From 269490b0553e59bf224ab96009809ae8908d8f74 Mon Sep 17 00:00:00 2001
From: Jeremy Kothe <jeremy.robert.kothe@gmail.com>
Date: Mon, 12 Oct 2026 21:13:31 +1100
Subject: [PATCH 1/2] Conditional kappa 0.001600951400768614: PR568 kernels and
 eight-cold provider on PR571's prefix word

---
 research/complex-571-three-provider/LICENSE   |   201 +
 .../complex-571-three-provider/MANIFEST.json  |    18 +
 research/complex-571-three-provider/NOTICE.md |    15 +
 .../code/assemble.py                          |   210 +
 .../code/assembly_controls.py                 |   251 +
 .../code/audit_allcold.py                     |   223 +
 .../code/bind_providers_portable.py           |    63 +
 .../code/emit_allcold.py                      |   144 +
 .../code/invoice_allcold.py                   |   316 +
 .../code/phase_timing_controls.py             |    34 +
 .../code/witness.py                           |    35 +
 .../data/OWNERS.json.gz                       |   Bin 0 -> 419252 bytes
 .../data/P571K-MULTICOLD.json                 |   550 +
 .../complex-571-three-provider/data/PINS.json |    30 +
 .../complex-571-three-provider/data/PLAN.json | 43304 ++++++++++++++++
 .../data/WITNESS-SPEC.json                    |   873 +
 research/complex-571-three-provider/verify.py |    99 +
 17 files changed, 46366 insertions(+)
 create mode 100644 research/complex-571-three-provider/LICENSE
 create mode 100644 research/complex-571-three-provider/MANIFEST.json
 create mode 100644 research/complex-571-three-provider/NOTICE.md
 create mode 100644 research/complex-571-three-provider/code/assemble.py
 create mode 100644 research/complex-571-three-provider/code/assembly_controls.py
 create mode 100644 research/complex-571-three-provider/code/audit_allcold.py
 create mode 100644 research/complex-571-three-provider/code/bind_providers_portable.py
 create mode 100644 research/complex-571-three-provider/code/emit_allcold.py
 create mode 100644 research/complex-571-three-provider/code/invoice_allcold.py
 create mode 100644 research/complex-571-three-provider/code/phase_timing_controls.py
 create mode 100644 research/complex-571-three-provider/code/witness.py
 create mode 100644 research/complex-571-three-provider/data/OWNERS.json.gz
 create mode 100644 research/complex-571-three-provider/data/P571K-MULTICOLD.json
 create mode 100644 research/complex-571-three-provider/data/PINS.json
 create mode 100644 research/complex-571-three-provider/data/PLAN.json
 create mode 100644 research/complex-571-three-provider/data/WITNESS-SPEC.json
 create mode 100644 research/complex-571-three-provider/verify.py

diff --git a/research/complex-571-three-provider/LICENSE b/research/complex-571-three-provider/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/complex-571-three-provider/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/complex-571-three-provider/MANIFEST.json b/research/complex-571-three-provider/MANIFEST.json
new file mode 100644
index 0000000000..eebb212aaa
--- /dev/null
+++ b/research/complex-571-three-provider/MANIFEST.json
@@ -0,0 +1,18 @@
+{
+  "code/assemble.py": "bbced1b47d689b32f5b6e652133713f315d683536f2dc9ae38f47c5604ba1bda",
+  "code/assembly_controls.py": "7ec40d7a223b3525ef672b2d491979f11d9be913b90c9fe5ae54160ae91538a2",
+  "code/audit_allcold.py": "10ec1cfeec49b1a295d6871e13b77e8ff645dc946902168b0187c905a0e5561a",
+  "code/bind_providers_portable.py": "ff989ae9cb57a2752e5ab12d983eaa77e12b9078bdc9c51d8815de2d7f6dddba",
+  "code/emit_allcold.py": "c3d7eb6ee86eebe4b389b9fa07fc8b00f1d6fdbb2d180b90ff50e55a5c78c531",
+  "code/invoice_allcold.py": "b1f0857371401432f47011f61ebf3b8875bb554175905de5f993c19f3ab89693",
+  "code/phase_timing_controls.py": "f02d0d0a6d84174d1706032401eb1c7140685ec24ce1ad22fc3e68ad4bfe6f85",
+  "code/witness.py": "4f6d445f4796e9e7c0ef388370020119d4fdb929c006b2101aecb203ece8ab61",
+  "data/OWNERS.json.gz": "f78fe84137f3c4541252f9b0a298c5761afb4e9004c11eb9108bd680415b0c55",
+  "data/P571K-MULTICOLD.json": "c839199d0e6f8e976978fe97bc0c5579a65ba69dfb6864585b448cccc1113056",
+  "data/PINS.json": "d229e7f4e9f290f8974a14b1f01fae4796e74e45f3ba66208c54a1dcf3226c8a",
+  "data/PLAN.json": "d0ca30bde3cd73f40d94813715e1d0a6255e2d7840e9bb0abf74e8e1cac11cd5",
+  "data/WITNESS-SPEC.json": "f1a3c9fab1d9e803f00c842034b2115d3aca6e977530d3a16fb527e0975c12b3",
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "NOTICE.md": "0fb9f292f903f2d453dac51bdca676e0266e9b91b8e03786f6ed9538c00ce057",
+  "verify.py": "21857d5aea3763fb1b1c3abdf5d84204c783318f8d41fb1fa6076501f4b53f8e"
+}
diff --git a/research/complex-571-three-provider/NOTICE.md b/research/complex-571-three-provider/NOTICE.md
new file mode 100644
index 0000000000..331ea5c95e
--- /dev/null
+++ b/research/complex-571-three-provider/NOTICE.md
@@ -0,0 +1,15 @@
+# Attribution and scope
+
+This package combines three providers under a new literal owner map (54 P571, 8 P571K, 10 E8 calls):
+
+- #571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`): the combined-prefix width-seven provider word `frontier-composition/combined-prefix-word/FULL-WORD.json.gz`, its retained local (`frontier-composition/combined-prefix-local`), its dispatch of 63 width-seven and 9 plain calls, and the global admission scripts in `frontier-composition/global-code/`. #571 was prepared with OpenAI Codex assistance under Apache-2.0.
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`): the eight-cold multi-cut eight-pivot provider word, rebuilt by its unchanged scripts. It is rebuilt by PR568's unchanged scripts and serves as the plain provider (E8).
+- P571K: #571's combined-prefix word with twelve additional multi-cut cold kernels, built by PR568's unchanged `code/build_multicut_kernels.py` from `data/P571K-MULTICOLD.json` (recipe derived by a greedy kernel search over #571's word), with PR568's unchanged omission controls `code/audit_multicold_controls.py`.
+
+Both packages are pinned external sources. `verify.py` checks their manifests and the exact file hashes it uses. It runs their unchanged scripts, rebuilds the width-seven local from #571's pinned word, and requires that rebuilt local to match #571's retained local byte for byte.
+
+The scripts in `code/` are adapted from #571's `frontier-composition/global-code/`. Every witness-specific value, including provider inventories, profiles, artifact and program hashes, dispatch, owner geometry, idle remainders, endpoints and kappa, is read from `data/WITNESS-SPEC.json` through `code/witness.py`. The spec was generated from audited global outputs, not hand-copied.
+
+The literal owner map was nominated by a HiGHS window MILP with large-neighbourhood search, adapted from PR569's `global/nominate_width7.py`. Lazy cross-time Hall cuts make every window literally decomposable. The admission scripts check the map independently.
+
+The kernel recipe, provider mix, literal owner assignment, spec-driven admission code and this package were prepared by Claude Code (Anthropic) research agents. Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of #571, PR568 and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
diff --git a/research/complex-571-three-provider/code/assemble.py b/research/complex-571-three-provider/code/assemble.py
new file mode 100644
index 0000000000..c554cab072
--- /dev/null
+++ b/research/complex-571-three-provider/code/assemble.py
@@ -0,0 +1,210 @@
+"""Hardened 63 width-seven (#571 prefix word) and 9 plain eight-cold (#568 E8) provider assembly with the native exact-complex moment.
+
+Prepared with OpenAI Codex assistance. The rational engines and outer
+constraints are retained from PR547/PR548 and their preserved ancestry.
+The bit operator is the cited unchanged PR543 supplier. The complex owner
+and invoice inputs must be freshly emitted by the packaged physical replay.
+All conservative admission guards and conservative moment/outer witnesses run
+before the PR559 native-complex correction. The bit surcharge is retained.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from decimal import Decimal, localcontext
+import argparse,json,hashlib,importlib.util,os,sys
+from collections import Counter
+assert __debug__, 'Assertions required'
+P=Path(sys.argv[1] if __name__=='__main__' else os.environ['GAIN_PR564_SOURCE']).resolve()
+read=lambda p:json.loads(p.read_text())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+hash_ok=lambda x:isinstance(x,str) and len(x)==64 and all(t in '0123456789abcdef'for t in x)
+digest=lambda x:hashlib.sha256(json.dumps(x,separators=(',',':')).encode()).hexdigest()
+def load(n):
+ s=importlib.util.spec_from_file_location(n,P/'engines'/(n+'.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,B,A=[load(n)for n in ('moment','base_two_moment','outer')]
+def dec(x):
+ with localcontext()as ctx:ctx.prec=70;return str(Decimal(x.numerator)/Decimal(x.denominator))
+from witness import DISPATCH,CALL_ORDER,COUNTS,PIDS,X,DISCOVER,pin
+
+
+def assemble(owner,invoice,owner_sha,invoice_sha):
+ # These are admission receipts, not optional collections of successful rows.
+ # Require both orientations and every finite check before pricing anything.
+ assert owner['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+ assert invoice['status']=='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE'
+ assert all(hash_ok(x)for x in (owner_sha,invoice_sha,owner['template_sha256'],owner['controller_audit_sha256'],invoice['parent_template_sha256']))
+ checks={'local_primitive_bound','logical','router','literal','mass','precision','tape','row','halving'}
+ assert set(invoice['strict_checks'])==checks
+ assert all(invoice['strict_checks'][name] is True for name in checks)
+ assert set(invoice['providers'])==set(PIDS)
+ assert invoice['provider_counts']==COUNTS
+ assert owner['all_live_owners_per_call_distinct'] is True
+ assert owner['owners_per_call']==728 and owner['actual_helper_owner_charts']==owner['hosted_residuals']==pin('expected.hosted_residuals',owner['hosted_residuals'])
+ pin('expected.rank_mass',owner['rank_mass'])
+ pin('expected.actual_73column_sigmas',owner['actual_73column_sigmas']);pin('expected.cross_replica_helper_roles',owner['cross_replica_helper_roles'])
+ pin('expected.idle_remainders',owner['explicit_idle_remainder_children'])
+ assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==72
+ assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+ assert invoice['helpers']==504 and invoice['centres']==8
+ assert invoice['physical_stock_identity']==dict(data_and_owner_families=7168,local_helpers=504,private_centres=8,coefficient_work=2)
+ assert sum(invoice['physical_stock_identity'].values())==invoice['physical']
+ assert invoice['controller_audit_sha256']==owner['controller_audit_sha256']
+ for pid,p in invoice['providers'].items():
+  assert set(p['local'])=={'forward','backward'}
+  assert p['helpers']==504 and p['centres']==8 and p['n']==728 and p['v']==112 and p['h']==9
+  K='providers.'+pid+'.';pin(K+'entering',p['entering_helpers']);pin(K+'entrance',p['entrance_rank'])
+  pin(K+'inventory',p['width_inventory'])
+  assert all(type(w) is int and 0<w<=9 for w in p['widths'])
+  assert Counter(p['widths'])==Counter({int(r):n for r,n in p['width_inventory'].items()})
+  assert sum(p['widths'])==9*504-p['entrance_rank'] and len(p['widths'])==504
+  pin(K+'width_digest',digest(p['widths']));assert all(p['widths'][h]==8 for h in (270,282,294,306))
+  pin(K+'expected_profile',p['paid_profile'])
+  assert p['children']==sum(p['paid_profile'].values())
+  pin(K+'program_hashes',p['program_hashes'])
+  for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+   assert hash_ok(p['artifacts'][name]) and p['artifacts'][name]==owner['source_artifacts']['providers/'+pid+'/'+name]
+   if name!='CLIFFORD-REVIEW.json':pin(K+'artifacts.'+name,p['artifacts'][name])
+  assert set(p['semantic_artifact_sha256'])=={'CLIFFORD-REVIEW.json'};pin(K+'semantic_phase_sha256',p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'])
+  assert owner['provider_phase_semantic_sha256'][pid]==invoice['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+  for name in ('forward','backward'):
+   z=p['local'][name];pinned=pin(K+'expected_local.'+name,{k:z[k]for k in('events','macros','real_component_primitives','prefix_l1','coefficient_work_primitive_count')});primitives=pinned['real_component_primitives'];coefficient_work=pinned['coefficient_work_primitive_count']
+   assert z['all_dirty_helper_columns_restored'] is True and z['private_centres_and_coefficient_work_cleared'] is True
+   assert z['all_exact_columns']==728 and z['dirty_helper_columns']==504
+   assert z['events']==pinned['events'] and z['macros']==pinned['macros']
+   assert z['real_component_primitives']==primitives and z['coefficient_work_primitive_count']==coefficient_work
+   assert z['pre_wrappers']==z['post_wrappers']==p['entering_helpers'];pin(K+'wrappers',z['pre_wrappers'])
+   assert 0<z['prefix_bits']<=192 and 0<Q(z['prefix_l1'])<2**192
+   peak=Q(z['prefix_l1']);assert z['prefix_bits']==peak.numerator.bit_length()-peak.denominator.bit_length()+1
+   assert peak==Q(pinned['prefix_l1'])
+  assert p['compiler']==64*74**3
+  assert p['local_adapters']==16*(max(z['macros']for z in p['local'].values())+p['children']+728+8)+64*73
+  assert p['local_primitive_bound']==max(z['real_component_primitives']for z in p['local'].values())+p['local_adapters']*p['compiler']
+ calls=invoice['selected_calls'];assert len(calls)==72
+ assert [(c['stage'],c['replica'])for c in calls]==CALL_ORDER
+ assert {(c['stage'],c['replica']) for c in calls}=={(s,r) for s in range(9) for r in range(8)}
+ for c in calls:
+  pid=DISPATCH[c['stage'],c['replica']]
+  assert c['provider_id']==pid
+  # The retained nine-stage recipe alternates its two reflected shears.
+  assert c['orientation']==('forward' if c['stage']%2==0 else 'backward')
+  p=invoice['providers'][pid];z=p['local'][c['orientation']]
+  assert c['program_sha256']==p['program_hashes'][c['orientation']]
+  for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+   assert c[name]==z[name]
+  assert c['entering_helpers']==p['entering_helpers'] and c['entrance_rank']==p['entrance_rank']
+ assert invoice['selected_real_component_primitives']==sum(c['real_component_primitives'] for c in calls)
+ assert invoice['selected_coefficient_work_primitive_count']==sum(c['coefficient_work_primitive_count'] for c in calls)
+ assert invoice['selected_scalar_macros']==sum(c['macros'] for c in calls)==sum(invoice['providers'][c['provider_id']]['local'][c['orientation']]['macros'] for c in calls)
+ assert invoice['factors_per_wrapper']==144
+ assert invoice['wrapper_elementary_factors_charged']==sum(c['pre_wrappers']+c['post_wrappers'] for c in calls)*144
+ paid=Counter()
+ for c in calls:paid.update({int(r):n for r,n in invoice['providers'][c['provider_id']]['paid_profile'].items()})
+ assert dict(paid)=={int(r):n for r,n in invoice['selected_local_paid_profile'].items()}
+ idle=Counter({int(r):n for r,n in owner['paid_profile'].items()});idle.subtract(paid);assert all(n>=0 for n in idle.values())
+ idle=+idle;assert sum(idle.values())==owner['explicit_idle_remainder_children']
+ pin('expected.idle_remainder_profile',{str(r):n for r,n in sorted(idle.items())})
+ paid.update(idle)
+ assert dict(paid)=={int(r):n for r,n in owner['paid_profile'].items()}
+ assert invoice['compiler']==64*74**3
+ assert invoice['local_adapters']==max(p['local_adapters']for p in invoice['providers'].values())
+ assert invoice['local_primitive_bound']==max(p['local_primitive_bound']for p in invoice['providers'].values())
+ # Recount the retained dedicated-bank envelope independently. Its geometry
+ # stays fixed, while every local primitive and wrapper comes from the actual
+ # selected provider/orientation sums above.
+ parent_live,parent_physical,parent_idle=11704,12218,16128
+ assert owner['source_idle_children_charged']==parent_idle
+ bridges,shifts=2*112*72,4*112*8;moves=2*shifts
+ nonlocal_items=(4*112*8*9+2*112*8*9+2*72*504+parent_idle+9*504+bridges+shifts+moves+parent_live+parent_physical+invoice['wrapper_elementary_factors_charged'])
+ outside=8*nonlocal_items+64*73
+ pervertex=(invoice['selected_real_component_primitives']+bridges+shifts+moves+parent_live+(72*invoice['local_adapters']+outside)*invoice['compiler']+64*parent_physical)
+ rebased=pervertex+65*(invoice['physical']-parent_physical)+(invoice['live']-parent_live)
+ assert invoice['unhosted_pervertex']==pervertex and invoice['hosted_rebased_pervertex']==rebased
+ used=max(pervertex,rebased)
+ prior=invoice['retained_prior_overcharge']
+ if prior is not None:
+  assert hash_ok(prior['sha256']) and type(prior['previous_pervertex_allowance']) is int and prior['previous_pervertex_allowance']>0
+  assert prior['added_complete_new_pervertex']==pervertex
+  assert prior['policy']=='Retain old allowance and add entire fresh mixed recount.'
+  used=max(used,prior['previous_pervertex_allowance']+pervertex)
+ assert invoice['conservative_pervertex_used']==used
+ finite=invoice['finite']
+ assert 0<finite['physical_row_coefficient']<finite['retained_row_coefficient']==20161
+ assert 0<finite['required_C0_bits']<finite['C0_exponent']==210000
+ assert finite['G_exponent']==30000 and finite['E_exponent']==100000
+ assert finite['halving_integer_inequality']==[5329,4608]
+ assert 0<invoice['global_prefix_bits']<=invoice['charged_prefix_bits']==512
+ assert invoice['row_prefix_extra']==1024
+ assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+72+72+4
+ group=2**(36*36)
+ for j in range(1,37):group*=2**(2*j)-1
+ stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']
+ logical=group*used+64;router=invoice['compiler']*(logical+1)*(stock+1)**2
+ literal=2*2**30000*stock**2+8*streamed_mass+4*stock+4+32*73
+ total_mass=streamed_mass+2**100000
+ assert finite['physical_stock_bits']==stock.bit_length() and finite['router_bits']==router.bit_length() and finite['literal_bits']==literal.bit_length()
+ assert finite['physical_row_coefficient']==2*stock.bit_length()+9909+252+1024
+ assert finite['required_C0_bits']==(32*73*total_mass*total_mass).bit_length()
+ actual_checks=dict(local_primitive_bound=invoice['local_primitive_bound']<2**48,logical=logical<2**6050,router=router<2**30000,literal=literal<2**100000,mass=total_mass<2**100001,precision=32*73*total_mass*total_mass<2**210000,tape=2*total_mass+18<2**210000,row=finite['physical_row_coefficient']<20161,halving=73*73>2*48*48)
+ assert actual_checks==invoice['strict_checks'] and all(actual_checks.values())
+ bit_path=P/'inputs/PR543-EXPECTED.json';bit_data=bit_path.read_bytes()
+ assert hashlib.sha1(b'blob '+str(len(bit_data)).encode()+b'\0'+bit_data).hexdigest()=='b61d859826246e0c3dabbe096e57ad7015eadfd5'
+ bit=json.loads(bit_data)['nine']
+ c=Q(bit['bit_lower'])
+ H={int(r):n for r,n in owner['paid_profile'].items()};pin('expected.global_profile',owner['paid_profile'])
+ # Claimed lower endpoints come from the spec; discovery derives them with the same certified moment engine.
+ # Either way they are verified below (accepted at b, rejected at b+1e-24).
+ if DISCOVER:b=Q(M.certify(H,73,owner['live'],False)['lower']);conservative_b=Q(M.certify(H,73,owner['live'],True)['lower'])
+ else:b=Q(X['complex_lower']);conservative_b=Q(X['conservative_complex_lower'])
+ assert owner['template_sha256']==invoice['template_sha256'] and owner_sha==invoice['owner_audit_sha256']
+ pin('expected.live',owner['live']);pin('expected.physical',owner['physical']);assert owner['deficit']==2560
+ assert owner['banked_residuals']==0
+ def check_moment(side,h,m,W,lower,deficit,bad):
+  assert m*W-sum(r*n for r,n in h.items())==deficit and m*m>2*max(h)**2
+  rows=[]
+  for z,accept in [(lower,True),(lower+Q(1,10**24),False)]:
+   l,u=M.moment(h,m,W,z,bad);ll,uu=B.moment(m,W,list(h.items()),z)
+   if bad:
+    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 accept else(l>1 and ll>1)
+   rows.append(dict(side=side,surcharge=bad,endpoint=str(z),accept=accept,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)]))
+  return rows
+ bitH={int(r):n for r,n in bit['profile'].items()}
+ bit_moments=check_moment('bit',bitH,64,bit['bit']['live'],c,9984,True)
+ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,2560,True)
+ assert bit['bit']['two_level_coefficient_bits']<bit['bit']['charged_two_level_coefficient_bits']==512 and bit['bit']['row_coefficient']<20161
+ def outer_witness(bb):
+  eta=beta=Q(1,10**24);s=min(c,(1-beta)*bb)-Q(1,10**27);assert 0<s<c and s<(1-beta)*bb
+  chain=[Q(384599,10**10)];cuts=[]
+  for _ in range(7):
+   old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+   ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512)
+   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)}}
+  outer=A.assembly(chain[-1],bb,bridge,k,eta=eta,beta=beta);assert len(outer['strict_constraints'])==47 and all(v>0 for v in outer['strict_constraints'].values())
+  controls=[]
+  for name,kk,ee,be 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],bb,bridge,kk,eta=ee,beta=be)
+   except AssertionError:controls.append(name)
+   else:raise AssertionError(name)
+  return k,cuts,outer,controls
+ conservative_k,conservative_cuts,conservative_outer,conservative_controls=outer_witness(conservative_b)
+ pin('expected.conservative_kappa_decimal',dec(conservative_k))
+ # Only after every conservative supplier/admission/outer check succeeds is
+ # the reviewed native exact-complex recurrence selected. Bit charge stays.
+ native_moments=check_moment('complex',H,73,owner['live'],b,2560,False)
+ k,cuts,outer,controls=outer_witness(b)
+ pin('expected.kappa_decimal',dec(k))
+ assert M.moment(H,73,owner['live'],b,True)[0]>1
+ assert M.moment(bitH,64,bit['bit']['live'],c+Q(1,10**24),False)[1]<1
+ model_controls=['native_complex_endpoint_rejected_with_old_surcharge','omitting_bit_surcharge_would_fail_next_endpoint_rejection']
+ moments=bit_moments+native_moments
+ input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'inputs/PR543-EXPECTED.json':sha(bit_path)}
+ input_hashes.update({'engines/'+name+'.py':sha(P/'engines'/(name+'.py'))for name in ('moment','base_two_moment','outer')})
+ return dict(status='PASS_FRESH_MIXED_048_ALLCOLD_NATIVE_EXACT_ASSEMBLY',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',gain_over_pinned569_percent=dec(100*(k/Q(X['gain_baseline_kappa'])-1)),complex_profile=H,provider_counts=invoice['provider_counts'],surcharge_model={'complex':False,'bit':True},conservative_complex_lower=str(conservative_b),conservative_complex_decimal=dec(conservative_b),conservative_kappa=str(conservative_k),conservative_kappa_decimal=dec(conservative_k),conservative_moments=conservative_moments,conservative_bootstrap=conservative_cuts,conservative_outer={n:str(v)for n,v in conservative_outer['strict_constraints'].items()},conservative_controls=conservative_controls,model_controls=model_controls,native_correction_gain=dec(k-conservative_k),template_sha256=owner['template_sha256'],input_sha256=input_hashes,bit_supplier=dict(pr=543,repository='eumemic/integer-mult-bounds',commit='2065fe4f72a914d907f1046603f5a36f17018535',path='research/e8-bit-r420/EXPECTED.json',git_blob_sha1='b61d859826246e0c3dabbe096e57ad7015eadfd5',replay_scope='Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit.'),moments=moments,bootstrap=cuts,outer={n:str(v)for n,v in outer['strict_constraints'].items()},controls=controls,scope='Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. Two fixed plain/composed-prefix-multicold per-invocation providers composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.')
+if __name__=='__main__':
+ import sys
+ package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists()
+ owner_path=C/'audit/OWNERS-AND-PROFILE.json';invoice_path=C/'audit/PREFIX-AND-INVOICE.json'
+ owner,invoice=read(owner_path),read(invoice_path)
+ assert owner['template_sha256']==read(C/'hosted/HOSTED.json')['template_sha256']
+ r=assemble(owner,invoice,sha(owner_path),sha(invoice_path));out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],r['kappa_decimal'])
diff --git a/research/complex-571-three-provider/code/assembly_controls.py b/research/complex-571-three-provider/code/assembly_controls.py
new file mode 100644
index 0000000000..fdc35bb4c9
--- /dev/null
+++ b/research/complex-571-three-provider/code/assembly_controls.py
@@ -0,0 +1,251 @@
+"""Independent admission controls for the N-provider native-complex assembly (per-provider controls).
+
+Prepared with OpenAI Codex assistance; Apache-2.0. Mutation receipts are
+rebound to their new owner digest, so unrelated stale hashes cannot conceal
+an incomplete width, provider, orientation, paid-profile or finite check.
+The fresh physical replay remains a separate prerequisite.
+"""
+import argparse
+import copy
+import itertools
+import math
+import hashlib
+import json
+import os
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+
+assert __debug__, 'Assertions required'
+P = Path(__file__).resolve().parent
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+digest = lambda x: hashlib.sha256(json.dumps(x, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    from assemble import assemble
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    baseline = assemble(owner, invoice, sha(owner_path), sha(invoice_path))
+
+    def empty_maps(o, i):
+        i['strict_checks'] = {}
+        i['providers'] = {}
+
+    def understated_stock(o, i):
+        o['physical'] -= 1
+        i['physical'] -= 1
+        i['physical_stock_identity']['coefficient_work'] -= 1
+
+    def changed_profile(o, i):
+        o['paid_profile']['1'] += 2
+        o['paid_profile']['2'] -= 1
+
+    def wrong_orientation(o, i):
+        c = next(c for c in i['selected_calls'] if c['stage'] == 0)
+        c['orientation'] = 'backward'
+        p = i['providers'][c['provider_id']]
+        z = p['local']['backward']
+        c['program_sha256'] = p['program_hashes']['backward']
+        for name in ('events', 'macros', 'real_component_primitives',
+                     'coefficient_work_primitive_count', 'pre_wrappers', 'post_wrappers'):
+            c[name] = z[name]
+        i['selected_real_component_primitives'] = sum(c['real_component_primitives'] for c in i['selected_calls'])
+        i['selected_coefficient_work_primitive_count'] = sum(c['coefficient_work_primitive_count'] for c in i['selected_calls'])
+
+    def understated_prefix(o, i):
+        for p in i['providers'].values():
+            for z in p['local'].values():
+                z['prefix_bits'], z['prefix_l1'] = 1, '1'
+        i['global_prefix_bits'] = 1 + 37 + 72 + 72 + 4
+
+    def reordered_calls(o, i):
+        i['selected_calls'][0], i['selected_calls'][1] = i['selected_calls'][1], i['selected_calls'][0]
+
+    def no_cold_wrappers(o, i):
+        for p in i['providers'].values():
+            p['entering_helpers'] -= 4
+            for z in p['local'].values():z['pre_wrappers'] = z['post_wrappers'] = p['entering_helpers']
+        for c in i['selected_calls']:
+            c['entering_helpers'] = c['pre_wrappers'] = c['post_wrappers'] = i['providers'][c['provider_id']]['entering_helpers']
+        i['wrapper_elementary_factors_charged'] = sum(2*c['pre_wrappers'] for c in i['selected_calls'])*i['factors_per_wrapper']
+
+    controls = [
+        ('empty_certification_maps', empty_maps),
+        ('failed_invoice_status', lambda o, i: i.__setitem__('status', 'FAIL')),
+        ('nonboolean_precision_check', lambda o, i: i['strict_checks'].__setitem__('precision', 'true')),
+        ('wrong_owner_role_count', lambda o, i: o.__setitem__('actual_helper_owner_charts', o['actual_helper_owner_charts'] - 1)),
+        ('understated_physical_stock', understated_stock),
+        ('changed_profile_same_rank_mass', changed_profile),
+        ('insufficient_finite_C0', lambda o, i: i['finite'].__setitem__('required_C0_bits', 210001)),
+        ('missing_finite_check', lambda o, i: i['strict_checks'].pop('halving')),
+        ('wrong_reflected_orientation_selfconsistent_totals', wrong_orientation),
+        ('missing_selected_call', lambda o, i: i['selected_calls'].pop()),
+        ('wrong_selected_primitive_sum', lambda o, i: i.__setitem__('selected_real_component_primitives', i['selected_real_component_primitives'] - 1)),
+        ('wrong_selected_coefficient_work_sum', lambda o, i: i.__setitem__('selected_coefficient_work_primitive_count', i['selected_coefficient_work_primitive_count'] - 1)),
+        ('unpaid_wrapper_factors', lambda o, i: i.__setitem__('wrapper_elementary_factors_charged', i['wrapper_elementary_factors_charged'] - 144)),
+        ('wrong_global_compiler', lambda o, i: i.__setitem__('compiler', 1)),
+        ('wrong_global_adapter_maximum', lambda o, i: i.__setitem__('local_adapters', 1)),
+        ('understated_exact_prefix_and_global_sum', understated_prefix),
+        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),
+        ('wrong_row_prefix_reserve', lambda o, i: i.__setitem__('row_prefix_extra', 0)),
+        ('wrong_parent_geometry_charge', lambda o, i: i.__setitem__('unhosted_pervertex', 1)),
+        ('wrong_rebased_geometry_charge', lambda o, i: i.__setitem__('hosted_rebased_pervertex', 1)),
+        ('wrong_complete_pervertex_envelope', lambda o, i: i.__setitem__('conservative_pervertex_used', 1)),
+        ('wrong_prior_added_complete_invoice', lambda o, i: i['retained_prior_overcharge'].__setitem__('added_complete_new_pervertex', 1)),
+        ('wrong_finite_router_bits', lambda o, i: i['finite'].__setitem__('router_bits', 1)),
+        ('wrong_finite_literal_bits', lambda o, i: i['finite'].__setitem__('literal_bits', 1)),
+        ('wrong_finite_physical_stock_bits', lambda o, i: i['finite'].__setitem__('physical_stock_bits', 1)),
+        ('wrong_finite_row_coefficient', lambda o, i: i['finite'].__setitem__('physical_row_coefficient', 1)),
+        ('reordered_complete_calls', reordered_calls),
+        ('understated_explicit_idle_remainders', lambda o, i: o.__setitem__('explicit_idle_remainder_children', o['explicit_idle_remainder_children']-1)),
+        ('understated_actual_chart_types', lambda o, i: o.__setitem__('actual_73column_sigmas', o['actual_73column_sigmas']-1)),
+        ('wrong_cross_replica_role_count', lambda o, i: o.__setitem__('cross_replica_helper_roles', o['cross_replica_helper_roles']-1)),
+        ('old_no_cold_wrapper_counts_selfconsistent', no_cold_wrappers),
+    ]
+
+    def resync(i, c):
+        p = i['providers'][c['provider_id']]
+        c['program_sha256'] = p['program_hashes'][c['orientation']]
+        c['entering_helpers'], c['entrance_rank'] = p['entering_helpers'], p['entrance_rank']
+        for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+            c[name] = p['local'][c['orientation']][name]
+
+    # Every provider gets the full per-provider control set, substituting a partner provider where needed.
+    for P in PIDS:
+        Qp = partner(P)
+        widths = invoice['providers'][P]['widths']
+
+        def forged_program_hash(o, i, P=P):
+            i['providers'][P]['program_hashes']['forward'] = '0' * 64
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = '0' * 64
+
+        def wrong_selected_call(o, i, P=P):
+            c = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            d = next(d for d in i['selected_calls'] if d['provider_id'] != P and (d['stage'] - c['stage']) % 2 == 0)
+            c['stage'], d['stage'], c['replica'], d['replica'] = d['stage'], c['stage'], d['replica'], c['replica']
+
+        def stale_program(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['program_hashes'] = copy.deepcopy(i['providers'][Qp]['program_hashes'])
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = p['program_hashes'][c['orientation']]
+
+        def stale_profile(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['paid_profile'] = copy.deepcopy(i['providers'][Qp]['paid_profile'])
+            p['children'] = sum(p['paid_profile'].values())
+
+        def moved(o, i, P=P):
+            a = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            b = next(c for c in i['selected_calls'] if c['provider_id'] != P and c['orientation'] == a['orientation'])
+            a['provider_id'], b['provider_id'] = b['provider_id'], a['provider_id']
+            resync(i, a); resync(i, b)
+
+        def compensating(o, i, P=P, Qp=Qp):
+            # Two dishonest profiles that cancel exactly in the dispatch-weighted aggregate.
+            g = math.gcd(COUNTS[P], COUNTS[Qp]); dp, dq = COUNTS[Qp] // g, COUNTS[P] // g
+            p, q = i['providers'][P], i['providers'][Qp]
+            p['paid_profile']['1'] += dp; q['paid_profile']['1'] -= dq
+            p['children'] += dp; q['children'] -= dq
+
+        def forged_recipe(o, i, P=P):
+            name = 'CLIFFORD-RECIPES.json'
+            i['providers'][P]['artifacts'][name] = '0'*64
+            o['source_artifacts']['providers/'+P+'/'+name] = '0'*64
+
+        def forged_phase(o, i, P=P):
+            i['providers'][P]['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'] = '0'*64
+            o['provider_phase_semantic_sha256'][P] = i['provider_phase_semantic_sha256'][P] = '0'*64
+
+        controls += [
+            (P + ':missing_provider', lambda o, i, P=P: i['providers'].pop(P)),
+            (P + ':missing_backward_orientation', lambda o, i, P=P: i['providers'][P]['local'].pop('backward')),
+            (P + ':unpaid_scalar_primitive', lambda o, i, P=P: i['providers'][P]['local']['forward'].__setitem__('real_component_primitives', i['providers'][P]['local']['forward']['real_component_primitives'] - 1)),
+            (P + ':wrong_local_artifact_binding', lambda o, i, P=P: i['providers'][P]['artifacts'].__setitem__('LOCAL-PROGRAMS.json.gz', '0' * 64)),
+            (P + ':false_dirty_restoration', lambda o, i, P=P: i['providers'][P]['local']['backward'].__setitem__('all_dirty_helper_columns_restored', False)),
+            (P + ':wrong_declared_provider_count', lambda o, i, P=P: i['provider_counts'].__setitem__(P, i['provider_counts'][P] + 1)),
+            (P + ':wrong_local_compiler', lambda o, i, P=P: i['providers'][P].__setitem__('compiler', 1)),
+            (P + ':wrong_local_adapter_charge', lambda o, i, P=P: i['providers'][P].__setitem__('local_adapters', 1)),
+            (P + ':wrong_local_primitive_bound', lambda o, i, P=P: i['providers'][P].__setitem__('local_primitive_bound', 1)),
+            (P + ':forged_provider_and_call_program_hash', forged_program_hash),
+            (P + ':provider_at_wrong_call', wrong_selected_call),
+            (P + ':stale_partner_program_consistent_call_hashes', stale_program),
+            (P + ':stale_partner_profile_consistent_child_total', stale_profile),
+            (P + ':relocated_against_partner_same_counts', moved),
+            (P + ':compensating_false_profiles_with_' + Qp, compensating),
+            (P + ':synchronized_forged_source_recipe_hash', forged_recipe),
+            (P + ':synchronized_forged_phase_review_semantics', forged_phase),
+        ]
+        # Width order and inventory: swap the first helper of every pair of distinct widths (same inventory),
+        # and shift one unit between them (same total).
+        first = {}
+        for h, w in enumerate(widths):
+            first.setdefault(w, h)
+        for wa, wb in itertools.combinations(sorted(first), 2):
+            def swap(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a], w[b] = w[b], w[a]
+            def shift(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a] += 1; w[b] -= 1
+            controls.append((P + ':width_order_swap_%d_%d' % (wa, wb), swap))
+            controls.append((P + ':width_inventory_shift_%d_%d' % (wa, wb), shift))
+        for h in (270, 282, 294, 306):
+            def cold_swap(o, i, P=P, h=h):
+                w = i['providers'][P]['widths']; j = w.index(9); w[h], w[j] = w[j], w[h]
+            controls.append((P + ':cold_helper_width_swap_%d' % h, cold_swap))
+    rejected = []
+    accepted = []
+    for name, mutate in controls:
+        o, i = copy.deepcopy(owner), copy.deepcopy(invoice)
+        mutate(o, i)
+        oh = digest(o)
+        i['owner_audit_sha256'] = oh
+        try:
+            assemble(o, i, oh, digest(i))
+        except (AssertionError, KeyError):
+            rejected.append(name)
+        else:
+            # Discovery has no pinned values to reject spec-only mutations; the strict run must reject every control.
+            if not DISCOVER:
+                raise AssertionError('Invalid admission receipt accepted: ' + name)
+            accepted.append(name)
+    try:
+        assemble(owner, invoice, '0' * 64, sha(invoice_path))
+    except AssertionError:
+        rejected.append('wrong_owner_receipt_hash')
+    else:
+        raise AssertionError('Wrong owner digest accepted')
+    pin('expected.assembly_controls_rejected', len(rejected))
+    assert baseline['controls'] == ['next_grid', 'zero_eta', 'zero_beta', 'unit_beta']
+    assert baseline['conservative_controls'] == baseline['controls']
+    assert baseline['surcharge_model'] == {'complex': False, 'bit': True}
+    assert len(baseline['model_controls']) == 2
+    return dict(
+        status='PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS',
+        valid_receipt_kappa=baseline['kappa'],
+        input_sha256=baseline['input_sha256'],
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+        rejected_controls=rejected,
+        discovery_accepted_controls=accepted,
+        exact_outer_controls=baseline['controls'],
+        conservative_outer_controls=baseline['conservative_controls'],
+        recurrence_model_controls=baseline['model_controls'],
+        scope='Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay.',
+    )
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--source-package', type=Path, required=True)
+    ap.add_argument('--owner', type=Path, required=True)
+    ap.add_argument('--invoice', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    assert not a.out.exists()
+    result = verify(a.owner, a.invoice, a.source_package)
+    a.out.write_text(json.dumps(result, indent=2) + '\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/complex-571-three-provider/code/audit_allcold.py b/research/complex-571-three-provider/code/audit_allcold.py
new file mode 100644
index 0000000000..f92f15341a
--- /dev/null
+++ b/research/complex-571-three-provider/code/audit_allcold.py
@@ -0,0 +1,223 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: BASE HOSTED REPORT [--mutation-controls]
+Each provider is independently read from BASE/providers, never from a baseline width histogram.
+OpenAI Codex two-provider width-seven extension; retains all inherited independent controller checks.
+The exact 63 width-seven and 9 plain calls are frozen below.
+"""
+import sys,json,gzip,hashlib,copy
+assert __debug__, 'Assertions must remain enabled'
+from pathlib import Path
+from collections import Counter,defaultdict
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+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')
+ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json')
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_ids=PIDS
+providers={};registry={};phase_semantic_hashes={}
+required_artifacts={'work/complex-nine-native/DATA-PHASES.json'}
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+ 'INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+for pid in provider_ids:
+ p=BASE/'providers'/pid
+ c=read(p/'CANONICAL-WORD.json.gz');checks=read(p/'LOCAL-CHECKS.json')
+ programs=read(p/'LOCAL-PROGRAMS.json.gz');replay=read(p/'INDEPENDENT-LOCAL-REPLAY.json')
+ phase=read(p/'CLIFFORD-REVIEW.json');adapters=read(p/'RESIDUAL-ADAPTERS.json')['recipes']
+ widths=[c['h']-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])]
+ assert all(widths[h]==8 for h in (270,282,294,306));pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ canonical_sha=sha(p/'CANONICAL-WORD.json.gz');programs_sha=sha(p/'LOCAL-PROGRAMS.json.gz')
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==canonical_sha and replay['local_programs_sha256']==programs_sha
+ assert replay['v']==c['v'] and replay['helpers']==c['R']
+ assert set(programs)==set(checks)==set(replay['local'])==set(replay['paid_profiles'])=={'forward','backward'}
+ for orientation,events in programs.items():
+  ck=checks[orientation];rr=replay['local'][orientation]
+  assert hashlib.sha256(json.dumps(events,sort_keys=True,separators=(',',':')).encode()).hexdigest()==ck['sha256']
+  assert ck['events']==len(events) and ck['all_columns']==2*c['v']+c['R']
+  assert ck['private_centers_cleared'] and ck['private_coefficient_stream_cleared_after_each_macro']
+  assert rr['all_exact_columns']==2*c['v']+c['R'] and rr['private_work_erased']
+  literal=Counter(e[-1]for e in events if e[0]in('climb','center'))
+  assert dict(literal)=={int(r):n for r,n in ck['paid_profile'].items()}=={int(r):n for r,n in c['local_profile'].items()}
+  assert ck['paid_profile']==replay['paid_profiles'][orientation]
+ assert phase['canonical_word_sha256']==canonical_sha and phase['recipe_sha256']==sha(p/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase']
+ phase_semantic_hashes[pid]=hashlib.sha256(json.dumps({k:v for k,v in phase.items()if k!='seconds'},sort_keys=True,separators=(',',':')).encode()).hexdigest()
+ for h,w in enumerate(widths):
+  assert 0<w<=c['h']
+  if w<c['h']:
+   f=c['start'][2*c['v']+h];a=adapters[str(f)]
+   assert a['frame']==f and a['vectors']==c['frames'][f] and a['rank']==w and a['entrance_rank']==c['h']-w
+ providers[pid]=dict(canonical=c,checks=checks,widths=widths)
+ registry[pid]=dict(local_programs=programs,canonical_word_sha256=canonical_sha,local_programs_sha256=programs_sha,
+  local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(p/'CLIFFORD-RECIPES.json'),
+  residual_adapter_sha256=sha(p/'RESIDUAL-ADAPTERS.json'),
+  **{k:c[k]for k in('v','h','R','ports','centers')},widths=widths)
+ required_artifacts.update('providers/'+pid+'/'+fn for fn in provider_files)
+canon=providers[provider_ids[0]]['canonical'];V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers'])
+assert V==112 and canon['h']==9
+assert all(providers[p]['canonical'][k]==canon[k]for p in provider_ids for k in('v','h','R','ports','centers'))
+assert required_artifacts<=set(summary['source_artifacts'])
+prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R
+# The selected map is an input to check, not a claim from the emitter.
+
+assert len(DISPATCH)==72 and Counter(DISPATCH.values())==COUNTS
+expected_provider=lambda stage,replica:DISPATCH[stage,replica]
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(V)]
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_providers']==registry and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert not any(k in t for k in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'))
+ assert len(t['calls'])==72 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','adapter_policy'):assert t[key]==parent[key]
+ assert t['exact_data_phase_recipe_sha256']==sha(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==72
+ all_local=[];perrep={r:[]for r in range(8)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<8 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   if e['kind']=='local_cover_sweep':expected['provider_id']=expected_provider(e['stage'],r)
+   assert e==expected
+   assert 0<=e['time']<72 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[DATA,DATA]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,DATA],charged_calls_per_cover=DATA)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[],children=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,DATA],charged_calls_per_cover=DATA)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time','provider_id','local_program_sha256')}=={k:v for k,v in old.items()if k not in('owners','local_program_sha256')}
+  pid=expected_provider(call['stage'],call['replica']);assert call['provider_id']==pid
+  width=providers[pid]['widths'];checks=providers[pid]['checks']
+  assert call['local_program_sha256']==checks[call['orientation']]['sha256']
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:(2*V)]==old['owners'][:(2*V)]
+  for h,(family,route)in enumerate(own[(2*V):]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,(8*V));fampair,sub=divmod(sub,(2*V));side,port=divmod(sub,V)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*V+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(8)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*(8*V)+(2*pairs[i]+sides[i])*V+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==2560 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ if '--mutation-controls' not in sys.argv[4:]:return
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA))
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+# Per-provider substitution controls: every provider is swapped against a partner provider.
+for P in provider_ids:
+ Qp=partner(P)
+ at_p=lambda q,P=P:next(c for c in q['calls']if c['provider_id']==P)
+ diff=[h for h in range(R)if providers[P]['widths'][h]!=providers[Qp]['widths'][h]]
+ narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+ reject(P+': wrong provider at its invocation',lambda q,P=P,Qp=Qp,at_p=at_p:at_p(q).__setitem__('provider_id',Qp))
+ reject(P+': stale per-call local program hash',lambda q,Qp=Qp,at_p=at_p:at_p(q).__setitem__('local_program_sha256',registry[Qp]['local_program_checks'][at_p(q)['orientation']]['sha256']))
+ reject(P+': stale serialized provider program',lambda q,P=P,Qp=Qp:q['local_providers'][P].__setitem__('local_programs',registry[Qp]['local_programs']))
+ reject(P+': unbound residual adapter hash',lambda q,P=P:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+ if diff:reject(P+': partner width in provider width registry',lambda q,P=P,Qp=Qp,h=diff[0]:q['local_providers'][P]['widths'].__setitem__(h,providers[Qp]['widths'][h]))
+ reject(P+': wrong per-call residual width',lambda q,at_p=at_p,h=narrow:at_p(q)['owners'][2*V+h][1].__setitem__(3,at_p(q)['owners'][2*V+h][1][3]-1))
+ reject(P+': wrong sweep provider',lambda q,P=P,Qp=Qp:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep'and DISPATCH[e['stage'],e['replica']]==P).__setitem__('provider_id',Qp))
+ reject(P+': entering helper width silently restored to nine',lambda q,P=P,h=narrow:q['local_providers'][P]['widths'].__setitem__(h,9))
+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:],provider_phase_semantic_sha256=phase_semantic_hashes,widths_by_provider={pid:dict(sorted(Counter(providers[pid]['widths']).items()))for pid in provider_ids},provider_counts=dict(Counter(c['provider_id']for c in ct['calls'])),all_provider_program_phase_and_wrapper_bindings=True,scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.parent.mkdir(parents=True,exist_ok=True)
+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'],provider_phase_semantic_sha256=phase_semantic_hashes,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()
+portable=bytearray(gzip.compress(frame_raw,mtime=0));portable[9]=255
+(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(bytes(portable))
+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/complex-571-three-provider/code/bind_providers_portable.py b/research/complex-571-three-provider/code/bind_providers_portable.py
new file mode 100644
index 0000000000..07f798629c
--- /dev/null
+++ b/research/complex-571-three-provider/code/bind_providers_portable.py
@@ -0,0 +1,63 @@
+"""Bind freshly verified plain and width-seven four-cold providers to the frozen literal owner plan.
+Prepared with OpenAI Codex assistance; Apache-2.0. All byte-stable native
+files are pinned to the plan. Only validated phase-receipt timing/serialization
+and directory fields are rebound; no dispatch, width or owner choice changes.
+"""
+import argparse,copy,gzip,hashlib,json,shutil
+from collections import Counter
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('baseline','plan','out'):ap.add_argument('--'+name,type=Path,required=True)
+ap.add_argument('--provider',action='append',required=True,help='PID=DIR');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 sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+base=a.out/'base';shutil.copytree(a.baseline/'complex-global/base',base)
+ap2=dict(x.split('=',1)for x in a.provider);dirs={k:Path(v)for k,v in ap2.items()};assert set(dirs)==set(PIDS)
+for pid,src in dirs.items():shutil.copytree(src,base/'providers'/pid)
+pin('data.plan_sha256',sha(a.plan))
+plan=read(a.plan);original=copy.deepcopy(plan);sources={}
+assert set(plan['provider_registry'])==set(dirs)
+assert {(c['stage'],c['replica']):c['provider']for c in plan['provider_calls']}==DISPATCH,'PLAN dispatch differs from spec dispatch'
+stable=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json')
+for pid,desc in plan['provider_registry'].items():
+ d=base/'providers'/pid
+ word,program,checks,native,phase=[read(d/name)for name in('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json')]
+ assert (word['v'],word['h'],word['R'],len(word['centers']))==(112,9,504,8)
+ assert word['ports']==desc['ports'] and word['centers']==desc['centers']
+ widths=[9-len(word['frames'][f])for f in word['start'][224:]]
+ assert all(widths[h]==8 for h in (270,282,294,306))
+ assert widths==desc['widths'];pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ assert native['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ pin('providers.%s.native_negative_controls'%pid,len(native['negative_controls_rejected']))
+ assert native['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and native['local_programs_sha256']==sha(d/'LOCAL-PROGRAMS.json.gz')
+ assert phase['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES'
+ assert phase['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and phase['recipe_sha256']==sha(d/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase'] is True and phase['endpoint_adapters']==224 
+ pin('providers.%s.phase_edges'%pid,phase['directed_edges'])
+ assert set(program)==set(checks)=={'forward','backward'}
+ expected={int(r):n for r,n in checks['forward']['paid_profile'].items()};pin('providers.%s.expected_profile'%pid,checks['forward']['paid_profile'])
+ for orientation,events in program.items():
+  profile=Counter()
+  for e in events:
+   if e[0]=='climb':profile[e[5]]+=1
+   elif e[0]=='center':profile[e[4]]+=1
+  assert dict(profile)==expected=={int(r):n for r,n in checks[orientation]['paid_profile'].items()}=={int(r):n for r,n in native['paid_profiles'][orientation].items()}
+  assert hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()==checks[orientation]['sha256']
+ for name in stable:
+  assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-timing artifact')
+  if name.endswith('.gz'):assert(d/name).read_bytes()[9]==255,(pid,name,'nonportable gzip header')
+ for c in plan['provider_calls']:
+  if c['provider']==pid:
+   assert c['orientation']==('forward'if c['stage']%2==0 else'backward')
+   assert c['local_program_sha256']==checks[c['orientation']]['sha256']
+ desc['directory']='providers/'+pid
+ desc['artifact_sha256']={name:sha(d/name)for name in desc['artifact_sha256']}
+ sources[pid]=dict(artifact_sha256=desc['artifact_sha256'],canonical_content_sha256=hashlib.sha256(json.dumps(word,sort_keys=True,separators=(',',':')).encode()).hexdigest(),all_phase_edges=phase['directed_edges'])
+plan['runtime_source_plan_sha256']=sha(a.plan)
+(a.out/'PLAN.json').write_text(json.dumps(plan,indent=2)+'\n')
+receipt=dict(status='PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING',source_plan_sha256=sha(a.plan),runtime_plan_sha256=sha(a.out/'PLAN.json'),providers=sources,only_rebound_fields=['provider_registry.directory','provider_registry.artifact_sha256.CLIFFORD-REVIEW.json','runtime_source_plan_sha256'])
+(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(receipt['status'])
diff --git a/research/complex-571-three-provider/code/emit_allcold.py b/research/complex-571-three-provider/code/emit_allcold.py
new file mode 100644
index 0000000000..d8fd22469a
--- /dev/null
+++ b/research/complex-571-three-provider/code/emit_allcold.py
@@ -0,0 +1,144 @@
+"""Two-provider width-seven whole-owner derivative, adapted with OpenAI Codex assistance.
+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
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--base',type=Path,required=True);parser.add_argument('--owners',type=Path,required=True);parser.add_argument('--plan',type=Path,required=True);parser.add_argument('--out',type=Path,required=True)
+a=parser.parse_args();BASE,MAP,PLAN,OUT=(p.resolve()for p in(a.base,a.owners,a.plan,a.out));assert not OUT.exists();OUT.mkdir(parents=True)
+class OH:
+ @staticmethod
+ def idle_basis(q):
+  z=next(i for i in range(9)if not(q>>i)&1);u=q^(1<<z);order=list(range(9));order[0],order[z]=order[z],order[0]
+  return[(1<<i)^(u if u>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ @staticmethod
+ def spectators(q,pending,off,w):
+  B=OH.idle_basis(q);occ=[B.index(v)for v in pending[off:off+w]]
+  return[j for j in range(73)if j not in occ][:9-w]
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+assert hashlib.sha256(MAP.read_bytes()).hexdigest()==SPEC['data']['owners_sha256'],'OWNERS not pinned by spec'
+plan=read(PLAN);assert plan['runtime_source_plan_sha256']==SPEC['data']['plan_sha256'],'PLAN not pinned by spec'
+call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==72;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);T=8;V=canon['v'];M=73;R=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)
+assert(len(roles),len(canon['start']),len(ph['recipes']))==(72*R,2*V+R,V)
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+registry={};source_artifacts={'work/complex-nine-native/DATA-PHASES.json':sha(BASE/'work/complex-nine-native/DATA-PHASES.json')}
+for provider_id in sorted(plan['provider_registry']):
+ assert provider_id in PIDS
+ directory=BASE/'providers'/provider_id
+ assert all((directory/f).is_file()for f in provider_files)
+ pc=read(directory/'CANONICAL-WORD.json.gz');checks=read(directory/'LOCAL-CHECKS.json');programs=read(directory/'LOCAL-PROGRAMS.json.gz');replay=read(directory/'INDEPENDENT-LOCAL-REPLAY.json')
+ assert(pc['v'],pc['h'],pc['R'],pc['ports'],pc['centers'])==(V,9,R,canon['ports'],canon['centers'])
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz')and replay['local_programs_sha256']==sha(directory/'LOCAL-PROGRAMS.json.gz')
+ widths=[9-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)]
+ assert widths==plan['provider_registry'][provider_id]['widths']
+ for name in provider_files:
+  value=sha(directory/name);assert value==plan['provider_registry'][provider_id]['artifact_sha256'][name]
+  source_artifacts[f'providers/{provider_id}/{name}']=value
+ registry[provider_id]=dict(local_programs=programs,canonical_word_sha256=sha(directory/'CANONICAL-WORD.json.gz'),local_programs_sha256=sha(directory/'LOCAL-PROGRAMS.json.gz'),local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(directory/'CLIFFORD-RECIPES.json'),residual_adapter_sha256=sha(directory/'RESIDUAL-ADAPTERS.json'),v=V,h=9,R=R,ports=pc['ports'],centers=pc['centers'],widths=widths)
+selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+assert len(selected)==72 and set(selected)==set(call_order)
+assert Counter(c['provider']for c in selected.values())==COUNTS
+per_call_widths={(c['stage'],c['replica']):c['widths']for c in plan['per_call_widths']}
+for key,c in selected.items():
+ assert c['time']==at[key] and c['provider']in registry
+ assert per_call_widths[key]==registry[c['provider']]['widths']
+for key in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'):t.pop(key)
+t['local_providers']=registry
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==registry[selected[s,rep]['provider']]['widths'][h] and 0<=orp<T
+ assert f==orp*(8*V)+(2*pairs[i]+side[i])*V+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f<DATA for f,r in c['owners'])
+ pc=selected[k];provider_id=pc['provider'];assert c['orientation']==pc['orientation']
+ c['provider_id']=provider_id;c['local_program_sha256']=registry[provider_id]['local_program_checks'][c['orientation']]['sha256']
+ assert c['local_program_sha256']==pc['local_program_sha256']
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in registry[c['provider_id']]['local_program_checks'][c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*(8*V)+(2*pairs[i]+side[i])*V+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==2560
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='round20-R504-asynchronous-whole-owner-v1',live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['bank_padding']['children']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  if ne['kind']=='local_cover_sweep':ne['provider_id']=selected[s,rep]['provider']
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert all(c['local_program_sha256']==registry[c['provider_id']]['local_program_checks'][c['orientation']]['sha256']for c in t['calls'])
+t['provider_dispatch']='For each indivisible local_cover_sweep, execute local_providers[call.provider_id].local_programs[call.orientation] with that provider residual adapters and Clifford recipes. The sweep provider_id must equal its call provider_id.'
+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_MIXED_PROVIDER_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=source_artifacts,provider_counts=dict(Counter(c['provider_id']for c in t['calls'])),
+ scope='Two actual verified plain/width-seven providers dispatched per complete invocation; 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/complex-571-three-provider/code/invoice_allcold.py b/research/complex-571-three-provider/code/invoice_allcold.py
new file mode 100644
index 0000000000..863e787540
--- /dev/null
+++ b/research/complex-571-three-provider/code/invoice_allcold.py
@@ -0,0 +1,316 @@
+"""Fresh call-specific mixed-provider finite invoice.
+
+Prepared with OpenAI Codex assistance, Apache-2.0. The scalar/Horner recount
+and finite inequalities are adapted from the retained PR558 -> PR552 ->
+PR531 invoice_final.py, whose notices and sources are preserved in the package.
+Every call selects a hash-bound provider. Shared compiler reserves use maxima;
+primitive work, coefficient work, local children and wrappers are also summed
+from actual selected provider/orientation records.
+"""
+import argparse, gzip, hashlib, json
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+assert __debug__, 'Assertions required'
+
+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 programhash(events):
+    return hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()
+
+def recount_provider(local_dir, registry):
+    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)==registry['canonical_word_sha256']
+    assert replay['local_programs_sha256']==filehash(pp)==registry['local_programs_sha256']
+    assert programs==registry['local_programs']
+    assert checks==registry['local_program_checks']
+    assert filehash(local_dir/'CLIFFORD-RECIPES.json')==registry['exact_local_clifford_recipe_sha256']
+    assert filehash(local_dir/'RESIDUAL-ADAPTERS.json')==registry['residual_adapter_sha256']
+    v,helpers,h,m=w['v'],w['R'],w['h'],73
+    assert (v,helpers,h)==(112,504,9)
+    assert registry['v']==v and registry['R']==helpers and registry['h']==h
+    assert registry['ports']==w['ports'] and registry['centers']==w['centers']
+    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
+
+    assert widths==registry['widths']
+    artifacts={f.name:filehash(f) for f in local_dir.iterdir() if f.is_file()}
+    phase_review=read(local_dir/'CLIFFORD-REVIEW.json')
+    semantic_phase=hashlib.sha256(json.dumps({k:v for k,v in phase_review.items()if k!='seconds'},sort_keys=True,separators=(',',':')).encode()).hexdigest()
+    return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n,
+                entering_helpers=entering,entrance_rank=sum(h-width for width in widths),
+                width_inventory=dict(sorted(Counter(widths).items())),widths=widths,
+                local_adapters=adapters,local_primitive_bound=primitive_bound,
+                compiler=compiler,children=children,artifacts=artifacts,
+                paid_profile=checks['forward']['paid_profile'],
+                program_hashes={o:programhash(events) for o,events in programs.items()},semantic_artifact_sha256={'CLIFFORD-REVIEW.json':semantic_phase})
+
+
+def run(base, hosted, audit, out, 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); summary=read(hosted/'HOSTED.json')
+    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']==summary['template_sha256']
+    assert owners['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+    assert template['recipe']==parent['recipe']
+    assert 'local_programs' not in template
+    assert set(template['local_providers'])==set(PIDS)
+    providers={pid:recount_provider(base/'providers'/pid,registry)
+               for pid,registry in template['local_providers'].items()}
+    for pid,p in providers.items():
+        assert owners['provider_phase_semantic_sha256'][pid]==control['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+        # The fresh controller admission must cite precisely these provider bytes.
+        for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+                     'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+                     'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+            path='providers/'+pid+'/'+name
+            assert summary['source_artifacts'][path]==p['artifacts'][name]
+            assert owners['source_artifacts'][path]==p['artifacts'][name]
+    v,helpers,h,m,centres,n=112,504,9,73,8,728
+    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']
+    assert len({(c['stage'],c['replica']) for c in template['calls']})==call_count
+    parent_calls={(c['stage'],c['replica']):c for c in parent['calls']}
+    sweeps=[e for e in template['execution_schedule'] if e['kind']=='local_cover_sweep']
+    assert len(sweeps)==call_count
+    selected=[]; selected_paid=Counter(); provider_counts=Counter(); orientation_counts=Counter()
+    scalar=coefficient_work=macros=0; wrapper_factors=0
+    factors_per_wrapper=2*(m-1)
+    for c in template['calls']:
+        pid,orientation=c['provider_id'],c['orientation']; p=providers[pid]
+        old=parent_calls[(c['stage'],c['replica'])]
+        assert orientation==old['orientation'] and c['owners'][:2*v]==old['owners'][:2*v]
+        assert c['local_program_sha256']==p['program_hashes'][orientation]
+        r=p['local'][orientation]
+        scalar+=r['real_component_primitives']; coefficient_work+=r['coefficient_work_primitive_count']; macros+=r['macros']
+        wrapper_factors+=(r['pre_wrappers']+r['post_wrappers'])*factors_per_wrapper
+        provider_counts[pid]+=1; orientation_counts[(pid,orientation)]+=1
+        selected_paid.update({int(k):v for k,v in p['paid_profile'].items()})
+        selected.append(dict(stage=c['stage'],replica=c['replica'],provider_id=pid,orientation=orientation,
+                             program_sha256=c['local_program_sha256'],events=r['events'],macros=r['macros'],
+                             real_component_primitives=r['real_component_primitives'],
+                             coefficient_work_primitive_count=r['coefficient_work_primitive_count'],
+                             entering_helpers=p['entering_helpers'],entrance_rank=p['entrance_rank'],
+                             pre_wrappers=r['pre_wrappers'],post_wrappers=r['post_wrappers']))
+    assert provider_counts==COUNTS
+    # The sweep registry is executable: no hidden use of the historical supplier.
+    by_call={(c['stage'],c['replica']):c for c in template['calls']}
+    for e in sweeps:
+        c=by_call[(e['stage'],e['replica'])]
+        assert e['provider_id']==c['provider_id']
+    assert set(p['compiler'] for p in providers.values())=={64*(m+1)**3}
+    compiler=64*(m+1)**3
+    adapters=max(p['local_adapters'] for p in providers.values())
+    primitive_bound=max(p['local_primitive_bound'] for p in providers.values())
+    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 and parent_physical==parent_live+helpers+centres+2
+    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']
+    # The old dedicated-bank geometry is only a conservative reserve envelope.
+    # Its singular program is never used as evidence for a mixed invocation.
+    rebased=parent_pervertex+65*(physical-parent_physical)+(live-parent_live)
+    used=max(rebased,parent_pervertex); retained=None; payload=512
+    if retained_invoice is not None:
+        previous=read(retained_invoice)
+        assert previous['compiler']==compiler and previous['charged_prefix_bits']==payload
+        previous_bound=previous['conservative_pervertex_used']
+        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 entire fresh mixed 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(r['prefix_bits'] for p in providers.values() for r in p['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_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'),
+        providers=providers,provider_phase_semantic_sha256={pid:p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']for pid,p in providers.items()},provider_counts=dict(provider_counts),selected_calls=selected,
+        selected_local_paid_profile=dict(sorted(selected_paid.items())),
+        selected_real_component_primitives=scalar,selected_coefficient_work_primitive_count=coefficient_work,
+        selected_scalar_macros=macros,global_prefix_bits=required_prefix,charged_prefix_bits=payload,
+        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,
+        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),
+        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='Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional.')
+    prefix=dict(status='PASS_MIXED_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'),
+        proof='Each selected normalized provider restores all arbitrary dirty helper columns and gives the same data shear endpoints. Actual whole-owner charts are right-translation bijections. Sum all 72 invocation and 72 bridge sweeps and take maximum local scalar/Horner prefix over all three providers and orientations. Idle children, phases, spectator endpoints and terminal translations are unitary. Retained all-size interfaces are conditional.')
+    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({k:receipt[k] for k in ['status','provider_counts','selected_real_component_primitives',
+          'selected_coefficient_work_primitive_count','global_prefix_bits','finite','strict_checks']},indent=2))
+    return receipt
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    for name in ('base','hosted','audit','out'):parser.add_argument('--'+name,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/complex-571-three-provider/code/phase_timing_controls.py b/research/complex-571-three-provider/code/phase_timing_controls.py
new file mode 100644
index 0000000000..1e38d20149
--- /dev/null
+++ b/research/complex-571-three-provider/code/phase_timing_controls.py
@@ -0,0 +1,34 @@
+"""Accept timing-only phase receipt differences; reject semantic differences.
+OpenAI Codex assistance; Apache-2.0. Only seconds is excluded from semantic pins.
+"""
+from pathlib import Path
+import sys,json,copy,hashlib,os
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+source,base,audit,out=map(Path,sys.argv[1:5]);assert not out.exists()
+os.environ['GAIN_PR564_SOURCE']=str(source.resolve())
+from assemble import assemble
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+digest=lambda v:hashlib.sha256(json.dumps(v,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+op=audit/'OWNERS-AND-PROFILE.json';ip=audit/'PREFIX-AND-INVOICE.json';owner=json.loads(op.read_text());invoice=json.loads(ip.read_text());baseline=assemble(owner,invoice,sha(op),sha(ip));accepted=[];rejected=[]
+for pid in invoice['providers']:
+ original=json.loads((base/'providers'/pid/'CLIFFORD-REVIEW.json').read_text())
+ for kind in('timing_only','substantive_phase_failure'):
+  phase=copy.deepcopy(original)
+  if kind=='timing_only':phase['seconds']+=123.456789
+  else:phase['all_child_equalities_include_global_phase']=False
+  raw=(json.dumps(phase,indent=2)+'\n').encode();rawsha=hashlib.sha256(raw).hexdigest();semantic=digest({k:v for k,v in phase.items()if k!='seconds'})
+  o,i=copy.deepcopy(owner),copy.deepcopy(invoice);name='CLIFFORD-REVIEW.json';o['source_artifacts']['providers/'+pid+'/'+name]=i['providers'][pid]['artifacts'][name]=rawsha
+  o['provider_phase_semantic_sha256'][pid]=i['provider_phase_semantic_sha256'][pid]=i['providers'][pid]['semantic_artifact_sha256'][name]=semantic
+  oh=digest(o);i['owner_audit_sha256']=oh
+  assert rawsha!=owner['source_artifacts']['providers/'+pid+'/'+name]
+  if kind=='timing_only':
+   assert semantic==invoice['provider_phase_semantic_sha256'][pid]
+   r=assemble(o,i,oh,digest(i));assert r['kappa']==baseline['kappa'];accepted.append(pid)
+  else:
+   assert semantic!=invoice['provider_phase_semantic_sha256'][pid]
+   try:assemble(o,i,oh,digest(i))
+   except AssertionError:rejected.append(pid)
+   else:raise AssertionError('semantic phase failure accepted')
+assert len(accepted)==len(rejected)==len(PIDS)
+out.write_text(json.dumps(dict(status='PASS_PHASE_REVIEW_TIMING_PORTABILITY_AND_SEMANTIC_REJECTION',timing_only_accepted=accepted,substantive_phase_failure_rejected=rejected,kappa=baseline['kappa'],source_owner_sha256=sha(op),source_invoice_sha256=sha(ip),scope='Actual phase receipt JSON is changed, raw artifact bindings and owner digest are consistently recomputed, and all substantive semantics are freshly hashed. Only seconds may vary; no phase correctness field is omitted from the frozen digest.'),indent=2)+'\n');print('PASS',len(accepted),len(rejected))
diff --git a/research/complex-571-three-provider/code/witness.py b/research/complex-571-three-provider/code/witness.py
new file mode 100644
index 0000000000..84eff298c4
--- /dev/null
+++ b/research/complex-571-three-provider/code/witness.py
@@ -0,0 +1,35 @@
+"""Spec loader: spec values are EXPECTED values, compared only after independent recomputation.
+WITNESS_DISCOVER=1 runs the same recomputation without comparing pinned values (pin() records only);
+it is used once to produce outputs for generate_spec.py, after which the strict run must pass.
+"""
+import json,os
+from collections import Counter
+from pathlib import Path
+SPEC=json.loads(Path(os.environ['WITNESS_SPEC']).read_text())
+DISCOVER=os.environ.get('WITNESS_DISCOVER')=='1'
+X=SPEC.get('expected',{})
+PROVIDERS=SPEC.get('providers',{})
+DISPATCH={(s,r):p for s,r,p in SPEC['dispatch']}
+CALL_ORDER=[tuple(x)for x in SPEC['call_order']]
+PIDS=tuple(sorted(set(DISPATCH.values())))
+COUNTS=dict(Counter(DISPATCH.values()))
+assert DISCOVER or set(PROVIDERS)==set(PIDS),'spec providers differ from dispatch providers'
+def lookup(key):
+ """Dotted spec path; a segment may itself contain dots when it names a file (split at most once per known file suffix)."""
+ v=SPEC;parts=key.split('.')
+ while parts:
+  for n in range(len(parts),0,-1):
+   k='.'.join(parts[:n])
+   if isinstance(v,dict) and k in v:v=v[k];parts=parts[n:];break
+  else:raise KeyError('spec has no key %s'%key)
+ return v
+def pin(key,got):
+ """Strict mode: got must equal the spec value at dotted key; the failure names the key."""
+ if DISCOVER:return got
+ want=lookup(key)
+ assert got==want,'SPEC MISMATCH %s: expected %s got %s'%(key,json.dumps(want)[:400],json.dumps(got,default=str)[:400])
+ return got
+def partner(pid):
+ """A different provider for substitution controls (next in sorted order)."""
+ assert len(PIDS)>1
+ return PIDS[(PIDS.index(pid)+1)%len(PIDS)]
diff --git a/research/complex-571-three-provider/data/OWNERS.json.gz b/research/complex-571-three-provider/data/OWNERS.json.gz
new file mode 100644
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new file mode 100644
index 0000000000..07b1b8206b
--- /dev/null
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new file mode 100644
index 0000000000..acc2dd6d1e
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+  "source_owners_sha256": "35ce2ebf98907d0fbe1c3759dd58f2fa0e8a1bd3b97f65fb101092df657ce4b8"
+}
diff --git a/research/complex-571-three-provider/data/WITNESS-SPEC.json b/research/complex-571-three-provider/data/WITNESS-SPEC.json
new file mode 100644
index 0000000000..17ddce2207
--- /dev/null
+++ b/research/complex-571-three-provider/data/WITNESS-SPEC.json
@@ -0,0 +1,873 @@
+{
+ "schema": "witness-spec/1",
+ "name": "big571-three-provider",
+ "data": {
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+ },
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+   },
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+  ],
+  [
+   2,
+   7,
+   "width7_eight"
+  ],
+  [
+   8,
+   0,
+   "width7_eight"
+  ],
+  [
+   3,
+   6,
+   "fourcold_eight"
+  ],
+  [
+   4,
+   5,
+   "width7_eight"
+  ],
+  [
+   5,
+   4,
+   "width7_eight"
+  ],
+  [
+   6,
+   3,
+   "fourcold_eight"
+  ],
+  [
+   7,
+   2,
+   "width7_eight"
+  ],
+  [
+   8,
+   1,
+   "width7_eight"
+  ],
+  [
+   3,
+   7,
+   "width7_eight"
+  ],
+  [
+   4,
+   6,
+   "width7_eight"
+  ],
+  [
+   5,
+   5,
+   "fourcold_eight"
+  ],
+  [
+   6,
+   4,
+   "fourcold_eight"
+  ],
+  [
+   7,
+   3,
+   "width7_eight"
+  ],
+  [
+   8,
+   2,
+   "width7_eight"
+  ],
+  [
+   4,
+   7,
+   "width7_eight"
+  ],
+  [
+   5,
+   6,
+   "width7_eight"
+  ],
+  [
+   6,
+   5,
+   "width7_eight"
+  ],
+  [
+   7,
+   4,
+   "width7_eight"
+  ],
+  [
+   8,
+   3,
+   "width7_eight"
+  ],
+  [
+   5,
+   7,
+   "width7_eight"
+  ],
+  [
+   6,
+   6,
+   "width7_eight"
+  ],
+  [
+   7,
+   5,
+   "width7_eight"
+  ],
+  [
+   8,
+   4,
+   "width7_eight"
+  ],
+  [
+   6,
+   7,
+   "width7_eight"
+  ],
+  [
+   7,
+   6,
+   "width7_eight"
+  ],
+  [
+   8,
+   5,
+   "width7_eight"
+  ],
+  [
+   7,
+   7,
+   "width7_eight"
+  ],
+  [
+   8,
+   6,
+   "width7_eight"
+  ],
+  [
+   8,
+   7,
+   "width7_eight"
+  ]
+ ],
+ "call_order": [
+  [
+   0,
+   0
+  ],
+  [
+   0,
+   1
+  ],
+  [
+   1,
+   0
+  ],
+  [
+   0,
+   2
+  ],
+  [
+   1,
+   1
+  ],
+  [
+   2,
+   0
+  ],
+  [
+   0,
+   3
+  ],
+  [
+   1,
+   2
+  ],
+  [
+   2,
+   1
+  ],
+  [
+   3,
+   0
+  ],
+  [
+   0,
+   4
+  ],
+  [
+   1,
+   3
+  ],
+  [
+   2,
+   2
+  ],
+  [
+   3,
+   1
+  ],
+  [
+   4,
+   0
+  ],
+  [
+   0,
+   5
+  ],
+  [
+   1,
+   4
+  ],
+  [
+   2,
+   3
+  ],
+  [
+   3,
+   2
+  ],
+  [
+   4,
+   1
+  ],
+  [
+   5,
+   0
+  ],
+  [
+   0,
+   6
+  ],
+  [
+   1,
+   5
+  ],
+  [
+   2,
+   4
+  ],
+  [
+   3,
+   3
+  ],
+  [
+   4,
+   2
+  ],
+  [
+   5,
+   1
+  ],
+  [
+   0,
+   7
+  ],
+  [
+   6,
+   0
+  ],
+  [
+   1,
+   6
+  ],
+  [
+   2,
+   5
+  ],
+  [
+   3,
+   4
+  ],
+  [
+   4,
+   3
+  ],
+  [
+   5,
+   2
+  ],
+  [
+   6,
+   1
+  ],
+  [
+   1,
+   7
+  ],
+  [
+   7,
+   0
+  ],
+  [
+   2,
+   6
+  ],
+  [
+   3,
+   5
+  ],
+  [
+   4,
+   4
+  ],
+  [
+   5,
+   3
+  ],
+  [
+   6,
+   2
+  ],
+  [
+   7,
+   1
+  ],
+  [
+   2,
+   7
+  ],
+  [
+   8,
+   0
+  ],
+  [
+   3,
+   6
+  ],
+  [
+   4,
+   5
+  ],
+  [
+   5,
+   4
+  ],
+  [
+   6,
+   3
+  ],
+  [
+   7,
+   2
+  ],
+  [
+   8,
+   1
+  ],
+  [
+   3,
+   7
+  ],
+  [
+   4,
+   6
+  ],
+  [
+   5,
+   5
+  ],
+  [
+   6,
+   4
+  ],
+  [
+   7,
+   3
+  ],
+  [
+   8,
+   2
+  ],
+  [
+   4,
+   7
+  ],
+  [
+   5,
+   6
+  ],
+  [
+   6,
+   5
+  ],
+  [
+   7,
+   4
+  ],
+  [
+   8,
+   3
+  ],
+  [
+   5,
+   7
+  ],
+  [
+   6,
+   6
+  ],
+  [
+   7,
+   5
+  ],
+  [
+   8,
+   4
+  ],
+  [
+   6,
+   7
+  ],
+  [
+   7,
+   6
+  ],
+  [
+   8,
+   5
+  ],
+  [
+   7,
+   7
+  ],
+  [
+   8,
+   6
+  ],
+  [
+   8,
+   7
+  ]
+ ],
+ "expected": {
+  "provider_counts": {
+   "prefixk_eight": 8,
+   "fourcold_eight": 10,
+   "width7_eight": 54
+  },
+  "global_profile": {
+   "1": 169688,
+   "2": 40194,
+   "3": 26384,
+   "4": 13824,
+   "5": 4032,
+   "6": 4032,
+   "7": 10,
+   "8": 576,
+   "30": 1,
+   "48": 1815
+  },
+  "owners_per_call": 728,
+  "hosted_residuals": 36288,
+  "rank_mass": 520704,
+  "actual_73column_sigmas": 6044,
+  "cross_replica_helper_roles": 28676,
+  "idle_remainders": 3028,
+  "live": 7168,
+  "physical": 7682,
+  "deficit": 2560,
+  "entering_helper_roles": 15688,
+  "idle_remainder_profile": {
+   "2": 2,
+   "3": 1200,
+   "7": 10,
+   "30": 1,
+   "48": 1815
+  },
+  "complex_lower": "320703711209415224549/200000000000000000000000",
+  "conservative_complex_lower": "1603518553252880887409/1000000000000000000000000",
+  "kappa": "800475700384307/500000000000000000",
+  "kappa_decimal": "0.001600951400768614",
+  "conservative_kappa_decimal": "0.001600951397983358",
+  "gain_baseline_kappa": "0.00160073442456167",
+  "mutations_rejected": 31,
+  "assembly_controls_rejected": 147
+ }
+}
diff --git a/research/complex-571-three-provider/verify.py b/research/complex-571-three-provider/verify.py
new file mode 100644
index 0000000000..e433d0ef90
--- /dev/null
+++ b/research/complex-571-three-provider/verify.py
@@ -0,0 +1,99 @@
+"""Admit the three-provider literal witness: #571's width-seven prefix word (P571), the same word with twelve PR568 multi-cut cold kernels (P571K), and PR568's eight-cold eight-pivot provider (E8).
+Prepared with Claude Code assistance. Apache-2.0; see NOTICE.md.
+The unchanged PR568 package (research/complex-multicold) and #571 package (research/structural-gain) are pinned external sources.
+P571K is built by PR568's unchanged build_multicut_kernels.py from #571's pinned word and data/P571K-MULTICOLD.json.
+Global stages are spec-driven: every pinned witness value is in data/WITNESS-SPEC.json (read by code/witness.py).
+"""
+import argparse,gzip,hashlib,json,os,subprocess,sys,time,shutil
+from pathlib import Path
+from fractions import Fraction as Q
+assert __debug__, 'Assertions required'
+P=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser();ap.add_argument('--work',type=Path,required=True)
+ap.add_argument('--multicold',type=Path,default=P.parent/'complex-multicold',help='unchanged PR568 package')
+ap.add_argument('--structural-gain',type=Path,default=P.parent/'structural-gain',help='unchanged #571 package')
+a=ap.parse_args();O=a.work.resolve();S=a.multicold.resolve();L=a.structural_gain.resolve()
+assert not O.exists() and not any(O.is_relative_to(x)for x in (P,S,L))
+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,x):p.write_text(json.dumps(x,indent=2)+'\n')
+def tree(root,skip):return{f.relative_to(root).as_posix():sha(f)for f in root.rglob('*')if f.is_file()and f!=root/skip and'__pycache__'not in f.parts}
+assert tree(P,'MANIFEST.json')==read(P/'MANIFEST.json')
+pins=read(P/'data/PINS.json');spec=read(P/'data/WITNESS-SPEC.json');X=spec['expected']
+assert spec['data']['plan_sha256']==sha(P/'data/PLAN.json') and spec['data']['owners_sha256']==sha(P/'data/OWNERS.json.gz')
+assert sha(S/'MANIFEST.json')==pins['multicold_source']['manifest_sha256'] and tree(S,'MANIFEST.json')==read(S/'MANIFEST.json')
+assert sha(L/'MANIFEST.json')==pins['structural_gain_source']['manifest_sha256']
+for name,value in pins['structural_gain_source']['files'].items():assert sha(L/name)==value==read(L/'MANIFEST.json')['files'][name]
+O.mkdir(parents=True);steps=[];start=time.monotonic()
+env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONUTF8='1',PYTHONINTMAXSTRDIGITS='0',MULTICOLD_SOURCE=str(S),GAIN_PR564_SOURCE=str(S),WITNESS_SPEC=str(P/'data/WITNESS-SPEC.json'));env.pop('WITNESS_DISCOVER',None);env.pop('PYTHONOPTIMIZE',None)
+def begin(name,script,*args):
+ log=O/(name+'.log');f=log.open('w');t=time.monotonic();print('RUN',name,flush=True)
+ proc=subprocess.Popen([sys.executable,'-B',str(S/'code/run_portable.py'),str(script),*map(str,args)],stdout=f,stderr=subprocess.STDOUT,env=env)
+ return name,log,f,t,proc
+def finish(job):
+ name,log,f,t,proc=job;code=proc.wait();f.close();steps.append(dict(name=name,exit_code=code,seconds=time.monotonic()-t,log_sha256=sha(log)));dump(O/'STAGES.json',steps)
+ if code:raise RuntimeError(name+' failed\n'+log.read_text()[-6000:])
+ print('PASS',name,flush=True)
+def run(name,script,*args):finish(begin(name,script,*args))
+B=S/'vendor/pr558';F=B/'vendor/pr552';V=F/'complex-global/vendor531';GK=F/'complex-local/static44/gk';baseline=O/'baseline558';SEL=baseline/'reconstruction/static44/SELECTION.json';G=O/'mixed-global'
+run('frozen558-full-replay',B/'verify.py','--work',baseline)
+# PR568's eight-pivot provider, rebuilt exactly as research/complex-multicold/verify.py does.
+raw=baseline/'reconstruction/promoted/FULL-WORD.json.gz';cold=O/'eight-cold-word';word=O/'eight-multicold-word';recipe=S/'data/EIGHT-COLD.json';multi=S/'data/EIGHT-MULTICOLD.json'
+run('eight-cold-construction',S/'code/build_cold_kernel.py','--input',raw,'--recipe',recipe,'--gk-dir',GK,'--out',cold)
+run('eight-cold-kernel-omissions',S/'code/audit_kernel_controls.py','--word',cold/'FULL-WORD.json.gz','--recipe',recipe,'--out',cold/'KERNEL-OMISSION-CONTROLS.json')
+run('eight-multicold-construction',S/'code/build_multicut_kernels.py','--input',cold/'FULL-WORD.json.gz','--recipe',multi,'--gk-dir',GK,'--out',word)
+run('eight-multicold-kernel-omissions',S/'code/audit_multicold_controls.py','--word',word/'FULL-WORD.json.gz','--recipe',multi,'--out',word/'MULTICOLD-OMISSION-CONTROLS.json')
+run('eight-inherited-44-omissions',F/'complex-local/static44/audit_scalar.py',word/'FULL-WORD.json.gz',SEL,word/'STATIC44-SCALAR-AUDIT.json')
+shutil.copyfile(raw.parent/'PROMOTION.json',word/'PROMOTION.json')
+run('eight-promoted-omissions',B/'code/audit_promoted_scalar.py',word/'FULL-WORD.json.gz',SEL,word/'PROMOTED-SCALAR-AUDIT.json')
+assert hashlib.sha256(gzip.decompress((word/'FULL-WORD.json.gz').read_bytes())).hexdigest()==pins['eight_multicold_word_content_sha256']
+# #571's admitted combined-prefix word (pinned by its manifest), localized by the same unchanged vendor pipeline #571 uses.
+w7src=L/'frontier-composition/combined-prefix-word';w7retained=L/'frontier-composition/combined-prefix-local'
+assert hashlib.sha256(gzip.decompress((w7src/'FULL-WORD.json.gz').read_bytes())).hexdigest()==pins['width7_word_content_sha256']
+# P571K: PR568's unchanged multi-cut kernel constructor applied to #571's pinned word, then its omission controls.
+kword=O/'prefixk-word'
+run('prefixk-multicold-construction',S/'code/build_multicut_kernels.py','--input',w7src/'FULL-WORD.json.gz','--recipe',P/'data/P571K-MULTICOLD.json','--gk-dir',GK,'--out',kword)
+assert hashlib.sha256(gzip.decompress((kword/'FULL-WORD.json.gz').read_bytes())).hexdigest()==pins['prefixk_word_content_sha256']
+run('prefixk-multicold-kernel-omissions',S/'code/audit_multicold_controls.py','--word',kword/'FULL-WORD.json.gz','--recipe',P/'data/P571K-MULTICOLD.json','--out',kword/'MULTICOLD-OMISSION-CONTROLS.json')
+providers={'eight':(word,O/'eight-cold-local'),'width7':(w7src,O/'width7-local'),'prefixk':(kword,O/'prefixk-local')}
+for name,(src,local) in providers.items():
+ run(name+'-all-columns-native-frames',V/'code/audit_and_transport.py','--raw',src/'FULL-WORD.json.gz','--routing',F/'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz','--out',local)
+ run(name+'-both-reflected-ledgers',V/'code/emit_local.py',local)
+ run(name+'-independent-local-controls',V/'code/audit_local.py',local)
+ run(name+'-normalized-wrappers',V/'code/adapters_local.py',local/'CANONICAL-WORD.json.gz',local/'RESIDUAL-ADAPTERS.json',local/'WRAPPER-CHECKS.json')
+phase_jobs=[begin(name+'-all-phase-edges',B/'code/phases_full.py',local,V/'vendor/clifford')for name,(src,local) in providers.items()]
+for job in phase_jobs:finish(job)
+eight,width7,prefixk=(providers[n][1] for n in ('eight','width7','prefixk'))
+# The fresh width-seven local is byte-identical to #571's retained, manifest-pinned local (phase review up to timing).
+for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','WRAPPER-CHECKS.json','CLIFFORD-RECIPES.json'):
+ assert sha(width7/name)==sha(w7retained/name),name
+fresh,kept=read(width7/'CLIFFORD-REVIEW.json'),read(w7retained/'CLIFFORD-REVIEW.json')
+assert {k:v for k,v in fresh.items()if k!='seconds'}=={k:v for k,v in kept.items()if k!='seconds'}
+locals_={'fourcold_eight':eight,'width7_eight':width7,'prefixk_eight':prefixk}
+assert set(locals_)==set(spec['providers'])
+run('bind-three-providers',P/'code/bind_providers_portable.py','--baseline',baseline,*[x for pid,d in sorted(locals_.items()) for x in ('--provider','%s=%s'%(pid,d))],'--plan',P/'data/PLAN.json','--out',G)
+run('emit-three-provider-controller',P/'code/emit_allcold.py','--base',G/'base','--owners',P/'data/OWNERS.json.gz','--plan',G/'PLAN.json','--out',G/'hosted')
+(G/'audit').mkdir()
+run('independent-controller-and-controls',P/'code/audit_allcold.py',G/'base',G/'hosted',G/'audit/ASYNC-AUDIT.json','--mutation-controls')
+run('fresh-three-provider-invoice',P/'code/invoice_allcold.py','--base',G/'base','--hosted',G/'hosted','--audit',G/'audit','--out',G/'audit','--retained-invoice',V/'evidence/audit/PREFIX-AND-INVOICE.json')
+run('conservative-and-native-exact-assembly',P/'code/assemble.py',S,G,O/'ASSEMBLY.json')
+run('admission-controls',P/'code/assembly_controls.py','--source-package',S,'--owner',G/'audit/OWNERS-AND-PROFILE.json','--invoice',G/'audit/PREFIX-AND-INVOICE.json','--out',O/'ASSEMBLY-CONTROLS.json')
+run('phase-timing-portability-controls',P/'code/phase_timing_controls.py',S,G/'base',G/'audit',O/'PHASE-TIMING-CONTROLS.json')
+for pid,local in locals_.items():
+ r=read(local/'INDEPENDENT-LOCAL-REPLAY.json');ph=read(local/'CLIFFORD-REVIEW.json');sp=spec['providers'][pid]
+ assert len(r['negative_controls_rejected'])==sp['native_negative_controls']==11 and r['paid_profiles']['forward']==r['paid_profiles']['backward']
+ assert ph['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES' and ph['all_child_equalities_include_global_phase']is True and ph['directed_edges']==sp['phase_edges'] and ph['endpoint_adapters']==224
+assert len(read(kword/'MULTICOLD-OMISSION-CONTROLS.json')['controls'])==pins['prefixk_multicold_omission_controls']
+assert len(read(cold/'KERNEL-OMISSION-CONTROLS.json')['controls'])==6
+assert len(read(word/'MULTICOLD-OMISSION-CONTROLS.json')['controls'])==32
+assert len(read(G/'audit/ASYNC-AUDIT.json')['mutations_rejected'])==X['mutations_rejected']
+assert len(read(O/'ASSEMBLY-CONTROLS.json')['rejected_controls'])==X['assembly_controls_rejected']
+z=read(O/'ASSEMBLY.json');assert Q(z['kappa_decimal'])==Q(X['kappa_decimal']) and Q(z['conservative_kappa_decimal'])==Q(X['conservative_kappa_decimal'])
+assert {str(k):v for k,v in z['complex_profile'].items()}==X['global_profile'] and z['provider_counts']==X['provider_counts']
+r=dict(status='PASS_PR571_PREFIX_WORD_PREFIXK_AND_PR568_EIGHT_COLD_THREE_PROVIDER_NATIVE_COMPLEX_AND_CITED_BIT',kappa=z['kappa'],kappa_decimal=z['kappa_decimal'],complex_lower=z['complex_lower'],bit_lower=z['bit_lower'],conservative_kappa_decimal=z['conservative_kappa_decimal'],conservative_complex_lower=z['conservative_complex_lower'],global_profile=z['complex_profile'],provider_counts=z['provider_counts'],surcharge_model=z['surcharge_model'],seconds=time.monotonic()-start,scope=z['scope']);dump(O/'RESULT.json',r)
+paths=['PHASE-TIMING-CONTROLS.json','mixed-global/audit/IDLE-REMAINDER-FRAMES.json','RESULT.json','ASSEMBLY.json','ASSEMBLY-CONTROLS.json','mixed-global/BINDING.json','mixed-global/audit/ASYNC-AUDIT.json','mixed-global/audit/OWNERS-AND-PROFILE.json','mixed-global/audit/PREFIX-AND-INVOICE.json',
+ 'eight-cold-word/KERNEL-CONSTRUCTION.json','eight-cold-word/KERNEL-OMISSION-CONTROLS.json','eight-multicold-word/KERNEL-CONSTRUCTION.json','eight-multicold-word/MULTICOLD-OMISSION-CONTROLS.json','eight-multicold-word/STATIC44-SCALAR-AUDIT.json','eight-multicold-word/PROMOTED-SCALAR-AUDIT.json','prefixk-word/KERNEL-CONSTRUCTION.json','prefixk-word/MULTICOLD-OMISSION-CONTROLS.json']
+for name in ('eight-cold-local','width7-local','prefixk-local'):
+ for fn in ('INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json','WRAPPER-CHECKS.json'):paths.append(name+'/'+fn)
+dump(O/'RECEIPT.json',dict(status=r['status'],steps=steps,artifacts={name:sha(O/name)for name in paths},manifest_sha256=sha(P/'MANIFEST.json'),multicold_manifest_sha256=sha(S/'MANIFEST.json'),structural_gain_manifest_sha256=sha(L/'MANIFEST.json'),witness_spec_sha256=sha(P/'data/WITNESS-SPEC.json')))
+print(json.dumps(r,indent=2))

From f4e9f7e85e9211cf6ba6c5789da2aa0902d9121e Mon Sep 17 00:00:00 2001
From: Jeremy Kothe <jeremy.robert.kothe@gmail.com>
Date: Mon, 12 Oct 2026 21:22:01 +1100
Subject: [PATCH 2/2] Raise to kappa 0.00160109005167629: improved literal
 owner map for the three-provider witness

---
 .../complex-571-three-provider/MANIFEST.json  |   6 +--
 .../data/OWNERS.json.gz                       | Bin 419252 -> 420241 bytes
 .../complex-571-three-provider/data/PLAN.json |  10 ++---
 .../data/WITNESS-SPEC.json                    |  40 ++++++++----------
 4 files changed, 25 insertions(+), 31 deletions(-)

diff --git a/research/complex-571-three-provider/MANIFEST.json b/research/complex-571-three-provider/MANIFEST.json
index eebb212aaa..ed831c1952 100644
--- a/research/complex-571-three-provider/MANIFEST.json
+++ b/research/complex-571-three-provider/MANIFEST.json
@@ -7,11 +7,11 @@
   "code/invoice_allcold.py": "b1f0857371401432f47011f61ebf3b8875bb554175905de5f993c19f3ab89693",
   "code/phase_timing_controls.py": "f02d0d0a6d84174d1706032401eb1c7140685ec24ce1ad22fc3e68ad4bfe6f85",
   "code/witness.py": "4f6d445f4796e9e7c0ef388370020119d4fdb929c006b2101aecb203ece8ab61",
-  "data/OWNERS.json.gz": "f78fe84137f3c4541252f9b0a298c5761afb4e9004c11eb9108bd680415b0c55",
+  "data/OWNERS.json.gz": "b8c4bbfbcf9869d3f1af8c50556d3ec0a8b2577fba6377b0ce8a2ec8b883798e",
   "data/P571K-MULTICOLD.json": "c839199d0e6f8e976978fe97bc0c5579a65ba69dfb6864585b448cccc1113056",
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-  "data/WITNESS-SPEC.json": "f1a3c9fab1d9e803f00c842034b2115d3aca6e977530d3a16fb527e0975c12b3",
+  "data/PLAN.json": "4707d897d24e85d24897618264da0687634ffc5e1463926e790475d6be1d9b96",
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   "verify.py": "21857d5aea3763fb1b1c3abdf5d84204c783318f8d41fb1fa6076501f4b53f8e"
diff --git a/research/complex-571-three-provider/data/OWNERS.json.gz b/research/complex-571-three-provider/data/OWNERS.json.gz
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diff --git a/research/complex-571-three-provider/data/PLAN.json b/research/complex-571-three-provider/data/PLAN.json
index acc2dd6d1e..a0308e6e4a 100644
--- a/research/complex-571-three-provider/data/PLAN.json
+++ b/research/complex-571-three-provider/data/PLAN.json
@@ -9,15 +9,13 @@
   "deficit": 2560,
   "profile": {
     "1": 169688,
-    "2": 40194,
-    "3": 26384,
+    "2": 40193,
+    "3": 26386,
     "4": 13824,
     "5": 4032,
     "6": 4032,
-    "7": 10,
     "8": 576,
-    "30": 1,
-    "48": 1815
+    "48": 1817
   },
   "order": [
     [
@@ -43299,6 +43297,6 @@
     }
   },
   "source_plan_sha256": "0c86ebfa5fd9d657834036b620f05742c0b5713efbf47ec0964eb7229e1cd53f",
-  "assignment_sha256": "f78fe84137f3c4541252f9b0a298c5761afb4e9004c11eb9108bd680415b0c55",
+  "assignment_sha256": "b8c4bbfbcf9869d3f1af8c50556d3ec0a8b2577fba6377b0ce8a2ec8b883798e",
   "source_owners_sha256": "35ce2ebf98907d0fbe1c3759dd58f2fa0e8a1bd3b97f65fb101092df657ce4b8"
 }
diff --git a/research/complex-571-three-provider/data/WITNESS-SPEC.json b/research/complex-571-three-provider/data/WITNESS-SPEC.json
index 17ddce2207..118b363856 100644
--- a/research/complex-571-three-provider/data/WITNESS-SPEC.json
+++ b/research/complex-571-three-provider/data/WITNESS-SPEC.json
@@ -1,9 +1,9 @@
 {
  "schema": "witness-spec/1",
- "name": "big571-three-provider",
+ "name": "big571-ch0_2",
  "data": {
-  "plan_sha256": "d0ca30bde3cd73f40d94813715e1d0a6255e2d7840e9bb0abf74e8e1cac11cd5",
-  "owners_sha256": "f78fe84137f3c4541252f9b0a298c5761afb4e9004c11eb9108bd680415b0c55"
+  "plan_sha256": "4707d897d24e85d24897618264da0687634ffc5e1463926e790475d6be1d9b96",
+  "owners_sha256": "b8c4bbfbcf9869d3f1af8c50556d3ec0a8b2577fba6377b0ce8a2ec8b883798e"
  },
  "providers": {
   "fourcold_eight": {
@@ -834,39 +834,35 @@
   },
   "global_profile": {
    "1": 169688,
-   "2": 40194,
-   "3": 26384,
+   "2": 40193,
+   "3": 26386,
    "4": 13824,
    "5": 4032,
    "6": 4032,
-   "7": 10,
    "8": 576,
-   "30": 1,
-   "48": 1815
+   "48": 1817
   },
   "owners_per_call": 728,
   "hosted_residuals": 36288,
   "rank_mass": 520704,
-  "actual_73column_sigmas": 6044,
-  "cross_replica_helper_roles": 28676,
-  "idle_remainders": 3028,
+  "actual_73column_sigmas": 6104,
+  "cross_replica_helper_roles": 28841,
+  "idle_remainders": 3020,
   "live": 7168,
   "physical": 7682,
   "deficit": 2560,
   "entering_helper_roles": 15688,
   "idle_remainder_profile": {
-   "2": 2,
-   "3": 1200,
-   "7": 10,
-   "30": 1,
-   "48": 1815
+   "2": 1,
+   "3": 1202,
+   "48": 1817
   },
-  "complex_lower": "320703711209415224549/200000000000000000000000",
-  "conservative_complex_lower": "1603518553252880887409/1000000000000000000000000",
-  "kappa": "800475700384307/500000000000000000",
-  "kappa_decimal": "0.001600951400768614",
-  "conservative_kappa_decimal": "0.001600951397983358",
-  "gain_baseline_kappa": "0.00160073442456167",
+  "complex_lower": "400914412997296205799/250000000000000000000000",
+  "conservative_complex_lower": "1603657649194832248739/1000000000000000000000000",
+  "kappa": "160109005167629/100000000000000000",
+  "kappa_decimal": "0.00160109005167629",
+  "conservative_kappa_decimal": "0.001601090048890878",
+  "gain_baseline_kappa": "0.001600067494703216",
   "mutations_rejected": 31,
   "assembly_controls_rejected": 147
  }