From 511c183545c5e10e460119407135c80f2227d811 Mon Sep 17 00:00:00 2001 From: Dugongue <49054532+Dugongue@users.noreply.github.com> Date: Sun, 11 Oct 2026 23:05:44 -0700 Subject: [PATCH 1/4] Add files via upload --- .../code/alien-avalanche80.cpp | 7 + .../code/alien-flags.cpp | 11 + .../code/assemble.py | 49 + .../code/build_wave.py | 34 + .../complex-global/MIXED-RESOURCE-PROOF.md | 15 + .../complex-global/OAI-SOURCES.json | 23 + .../complex-global/README.md | 15 + .../complex-global/RESOURCE-PROOF.md | 21 + .../complex-global/RESOURCE-RESEARCH.md | 13 + .../complex-global/RESOURCE-TRANSFERS.md | 46 + .../complex-global/SAT-OWNERS.json.gz | Bin 0 -> 409252 bytes .../complex-global/SAT534-PLAN.json | 11389 ++++++++++++++ .../complex-global/SCREEN-RECEIPT.json | 16 + .../complex-global/SOURCE-TRANSFERS.json | 21 + .../complex-global/SOURCES.json | 21 + .../complex-global/TWO-RESOURCE-TECHNIQUES.md | 67 + .../complex-global/audit_clone.py | 155 + .../complex-global/audit_clone_lift.py | 80 + .../complex-global/audit_mixed.py | 186 + .../complex-global/build_clone.py | 65 + .../complex-global/build_mixed72.py | 37 + .../complex-global/build_mixed_clone.py | 66 + .../complex-global/emit_clone.py | 100 + .../complex-global/emit_mixed.py | 127 + .../complex-global/inputs558/OWNERS.json.gz | Bin 0 -> 414100 bytes .../complex-global/inputs558/PLAN.json | 12546 ++++++++++++++++ .../complex-global/invoice_clone.py | 304 + .../complex-global/invoice_mixed.py | 260 + .../complex-global/replay.py | 32 + .../complex-global/run_complex44.py | 29 + .../complex-global/run_portable.py | 24 + .../vendor531/code/adapters_local.py | 60 + .../vendor531/code/audit_and_transport.py | 222 + .../vendor531/code/audit_local.py | 144 + .../vendor531/code/audit_supplier_hosted.py | 155 + .../vendor531/code/emit_local.py | 156 + .../vendor531/code/emit_supplier_hosted.py | 100 + .../vendor531/code/invoice_final.py | 299 + .../vendor531/code/phases_delta.py | 158 + .../vendor531/code/prepare_supplier_base.py | 95 + 40 files changed, 27148 insertions(+) create mode 100644 research/contextual-provider-pooling/code/alien-avalanche80.cpp create mode 100644 research/contextual-provider-pooling/code/alien-flags.cpp create mode 100644 research/contextual-provider-pooling/code/assemble.py create mode 100644 research/contextual-provider-pooling/code/build_wave.py create mode 100644 research/contextual-provider-pooling/complex-global/MIXED-RESOURCE-PROOF.md create mode 100644 research/contextual-provider-pooling/complex-global/OAI-SOURCES.json create mode 100644 research/contextual-provider-pooling/complex-global/README.md create mode 100644 research/contextual-provider-pooling/complex-global/RESOURCE-PROOF.md create mode 100644 research/contextual-provider-pooling/complex-global/RESOURCE-RESEARCH.md create mode 100644 research/contextual-provider-pooling/complex-global/RESOURCE-TRANSFERS.md create mode 100644 research/contextual-provider-pooling/complex-global/SAT-OWNERS.json.gz create mode 100644 research/contextual-provider-pooling/complex-global/SAT534-PLAN.json create mode 100644 research/contextual-provider-pooling/complex-global/SCREEN-RECEIPT.json create mode 100644 research/contextual-provider-pooling/complex-global/SOURCE-TRANSFERS.json create mode 100644 research/contextual-provider-pooling/complex-global/SOURCES.json create mode 100644 research/contextual-provider-pooling/complex-global/TWO-RESOURCE-TECHNIQUES.md create mode 100644 research/contextual-provider-pooling/complex-global/audit_clone.py create mode 100644 research/contextual-provider-pooling/complex-global/audit_clone_lift.py create mode 100644 research/contextual-provider-pooling/complex-global/audit_mixed.py create mode 100644 research/contextual-provider-pooling/complex-global/build_clone.py create mode 100644 research/contextual-provider-pooling/complex-global/build_mixed72.py create mode 100644 research/contextual-provider-pooling/complex-global/build_mixed_clone.py create mode 100644 research/contextual-provider-pooling/complex-global/emit_clone.py create mode 100644 research/contextual-provider-pooling/complex-global/emit_mixed.py create mode 100644 research/contextual-provider-pooling/complex-global/inputs558/OWNERS.json.gz create mode 100644 research/contextual-provider-pooling/complex-global/inputs558/PLAN.json create mode 100644 research/contextual-provider-pooling/complex-global/invoice_clone.py create mode 100644 research/contextual-provider-pooling/complex-global/invoice_mixed.py create mode 100644 research/contextual-provider-pooling/complex-global/replay.py create mode 100644 research/contextual-provider-pooling/complex-global/run_complex44.py create mode 100644 research/contextual-provider-pooling/complex-global/run_portable.py create mode 100644 research/contextual-provider-pooling/complex-global/vendor531/code/adapters_local.py create mode 100644 research/contextual-provider-pooling/complex-global/vendor531/code/audit_and_transport.py create mode 100644 research/contextual-provider-pooling/complex-global/vendor531/code/audit_local.py create mode 100644 research/contextual-provider-pooling/complex-global/vendor531/code/audit_supplier_hosted.py create mode 100644 research/contextual-provider-pooling/complex-global/vendor531/code/emit_local.py create mode 100644 research/contextual-provider-pooling/complex-global/vendor531/code/emit_supplier_hosted.py create mode 100644 research/contextual-provider-pooling/complex-global/vendor531/code/invoice_final.py create mode 100644 research/contextual-provider-pooling/complex-global/vendor531/code/phases_delta.py create mode 100644 research/contextual-provider-pooling/complex-global/vendor531/code/prepare_supplier_base.py 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 +using namespace std;using B=bitset<512>;struct N{bool fixed;B s;int d;vector pre,nxt,regs;};vectora;vectorhyper(512);long double pc[11]; +int main(int argc,char**argv){ifstream in(argv[1]);int nf,nn,nr;in>>nf>>nn>>nr;vectorfs(nf);vectordims(nf);for(int f=0;f>n;dims[f]=round(log2(n));while(n--){in>>x;fs[f][x]=1;}}a.resize(nn);vectorlast(nr,-1);for(int i=0;i>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);vectormark(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;vectorbst;int bv=0,bs=0;for(int sign:{1,-1})for(int v=1;v<512;v++){vectoractive(nn);for(int i=0;iq{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 +using namespace std; using B=bitset<512>; +struct F{B s;int d;};struct N{bool fixed;int f;vector regs,pre,nxt;}; +vector fs;vector ns;long double pc[10]; +bool sub(int a,int b){return (fs[a].s & ~fs[b].s).none();} +long double change(const vector&v,int f){unordered_setS(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;}}vectorlast(nr,-1);for(int i=0;i>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);vectororig;for(auto &n:ns)orig.push_back(n.f);mt19937 rng(20261011);int accepted=0;long double gain=0; +auto trygroup=[&](vectorv){unordered_setS(v.begin(),v.end());vectorlo,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;ford(nn);iota(ord.begin(),ord.end(),0);shuffle(ord.begin(),ord.end(),rng);for(int i:ord)if(!ns[i].fixed)trygroup({i});vectorseen(nn);for(int i:ord)if(!seen[i]&&!ns[i].fixed){vectorv{i};seen[i]=1;for(int k=0;k<(int)v.size();k++){int t=v[k];vectoradj=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<oldh,newh;for(int i=0;i=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;i2*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']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= 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. 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z+^X~Gij&MfWTJ_MWCT(zGQ#~caRFTgGRBP;38DO~rr$%?3oXrOY?+EPzU~T@3-)*3 z77ClmV&!NM#PmL1kdNpd8#Fal 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 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/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<>i&1 else 0)for i in order]+[1<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<=fD + def fam(f,c): + assert 0<=c>i)&1==0);a=q^(1<>i&1 else 0)for i in order]+[1<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=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>i)&1);u=q^(1<>i&1 else 0)for i in order]+[1<=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(f2*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<>i&1 else 0)for i in order]+[1<=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(f2*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 0000000000000000000000000000000000000000..eeb01317d735847c932373cd864d93ca6dbdece8 GIT 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z+I&)~x_X_Ns++RN1_K6zTZ6%B<@QxV#JMQn(dXEJN&)Uhza%-K7BFAA}+kF z9QQ$w1@M^nc{x@cGxuY&LBB^*xu=@lsZf2&LV3-CoSoa&rigkA$DE!TW^$AultT^e z@G{){-rSnzJbiX&`1Kd`Q}2O0gEj2A%>iWs5_2S6b)0<=5wjH@jZ0L(hA|z)ZgH@% zbOjDxG zkyD1+(NzGq1x$0cTr@AdxYbwmX+LXz@FV2s2}8N011h|yIYP`$aUV2t0kwIbCoJ}s z(V`{l?5;PSI>Hr`z_(9dGGJ=mw`n%hbbwo6O@L%rg;i{<(R5;yLDp3$acN8lwH=3P zVFOfYi5><{MZ06mDaTu}snd!7Jp2;^Y9nuPIuH4M&Tw%Voc6cl??%t@V7@-yJD3Af zX~Klvybe8dU@o%GL3p%tI2HdDpbZuau3>Msy`ffg8+F)+qkZ;{XwmxEauSrL`1SaBez#Kf=J(6u+dhd3qJ)DXItMSJNph%SPEnZFBw%|d28xDz0oA*e7*PBL kE= 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/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>i)&1==0);a=q^(1<>i&1 else 0)for i in order]+[1<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>i)&1);u=q^(1<>i&1 else 0)for i in order]+[1<=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(f2*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 02*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) From 24ea5c4e288ecc0012a40ba5622f0560819a1269 Mon Sep 17 00:00:00 2001 From: Dugongue <49054532+Dugongue@users.noreply.github.com> Date: Sun, 11 Oct 2026 23:05:51 -0700 Subject: [PATCH 2/4] Add files via upload --- .../complex-local/static44/PROOF.md | 61 +++ .../complex-local/static44/README.md | 7 + .../complex-local/static44/RECIPE.json | 168 +++++++ .../static44/SOURCE-MANIFEST.json | 16 + .../complex-local/static44/replay.py | 9 + .../docs/CURRENT-SOURCE-PINS.json | 17 + .../docs/DAG-STRUCTURES.json | 208 ++++++++ ...MINATION-AVALANCHE-INDEPENDENT-REVIEW.json | 112 +++++ .../docs/ELIMINATION-CODIM2.json | 1 + ...IMINATION-ELIMINATION-AND-PATH-TRANSFER.md | 41 ++ .../docs/ELIMINATION-SCREEN-REVIEW.json | 15 + .../docs/ELIMINATION-SOURCES.json | 34 ++ .../docs/FIVEFOLD-DIRECT-SUM-REVIEW.md | 59 +++ .../docs/FRAME-SOURCES.json | 12 + .../docs/FRAME-TRANSFERS.md | 66 +++ .../docs/MIXTURE-SOURCE-PINS.json | 14 + .../docs/NESTED-PROMOTION-AND-MIXTURE.md | 33 ++ .../docs/OAI-BLOCK-NORM.md | 9 + .../docs/PR-LINEAGE.md | 17 + .../docs/PR552-PREVIOUS-README.md | 62 +++ .../docs/PRIOR-TN27-README.md | 29 ++ .../docs/PUBLIC-PINS.json | 447 ++++++++++++++++++ .../engines/base_two_moment.py | 63 +++ .../engines/moment.py | 113 +++++ .../engines/outer.py | 58 +++ .../epoch/EPOCH-PROOF.md | 67 +++ .../epoch/EPOCH-SELECTION.json | 22 + .../epoch/MANIFEST.json | 7 + .../epoch/SOURCES.json | 15 + .../epoch/audit_epoch.cpp | 7 + .../epoch/build_epoch14.py | 88 ++++ .../evidence/CLONE-ASSEMBLY.json | 168 +++++++ .../evidence/CLONE-INVOICE.json | 106 +++++ .../evidence/CLONE-LIFT.json | 54 +++ .../evidence/COMPLEX-INVOICE.json | 106 +++++ .../evidence/EXACT-ASSEMBLY.json | 169 +++++++ .../evidence/FINAL-MIXTURE-REVIEW.json | 97 ++++ .../evidence/FINAL-RESOURCE.json | 44 ++ .../evidence/MIXED-ASSEMBLY.json | 173 +++++++ .../evidence/MIXED-INVOICE.json | 243 ++++++++++ 40 files changed, 3037 insertions(+) create mode 100644 research/contextual-provider-pooling/complex-local/static44/PROOF.md create mode 100644 research/contextual-provider-pooling/complex-local/static44/README.md create mode 100644 research/contextual-provider-pooling/complex-local/static44/RECIPE.json create mode 100644 research/contextual-provider-pooling/complex-local/static44/SOURCE-MANIFEST.json create mode 100644 research/contextual-provider-pooling/complex-local/static44/replay.py create mode 100644 research/contextual-provider-pooling/docs/CURRENT-SOURCE-PINS.json create mode 100644 research/contextual-provider-pooling/docs/DAG-STRUCTURES.json create mode 100644 research/contextual-provider-pooling/docs/ELIMINATION-AVALANCHE-INDEPENDENT-REVIEW.json create mode 100644 research/contextual-provider-pooling/docs/ELIMINATION-CODIM2.json create mode 100644 research/contextual-provider-pooling/docs/ELIMINATION-ELIMINATION-AND-PATH-TRANSFER.md create mode 100644 research/contextual-provider-pooling/docs/ELIMINATION-SCREEN-REVIEW.json create mode 100644 research/contextual-provider-pooling/docs/ELIMINATION-SOURCES.json create mode 100644 research/contextual-provider-pooling/docs/FIVEFOLD-DIRECT-SUM-REVIEW.md create mode 100644 research/contextual-provider-pooling/docs/FRAME-SOURCES.json create mode 100644 research/contextual-provider-pooling/docs/FRAME-TRANSFERS.md create mode 100644 research/contextual-provider-pooling/docs/MIXTURE-SOURCE-PINS.json create mode 100644 research/contextual-provider-pooling/docs/NESTED-PROMOTION-AND-MIXTURE.md create mode 100644 research/contextual-provider-pooling/docs/OAI-BLOCK-NORM.md create mode 100644 research/contextual-provider-pooling/docs/PR-LINEAGE.md create mode 100644 research/contextual-provider-pooling/docs/PR552-PREVIOUS-README.md create mode 100644 research/contextual-provider-pooling/docs/PRIOR-TN27-README.md create mode 100644 research/contextual-provider-pooling/docs/PUBLIC-PINS.json create mode 100644 research/contextual-provider-pooling/engines/base_two_moment.py create mode 100644 research/contextual-provider-pooling/engines/moment.py create mode 100644 research/contextual-provider-pooling/engines/outer.py create mode 100644 research/contextual-provider-pooling/epoch/EPOCH-PROOF.md create mode 100644 research/contextual-provider-pooling/epoch/EPOCH-SELECTION.json create mode 100644 research/contextual-provider-pooling/epoch/MANIFEST.json create mode 100644 research/contextual-provider-pooling/epoch/SOURCES.json create mode 100644 research/contextual-provider-pooling/epoch/audit_epoch.cpp create mode 100644 research/contextual-provider-pooling/epoch/build_epoch14.py create mode 100644 research/contextual-provider-pooling/evidence/CLONE-ASSEMBLY.json create mode 100644 research/contextual-provider-pooling/evidence/CLONE-INVOICE.json create mode 100644 research/contextual-provider-pooling/evidence/CLONE-LIFT.json create mode 100644 research/contextual-provider-pooling/evidence/COMPLEX-INVOICE.json create mode 100644 research/contextual-provider-pooling/evidence/EXACT-ASSEMBLY.json create mode 100644 research/contextual-provider-pooling/evidence/FINAL-MIXTURE-REVIEW.json create mode 100644 research/contextual-provider-pooling/evidence/FINAL-RESOURCE.json create mode 100644 research/contextual-provider-pooling/evidence/MIXED-ASSEMBLY.json create mode 100644 research/contextual-provider-pooling/evidence/MIXED-INVOICE.json 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/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(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 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. 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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]<10 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 +#include +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>base;vectordiffs,targetdiffs; +for(int run=0;run>A(n,vector(n));for(int i=0;i>m;for(int k=0;k>kind>>t>>s>>a>>b;assert(t>=0&&t=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\":"<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 Date: Sun, 11 Oct 2026 23:05:57 -0700 Subject: [PATCH 3/4] Add files via upload --- .../complex-global/WAVE-MAJORISATION.json | 32 + .../complex-global/vendor531/LICENSE | 201 +++ .../complex-global/vendor531/NOTICE.md | 24 + .../complex-global/vendor531/SOURCES.json | 63 + 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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]<10 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&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 for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<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)&1)<>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;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<>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&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>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<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< 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 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zn@Rnth_mtF>(lk_EJ=y?<34DwGLcNL1Eu%3eUAmb&#kuFtMB`>m)<WgLTi{S4b2W}^A^q#U#1*INCE(MJ?)@Q;<66s1*hr4wQk5^|=*WCrHPjx7E z;c3(D{H1rz!V4-TdKE0fWfk71?^Z*{G;r4C<<9jYWpAgZvk1Mxe)aRzV!bLVRBUUcI7aKiSZuEZ$SqAIeFV_^2 zSr0AUx>J2Pa*C=zXW43dpRY?ir9SnToi$=le5(eI;RNg1)IZNy6nimP+6j=lfYl>-Cr5_IK~F`B6D36>hNq2gpg9uK)l5 literal 0 HcmV?d00001 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. 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