\\replay\\audit\\PREFIX-AND-INVOICE.json": "8e9a1febf2b9f1212c6e36f4155dec72c2a805ee7173a71ba99dc5f7cdc5d714",
+    "lead\\FINAL-ASSEMBLY.json": "c4164d982d6d974744146f88e4f5bcf8464b702c1832fd6cb099574f4ff212ce"
+  },
+  "scope": "Independent source review, per-call selected canonical/program/phase/width binding, receipt hash chain, finite invoice and47 exact rational sign checks. Existing fresh physical pipeline supplies the expensive chronology/sigma/column checks; this review did not rerun them. Bit supplier remains cited; all inherited all-size interfaces remain conditional.",
+  "research_scope": "All48 distinct local promotion signatures independently checked; partial groups strictly dominated by whole-group mixtures in the fractional resource problem. No separate numerical gain attributed to this lane or to imported Lean statements."
+}
diff --git a/research/contextual-provider-pooling/evidence/FINAL-RESOURCE.json b/research/contextual-provider-pooling/evidence/FINAL-RESOURCE.json
new file mode 100644
index 0000000000..694d910171
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/FINAL-RESOURCE.json
@@ -0,0 +1,44 @@
+{
+  "status": "PASS_FINAL_WEIGHTED_COSET_WAVE_RESOURCE_AND_INVOICE",
+  "complex_lower": "1594507308884431019637/1000000000000000000000000",
+  "template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0",
+  "roles": 36288,
+  "charts": 2972,
+  "profile": {
+    "1": 165600,
+    "2": 32128,
+    "3": 35907,
+    "4": 13248,
+    "5": 4032,
+    "6": 4032,
+    "7": 208,
+    "8": 576,
+    "39": 1,
+    "48": 1660
+  },
+  "prefix_required": 225,
+  "prefix_charged": 512,
+  "row": 16467,
+  "local": {
+    "backward": {
+      "events": 21483,
+      "prefix_bits": 40,
+      "all_exact_columns": 728
+    },
+    "forward": {
+      "events": 21483,
+      "prefix_bits": 37,
+      "all_exact_columns": 728
+    }
+  },
+  "negative_controls": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve"
+  ],
+  "frozen_manifest_sha256": "af4e9eecb006a98f78a024ee6558f27641b3be8c8b0771e6fa22d0c7cddf38cf"
+}
diff --git a/research/contextual-provider-pooling/evidence/MIXED-ASSEMBLY.json b/research/contextual-provider-pooling/evidence/MIXED-ASSEMBLY.json
new file mode 100644
index 0000000000..d4064ec876
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/MIXED-ASSEMBLY.json
@@ -0,0 +1,173 @@
+{
+  "status": "PASS_MIXED_PROVIDER_NATIVE_COMPLEX_AND_CITED_P111_COMPOSITION",
+  "kappa": "318515327278119/200000000000000000",
+  "kappa_decimal": "0.001592576636390595",
+  "complex_lower": "7975584912145610089/5000000000000000000000",
+  "complex_decimal": "0.0015951169824291220178",
+  "bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "bit_decimal": "0.001733052823330162099157",
+  "binding": "complex",
+  "gain_over_frozen559_percent": "0.00368877094280285994459430052526845178816071498952442314334055",
+  "gain_over_prior_delivery_percent": "0.0377757066681351028435525135708134639795354373564308481153138",
+  "complex_template_sha256": "94e14dfce4808c7f1c156b22a8bc0aec159a761b39946f030d485734331e0243",
+  "complex_owner_audit_sha256": "0918cdfb307dd9b89e7565eb86fcb0a961e1d0bb832efa5d793a6517ae9d9f82",
+  "complex_invoice_sha256": "8e9a1febf2b9f1212c6e36f4155dec72c2a805ee7173a71ba99dc5f7cdc5d714",
+  "complex_profile": {
+    "1": 832540,
+    "2": 153900,
+    "3": 179556,
+    "4": 68460,
+    "5": 20160,
+    "6": 20160,
+    "7": 1040,
+    "8": 2880,
+    "48": 8304
+  },
+  "moments": [
+    {
+      "side": "bit",
+      "endpoint": "1733052823330162099157/1000000000000000000000000",
+      "accept": true,
+      "mercator": [
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+        "-4603911776979020866873882688005282877972055/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "-1707686990214702474933/2500000000000000000000000000000000000000000000",
+        "-6830737960858809899617/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "bit",
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+      "accept": false,
+      "mercator": [
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+      ],
+      "base_two": [
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+        "12928406019707192501991/5000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "complex",
+      "endpoint": "7975584912145610089/5000000000000000000000",
+      "accept": true,
+      "mercator": [
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+      ],
+      "base_two": [
+        "-45199/500000000000000000000000000000",
+        "-90397/1000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "complex",
+      "endpoint": "1595116982429122017801/1000000000000000000000000",
+      "accept": false,
+      "mercator": [
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+      ],
+      "base_two": [
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+    }
+  ],
+  "bootstrap": [
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+    "bulk_exposure_above_kappa": "992322671299615688664600559411580346304306298689308629357666225216818026007512499464183040302837723518978273274422543237894037361845308803820248822139147277493718333839446834555840235661030500872525895393973301979252061860917374808264335328835257887024012661968510548288485384296170990225283408551029056572777919/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "281254435534127811468580680989500672033351096397539012558121993591416537103708864081417005522828107777356838886845032371059055763767160126159596472293873411902413568978175236472998124271860948232570761650006210607940678191245751156791500824686189257510863209277664852831660289042346056229715898994921330977625381781002717858088053212807/312998474057009100629053983566429328004175180084143892918349399242902270560613833744039224437590630250179672489754134997676959949992650400177862425739278758823735882576551648921823654722854385709465408676339257529840187360216858376616679808169285600406616396273603438395819392368048287319914918650111966949660897768881518353509483555329600000000000000000",
+    "scalar_work_above_kappa": "2188768362813161808915538363863576680177193432198054795086483466064338361920078904767183088708117114512233375658610499349487678693817426631242638425817563956571407551332255304669549758166440705436517329940879196864303859356770901725499203643854160288570857037072332860147849926131850999448366791599886572262279153327217385174213974952359/1564992370285045503145269917832146640020875900420719464591746996214511352803069168720196122187953151250898362448770674988384799749963252000889312128696393794118679412882758244609118273614271928547327043381696287649200936801084291883083399040846428002033081981368017191979096961840241436599574593250559834748304488844407591767547417776648000000000000000000",
+    "dimension_above_kappa": "39000190742873862402853062281666146419695530079296888639701398088403334383934566796773903970812734990157731038321014585755271780368589543053661663346660983430878075725546373405678105108208203917459062474663210221393306839062673523434264435401500255221288663564798664921147383072577339313641561327783033606875228172794973995956744916403008353628935054361/39124809257126137578631747945803666000521897510517986614793674905362783820076729218004903054698828781272459061219266874709619993749081300022232803217409844852966985322068956115227956840356798213683176084542407191230023420027107297077084976021160700050827049534200429799477424046006035914989364831263995868707612221110189794188685444416200000000000000000"
+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Exact composition of the freshly rebuilt selected kernel-promotion providers and their complete mixed-provider controller using the native complex moment from PR559 with the pinned PR555 published bit receipt. The unchanged bit operator is cited, not rebuilt in this package. Inherited all-size compiler, common-label/mutable-source, hosting, precision/tape and analytic interfaces remain conditional. PR555 interleaved phase-B source writes and111 live ports retain its stated H1-H5 and punctured-supplier interface arguments."
+}
diff --git a/research/contextual-provider-pooling/evidence/MIXED-INVOICE.json b/research/contextual-provider-pooling/evidence/MIXED-INVOICE.json
new file mode 100644
index 0000000000..4b68e3baae
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/MIXED-INVOICE.json
@@ -0,0 +1,243 @@
+{
+  "status": "PASS_INDEPENDENT_MIXED_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "94e14dfce4808c7f1c156b22a8bc0aec159a761b39946f030d485734331e0243",
+  "parent_template_sha256": "b0671ac778e366abf27d9097dd2804637b41191cdeef4216895f79a46d1ed3df",
+  "owner_audit_sha256": "0918cdfb307dd9b89e7565eb86fcb0a961e1d0bb832efa5d793a6517ae9d9f82",
+  "controller_audit_sha256": "e1ed47a87e9be101bdbca694c70fabdc340901f153bf39596ab0eec493a0cb2c",
+  "provider_bindings": {
+    "n0": {
+      "canonical_word_sha256": "bdc28338d65fee98fbf00bb2b7dfe70da8def857187712a065ee2500fd13a5e3",
+      "local_programs_sha256": "8f17ffb28cd71d501fb437aecc113d29e30b6b8d7a7cc044475aaf169ed3d2b0",
+      "local_checks_sha256": "75fc20d2c9fce6348a3fdbef7c64c2ccddff9c9236120f3bf51be44daae9cde4",
+      "independent_local_replay_sha256": "6bcb26454d545c16cd15f2a3058c0b9c38cbce27e3943a1f074f607ef0660725"
+    },
+    "n2": {
+      "canonical_word_sha256": "b25777f599727cd5d320ae23bd1198d97c2eb35a29ab90c0f7e3250b6540cdf3",
+      "local_programs_sha256": "8c0f306abc36b0bf3c5a63141a5c9b78794264fc51ab30b70775734d7783d45a",
+      "local_checks_sha256": "6f02241e70220b8ef80a8e9817004e2affeaef6536f0f8e6a314096bcee9dbf8",
+      "independent_local_replay_sha256": "c4fe1c5c25ff5f5965577a4f12056c110eebc5f5a59ce17adcd0ce8996da8666"
+    },
+    "n6": {
+      "canonical_word_sha256": "79286d7f352f9e88e47ca4e616f97a99cea577a6868a5aed2998217d730d19ea",
+      "local_programs_sha256": "2a6b8a081b45b60470da99fc1306c08293dac92160815ec0d9540ab183967a48",
+      "local_checks_sha256": "99fd2effc0f45b4eb212e3f467c53e4e36ca7c3687c7377322b20ecce1f80ee6",
+      "independent_local_replay_sha256": "be7a950a103471da3864362f8315e9e07cbde8d0a0eb0f8afff2407437ab82af"
+    },
+    "n8": {
+      "canonical_word_sha256": "e58decc71478c1e5623776a1a0ce0a918fe778e47fb6a4d2656a330a6235d1af",
+      "local_programs_sha256": "c13c308504373160bf233e53a289e98a46a83b369f8f8e3133ea23b52e904a15",
+      "local_checks_sha256": "285aa85e567abb3ef865d37fdab2949855fd46d06bca05d78b56691aa9a65a09",
+      "independent_local_replay_sha256": "520be60830f40f6fc90ceaa35090f8ebb01b616dce39e8402f7633070b264cc3"
+    }
+  },
+  "provider_counts": {
+    "n8": 275,
+    "n0": 75,
+    "n6": 5,
+    "n2": 5
+  },
+  "global_prefix_bits": 801,
+  "charged_prefix_bits": 1024,
+  "complete_invocation_sweeps": 360,
+  "bridge_sweeps": 360,
+  "row_prefix_extra": 2048,
+  "local": {
+    "n0:backward": {
+      "events": 21455,
+      "macros": 16262,
+      "real_component_primitives": 161184,
+      "prefix_l1": "1044730572396",
+      "prefix_bits": 40,
+      "coefficient_work_primitive_count": 79820,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "n0:forward": {
+      "events": 21455,
+      "macros": 16262,
+      "real_component_primitives": 161136,
+      "prefix_l1": "88876257700",
+      "prefix_bits": 37,
+      "coefficient_work_primitive_count": 79788,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "n2:backward": {
+      "events": 21459,
+      "macros": 16262,
+      "real_component_primitives": 161184,
+      "prefix_l1": "1044730572396",
+      "prefix_bits": 40,
+      "coefficient_work_primitive_count": 79820,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "n2:forward": {
+      "events": 21459,
+      "macros": 16262,
+      "real_component_primitives": 161136,
+      "prefix_l1": "88876257700",
+      "prefix_bits": 37,
+      "coefficient_work_primitive_count": 79788,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "n6:backward": {
+      "events": 21459,
+      "macros": 16262,
+      "real_component_primitives": 161184,
+      "prefix_l1": "1044730572396",
+      "prefix_bits": 40,
+      "coefficient_work_primitive_count": 79820,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "n6:forward": {
+      "events": 21459,
+      "macros": 16262,
+      "real_component_primitives": 161136,
+      "prefix_l1": "88876257700",
+      "prefix_bits": 37,
+      "coefficient_work_primitive_count": 79788,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "n8:backward": {
+      "events": 21455,
+      "macros": 16262,
+      "real_component_primitives": 161184,
+      "prefix_l1": "1044730572396",
+      "prefix_bits": 40,
+      "coefficient_work_primitive_count": 79820,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "n8:forward": {
+      "events": 21455,
+      "macros": 16262,
+      "real_component_primitives": 161136,
+      "prefix_l1": "88876257700",
+      "prefix_bits": 37,
+      "coefficient_work_primitive_count": 79788,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 212,
+      "post_wrappers": 212,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    }
+  },
+  "helpers": 504,
+  "centres": 8,
+  "live": 35840,
+  "physical": 36354,
+  "physical_stock_identity": {
+    "data_and_owner_families": 35840,
+    "local_helpers": 504,
+    "private_centres": 8,
+    "coefficient_work": 2
+  },
+  "provider_widths": {
+    "n0": {
+      "5": 56,
+      "8": 156,
+      "9": 292
+    },
+    "n2": {
+      "4": 2,
+      "5": 54,
+      "8": 156,
+      "9": 292
+    },
+    "n6": {
+      "4": 6,
+      "5": 50,
+      "8": 156,
+      "9": 292
+    },
+    "n8": {
+      "4": 8,
+      "5": 48,
+      "8": 156,
+      "9": 292
+    }
+  },
+  "local_adapters": 332960,
+  "local_primitive_bound": 8635096675744,
+  "wrapper_elementary_factors_charged": 21980160,
+  "factors_per_wrapper": 144,
+  "compiler": 25934336,
+  "unhosted_pervertex": 7873054081055640,
+  "hosted_rebased_pervertex": 7873054079558760,
+  "conservative_pervertex_used": 10751001070780208,
+  "retained_prior_overcharge": {
+    "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+    "previous_pervertex_allowance": 2877946989724568,
+    "added_complete_new_pervertex": 7873054081055640,
+    "policy": "Retain old allowance and add the entire fresh recount."
+  },
+  "registry_dispatch_charge": 184320,
+  "finite": {
+    "physical_stock_bits": 2643,
+    "router_bits": 7991,
+    "literal_bits": 35287,
+    "physical_row_coefficient": 17495,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Fresh independent recount of every selected local supplier, full calls/bridges, maximum adapters and explicit finite registry dispatch. All-size compiler, precision/tape and analytic interfaces remain conditional."
+}
diff --git a/research/contextual-provider-pooling/evidence/MIXED72-REVIEW.json b/research/contextual-provider-pooling/evidence/MIXED72-REVIEW.json
new file mode 100644
index 0000000000..c01a8b9142
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/MIXED72-REVIEW.json
@@ -0,0 +1,27 @@
+{
+  "status": "PASS_INDEPENDENT_MIXED72_RESOURCE_AND_PROVIDER_BINDING",
+  "provider_counts": {
+    "n8": 55,
+    "n0": 15,
+    "n6": 1,
+    "n2": 1
+  },
+  "helper_roles": 36288,
+  "calls": 72,
+  "profile": {
+    "1": 166508,
+    "2": 30780,
+    "3": 35911,
+    "4": 13692,
+    "5": 4032,
+    "6": 4032,
+    "8": 576,
+    "7": 208,
+    "48": 1660,
+    "39": 1
+  },
+  "profile_mass": 520704,
+  "plan_sha256": "7990289ef5b8766ab036a1e7ef71c9195703c6fe5e568f486e841e66ff484ac6",
+  "owners_sha256": "3e9901234c1c095bc8bb753df80fd0fe2e18a6226d4cad7b87745955bed4175a",
+  "scope": "Literal resource/provider/profile binding. Physical sigma geometry, reconstructed timeline admission, final mixed emitted stream and invoice still require final audit."
+}
diff --git a/research/contextual-provider-pooling/evidence/PROMOTION-FULLCHAIN-CHECK.json b/research/contextual-provider-pooling/evidence/PROMOTION-FULLCHAIN-CHECK.json
new file mode 100644
index 0000000000..ed3775fc91
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/PROMOTION-FULLCHAIN-CHECK.json
@@ -0,0 +1,391 @@
+{
+  "status": "PASS",
+  "cases": 48,
+  "source_sha256": "71e3f161f4b8b5c7d955a2504640bd3cfeda535bd908f947a4b9e394d84cf8b6",
+  "checks": [
+    {
+      "group": 0,
+      "delta": {
+        "1": 7,
+        "2": -4
+      }
+    },
+    {
+      "group": 0,
+      "delta": {
+        "1": 10,
+        "2": -6
+      }
+    },
+    {
+      "group": 0,
+      "delta": {
+        "1": 10,
+        "2": -7,
+        "3": -1,
+        "4": 1
+      }
+    },
+    {
+      "group": 0,
+      "delta": {
+        "1": 8,
+        "2": -8,
+        "3": -4,
+        "4": 4
+      }
+    },
+    {
+      "group": 1,
+      "delta": {
+        "1": 7,
+        "2": -4
+      }
+    },
+    {
+      "group": 1,
+      "delta": {
+        "1": 10,
+        "2": -6
+      }
+    },
+    {
+      "group": 1,
+      "delta": {
+        "1": 10,
+        "2": -7,
+        "3": -1,
+        "4": 1
+      }
+    },
+    {
+      "group": 1,
+      "delta": {
+        "1": 8,
+        "2": -8,
+        "3": -4,
+        "4": 4
+      }
+    },
+    {
+      "group": 3,
+      "delta": {
+        "1": 7,
+        "2": -4
+      }
+    },
+    {
+      "group": 3,
+      "delta": {
+        "1": 10,
+        "2": -6
+      }
+    },
+    {
+      "group": 3,
+      "delta": {
+        "1": 10,
+        "2": -7,
+        "3": -1,
+        "4": 1
+      }
+    },
+    {
+      "group": 3,
+      "delta": {
+        "1": 8,
+        "2": -8,
+        "3": -4,
+        "4": 4
+      }
+    },
+    {
+      "group": 4,
+      "delta": {
+        "1": 7,
+        "2": -4
+      }
+    },
+    {
+      "group": 4,
+      "delta": {
+        "1": 10,
+        "2": -6
+      }
+    },
+    {
+      "group": 4,
+      "delta": {
+        "1": 10,
+        "2": -7,
+        "3": -1,
+        "4": 1
+      }
+    },
+    {
+      "group": 4,
+      "delta": {
+        "1": 8,
+        "2": -8,
+        "3": -4,
+        "4": 4
+      }
+    },
+    {
+      "group": 5,
+      "delta": {
+        "1": 7,
+        "2": -4
+      }
+    },
+    {
+      "group": 5,
+      "delta": {
+        "1": 10,
+        "2": -6
+      }
+    },
+    {
+      "group": 5,
+      "delta": {
+        "1": 10,
+        "2": -7,
+        "3": -1,
+        "4": 1
+      }
+    },
+    {
+      "group": 5,
+      "delta": {
+        "1": 8,
+        "2": -8,
+        "3": -4,
+        "4": 4
+      }
+    },
+    {
+      "group": 6,
+      "delta": {
+        "1": 7,
+        "2": -4
+      }
+    },
+    {
+      "group": 6,
+      "delta": {
+        "1": 10,
+        "2": -6
+      }
+    },
+    {
+      "group": 6,
+      "delta": {
+        "1": 10,
+        "2": -7,
+        "3": -1,
+        "4": 1
+      }
+    },
+    {
+      "group": 6,
+      "delta": {
+        "1": 8,
+        "2": -8,
+        "3": -4,
+        "4": 4
+      }
+    },
+    {
+      "group": 7,
+      "delta": {
+        "1": 7,
+        "2": -4
+      }
+    },
+    {
+      "group": 7,
+      "delta": {
+        "1": 10,
+        "2": -6
+      }
+    },
+    {
+      "group": 7,
+      "delta": {
+        "1": 10,
+        "2": -7,
+        "3": -1,
+        "4": 1
+      }
+    },
+    {
+      "group": 7,
+      "delta": {
+        "1": 8,
+        "2": -8,
+        "3": -4,
+        "4": 4
+      }
+    },
+    {
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diff --git a/research/contextual-provider-pooling/evidence/WAVE-REVIEW.json b/research/contextual-provider-pooling/evidence/WAVE-REVIEW.json
new file mode 100644
index 0000000000..434c9c1de3
--- /dev/null
+++ b/research/contextual-provider-pooling/evidence/WAVE-REVIEW.json
@@ -0,0 +1,228 @@
+{
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+}
diff --git a/research/contextual-provider-pooling/inputs/PR543-EXPECTED.json b/research/contextual-provider-pooling/inputs/PR543-EXPECTED.json
new file mode 100644
index 0000000000..b61d859826
--- /dev/null
+++ b/research/contextual-provider-pooling/inputs/PR543-EXPECTED.json
@@ -0,0 +1,239 @@
+{
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diff --git a/research/contextual-provider-pooling/inputs/PR555-EXPECTED.json b/research/contextual-provider-pooling/inputs/PR555-EXPECTED.json
new file mode 100644
index 0000000000..c8ad4439e8
--- /dev/null
+++ b/research/contextual-provider-pooling/inputs/PR555-EXPECTED.json
@@ -0,0 +1,221 @@
+{
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+  "profile": {
+   "1": 380448,
+   "2": 400416,
+   "3": 23040,
+   "4": 27744,
+   "5": 29376,
+   "6": 17088,
+   "7": 26496,
+   "42": 288
+  },
+  "bit": {
+   "live": 28416,
+   "physical": 28425,
+   "maxchild": 42,
+   "rank_mass": 1808352,
+   "hosted_residuals": 126432,
+   "bank_assignments": 0,
+   "prefix_bits": 177,
+   "charged_prefix_bits": 192,
+   "coefficient_bits": 177,
+   "two_level_coefficient_bits": 393,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "eleven": {
+  "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting), parameterised by PR #545's code/adapt.py",
+  "bit_lower": "427652201524503168379/250000000000000000000000",
+  "bit_lower_decimal": "0.001710608806098012673516",
+  "profile": {
+   "1": 116248,
+   "2": 121648,
+   "3": 7040,
+   "4": 7688,
+   "5": 8976,
+   "6": 4432,
+   "7": 8688,
+   "56": 2600
+  },
+  "bit": {
+   "live": 8880,
+   "physical": 8889,
+   "maxchild": 56,
+   "rank_mass": 689304,
+   "hosted_residuals": 38632,
+   "prefix_bits": 4304,
+   "charged_prefix_bits": 4352,
+   "coefficient_bits": 4304,
+   "three_level_coefficient_bits": 12966,
+   "charged_three_level_coefficient_bits": 12992,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "790bbd2d8ef4e1169fca344c76b1965ee2fe78e34e74d16d458e4849cc2ba3b6",
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ }
+}
diff --git a/research/contextual-provider-pooling/inputs/WAVES.json b/research/contextual-provider-pooling/inputs/WAVES.json
new file mode 100644
index 0000000000..5008a0a452
--- /dev/null
+++ b/research/contextual-provider-pooling/inputs/WAVES.json
@@ -0,0 +1,361 @@
+{
+  "source_canonical_sha256": "7f7bf2315c83eb5dc0bb3502ceae575bfcffa00ad37fd32839114744ac18182c",
+  "passes": [
+    {
+      "v": 33,
+      "sign": -1,
+      "events": [
+        [
+          "B",
+          1461
+        ],
+        [
+          "B",
+          1460
+        ],
+        [
+          "B",
+          1049
+        ],
+        [
+          "B",
+          1054
+        ],
+        [
+          "B",
+          937
+        ],
+        [
+          "B",
+          942
+        ],
+        [
+          "B",
+          851
+        ],
+        [
+          "B",
+          905
+        ],
+        [
+          "B",
+          897
+        ]
+      ]
+    },
+    {
+      "v": 33,
+      "sign": -1,
+      "events": [
+        [
+          "B",
+          1469
+        ],
+        [
+          "B",
+          1468
+        ],
+        [
+          "B",
+          1051
+        ],
+        [
+          "B",
+          1052
+        ],
+        [
+          "B",
+          939
+        ],
+        [
+          "B",
+          940
+        ],
+        [
+          "B",
+          875
+        ],
+        [
+          "B",
+          867
+        ],
+        [
+          "B",
+          889
+        ],
+        [
+          "B",
+          881
+        ]
+      ]
+    },
+    {
+      "v": 39,
+      "sign": -1,
+      "events": [
+        [
+          "B",
+          1457
+        ],
+        [
+          "B",
+          1456
+        ],
+        [
+          "B",
+          1048
+        ],
+        [
+          "B",
+          1055
+        ],
+        [
+          "B",
+          936
+        ],
+        [
+          "B",
+          943
+        ],
+        [
+          "B",
+          907
+        ],
+        [
+          "B",
+          899
+        ]
+      ]
+    },
+    {
+      "v": 39,
+      "sign": -1,
+      "events": [
+        [
+          "B",
+          1465
+        ],
+        [
+          "B",
+          1464
+        ],
+        [
+          "B",
+          1050
+        ],
+        [
+          "B",
+          1053
+        ],
+        [
+          "B",
+          938
+        ],
+        [
+          "B",
+          941
+        ],
+        [
+          "B",
+          873
+        ],
+        [
+          "B",
+          865
+        ],
+        [
+          "B",
+          891
+        ],
+        [
+          "B",
+          883
+        ]
+      ]
+    },
+    {
+      "v": 192,
+      "sign": -1,
+      "events": [
+        [
+          "B",
+          1877
+        ],
+        [
+          "B",
+          1876
+        ],
+        [
+          "B",
+          1153
+        ],
+        [
+          "B",
+          1158
+        ],
+        [
+          "B",
+          1041
+        ],
+        [
+          "B",
+          1046
+        ],
+        [
+          "B",
+          902
+        ],
+        [
+          "B",
+          854
+        ],
+        [
+          "B",
+          908
+        ],
+        [
+          "B",
+          860
+        ]
+      ]
+    },
+    {
+      "v": 192,
+      "sign": -1,
+      "events": [
+        [
+          "B",
+          1885
+        ],
+        [
+          "B",
+          1884
+        ],
+        [
+          "B",
+          1155
+        ],
+        [
+          "B",
+          1156
+        ],
+        [
+          "B",
+          1043
+        ],
+        [
+          "B",
+          1044
+        ],
+        [
+          "B",
+          886
+        ],
+        [
+          "B",
+          870
+        ],
+        [
+          "B",
+          892
+        ],
+        [
+          "B",
+          876
+        ]
+      ]
+    },
+    {
+      "v": 198,
+      "sign": -1,
+      "events": [
+        [
+          "B",
+          1873
+        ],
+        [
+          "B",
+          1872
+        ],
+        [
+          "B",
+          1152
+        ],
+        [
+          "B",
+          1159
+        ],
+        [
+          "B",
+          1040
+        ],
+        [
+          "B",
+          1047
+        ],
+        [
+          "B",
+          900
+        ],
+        [
+          "B",
+          852
+        ],
+        [
+          "B",
+          910
+        ],
+        [
+          "B",
+          862
+        ]
+      ]
+    },
+    {
+      "v": 198,
+      "sign": -1,
+      "events": [
+        [
+          "B",
+          1881
+        ],
+        [
+          "B",
+          1880
+        ],
+        [
+          "B",
+          1154
+        ],
+        [
+          "B",
+          1157
+        ],
+        [
+          "B",
+          1042
+        ],
+        [
+          "B",
+          1045
+        ],
+        [
+          "B",
+          884
+        ],
+        [
+          "B",
+          868
+        ],
+        [
+          "B",
+          894
+        ],
+        [
+          "B",
+          878
+        ]
+      ]
+    }
+  ]
+}
diff --git a/research/contextual-provider-pooling/optional-audit/COSET-PATH-APPLICATION.md b/research/contextual-provider-pooling/optional-audit/COSET-PATH-APPLICATION.md
new file mode 100644
index 0000000000..d01ea9c4d0
--- /dev/null
+++ b/research/contextual-provider-pooling/optional-audit/COSET-PATH-APPLICATION.md
@@ -0,0 +1,35 @@
+# Independent path-transfer review of the twelve weighted-coset substitutions
+
+This review supplies an independent exact scalar audit of the selected provider. It does not claim an additional numerical gain, a new physical-frame theorem, or a replay of the unchanged bit supplier. The source hashes are in COSET-SOURCE-BINDING.json; the numerical receipt is COSET-PATH-REVIEW.json.
+
+## Sufficient transfer statement
+
+Let a finite linear straight-line circuit have initial coordinates split into protected inputs P and cold helper dirt C. Expand each assignment into a new register version, retaining unchanged versions by unit-weight edges. The coefficient of an initial coordinate in any output is the sum of all directed path weights from that input to the output. Induction on assignment order proves this statement: a scale multiplies the old paths, and an addition joins the old destination paths with the scaled source paths. Thus exact propagation of coefficient rows computes the boundary transfer matrix over the dyadic rationals, including all long paths and cancellation.
+
+Suppose a source rewrite at an addition preserves the destination and gate coefficient/frame, and its current prefix error has zero restriction to P. Subsequent linear maps cannot introduce a protected component into that error. Therefore the final difference is supported on C. If the retained compiler subtracts the actual cold response and then performs the inverse of the actual background program, the two compensated endpoints agree on every initial column and restore all background dirt. This conclusion requires checking the actual changed program, not merely the clean-input action or a source equality before earlier rewrites. When target decoding occurs after the background circuit it is included in the boundary map before deriving the cold response.
+
+In this witness P includes all 112 source coordinates, all 112 initial target coordinates, and 212 warm helper coordinates. The actual raw section named `precondition` is a final target decoder; it is included after A, cut, B. It is not mistaken for the compiler's initial cold-dirt compensation. The latter must be regenerated and charged by the physical pipeline.
+
+## Independent finite application
+
+A fresh C++ implementation, using Boost cpp_int dyadic arithmetic and no imported nomination, gk, or suffix-derivative routines, computes both complete 728-column boundary matrices. All 48,832 entries on 112 target rows and 436 protected columns agree exactly. The cold target-response nonzero count falls from 9,756 to 9,132, a saving of 624 entries. This is a compensation-count result, not an independent kappa increment.
+
+It separately reconstructs the current prefix at each of the twelve selected rewrites, incorporating every earlier rewrite, and checks all 728 coefficients of the stated source error. All 8,736 comparisons pass, and each error vanishes on P. The selected A indices are 205, 340, 1555, 1690, 207, 342, 475, 477, 610, 612, 745, and 747.
+
+The portable exporter proves that these exact twelve operations reconstruct the entire candidate A, that all fields other than A and cleanup remain equal, and that the 2,847 cleanup operations are precisely the reverse inverses of the actual nontarget A+B operations, at the full frame. The source audit is bound to candidate raw SHA-256 fd8ea67a1f4e8d754ffe29cc18a12aaa15c1704e58b688895e7ba51eb832b719.
+
+The path-algebra connection is actually used here as an independent exact boundary-transfer and version-error audit. Triangular elimination gives an alternative mathematical derivation of the same boundary matrix: eliminate internal time-expanded vertices, adding incoming times outgoing path weights. This is the relevant Schur/path relationship. The implementation does not separately run a second Schur-complement algorithm, and the earlier attempted register-elimination optimization had no admitted winner. There is one independent implementation, not two independent successful optimization techniques.
+
+Actual physical frame incidence, normalized operator endpoints, coefficient bounds, whole-owner maps and the assembly are checked separately by the changed-provider pipeline. This scalar audit does not replace those checks. Likewise, the source analogy is not a new Lean kernel certificate or a claim of global mathematical originality.
+
+## Optional reproduction
+
+The main verifier need not build this independent optional checker. With Python, a C++17 compiler, and genuine Boost headers installed:
+
+```
+python export_coset_paths.py --baseline BASELINE.json.gz --candidate CANDIDATE.json.gz --selection SELECTION.json --out audit-out
+c++ -O2 -std=c++17 -I BOOST_INCLUDE audit_coset_paths.cpp -o audit_coset_paths
+./audit_coset_paths audit-out/coset-path-input.txt audit-out/COSET-PATH-REVIEW.json
+```
+
+Do not compile with NDEBUG: the exact comparisons use C++ assertions. The included coset-path-input.txt is also a complete fixed independent arithmetic input; its SHA-256 is recorded by the source-binding receipt. The exporter accepts paths as arguments and contains no machine-specific locations. No executable binary is required in the submission.
diff --git a/research/contextual-provider-pooling/optional-audit/COSET-PATH-REVIEW.json b/research/contextual-provider-pooling/optional-audit/COSET-PATH-REVIEW.json
new file mode 100644
index 0000000000..db16f78ef3
--- /dev/null
+++ b/research/contextual-provider-pooling/optional-audit/COSET-PATH-REVIEW.json
@@ -0,0 +1 @@
+{"status":"PASS_INDEPENDENT_DYADIC_BOUNDARY_PATH_AND_VERSION_ERRORS","initial_columns":728,"target_rows":112,"protected_columns_including_targets":436,"protected_entries_checked":48832,"old_cold_response_nnz":9756,"new_cold_response_nnz":9132,"cold_response_nnz_saved":624,"changed_cold_entries":816,"version_witnesses":12,"exact_error_coefficients_checked":8736,"arithmetic":"independent cpp_int dyadics, no imported gk implementation"}
diff --git a/research/contextual-provider-pooling/optional-audit/COSET-SOURCE-BINDING.json b/research/contextual-provider-pooling/optional-audit/COSET-SOURCE-BINDING.json
new file mode 100644
index 0000000000..59a6b488a2
--- /dev/null
+++ b/research/contextual-provider-pooling/optional-audit/COSET-SOURCE-BINDING.json
@@ -0,0 +1,23 @@
+{
+  "status": "PASS_EXACT_SOURCE_BINDING_AND_LITERAL_CLEANUP",
+  "baseline_sha256": "931fa9d365eabacacbed055f00ce589ce29647ea904270dfe8943dd5d4ea609d",
+  "candidate_sha256": "fd8ea67a1f4e8d754ffe29cc18a12aaa15c1704e58b688895e7ba51eb832b719",
+  "selection_sha256": "d4f7ccff66f361adc06f63cdd4bafd44c0ea2dbaaf755fe619423a93a5bb1519",
+  "native_input_sha256": "779b497d52b6896a04f41d6c55424e65030a939945ca80858c369a3a3320a341",
+  "moves": 12,
+  "preserved_keys": [
+    "B",
+    "center_frames",
+    "centers",
+    "cut",
+    "ports",
+    "precondition",
+    "report",
+    "root_lines",
+    "scatter",
+    "start_extra",
+    "target_levels"
+  ],
+  "cleanup_count": 2847,
+  "all_cleanup_full_frame": true
+}
diff --git a/research/contextual-provider-pooling/optional-audit/audit_coset_paths.cpp b/research/contextual-provider-pooling/optional-audit/audit_coset_paths.cpp
new file mode 100644
index 0000000000..12bfd181ee
--- /dev/null
+++ b/research/contextual-provider-pooling/optional-audit/audit_coset_paths.cpp
@@ -0,0 +1,15 @@
+#include <bits/stdc++.h>
+#include <boost/multiprecision/cpp_int.hpp>
+using namespace std;using boost::multiprecision::cpp_int;
+struct D{cpp_int n=0;int e=0;D(){}D(long long x):n(x){}void norm(){if(n==0){e=0;return;}cpp_int a=n<0?-n:n;int k=min(e,(int)boost::multiprecision::lsb(a));n>>=k;e-=k;}D mul(long long a,long long b)const{assert(b>0&&(b&(b-1))==0);D x=*this;x.n*=a;x.e+=__builtin_ctzll((unsigned long long)b);x.norm();return x;}D operator+(const D&b)const{D c;c.e=max(e,b.e);c.n=(n<<(c.e-e))+(b.n<<(c.e-b.e));c.norm();return c;}D operator-(const D&b)const{return *this+b.mul(-1,1);}bool operator==(const D&b)const{return n==b.n&&e==b.e;}};
+struct Op{int kind,t,s;long long a,b;};int N,V;using Mat=vector<vector<D>>;
+Op readop(istream&in){Op e;in>>e.kind>>e.t>>e.s>>e.a>>e.b;return e;}
+Mat ident(){Mat x(N,vector<D>(N));for(int i=0;i<N;i++)x[i][i]=D(1);return x;}
+void apply_gate(Mat&x,const Op&e){for(int j=0;j<N;j++){if(e.kind)x[e.t][j]=x[e.t][j].mul(e.a,e.b);else if(x[e.s][j].n!=0)x[e.t][j]=x[e.t][j]+x[e.s][j].mul(e.a,e.b);}}
+int main(int argc,char**argv){ifstream in(argv[1]);int K,PN;in>>N>>V>>K>>PN;set<int>P;for(int i=0,r;i<PN;i++){in>>r;P.insert(r);}vector<Mat> results;for(int v=0;v<2;v++){int m;in>>m;Mat x=ident();for(int j=0;j<m;j++)apply_gate(x,readop(in));results.push_back(move(x));}
+long long oldcold=0,newcold=0,diffcold=0,protectedentries=0;for(int t=V;t<2*V;t++)for(int j=0;j<N;j++){if(P.count(j)){assert(results[0][t][j]==results[1][t][j]);protectedentries++;}else{oldcold+=results[0][t][j].n!=0;newcold+=results[1][t][j].n!=0;diffcold+=!(results[0][t][j]==results[1][t][j]);}}
+int ac;in>>ac;vector<Op> A(ac);for(auto&e:A)e=readop(in);long long exacterrors=0;
+for(int k=0;k<K;k++){int index,m;in>>index;Op change=readop(in);in>>m;vector<D>expected(N);for(int j=0,c;j<m;j++){long long a,b;in>>c>>a>>b;expected[c]=D(1).mul(a,b);}Mat x=ident();for(int j=0;j<index;j++)apply_gate(x,A[j]);Op old=A[index];assert(old.kind==0&&change.kind==0&&old.t==change.t);
+ for(int j=0;j<N;j++){D error=x[change.s][j].mul(change.a,change.b)-x[old.s][j].mul(old.a,old.b);assert(error==expected[j]);if(P.count(j))assert(error.n==0);exacterrors++;}A[index]=change;}
+assert(oldcold-newcold==624);ofstream out(argv[2]);out<<"{\"status\":\"PASS_INDEPENDENT_DYADIC_BOUNDARY_PATH_AND_VERSION_ERRORS\",\"initial_columns\":"<<N<<",\"target_rows\":"<<V<<",\"protected_columns_including_targets\":"<<PN<<",\"protected_entries_checked\":"<<protectedentries<<",\"old_cold_response_nnz\":"<<oldcold<<",\"new_cold_response_nnz\":"<<newcold<<",\"cold_response_nnz_saved\":"<<oldcold-newcold<<",\"changed_cold_entries\":"<<diffcold<<",\"version_witnesses\":"<<K<<",\"exact_error_coefficients_checked\":"<<exacterrors<<",\"arithmetic\":\"independent cpp_int dyadics, no imported gk implementation\"}\n";cout<<"PASS protected "<<protectedentries<<" old "<<oldcold<<" new "<<newcold<<" witnesses "<<K<<endl;
+}
diff --git a/research/contextual-provider-pooling/optional-audit/coset-path-input.txt b/research/contextual-provider-pooling/optional-audit/coset-path-input.txt
new file mode 100644
index 0000000000..0141a70a92
--- /dev/null
+++ b/research/contextual-provider-pooling/optional-audit/coset-path-input.txt
@@ -0,0 +1,10634 @@
+728 112 12 436
+0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 448 449 450 451 452 453 454 455 456 457 458 459 460 461 470 471 472 473 482 483 484 485 486 487 488 489 496 497 498 499 500 501 508 509 520 521 523 525 532 533 534 535 536 537 538 539 540 541 544 545 546 547 548 549 550 551 552 553 556 557 562 563 564 565 568 569 571 573 574 575 576 577 580 581 583 585 590 591 592 593 594 595 596 597 599 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727
+4287
+0 474 488 -1 1
+0 475 489 -1 1
+0 480 536 1 2
+0 481 537 1 2
+0 490 538 -1 1
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+0 478 548 1 2
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+0 468 546 1 2
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+0 492 552 -1 1
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+0 466 534 1 2
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diff --git a/research/contextual-provider-pooling/optional-audit/export_coset_paths.py b/research/contextual-provider-pooling/optional-audit/export_coset_paths.py
new file mode 100644
index 0000000000..b02c0127eb
--- /dev/null
+++ b/research/contextual-provider-pooling/optional-audit/export_coset_paths.py
@@ -0,0 +1,39 @@
+import argparse, gzip, hashlib, json
+from fractions import Fraction
+from pathlib import Path
+p=argparse.ArgumentParser();p.add_argument('--baseline',type=Path,required=True);p.add_argument('--candidate',type=Path,required=True);p.add_argument('--selection',type=Path,required=True);p.add_argument('--out',type=Path,required=True);a=p.parse_args()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+u,v,steps=read(a.baseline),read(a.candidate),read(a.selection)
+assert len(u['ports'])==112
+V=112;N=728
+P=set(range(2*V))|set(map(int,u['start_extra']))
+assert len(P)==436
+work=json.loads(json.dumps(u))
+for q in steps:
+ i=q['index'];assert work['A'][i]==q['old_operation'];work['A'][i]=q['new_operation']
+assert work['A']==v['A']
+assert all(u[k]==v[k] for k in u if k not in ['A','cleanup'])
+def inverse(e):
+ if e[0]=='add':return [e[0],e[1],e[2],-e[3],e[4],list(range(9))]
+ return [e[0],e[1],e[3],e[2],list(range(9))]
+def scalar(e):return e[:-1]
+expected=[inverse(e) for e in reversed(v['A']+v['B']) if not V<=e[1]<2*V]
+assert [scalar(e) for e in expected]==[scalar(e) for e in v['cleanup']]
+assert all(e[-1]==[256,128,64,32,16,8,4,2,1] for e in v['cleanup'])
+def op(e):
+ if e[0]=='add':return f'0 {e[1]} {e[2]} {e[3]} {e[4]}'
+ assert e[0]=='scale';return f'1 {e[1]} -1 {e[2]} {e[3]}'
+lines=[f'{N} {V} {len(steps)} {len(P)}',' '.join(map(str,sorted(P)))]
+for w in [u,v]:
+ seq=w['A']+w['cut']+w['B']+w['precondition'];lines+=[str(len(seq))]+list(map(op,seq))
+lines+=[str(len(u['A']))]+list(map(op,u['A']))
+for q in steps:
+ lines += [str(q['index']),op(q['new_operation']),str(len(q['cold_difference']))]
+ for j,x in q['cold_difference'].items():
+  z=Fraction(x);lines.append(f'{j} {z.numerator} {z.denominator}')
+a.out.mkdir(parents=True,exist_ok=True)
+x=('\n'.join(lines)+'\n').encode();(a.out/'coset-path-input.txt').write_bytes(x)
+sha=lambda x:hashlib.sha256(x).hexdigest()
+receipt={'status':'PASS_EXACT_SOURCE_BINDING_AND_LITERAL_CLEANUP','baseline_sha256':sha(a.baseline.read_bytes()),'candidate_sha256':sha(a.candidate.read_bytes()),'selection_sha256':sha(a.selection.read_bytes()),'native_input_sha256':sha(x),'moves':len(steps),'preserved_keys':[k for k in u if k not in ['A','cleanup']],'cleanup_count':len(expected),'all_cleanup_full_frame':True}
+(a.out/'COSET-SOURCE-BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n',encoding='utf-8')
+print(json.dumps(receipt))
diff --git a/research/contextual-provider-pooling/providers/MANIFEST.json b/research/contextual-provider-pooling/providers/MANIFEST.json
new file mode 100644
index 0000000000..de5c474f04
--- /dev/null
+++ b/research/contextual-provider-pooling/providers/MANIFEST.json
@@ -0,0 +1,9 @@
+{
+  "audit_promoted_scalar.py": "1994e7116065636b53bf740000ff78dce8ea62390e597d293d183f33c67eaa6d",
+  "build_promoted_epoch.py": "471ecdc704c7ef014230f7af5fd74034c58b4ca167c5b289cfaaa10d205eab23",
+  "build_providers.py": "a88707f15e1b2e3f1597d49adacc98d5ddc843bb0fa2f641f2e2333b5d19e317",
+  "PROMOTION.json": "9ad34faa8611a6ea7f161d2e1fe331ab1ba5ccec8fca3978e31c3e7bf789bc31",
+  "PROVIDER-PROOF.md": "51eaa725ce6939bb8d69fcce0a7503e19e397e897076bf2c873d1a50774a8b41",
+  "SOURCE-INSPECTION.json": "e848d67a145f217f465ab3e471f4098522195b12e994acddf734845af5e61fdd",
+  "VARIANTS.json": "d5af9008ed661ee2daa31e567212008ca1a27cab7f6184b4eda2beb3b6bfbc69"
+}
diff --git a/research/contextual-provider-pooling/providers/PROMOTION.json b/research/contextual-provider-pooling/providers/PROMOTION.json
new file mode 100644
index 0000000000..3910c5a057
--- /dev/null
+++ b/research/contextual-provider-pooling/providers/PROMOTION.json
@@ -0,0 +1,79 @@
+{
+  "status": "PASS_LITERAL_PARTIAL_RANK5_PROMOTION_FRAME_CHAIN",
+  "source_sha256": "a30810b755cf80e1128c0b932728bd51ca8e0bb31225fc415675afb42a766c8f",
+  "word_sha256": "375bd23001cd805707968005a9342827d5464e3f8e3a754197b31c46fc3f63c2",
+  "changes": [
+    {
+      "group": 10,
+      "old_E": [
+        260,
+        132,
+        96,
+        24
+      ],
+      "new_E": [
+        260,
+        132,
+        96,
+        24,
+        1
+      ],
+      "pivots": [
+        419,
+        421,
+        422,
+        423
+      ],
+      "gates": 12
+    },
+    {
+      "group": 6,
+      "old_E": [
+        267,
+        139,
+        96,
+        30
+      ],
+      "new_E": [
+        267,
+        139,
+        96,
+        25,
+        7
+      ],
+      "pivots": [
+        451,
+        453,
+        454,
+        455
+      ],
+      "gates": 12
+    }
+  ],
+  "local_before": {
+    "1": 2300,
+    "4": 184,
+    "8": 8,
+    "3": 472,
+    "2": 440,
+    "6": 56,
+    "5": 56
+  },
+  "local_after": {
+    "1": 2316,
+    "4": 192,
+    "8": 8,
+    "3": 464,
+    "2": 424,
+    "6": 56,
+    "5": 56
+  },
+  "widths": {
+    "9": 292,
+    "8": 156,
+    "5": 48,
+    "4": 8
+  },
+  "exploratory_gzip_sha256": "59eb1a2356b764544be4aab0432df1b07710ca57f8fe32fe6c0788e83aded4aa",
+  "word_content_sha256": "2b67fd69853dfc28f30ab5bb928f573077ae9d2bfa12cc36254d018d56133a5d"
+}
diff --git a/research/contextual-provider-pooling/providers/PROVIDER-PROOF.md b/research/contextual-provider-pooling/providers/PROVIDER-PROOF.md
new file mode 100644
index 0000000000..119ef7e187
--- /dev/null
+++ b/research/contextual-provider-pooling/providers/PROVIDER-PROOF.md
@@ -0,0 +1,53 @@
+# Epoch and selected-promotion provider construction
+
+The source is the frozen TN27 epoch word. PR558 supplies two sets of four
+post-center response-kernel pivots. This registry implements p0, p2, p4, p6,
+and p8, with helper-index sets fixed in VARIANTS.json. It does not infer a
+numerical result merely from entrance rank.
+
+## Sufficient composition argument
+
+The epoch rewrite changes the source presentation in A, with its exact terminal
+inverse, and preserves the full arbitrary-dirt linear operator. The promotion
+changes starting frames and 3 correction gates per selected pivot inside
+B[320:488]. All 168 gates there are elementary additions whose destination set
+and source set are disjoint. Their pairwise products therefore commute. Sorting
+these gates by frame dimension preserves the scalar operator, not just its clean
+input restriction. The constructor checks this disjointness and preserves the
+scalar multiset of B; A is unchanged from the already reconstructed epoch word.
+
+For each promoted helper, the new entrance contains its old rank-4 entrance and
+has rank 5. Every correction sourced by that helper is moved to the new frame.
+The exact nested-frame profile check validates every resulting chain. Cleanup is
+regenerated as the inverse of every background operation in reverse order.
+Since background operations do not read targets, their complete background
+transformation and inverse restore arbitrary initial helper dirt. The scalar
+replay also independently checks the compensation, endpoint, and dual endpoint
+on all 728 initial columns, plus omission controls for every promoted pivot.
+These checks do not certify physical owners, normalized adapters or the outer
+recurrence: the complete local and global replay must additionally certify them.
+
+## Nonlinear partial-group cost
+
+The complete p4 group has exactly half the local profile delta of p8 versus p0.
+The partial p2 and p6 choices do not interpolate that delta. Their combined
+histogram excess over p8+p0 is +12 rank-1 -4 rank-2 +4 rank-3 -4 rank-4 calls.
+This penalty must be included when pricing a time-dependent provider registry.
+Each constructor receipt contains the complete local histogram and ordered
+residual widths; no component gains may be added without that bill.
+
+## Reproduction
+
+Run:
+
+    python -B build_providers.py --input EPOCH/FULL-WORD.json.gz --gk-dir GK --out NEW_OUTPUT --audit
+
+EPOCH is the TN27 epoch constructor output. GK contains the preserved upstream
+gk_word.py and gk_common.py implementation. NEW_OUTPUT must not exist. Input,
+recipe, and output words are pinned by canonical JSON SHA-256 so CRLF and gzip
+implementation differences cannot disguise semantic changes. Newly emitted
+gzip uses compression level 9, mtime 0 and OS byte 255. p0 is copied unchanged.
+
+PR558 receives credit for the rank-5 promotion. The epoch presentation was
+already delivered in TN27. The new numerical mechanism, if fully admitted by
+the global replay, is resource-aware heterogeneous use of these providers.
diff --git a/research/contextual-provider-pooling/providers/SOURCE-INSPECTION.json b/research/contextual-provider-pooling/providers/SOURCE-INSPECTION.json
new file mode 100644
index 0000000000..dd30116048
--- /dev/null
+++ b/research/contextual-provider-pooling/providers/SOURCE-INSPECTION.json
@@ -0,0 +1,15 @@
+{
+  "sources": [
+    {
+      "source": "OAI/LinearAlgebra/MatrixMultiplication/Tensor/ComplexTensorRestrictionComposition.lean",
+      "sha256": "adf61335067c1e8b5f31ffac922f274950ffcfb2e91472672f08a400ddcb14d3",
+      "status": "source inspection; no new Lean compilation; not a numerical ingredient"
+    },
+    {
+      "source": "OAI/LinearAlgebra/MatrixMultiplication/Tensor/ComplexSeparatedTensorDecomposition.lean",
+      "sha256": "1c20cb73e7fb3c045c675884343c24fea0758289932cfd566f15d655f1ec2905",
+      "status": "source inspection; no new Lean compilation; not a numerical ingredient"
+    }
+  ],
+  "scope": "Restriction composition and separated tensor fibers suggested a multi-carrier delivery-block factorization. The paid bounded screen was not completed before the positive provider-mixture construction was frozen. No gain is attributed to these two analogies."
+}
diff --git a/research/contextual-provider-pooling/providers/VARIANTS.json b/research/contextual-provider-pooling/providers/VARIANTS.json
new file mode 100644
index 0000000000..dfbd8f0404
--- /dev/null
+++ b/research/contextual-provider-pooling/providers/VARIANTS.json
@@ -0,0 +1,2130 @@
+{
+  "p0": {
+    "pivots": [],
+    "word_semantic_sha256": "7d3b66098cf0b74cbbdc42993f4366f22f8e63302a2626628e2f753c68338e4e"
+  },
+  "p2": {
+    "word_semantic_sha256": "6be1e2b27127705f5672df5c87edece51746eb3d62c1bcd55b4f0bd4d27dc8c9",
+    "local_profile": {
+      "1": 2310,
+      "4": 184,
+      "8": 8,
+      "3": 472,
+      "2": 434,
+      "6": 56,
+      "5": 56
+    },
+    "width_counts": {
+      "9": 292,
+      "8": 156,
+      "5": 54,
+      "4": 2
+    },
+    "ordered_widths": [
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+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
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+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
+      9,
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+      5,
+      8,
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+      8,
+      5,
+      8,
+      5,
+      5,
+      5
+    ],
+    "pivots": [
+      419,
+      421,
+      422,
+      423,
+      451,
+      453,
+      454,
+      455
+    ]
+  }
+}
diff --git a/research/contextual-provider-pooling/providers/audit_promoted_scalar.py b/research/contextual-provider-pooling/providers/audit_promoted_scalar.py
new file mode 100644
index 0000000000..a532682863
--- /dev/null
+++ b/research/contextual-provider-pooling/providers/audit_promoted_scalar.py
@@ -0,0 +1,57 @@
+"""Independent exact scalar witness for a selected complex kernel word.
+Uses immutable correct-word compensation for omission controls; no repaired
+compensation is silently supplied to a mutant. No physical-hosting claim.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+p=Path(__file__).resolve().parent
+path=Path(sys.argv[1]);selection=Path(sys.argv[2]);out=Path(sys.argv[3]);w=json.loads(gzip.decompress(path.read_bytes()));sel=json.loads(selection.read_text());v=len(w['ports']);n=2*v+w['report']['R']
+def ident():return[{r:Q(1)}for r in range(n)]
+def apply(e,rows):
+ if e[0]=='scale':
+  _,t,a,b,*_=e;q=Q(a,b);rows[t]={j:q*x for j,x in rows[t].items()};return
+ _,t,s,a,b,*_=e;q=Q(a,b)
+ for j,x in list(rows[s].items()):
+  z=rows[t].get(j,Q(0))+q*x
+  if z:rows[t][j]=z
+  else:rows[t].pop(j,None)
+def inv(e,dual=False):
+ e=copy.deepcopy(e)
+ if e[0]=='add':
+  e[3]*=-1
+  if dual:e[1],e[2]=e[2],e[1]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def replay(es):
+ rows=ident()
+ for e in es:apply(e,rows)
+ return rows
+main=w['A']+w['cut']+w['B'];mx=replay(main);dirty=[{}for _ in range(n)]
+for r in range(v,2*v):dirty[r]={j:x for j,x in mx[r].items()if j>=2*v}
+for e in w['precondition']:apply(e,dirty)
+comp=[]
+for r in range(v,2*v):
+ for j,x in sorted(dirty[r].items()):
+  assert not w.get('start_extra',{}).get(str(j)),('nonzero-frame compensation',j)
+  comp.append(['add',r,j,-x.numerator,x.denominator,[]])
+cleanup=[inv(e)for e in reversed(w['A']+w['B'])if not v<=e[1]<2*v]
+assert[e[:-1]for e in cleanup]==[e[:-1]for e in w['cleanup']]
+program=w['precondition']+comp+main+cleanup;expected=ident()
+for t in range(v):expected[v+t][t]=Q(1)
+assert replay(program)==expected
+back=ident()
+for t in range(v):back[t][v+t]=Q(-1)
+assert replay([inv(e,True)for e in program])==back
+controls={}
+recipe=json.loads((path.parent/'PROMOTION.json').read_text())
+for change in recipe['changes']:
+ for h in change['pivots']:
+  bb=[e for e in w['B']if not(e[0]=='add'and e[2]==2*v+h and e[1]>=2*v and e[-1]==change['new_E'])]
+  assert len(bb)==len(w['B'])-3
+  cc=[inv(e)for e in reversed(w['A']+bb)if not v<=e[1]<2*v]
+  assert replay(w['precondition']+comp+w['A']+w['cut']+bb+cc)!=expected
+  controls[str(h)]='REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION'
+r=dict(status='PASS_EXACT_RATIONAL_FORWARD_AND_INVERSE_TRANSPOSE',word_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),selection_sha256=hashlib.sha256(selection.read_bytes()).hexdigest(),columns_each_orientation=n,compensations=len(comp),program_operations=len(program),kernel_pivots=len(controls),controls=controls,scope='Exact local scalar identity and preserved frame-zero compensation; physical owner routing, complete invoice and outer kappa separate.')
+out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],n,len(controls))
diff --git a/research/contextual-provider-pooling/providers/build_promoted_epoch.py b/research/contextual-provider-pooling/providers/build_promoted_epoch.py
new file mode 100644
index 0000000000..272887732f
--- /dev/null
+++ b/research/contextual-provider-pooling/providers/build_promoted_epoch.py
@@ -0,0 +1,40 @@
+from pathlib import Path
+import argparse,copy,json,gzip,hashlib,sys
+from collections import Counter
+ap=argparse.ArgumentParser();ap.add_argument('--input',required=True);ap.add_argument('--gk-dir',required=True);ap.add_argument('--promotion',required=True);ap.add_argument('--out',required=True);ap.add_argument('--pivots',default='all');a=ap.parse_args()
+sys.path.insert(0,a.gk_dir);import gk_word as g,gk_common as co
+g.V=co.V=112;g.DATA=co.DATA=7168
+canon=lambda v:json.dumps(v,sort_keys=True,separators=(',',':')).encode()
+w=json.loads(gzip.decompress(Path(a.input).read_bytes()));recipe=json.loads(Path(a.promotion).read_text())
+assert hashlib.sha256(canon(w)).hexdigest()=='7d3b66098cf0b74cbbdc42993f4366f22f8e63302a2626628e2f753c68338e4e'
+assert hashlib.sha256(canon(recipe)).hexdigest()=='857cbcfbcdd1ab31b276a825d98eaaa31e4c18e3abc48a5d0f37d4b046e6bff7','promotion recipe pin mismatch'
+full={h for c in recipe['changes']for h in c['pivots']}
+chosen=full if a.pivots=='all'else set(map(int,a.pivots.split(',')))if a.pivots else set()
+assert chosen<=full
+old=copy.deepcopy(w);kernel=w['B'][320:488]
+assert len(kernel)==168 and all(e[0]=='add'for e in kernel)
+assert not{e[1]for e in kernel}&{e[2]for e in kernel}
+changes=[]
+for ch in recipe['changes']:
+ pivots=[h for h in ch['pivots']if h in chosen]
+ if not pivots:continue
+ E0,E1=ch['old_E'],ch['new_E']
+ assert len(g.basis(E0))==4 and len(g.basis(E1))==5 and g.span(E0)<=g.span(E1)
+ for h in pivots:assert w['start_extra'][str(224+h)]==E0;w['start_extra'][str(224+h)]=E1
+ changed=0
+ for op in kernel:
+  if op[2]-224 in pivots:assert op[-1]==E0;op[-1]=E1;changed+=1
+ assert changed==3*len(pivots)
+ changes.append(dict(ch,pivots=pivots,gates=changed))
+w['B'][320:488]=sorted(kernel,key=lambda e:len(e[-1]))
+w['cleanup']=[g.inverse(e,g.FULL)for e in reversed(w['A']+w['B'])if not 112<=e[1]<224]
+assert w['A']==old['A']
+assert Counter(tuple(e[:-1])for e in old['B'])==Counter(tuple(e[:-1])for e in w['B'])
+H=g.profile(w);widths=Counter(g.widths_of(w))
+w['report'].update(local_profile=dict(H),width_inventory=dict(widths),local_rank_mass=sum(k*v for k,v in H.items()),status='EPOCH_SELECTED_RANK5_PROMOTION_PENDING_GLOBAL_ADMISSION')
+out=Path(a.out);out.mkdir(parents=True,exist_ok=False);raw=gzip.compress(gzip.decompress(g.dump(w)),compresslevel=9,mtime=0);raw=raw[:9]+bytes([255])+raw[10:];(out/'FULL-WORD.json.gz').write_bytes(raw)
+selected=dict(recipe,changes=changes,local_after=dict(H),widths=dict(widths))
+(out/'PROMOTION.json').write_text(json.dumps(selected,indent=2)+'\n')
+receipt=dict(status='PASS_FRAME_PROFILE_PENDING_SCALAR',selected_pivots=sorted(chosen),source_semantic_sha256=hashlib.sha256(canon(old)).hexdigest(),promotion_semantic_sha256=hashlib.sha256(canon(recipe)).hexdigest(),word_semantic_sha256=hashlib.sha256(canon(w)).hexdigest(),word_sha256=hashlib.sha256(raw).hexdigest(),local_profile=dict(H),width_counts=dict(widths),ordered_widths=g.widths_of(w),scalar_A_unchanged=True,scalar_B_multiset_unchanged=True)
+(out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(out.name,'pivots',len(chosen),'H',dict(H),'widths',dict(widths))
diff --git a/research/contextual-provider-pooling/providers/build_providers.py b/research/contextual-provider-pooling/providers/build_providers.py
new file mode 100644
index 0000000000..31571ff3d0
--- /dev/null
+++ b/research/contextual-provider-pooling/providers/build_providers.py
@@ -0,0 +1,23 @@
+"""Rebuild frozen rank-5 promotion providers from the TN27 epoch word."""
+import argparse,gzip,hashlib,json,shutil,subprocess,sys
+from pathlib import Path
+ap=argparse.ArgumentParser();ap.add_argument('--input',required=True);ap.add_argument('--gk-dir',required=True);ap.add_argument('--out',required=True);ap.add_argument('--audit',action='store_true');a=ap.parse_args()
+here=Path(__file__).resolve().parent
+registry=json.loads((here/'VARIANTS.json').read_text())
+def digest(path):
+ w=json.loads(gzip.decompress(Path(path).read_bytes()))
+ return hashlib.sha256(json.dumps(w,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+assert digest(a.input)==registry['p0']['word_semantic_sha256'],'wrong epoch source'
+out=Path(a.out);out.mkdir(parents=True,exist_ok=False)
+for name,item in registry.items():
+ dest=out/name
+ if name=='p0':
+  dest.mkdir();shutil.copyfile(a.input,dest/'FULL-WORD.json.gz')
+  (dest/'PROMOTION.json').write_text(json.dumps({'changes':[]})+'\n')
+ else:
+  subprocess.run([sys.executable,'-B',str(here/'build_promoted_epoch.py'),'--input',a.input,'--gk-dir',a.gk_dir,'--promotion',str(here/'PROMOTION.json'),'--out',str(dest),'--pivots',','.join(map(str,item['pivots']))],check=True)
+ assert digest(dest/'FULL-WORD.json.gz')==item['word_semantic_sha256'],('output pin',name)
+ if a.audit:
+  subprocess.run([sys.executable,'-B',str(here/'audit_promoted_scalar.py'),str(dest/'FULL-WORD.json.gz'),str(dest/'PROMOTION.json'),str(dest/'SCALAR-AUDIT.json')],check=True)
+(out/'REGISTRY.json').write_text(json.dumps({'status':'PASS_CANONICAL_SOURCE_AND_VARIANT_PINS','variants':registry,'scalar_replayed':a.audit},indent=2)+'\n')
+print('PASS',out)
diff --git a/research/contextual-provider-pooling/providers/run_variants.py b/research/contextual-provider-pooling/providers/run_variants.py
new file mode 100644
index 0000000000..f8d2d9945c
--- /dev/null
+++ b/research/contextual-provider-pooling/providers/run_variants.py
@@ -0,0 +1,18 @@
+"""Reconstruct selected local providers and replay every changed physical program."""
+from pathlib import Path
+import argparse,json,subprocess,sys
+if not __debug__:raise RuntimeError('Assertions required')
+p=Path(__file__).resolve().parent;root=p.parent;v=root/'complex-global/vendor531';g=root/'complex-local/static44/gk';launch=root/'complex-local/code/run_portable.py'
+a=argparse.ArgumentParser();a.add_argument('--source',type=Path,required=True);a.add_argument('--out',type=Path,required=True);a=a.parse_args();old=a.source.resolve();out=a.out.resolve();assert not out.exists();out.mkdir(parents=True)
+def run(script,*args):subprocess.run([sys.executable,'-B',str(launch),str(script),*map(str,args)],check=True)
+run(p/'build_providers.py','--input',old/'epoch/FULL-WORD.json.gz','--gk-dir',g,'--out',out/'raw','--audit')
+locations={'n0':str(old/'local')}
+for k in [2,6,8]:
+ local=out/f'n{k}/local';base=old/'local'
+ run(v/'code/audit_and_transport.py','--raw',out/f'raw/p{k}/FULL-WORD.json.gz','--routing',base/'CANONICAL-WORD.json.gz','--out',local)
+ run(v/'code/phases_delta.py','--local',local,'--baseline',base,'--compiler',v/'vendor/clifford')
+ run(v/'code/adapters_local.py',local/'CANONICAL-WORD.json.gz',local/'RESIDUAL-ADAPTERS.json',local/'WRAPPER-CHECKS.json')
+ run(v/'code/emit_local.py',local);run(v/'code/audit_local.py',local)
+ locations[f'n{k}']=str(local)
+(out/'PROVIDERS.json').write_text(json.dumps(locations,indent=2)+'\n',encoding='utf8',newline='\n')
+print('PASS selected provider source, omitted-pivot, phase and full-column audits')
diff --git a/research/contextual-provider-pooling/response/CROSS-FIELD-PROOFS.md b/research/contextual-provider-pooling/response/CROSS-FIELD-PROOFS.md
new file mode 100644
index 0000000000..18e0ec9eb2
--- /dev/null
+++ b/research/contextual-provider-pooling/response/CROSS-FIELD-PROOFS.md
@@ -0,0 +1,41 @@
+# Two cross-field sufficient constructions
+
+## Temporal observable-state merger
+
+Consider a cut in a finite linear circuit. Let r and s be two background registers that, after the cut, are neither written nor read by background operations. They may be read by target operations, and the target subsystem may have arbitrary subsequent invertible linear operations. Let O_r and O_s be their exact final target-response columns, computed by the backward adjoint of the entire remaining circuit. Suppose O_r = a O_s.
+
+Insert s += a r at the cut, and remove every subsequent target read of r. Since neither background state changes again, the original suffix's contribution is O_r r + O_s s. The changed suffix's contribution is O_s(s+a r), which is identical. The other states' contributions are unchanged by linearity. This argument incorporates target-to-target gates through the adjoint; simply summing coefficients by target would be insufficient.
+
+The added shear is invertible. Retain the stored register r, regenerate inverse background cleanup, and both arbitrary initial dirty values are restored. There is no erasure of an unobserved state. A sufficient native realization requires a common gate frame F containing both current frames and lying in the next frame of s; r needs no later delivery frame after its reads are removed. All remaining target chains and final frames must still be legal. Every extra shear, altered child rank and remainder is charged. Thus an explicit successful frame/column replay plus a lower complete moment suffices for an improved supplier.
+
+This is a causal one-dimensional specialization of state realization using future observations. A general rank factorization O=L R does not by itself prove an implementation: the state transform, extra coordinates, intermediate availability and physical frame schedule still require an explicit invertible circuit. We use the sufficient pair construction above, not a dimension-only claim. On the current witness 308 stable-cut positions yielded no proportional eligible pair; this restricted gate found no improvement.
+
+Source connections: Lall's Realization Theory notes explain reachability/observability and the Hankel operator. Mathlib's LinearRecurrence.toInit gives the explicit equivalence between a trajectory and its initial state, and proves trajectory uniqueness. Neither source supplies the native frame realization automatically.
+
+## Weighted coset decoding of a family of reads
+
+Keep the protected initial coordinates P (data and warm helper dirt) fixed. Cold helper dirt D is the only allowed quotient. At a read gate t += q s, choose another available register r and a coefficient a such that the exact current prefix rows satisfy row(s)|P = a row(r)|P. Replacing the gate by t += q a r changes the current state by a vector supported only on D. Consequently the final protected response is unchanged. Regenerated frame-zero compensation cancels the changed cold response, while literal inverse background cleanup restores all arbitrary background dirt.
+
+The new ingredient is a global cost and its exact update, rather than an isolated quotient identity. Let P_i be the actual prefix matrix before the gate and R_i the actual suffix matrix after it. The elementary-gate difference is e_t v^T, with v^T = q(a e_r^T-e_s^T). Therefore the complete matrix changes by
+
+Delta M = (R_i e_t) (v^T P_i).
+
+After applying the fixed target normalization L, the compensation table changes by the outer product
+
+Delta C = (L R_i e_t) (v^T P_i)|D.
+
+This identity is exact. It permits scoring a candidate by the weighted Hamming cost sum w[j,k] * 1(C[j,k] != 0), using only entries affected by that outer product. If its actual frame profile is preserved, a strict reduction in this cost reduces scalar compensation work. For an accepted family, recompute the prefix, suffix and table after each step; never add gains measured against incompatible original words. Induction proves that every accepted word preserves the protected response and admits the same sufficient compensation/cleanup construction.
+
+This is weighted coset representative selection: all admissible read representatives have the same protected syndrome, while their cold response is optimized against the existing table. Rational coefficients and dyadic compiler restrictions replace the usual finite-field alphabet. The method does not solve general minimum-weight decoding or claim global optimality. The search is a bounded exact greedy family decoder. Every selected representative is proved over the rationals; modular nominations are not certificates.
+
+Mathlib's hammingNorm is exactly the count of nonzero coordinates. Coding theory's coset-leader viewpoint supplies the optimization analogy. The new constructive outer-product update, explicit frame gate, and recomputation between accepted rewrites are proved here.
+
+## Discovery scope
+
+The fixed-frame and frame-interval source-family screens found no paid-rank improvement among 130 single alternatives, 50 lift-family trials and 10 interval-family trials. Two complete response-component retirement modes, across14 components, were sent for joint inventory pricing and were not selected by the complete capacity model. These are bounded negative searches, not universal barriers.
+
+The weighted family decoder's actual saving and complete local replay are recorded separately in weighted-coset/SCREEN.json and weighted-coset-local/. No scalar-operation saving is called a paid-rank improvement. The parent's independently proved collective frame contraction supplies the numerical rank-profile gain.
+
+## Certified concrete family
+
+The frozen twelve-step family reduces the compensation table from 9,756 to 9,132 nonzero entries, saving 624 scalar additions per local invocation. The full scalar program shrinks from 16,890 to 16,266 operations; each oriented emitted program shrinks from 22,107 to 21,483 events. The paid profile remains {1:2300,2:440,3:472,4:184,5:56,6:56,8:8}, with unchanged 504 helpers and all owner widths. Fresh native replay verifies every 728 formal column in both orientations, 2,929 phase edges, 23 residual adapters and 11 mutation controls. This is a scalar-work reduction composed with the separately proved collective-frame numerical gain.
diff --git a/research/contextual-provider-pooling/response/README.md b/research/contextual-provider-pooling/response/README.md
new file mode 100644
index 0000000000..4a201d36ea
--- /dev/null
+++ b/research/contextual-provider-pooling/response/README.md
@@ -0,0 +1 @@
+Run build_weighted_coset.py --input PARENT_AVALANCHE8_WORD --selection WEIGHTED-COSET-SELECTION.json --gk-dir SHARED_GK_DIRECTORY --out NEW_DIRECTORY. The fixed input/output semantic hashes exclude report metadata only. Every chosen quotient identity is recomputed exactly; no search runs. The enclosing verifier must run its unchanged native transport, phase, adapter, scalar and global checks on the output.
diff --git a/research/contextual-provider-pooling/response/SOURCE-MANIFEST.json b/research/contextual-provider-pooling/response/SOURCE-MANIFEST.json
new file mode 100644
index 0000000000..bdcde1589b
--- /dev/null
+++ b/research/contextual-provider-pooling/response/SOURCE-MANIFEST.json
@@ -0,0 +1,7 @@
+{
+  "build_weighted_coset.py": "563f3365c267a3d373b1a8135e0ebb2687a87e0ebffed8ec8c887e5e0811a1cd",
+  "CROSS-FIELD-PROOFS.md": "3d0a1b9ac989283400e7c1e3a025080a8f6837755baccdd55f5e51599ac0921e",
+  "README.md": "f64686b5807c4e6d08f42f7c615e204d63e264323976518e8020b8b516ce8cc5",
+  "SOURCES.json": "04f23772f3d5aaa27ef918d303eadf53e994c56189c3dec9a92bcd6aec934d84",
+  "WEIGHTED-COSET-SELECTION.json": "85cb5942943df762750a2f86c1812459172cffff61bba7955270b180bc4aff7e"
+}
diff --git a/research/contextual-provider-pooling/response/SOURCES.json b/research/contextual-provider-pooling/response/SOURCES.json
new file mode 100644
index 0000000000..992fb0946f
--- /dev/null
+++ b/research/contextual-provider-pooling/response/SOURCES.json
@@ -0,0 +1,30 @@
+[
+  {
+    "path": "Mathlib/Algebra/LinearRecurrence.lean",
+    "sha256": "78b01a4057af050e55bd9ff20180bd516ffbaeb93d04c3133852fcd7ae36c72b",
+    "declarations": [
+      "LinearRecurrence.toInit",
+      "LinearRecurrence.eq_mk_of_is_sol_of_eq_init"
+    ],
+    "scope": "Source inspection only; no Lean compilation"
+  },
+  {
+    "path": "Mathlib/InformationTheory/Hamming.lean",
+    "sha256": "2137a114bbbd90185eda5c8033b23c97f2610b7382b352da325ef903740a9a5a",
+    "declarations": [
+      "hammingNorm",
+      "hammingDist"
+    ],
+    "scope": "Source inspection only; no Lean compilation"
+  },
+  {
+    "url": "https://lall.stanford.edu/engr207c/lectures/realization_2008_11_15_03.pdf",
+    "source": "Sanjay Lall, Engr207C, Realization Theory",
+    "use": "Finite-horizon observability and state realization; our sufficient temporal pair lemma is proved separately."
+  },
+  {
+    "url": "https://personalpages.manchester.ac.uk/staff/yuri.bazlov/code/notes/ch4.html",
+    "source": "Yuri Bazlov, Coding Theory, Chapter4",
+    "use": "Coset leaders and minimum Hamming weight; adapted here to exact rational compensation tables, not a finite-field decoding complexity claim."
+  }
+]
diff --git a/research/contextual-provider-pooling/response/WEIGHTED-COSET-SELECTION.json b/research/contextual-provider-pooling/response/WEIGHTED-COSET-SELECTION.json
new file mode 100644
index 0000000000..fa156ce9fd
--- /dev/null
+++ b/research/contextual-provider-pooling/response/WEIGHTED-COSET-SELECTION.json
@@ -0,0 +1,366 @@
+{
+  "input_semantic_sha256": "00b355c231f8dd7431ddcfde1d7d633938c90975a4d806af08f7f46441bfc2bc",
+  "output_semantic_sha256": "a02c65df603a817c38568bb06b108a023e39ee27735aa60ebaf47b83e6ebeb85",
+  "selection": [
+    {
+      "index": 205,
+      "candidate": 26,
+      "old_operation": [
+        "add",
+        241,
+        24,
+        1,
+        1,
+        [
+          208
+        ]
+      ],
+      "new_operation": [
+        "add",
+        241,
+        240,
+        1,
+        1,
+        [
+          208
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "240": "1"
+      },
+      "compensation_saved": 60
+    },
+    {
+      "index": 340,
+      "candidate": 34,
+      "old_operation": [
+        "add",
+        257,
+        16,
+        1,
+        1,
+        [
+          400
+        ]
+      ],
+      "new_operation": [
+        "add",
+        257,
+        256,
+        1,
+        1,
+        [
+          400
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "256": "1"
+      },
+      "compensation_saved": 60
+    },
+    {
+      "index": 1555,
+      "candidate": 106,
+      "old_operation": [
+        "add",
+        401,
+        88,
+        1,
+        1,
+        [
+          265
+        ]
+      ],
+      "new_operation": [
+        "add",
+        401,
+        400,
+        1,
+        1,
+        [
+          265
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "400": "1"
+      },
+      "compensation_saved": 60
+    },
+    {
+      "index": 1690,
+      "candidate": 114,
+      "old_operation": [
+        "add",
+        417,
+        80,
+        1,
+        1,
+        [
+          73
+        ]
+      ],
+      "new_operation": [
+        "add",
+        417,
+        416,
+        1,
+        1,
+        [
+          73
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "416": "1"
+      },
+      "compensation_saved": 60
+    },
+    {
+      "index": 207,
+      "candidate": 27,
+      "old_operation": [
+        "add",
+        243,
+        25,
+        1,
+        1,
+        [
+          336
+        ]
+      ],
+      "new_operation": [
+        "add",
+        243,
+        242,
+        1,
+        1,
+        [
+          336
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "242": "1"
+      },
+      "compensation_saved": 48
+    },
+    {
+      "index": 342,
+      "candidate": 35,
+      "old_operation": [
+        "add",
+        259,
+        17,
+        1,
+        1,
+        [
+          8
+        ]
+      ],
+      "new_operation": [
+        "add",
+        259,
+        258,
+        1,
+        1,
+        [
+          8
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "258": "1"
+      },
+      "compensation_saved": 48
+    },
+    {
+      "index": 475,
+      "candidate": 42,
+      "old_operation": [
+        "add",
+        273,
+        8,
+        1,
+        1,
+        [
+          2
+        ]
+      ],
+      "new_operation": [
+        "add",
+        273,
+        272,
+        1,
+        1,
+        [
+          2
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "272": "1"
+      },
+      "compensation_saved": 48
+    },
+    {
+      "index": 477,
+      "candidate": 43,
+      "old_operation": [
+        "add",
+        275,
+        9,
+        1,
+        1,
+        [
+          412
+        ]
+      ],
+      "new_operation": [
+        "add",
+        275,
+        274,
+        1,
+        1,
+        [
+          412
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "274": "1"
+      },
+      "compensation_saved": 48
+    },
+    {
+      "index": 610,
+      "candidate": 50,
+      "old_operation": [
+        "add",
+        289,
+        32,
+        1,
+        1,
+        [
+          348
+        ]
+      ],
+      "new_operation": [
+        "add",
+        289,
+        288,
+        1,
+        1,
+        [
+          348
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "288": "1"
+      },
+      "compensation_saved": 48
+    },
+    {
+      "index": 612,
+      "candidate": 51,
+      "old_operation": [
+        "add",
+        291,
+        33,
+        1,
+        1,
+        [
+          196
+        ]
+      ],
+      "new_operation": [
+        "add",
+        291,
+        290,
+        1,
+        1,
+        [
+          196
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "290": "1"
+      },
+      "compensation_saved": 48
+    },
+    {
+      "index": 745,
+      "candidate": 58,
+      "old_operation": [
+        "add",
+        305,
+        64,
+        1,
+        1,
+        [
+          460
+        ]
+      ],
+      "new_operation": [
+        "add",
+        305,
+        304,
+        1,
+        1,
+        [
+          460
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "304": "1"
+      },
+      "compensation_saved": 48
+    },
+    {
+      "index": 747,
+      "candidate": 59,
+      "old_operation": [
+        "add",
+        307,
+        65,
+        1,
+        1,
+        [
+          84
+        ]
+      ],
+      "new_operation": [
+        "add",
+        307,
+        306,
+        1,
+        1,
+        [
+          84
+        ]
+      ],
+      "source_ratio": "1",
+      "cold_difference": {
+        "306": "1"
+      },
+      "compensation_saved": 48
+    }
+  ],
+  "profile": {
+    "1": 2300,
+    "2": 440,
+    "3": 472,
+    "4": 184,
+    "5": 56,
+    "6": 56,
+    "8": 8
+  },
+  "before_compensation": 9756,
+  "after_compensation": 9132,
+  "total_saved": 624
+}
diff --git a/research/contextual-provider-pooling/response/build_weighted_coset.py b/research/contextual-provider-pooling/response/build_weighted_coset.py
new file mode 100644
index 0000000000..d106b2b310
--- /dev/null
+++ b/research/contextual-provider-pooling/response/build_weighted_coset.py
@@ -0,0 +1,36 @@
+"""Frozen weighted coset representative construction. No search."""
+from pathlib import Path
+from fractions import Fraction as Q
+import argparse,copy,gzip,hashlib,json,sys
+if not __debug__:raise SystemExit('Assertions must remain enabled.')
+ap=argparse.ArgumentParser();ap.add_argument('--input',type=Path,required=True);ap.add_argument('--selection',type=Path,required=True);ap.add_argument('--gk-dir',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args()
+sys.path.insert(0,str(a.gk_dir));import gk_word as g,gk_common as c
+g.V=c.V=112;g.DATA=c.DATA=7168
+w=json.load(gzip.open(a.input));r=json.loads(a.selection.read_text());N=728;V=112
+def semantic(w):return hashlib.sha256(json.dumps({k:v for k,v in w.items()if k!='report'},sort_keys=True,separators=(',',':')).encode()).hexdigest()
+assert semantic(w)==r['input_semantic_sha256']
+protected=set(range(V))|set(map(int,w['start_extra']));assert len(protected)==324
+profile=g.profile(w);before=sum(map(len,g.responses(w)));assert before==r['before_compensation'];receipts=[]
+for move in r['selection']:
+ i=move['index'];old=w['A'][i];new=move['new_operation'];assert old==move['old_operation'];assert old[0]==new[0]=='add'and old[1]==new[1]and old[-1]==new[-1]and new[1]!=new[2]
+ rows=[{j:Q(1)}for j in range(N)]
+ for e in w['A'][:i]:g.apply_op(e,rows)
+ q=Q(old[3],old[4]);z=Q(new[3],new[4]);assert z.denominator&(z.denominator-1)==0
+ err={j:-q*x for j,x in rows[old[2]].items()}
+ for j,x in rows[new[2]].items():
+  y=err.get(j,Q(0))+z*x
+  if y:err[j]=y
+  else:err.pop(j,None)
+ assert all(j>=224 and j not in protected for j in err)
+ assert err=={int(j):Q(x)for j,x in move['cold_difference'].items()}
+ n0=sum(map(len,g.responses(w)));w['A'][i]=copy.deepcopy(new);assert g.profile(w)==profile
+ n1=sum(map(len,g.responses(w)));assert n0-n1==move['compensation_saved']>0
+ receipts.append(dict(index=i,compensation_before=n0,compensation_after=n1,cold_error_checked=True,protected_columns_preserved=True,frame_profile_unchanged=True))
+w['cleanup']=[g.inverse(e,g.FULL)for e in reversed(w['A']+w['B'])if not V<=e[1]<2*V]
+w['report']['local_profile']=dict(profile)
+assert semantic(w)==r['output_semantic_sha256']
+after=sum(map(len,g.responses(w)));assert after==r['after_compensation']and before-after==r['total_saved']==624
+assert dict(profile)=={int(k):v for k,v in r['profile'].items()}
+a.out.mkdir(parents=True,exist_ok=False);(a.out/'FULL-WORD.json.gz').write_bytes(g.dump(w))
+receipt=dict(status='PASS_FROZEN_WEIGHTED_COSET_FAMILY',input_semantic_sha256=r['input_semantic_sha256'],output_semantic_sha256=semantic(w),moves=receipts,compensation_before=before,compensation_after=after,total_saved=before-after,profile=dict(profile),scope='Exact rational prefix errors, all protected columns, frame chains and complete compensation table. Native phases, emitted programs and global assembly checked separately.')
+(a.out/'WEIGHTED-COSET-REPLAY.json').write_text(json.dumps(receipt,indent=2)+'\n');print('PASS frozen weighted coset family',len(receipts),before-after)
diff --git a/research/contextual-provider-pooling/verify.py b/research/contextual-provider-pooling/verify.py
new file mode 100644
index 0000000000..b920bb7cb1
--- /dev/null
+++ b/research/contextual-provider-pooling/verify.py
@@ -0,0 +1,40 @@
+"""Offline changed-word replay. No network and no optimizer are required."""
+import argparse,gzip,hashlib,json,os,shutil,subprocess,sys,time
+from pathlib import Path
+TEXT={'.py','.json','.md','.txt','.sh','.lean','.cpp','.h','.hpp','.sha256','.yml','.yaml','.toml'}
+def textfile(p):return p.suffix.lower()in TEXT or p.name in {'LICENSE','NOTICE','SOURCE'}
+def read(p):return json.loads(p.read_text(encoding='utf-8'))
+def dump(p,z):p.write_text(json.dumps(z,indent=2)+'\n',encoding='utf-8',newline='\n')
+def main():
+ if not __debug__:raise SystemExit('Assertions must be enabled; do not use Python -O.')
+ ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--work',type=Path,required=True);a=ap.parse_args()
+ root=Path(__file__).resolve().parent;work=a.work.resolve();assert not work.exists()and root not in work.parents
+ import numpy  # Required by the unchanged Clifford phase compiler.
+ man=read(root/'MANIFEST.json');assert man['format']=='sha256-lf-text-v1';expect=read(root/'EXPECTED.json')
+ present={x.relative_to(root).as_posix()for x in root.rglob('*')if x.is_file()and '__pycache__'not in x.parts}
+ assert present==set(man['files'])|{'MANIFEST.json'},('unlisted/missing',present^(set(man['files'])|{'MANIFEST.json'}))
+ for rel,z in man['files'].items():
+  f=(root/rel).resolve();assert root in f.parents;b=f.read_bytes()
+  if z['mode']=='lf-text':b=b.replace(b'\r\n',b'\n')
+  assert hashlib.sha256(b).hexdigest()==z['sha256'],('input hash changed',rel)
+ t=time.monotonic();work.mkdir(parents=True);src=work/'source';shutil.copytree(root,src,ignore=shutil.ignore_patterns('__pycache__'))
+ for f in src.rglob('*'):
+  if f.is_file()and textfile(f):f.write_bytes(f.read_bytes().replace(b'\r\n',b'\n'))
+ stages=[];env=dict(os.environ,PYTHONUTF8='1',PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0')
+ def run(name,script,*args):
+  began=time.monotonic()
+  with(work/(name+'.log')).open('w',encoding='utf-8')as log:r=subprocess.run([sys.executable,'-B',str(script),*map(str,args)],stdout=log,stderr=subprocess.STDOUT,env=env)
+  stages.append(dict(name=name,exit=r.returncode,seconds=time.monotonic()-began));dump(work/'STAGES.json',stages)
+  if r.returncode:print((work/(name+'.log')).read_text(encoding='utf-8'),file=sys.stderr);raise SystemExit(name+' failed')
+  print('PASS',name,round(stages[-1]['seconds'],2),flush=True)
+ local=work/'complex-local';cg=work/'complex-global';variants=work/'variants'
+ run('complex-reconstruction-and-local-checks',src/'complex-local/run_local.py','--out',local,'--vendor',src/'complex-global/vendor531')
+ run('selected-physical-providers',src/'providers/run_variants.py','--source',local,'--out',variants)
+ run('mixed-owner-physical-and-invoice',src/'complex-global/replay.py','--providers',variants/'PROVIDERS.json','--out',cg)
+ run('exact-two-supplier-assembly',src/'code/assemble.py',src,cg,work/'ASSEMBLY.json')
+ ans=read(work/'ASSEMBLY.json');ci=read(cg/'audit/PREFIX-AND-INVOICE.json');co=read(cg/'audit/OWNERS-AND-PROFILE.json');lift=read(cg/'audit/CLONE-LIFT.json');assert lift['status'].startswith('PASS')
+ result=dict(status='PASS_CONTEXTUAL_PROVIDER_POOLING',kappa=ans['kappa'],kappa_decimal=ans['kappa_decimal'],bit_lower=ans['bit_lower'],complex_lower=ans['complex_lower'],complex_template_sha256=ci['template_sha256'],provider_bindings=ci['provider_bindings'],provider_counts=ci['provider_counts'],complex_global_profile=co['paid_profile'],complex_prefix_bits=ci['global_prefix_bits'],charged_prefix_bits=ci['charged_prefix_bits'],physical_row=ci['finite']['physical_row_coefficient'],outer_constraints=len(ans['outer']),bit_operator='Pinned PR555 cited dependency, not physically replayed here',stages=stages,elapsed_seconds=time.monotonic()-t,scope=ans['scope'])
+ for k,x in expect.items():assert result[k]==x,('frozen result mismatch',k,result[k],x)
+ assert result['outer_constraints']==47
+ dump(work/'RESULT.json',result);print(json.dumps({k:result[k]for k in ['status','kappa_decimal','elapsed_seconds']}),flush=True)
+if __name__=='__main__':main()