diff --git a/research/k8-x54-t37/CERTIFICATE.json b/research/k8-x54-t37/CERTIFICATE.json
new file mode 100644
index 0000000000..7eb1ed453d
--- /dev/null
+++ b/research/k8-x54-t37/CERTIFICATE.json
@@ -0,0 +1,122 @@
+{
+  "replicas": 37,
+  "width_prices": {
+    "4": -1,
+    "5": -20,
+    "7": -8,
+    "8": -2,
+    "9": 4
+  },
+  "capacity_bonuses": {
+    "8": 2,
+    "16": 4,
+    "32": 8,
+    "48": -13
+  },
+  "packing": [
+    {
+      "capacity": 8,
+      "width_counts": [
+        0,
+        0,
+        0,
+        1,
+        0
+      ],
+      "bins": 24864
+    },
+    {
+      "capacity": 16,
+      "width_counts": [
+        0,
+        0,
+        0,
+        2,
+        0
+      ],
+      "bins": 3306
+    },
+    {
+      "capacity": 16,
+      "width_counts": [
+        0,
+        0,
+        1,
+        0,
+        1
+      ],
+      "bins": 9394
+    },
+    {
+      "capacity": 16,
+      "width_counts": [
+        2,
+        0,
+        0,
+        1,
+        0
+      ],
+      "bins": 3876
+    },
+    {
+      "capacity": 32,
+      "width_counts": [
+        0,
+        0,
+        2,
+        0,
+        2
+      ],
+      "bins": 298
+    },
+    {
+      "capacity": 32,
+      "width_counts": [
+        0,
+        1,
+        0,
+        0,
+        3
+      ],
+      "bins": 10656
+    },
+    {
+      "capacity": 32,
+      "width_counts": [
+        1,
+        0,
+        0,
+        0,
+        3
+      ],
+      "bins": 5622
+    },
+    {
+      "capacity": 48,
+      "width_counts": [
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "bins": 11302
+    },
+    {
+      "capacity": 48,
+      "width_counts": [
+        1,
+        0,
+        0,
+        1,
+        4
+      ],
+      "bins": 5274
+    }
+  ],
+  "root_interval": [
+    "0.001676945247549584231285",
+    "0.001676945247549584231286"
+  ],
+  "kappa_grid": "0.001674137810105185"
+}
diff --git a/research/k8-x54-t37/CODE-DERIVATION.json b/research/k8-x54-t37/CODE-DERIVATION.json
new file mode 100644
index 0000000000..510d91eb86
--- /dev/null
+++ b/research/k8-x54-t37/CODE-DERIVATION.json
@@ -0,0 +1,218 @@
+{
+  "emit_allcold.py": {
+    "source_sha256": "354367e1fd6185a67b04f4268bcae4d502e47b18cb2131e247f5bcab5b3a769e",
+    "derived_sha256": "3219e0706d497a2e6b595cec0a0d5bdbfbd1d991bf70136762eada44126a9ac1",
+    "edits": [
+      {
+        "before": "==144",
+        "after": "==333",
+        "count": 3
+      },
+      {
+        "before": "T=16;",
+        "after": "T=37;",
+        "count": 1
+      },
+      {
+        "before": "==5120",
+        "after": "==11840",
+        "count": 1
+      },
+      {
+        "before": "deficit=5120",
+        "after": "deficit=11840",
+        "count": 1
+      }
+    ]
+  },
+  "audit_allcold.py": {
+    "source_sha256": "1467a2acb654e62552c69fb9a7c4c85f70a02120881d222313865058ab71a6cc",
+    "derived_sha256": "a8d3c48e26957c5174ea35043545d3863a4c19c82422074ac42132b446533b4a",
+    "edits": [
+      {
+        "before": "T=16;",
+        "after": "T=37;",
+        "count": 1
+      },
+      {
+        "before": "144",
+        "after": "333",
+        "count": 6
+      },
+      {
+        "before": "range(16)",
+        "after": "range(37)",
+        "count": 2
+      },
+      {
+        "before": "r<16",
+        "after": "r<37",
+        "count": 1
+      },
+      {
+        "before": "5120",
+        "after": "11840",
+        "count": 3
+      }
+    ]
+  },
+  "assemble.py": {
+    "source_sha256": "15f6986a476bac76bcdc0bfcf51da115389b46f1950d2766b6822f757888b13a",
+    "derived_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a",
+    "edits": [
+      {
+        "before": "==144*R",
+        "after": "==333*R",
+        "count": 1
+      },
+      {
+        "before": "invoice['bridge_sweeps']==144",
+        "after": "invoice['bridge_sweeps']==333",
+        "count": 1
+      },
+      {
+        "before": "data_and_owner_families=14336",
+        "after": "data_and_owner_families=33152",
+        "count": 1
+      },
+      {
+        "before": "len(calls)==144",
+        "after": "len(calls)==333",
+        "count": 1
+      },
+      {
+        "before": "range(16)",
+        "after": "range(37)",
+        "count": 1
+      },
+      {
+        "before": "parent_live,parent_physical,parent_idle=23408,23922,32256",
+        "after": "parent_live,parent_physical,parent_idle=55832,56346,74592",
+        "count": 1
+      },
+      {
+        "before": "2*112*4*16",
+        "after": "2*112*4*37",
+        "count": 1
+      },
+      {
+        "before": "2*112*144,4*112*16",
+        "after": "2*112*333,4*112*37",
+        "count": 1
+      },
+      {
+        "before": "4*112*16*9+2*112*16*9+2*144*R",
+        "after": "4*112*37*9+2*112*37*9+2*333*R",
+        "count": 1
+      },
+      {
+        "before": "(144*invoice['local_adapters']",
+        "after": "(333*invoice['local_adapters']",
+        "count": 1
+      },
+      {
+        "before": "invoice['charged_prefix_bits']==512",
+        "after": "invoice['charged_prefix_bits']==1024",
+        "count": 1
+      },
+      {
+        "before": "invoice['row_prefix_extra']==1024",
+        "after": "invoice['row_prefix_extra']==2048",
+        "count": 1
+      },
+      {
+        "before": "+37+144+144+4",
+        "after": "+37+333+333+4",
+        "count": 1
+      },
+      {
+        "before": "+9909+252+1024",
+        "after": "+9909+252+2048",
+        "count": 1
+      },
+      {
+        "before": "5120",
+        "after": "11840",
+        "count": 3
+      },
+      {
+        "before": "(4+512)",
+        "after": "(4+1024)",
+        "count": 2
+      },
+      {
+        "before": "two independent bank groups, each with R0=504 helpers; restored private workspace is shared",
+        "after": "five bank groups with 8,8,8,8,5 active lanes and R0=504 helpers; shared private work is restored",
+        "count": 1
+      },
+      {
+        "before": "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. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. 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.",
+        "after": "Conditional R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain.",
+        "count": 1
+      }
+    ]
+  },
+  "assembly_controls.py": {
+    "source_sha256": "da7e981ae1b9f099d4e1524cb4f3ba1116011936ebe378692889b5dbfa99029d",
+    "derived_sha256": "29ba6742d899d2318a96745c8ec21de06ba3968d4641c3400a15bc714e0d7f9e",
+    "edits": [
+      {
+        "before": "1 + 37 + 144 + 144 + 4",
+        "after": "1 + 37 + 333 + 333 + 4",
+        "count": 1
+      }
+    ]
+  },
+  "freeze_spec.py": {
+    "source_sha256": "5971eecac6d6fbcb53244b80f1b9d7232012dc32876fab511214a5addebbe6c2",
+    "derived_sha256": "e9132a9d195c66123f2747a17f7ef404b4d1e3ef6263ab4c28c983a052cf10bd",
+    "edits": [
+      {
+        "before": "{'gauge44':144}",
+        "after": "{'gauge44':333}",
+        "count": 1
+      }
+    ]
+  },
+  "invoice_allcold.py": {
+    "source_sha256": "71eb57514e28ced97251e0507105f654f59885ec4d40486a780bf166098858a8",
+    "derived_sha256": "e97c74d1ccfb0b0e26260e65bb780fa0103f4c716647e238f943a2e840a1f566",
+    "edits": [
+      {
+        "before": "stages,replicas,blocks_per_stream=9,16,4",
+        "after": "stages,replicas,blocks_per_stream=9,37,4",
+        "count": 1
+      },
+      {
+        "before": "==5120",
+        "after": "==11840",
+        "count": 1
+      },
+      {
+        "before": "payload=512",
+        "after": "payload=1024",
+        "count": 1
+      },
+      {
+        "before": "previous['charged_prefix_bits']==payload",
+        "after": "previous['charged_prefix_bits']==512",
+        "count": 1
+      },
+      {
+        "before": "all 144 invocation and 144 bridge sweeps",
+        "after": "all 333 invocation and 333 bridge sweeps",
+        "count": 1
+      },
+      {
+        "before": "All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission.",
+        "after": "The fixed provider uses fresh hash-bound independent all-column/frame/phase/normalization admission.",
+        "count": 1
+      },
+      {
+        "before": "take maximum local scalar/Horner prefix over all three providers and orientations.",
+        "after": "take the maximum local scalar/Horner prefix over both orientations of the fixed provider.",
+        "count": 1
+      }
+    ]
+  }
+}
diff --git a/research/k8-x54-t37/CODE-DERIVATION.patch b/research/k8-x54-t37/CODE-DERIVATION.patch
new file mode 100644
index 0000000000..3089adb97c
--- /dev/null
+++ b/research/k8-x54-t37/CODE-DERIVATION.patch
@@ -0,0 +1,309 @@
+--- pr1074/code/emit_allcold.py
++++ r480-owner-optimum/code/emit_allcold.py
+@@ -24,8 +24,8 @@
+ 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))==144;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=16;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
++call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==333;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=37;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+ assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,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')
+@@ -49,9 +49,9 @@
+   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)
+-assert len(roles)==144*R   # one whole-owner role per (call, provider helper)
++assert len(roles)==333*R   # one whole-owner role per (call, provider helper)
+ selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+-assert len(selected)==144 and set(selected)==set(call_order)
++assert len(selected)==333 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():
+@@ -92,7 +92,7 @@
+   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())==5120
++assert M*DATA-sum(r*n for r,n in paid.items())==11840
+ C=len(canon['centers']);physical=DATA+C+R+2
+ assert parent['physical']-parent['live']==C+R0+2
+ # Local circuits, exact phase recipes, normalized wrappers and data routes stay
+@@ -140,7 +140,7 @@
+  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=5120,maxchild=max(paid),
++ rank_mass=sum(r*n for r,n in paid.items()),deficit=11840,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),
+--- pr1074/code/audit_allcold.py
++++ r480-owner-optimum/code/audit_allcold.py
+@@ -77,10 +77,10 @@
+ parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+ assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+ assert required_artifacts<=set(summary['source_artifacts'])
+-prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=16;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=144;HOSTED=CALLS*R
++prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=37;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=333;HOSTED=CALLS*R
+ # The selected map is an input to check, not a claim from the emitter.
+ 
+-assert len(DISPATCH)==144 and Counter(DISPATCH.values())==COUNTS
++assert len(DISPATCH)==333 and Counter(DISPATCH.values())==COUNTS
+ expected_provider=lambda stage,replica:DISPATCH[stage,replica]
+ 
+ def orthobasis(port):
+@@ -93,23 +93,23 @@
+  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'])==144 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
++ assert len(t['calls'])==333 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))==144
+- all_local=[];perrep={r:[]for r in range(16)};globals_=[]
++ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==333
++ all_local=[];perrep={r:[]for r in range(37)};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<16 and j<30;perrep[r].append(j)
++   r=e['replica'];assert 0<=r<37 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']<144 and order[e['time']][1]==r
++   assert 0<=e['time']<333 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:
+@@ -164,7 +164,7 @@
+    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(16)for h in range(R)}
++ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(37)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']:
+@@ -179,8 +179,8 @@
+    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==5120 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=144)
++ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==11840 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=333)
+ 
+ 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())
+@@ -228,11 +228,11 @@
+   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=5120,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,provider_artifact_semantic_sha256=artifact_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=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=11840,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,provider_artifact_semantic_sha256=artifact_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=5120,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,provider_artifact_semantic_sha256=artifact_semantic_hashes,controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
++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=11840,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,provider_artifact_semantic_sha256=artifact_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,
+--- pr1074/code/assemble.py
++++ r480-owner-optimum/code/assemble.py
+@@ -63,14 +63,14 @@
+  assert owner['all_live_owners_per_call_distinct'] is True
+  # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+  R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+- assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==144*R==pin('expected.hosted_residuals',owner['hosted_residuals'])
++ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==333*R==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']==144
++ assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==333
+  assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+  assert invoice['centres']==8
+- assert invoice['physical_stock_identity']==dict(data_and_owner_families=14336,local_helpers=R,private_centres=8,coefficient_work=2)
++ assert invoice['physical_stock_identity']==dict(data_and_owner_families=33152,local_helpers=R,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():
+@@ -106,9 +106,9 @@
+   assert p['compiler']==64*74**3
+   assert p['local_adapters']==16*(max(z['macros']for z in p['local'].values())+p['children']+2*112+R+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)==144
++ calls=invoice['selected_calls'];assert len(calls)==333
+  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(16)}
++ assert {(c['stage'],c['replica']) for c in calls}=={(s,r) for s in range(9) for r in range(37)}
+  for c in calls:
+   pid=DISPATCH[c['stage'],c['replica']]
+   assert c['provider_id']==pid
+@@ -138,13 +138,13 @@
+  # 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=23408,23922,32256
+- parent_banks,rem=divmod(parent_live-2*112*4*16,9);assert rem==0 and parent_physical==parent_live+504+8+2   # two independent bank groups, each with R0=504 helpers; restored private workspace is shared
++ parent_live,parent_physical,parent_idle=55832,56346,74592
++ parent_banks,rem=divmod(parent_live-2*112*4*37,9);assert rem==0 and parent_physical==parent_live+504+8+2   # five bank groups with 8,8,8,8,5 active lanes and R0=504 helpers; shared private work is restored
+  assert owner['source_idle_children_charged']==parent_idle
+- bridges,shifts=2*112*144,4*112*16;moves=2*shifts
+- nonlocal_items=(4*112*16*9+2*112*16*9+2*144*R+parent_idle+9*parent_banks+bridges+shifts+moves+parent_live+parent_physical+invoice['wrapper_elementary_factors_charged'])
++ bridges,shifts=2*112*333,4*112*37;moves=2*shifts
++ nonlocal_items=(4*112*37*9+2*112*37*9+2*333*R+parent_idle+9*parent_banks+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+(144*invoice['local_adapters']+outside)*invoice['compiler']+64*parent_physical)
++ pervertex=(invoice['selected_real_component_primitives']+bridges+shifts+moves+parent_live+(333*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)
+@@ -160,9 +160,9 @@
+  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+144+144+4
++ assert 0<invoice['global_prefix_bits']<=invoice['charged_prefix_bits']==1024
++ assert invoice['row_prefix_extra']==2048
++ assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+333+333+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']
+@@ -170,7 +170,7 @@
+  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['physical_row_coefficient']==2*stock.bit_length()+9909+252+2048
+  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())
+@@ -185,7 +185,7 @@
+  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']==5120
++ pin('expected.live',owner['live']);pin('expected.physical',owner['physical']);assert owner['deficit']==11840
+  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
+@@ -200,14 +200,14 @@
+  bitH={int(r):n for r,n in bit['profile'].items()}
+  assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+  bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+- conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,5120,True)
++ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,11840,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)
++   ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+1024)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+1024)
+    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)}}
+@@ -222,7 +222,7 @@
+  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,5120,False)
++ native_moments=check_moment('complex',H,73,owner['live'],b,11840,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
+@@ -231,7 +231,7 @@
+  moments=bit_moments+native_moments
+  input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'package:inputs/PR589-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_GAUGE44_NATIVE_EXACT_GLOBAL_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_pr635_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=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),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. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. 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.')
++ return dict(status='PASS_GAUGE44_NATIVE_EXACT_GLOBAL_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_pr635_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=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),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 R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain.')
+ if __name__=='__main__':
+  import sys
+  package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists()
+--- pr1074/code/assembly_controls.py
++++ r480-owner-optimum/code/assembly_controls.py
+@@ -58,7 +58,7 @@
+         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 + 144 + 144 + 4
++        i['global_prefix_bits'] = 1 + 37 + 333 + 333 + 4
+ 
+     def reordered_calls(o, i):
+         i['selected_calls'][0], i['selected_calls'][1] = i['selected_calls'][1], i['selected_calls'][0]
+--- pr1074/code/freeze_spec.py
++++ r480-owner-optimum/code/freeze_spec.py
+@@ -23,7 +23,7 @@
+ for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+     spec['expected'][key] = assembly[key]
+ spec['expected']['assembly_controls_rejected'] = 69
+-spec['expected']['provider_counts'] = {'gauge44':144}
++spec['expected']['provider_counts'] = {'gauge44':333}
+ spec['expected']['mutations_rejected'] = 15
+ a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+ print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
+--- pr1074/code/invoice_allcold.py
++++ r480-owner-optimum/code/invoice_allcold.py
+@@ -195,7 +195,7 @@
+     helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+     assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+     parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+-    stages,replicas,blocks_per_stream=9,16,4
++    stages,replicas,blocks_per_stream=9,37,4
+     call_count=len(template['calls'])
+     assert call_count==stages*replicas==control['complete_invocations']
+     assert control['one_owner_per_complete_invocation']
+@@ -250,7 +250,7 @@
+         +(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']==5120
++    assert m*live-mass==owners['deficit']==11840
+     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']
+@@ -260,10 +260,10 @@
+     # 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
++    used=max(rebased,parent_pervertex); retained=None; payload=1024
+     if retained_invoice is not None:
+         previous=read(retained_invoice)
+-        assert previous['compiler']==compiler and previous['charged_prefix_bits']==payload
++        assert previous['compiler']==compiler and previous['charged_prefix_bits']==512
+         previous_bound=previous['conservative_pervertex_used']
+         used=max(used,previous_bound+parent_pervertex)
+         retained=dict(sha256=filehash(retained_invoice),previous_pervertex_allowance=previous_bound,
+@@ -307,13 +307,13 @@
+                     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.')
++        scope='Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. The fixed provider uses 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 144 invocation and 144 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.')
++        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 333 invocation and 333 bridge sweeps and take the maximum local scalar/Horner prefix over both orientations of the fixed provider. 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')
diff --git a/research/k8-x54-t37/INDEPENDENT-DERIVATION.patch b/research/k8-x54-t37/INDEPENDENT-DERIVATION.patch
new file mode 100644
index 0000000000..3e8d9fed4e
--- /dev/null
+++ b/research/k8-x54-t37/INDEPENDENT-DERIVATION.patch
@@ -0,0 +1,137 @@
+--- base/research/complex-t21-owners/independent_check.py
++++ r480-owner-optimum/independent_owner.py
+@@ -1,30 +1,31 @@
+ #!/usr/bin/env python3
+ # SPDX-License-Identifier: Apache-2.0
+ # Prepared for haoyan with substantial OpenAI Codex assistance.
+-"""Independent variable-replica event, whole-helper, chart and finite-reserve audit.
++"""Independent source-event, owner, chart, and finite-reserve audit.
++
++This derivative fixes the R480 seven-slot k8 word and 37 replicas. It charges
++1024 complex prefix bits and checks disjoint pending children on each family.
++The source is Hao Yan's variable-replica checker at the pinned repository base.
++SOURCES.json and INDEPENDENT-DERIVATION.patch identify that source and all edits.
+ 
+ Inputs are read-only. No owner constructor or controller auditor is imported.
+---word is the canonical local supplier JSON.gz, with frame IDs and a native
+-INDEPENDENT-LOCAL-REPLAY.json alongside it (override with --local-replay).
++--word is the canonical local supplier JSON.gz, with a hash-bound native
++INDEPENDENT-LOCAL-REPLAY.json beside it (override with --local-replay).
+ --baseline-parent is the original eight-replica GLOBAL-TEMPLATE.json.gz.
+-Parameterized from Hao Yan's PR858 checker; the original source is vendored.
+-Only replica cardinalities, the nominated idle profile, and the two-copy
+-interleaving restriction change. Exact per-replica source projections remain.
+-Its sibling CANONICAL-WORD.json.gz supplies ports; DATA-PHASES.json defaults
+-to ../work/complex-nine-native/DATA-PHASES.json (override with --phases).
+-The PR741 and PR799/X4 suppliers share this width/owner interface. Their
+-local paid profiles and prefix exponents are read and recounted from the
+-provided canonical word and hash-bound native replay, never fixed to PR741.
++Its sibling CANONICAL-WORD.json.gz supplies the ports and centre frames.
++DATA-PHASES.json defaults to ../work/complex-nine-native/DATA-PHASES.json
++(override with --phases). The checker recounts local widths and paid ranks.
+ --out names a JSON receipt. Checks remain enabled under python -O.
+ """
+ import argparse
++import copy
+ from collections import Counter, defaultdict
+ import gzip
+ import hashlib
+ import json
+ from pathlib import Path
+ 
+-V, H, M, T, R = 112, 9, 73, 21, 504
++V, H, M, T, R = 112, 9, 73, 37, 480
+ EXPECTED_IDLE = None
+ 
+ 
+@@ -93,7 +94,7 @@
+     for orientation in ('forward', 'backward'):
+         require(dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}, 'local replay profile binding')
+     widths = [len(frames[word['final'][q]]) - len(frames[word['start'][q]]) for q in range(2 * V, n)]
+-    require(Counter(widths) == {4: 80, 5: 32, 7: 54, 8: 122, 9: 216}, 'current supplier width inventory')
++    require(Counter(widths) == {4: 56, 5: 32, 7: 30, 8: 122, 9: 240}, 'current supplier width inventory')
+     return widths, paid
+ 
+ 
+@@ -161,6 +162,21 @@
+                 bases=bases, phases=phases, bridges=bridges, event_count=len(events), replay=replay)
+ 
+ 
++def check_pending_axes(context):
++    checked = 0
++    for port, frame in enumerate(context['bases']):
++        used = defaultdict(set)
++        for child, rank in context['rank'].items():
++            axes = list(map(int, context['phases']['recipes'][port]['idle_children'][child]['orthogonal_axes']))
++            require(len(axes) == rank and len(set(axes)) == rank and set(axes) <= set(frame),
++                    'pending child orthogonal basis')
++            family = context['child_pair'][child], context['side'][child]
++            require(not used[family] & set(axes), 'overlapping pending children on one family')
++            used[family].update(axes)
++            checked += 1
++    return checked
++
++
+ def check_roles(context, roles):
+     c = context
+     live, physical = T * 8 * V, T * 8 * V + 8 + R + 2
+@@ -221,8 +237,8 @@
+     for i in range(1, 37):
+         group *= 2 ** (2 * i) - 1
+     stock = group * physical
+-    row = 2 * stock.bit_length() + 9909 + 252 + 2 * 512
+-    require(prefix < 512, 'prefix reserve')
++    row = 2 * stock.bit_length() + 9909 + 252 + 2 * 1024
++    require(prefix < 1024, 'prefix reserve')
+     require(row < 20161 and M * M > 2 * max(profile) ** 2, 'row or halving reserve')
+     return dict(status='PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW', roles=len(roles), calls=len(c['order']),
+                 source_events_per_replica=30, expanded_replica_events=c['event_count'], bridge_events=c['bridges'],
+@@ -233,7 +249,7 @@
+                 rank_mass=mass, deficit=320*T, namespace={'data':[0,live], 'centres':[live,live+8], 'tableau':[live+8,live+8+R], 'coefficient':[live+8+R,physical]},
+                 local_prefix_bits=localbits, local_prefix_from_native_receipt=True, local_profile_recounted=True,
+                 prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], margin=4),
+-                prefix_bits=prefix, charged_prefix_bits=512, physical_stock_bits=stock.bit_length(),
++                prefix_bits=prefix, charged_prefix_bits=1024, physical_stock_bits=stock.bit_length(),
+                 physical_row_coefficient=row, row_limit=20161,
+                 scope='Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.')
+ 
+@@ -271,6 +287,20 @@
+             rejected.append(dict(name=name, reason=str(exc)))
+         else:
+             raise ValueError('accepted negative control: ' + name)
++    bad = dict(context, phases=copy.deepcopy(context['phases']))
++    pair = next((a, b) for a in context['rank'] for b in context['rank']
++                if a < b and (context['child_pair'][a], context['side'][a]) ==
++                (context['child_pair'][b], context['side'][b]))
++    children = bad['phases']['recipes'][0]['idle_children']
++    children[pair[1]]['orthogonal_axes'][0] = children[pair[0]]['orthogonal_axes'][0]
++    try:
++        check_pending_axes(bad)
++    except ValueError as exc:
++        require(str(exc) == 'overlapping pending children on one family',
++                'pending-axis control rejected at unexpected predicate')
++        rejected.append(dict(name='cross_child_pending_axis_alias', reason=str(exc)))
++    else:
++        raise ValueError('accepted negative control: cross_child_pending_axis_alias')
+     return rejected
+ 
+ 
+@@ -287,7 +317,7 @@
+     parser.add_argument("--expected-idle", required=True)
+     args = parser.parse_args()
+     T = args.replicas
+-    require(1 <= T <= 22, "replica range")
++    require(T == 37, "replica range")
+     EXPECTED_IDLE = {int(k): v for k,v in json.loads(args.expected_idle).items()}
+     phases_path = args.phases or args.baseline_parent.parent.parent / 'work/complex-nine-native/DATA-PHASES.json'
+     canonical_path = args.baseline_parent.parent / 'CANONICAL-WORD.json.gz'
+@@ -300,7 +330,9 @@
+     require(len(word['center_frames']) == len(canonical['center_frames']) == 8, 'eight centre interfaces')
+     require([basis(word['frames'][f]) for f in word['center_frames']] == [basis(canonical['frames'][f]) for f in canonical['center_frames']], 'ordered centre-frame interface')
+     context = make_context(parent, phases, canonical['ports'], word, replay, roles)
++    pending = check_pending_axes(context)
+     receipt = check_roles(context, roles)
++    receipt['disjoint_pending_child_axis_checks'] = pending
+     receipt['controls_rejected'] = controls(context, roles)
+     receipt['input_sha256'] = {str(path): filehash(path) for path in (args.baseline_parent, phases_path, canonical_path, args.word, replay_path, args.owners)}
+     args.out.write_text(json.dumps(receipt, indent=2) + '\n', encoding='utf-8')
diff --git a/research/k8-x54-t37/NOTICE.md b/research/k8-x54-t37/NOTICE.md
new file mode 100644
index 0000000000..f6ad0970cf
--- /dev/null
+++ b/research/k8-x54-t37/NOTICE.md
@@ -0,0 +1,54 @@
+# Composition notice (this package)
+
+This package composes Ali Romman's R480 T37 owner optimum (#1129, package `research/r480-owner-optimum`,
+retained here with all notices) with Jeremy Kothe's eighth triangle-hybrid slot X54 (#1130,
+`RECIPE-X54-ends7.json`, rebased unchanged in edits and frames onto the seven-slot k8 word). The
+composition, the X54 rebase/pins/driver, the rebound provider identities and the re-frozen data are by
+Rohan Arun (@rohanarun) with Claude (Anthropic) assistance, under Apache-2.0. No authorship of the
+owner theorem, construction, slot or local chain is claimed.
+
+# Attribution and license
+
+New owner theorem, exact flow construction, checker, and package by
+Ali Romman <226877337+aliromman@users.noreply.github.com>, with substantial
+OpenAI Codex assistance. New work is under Apache-2.0.
+
+The fixed local supplier is Jeremy Kothe's seven-slot k8 word in PR1074,
+commit `052afc128954f7b6a2b3c409eb4d72248e4020f2`. The seven-slot step comes
+from PR1018 and credits Rohan Arun's PR987 search. The earlier local word and
+its scalar, frame, phase, and source-access construction retain all notices
+in `vendor/pr1074/NOTICE.md` and `vendor/pr1074/UPSTREAM-NOTICE.md`.
+This package does not claim authorship of those local changes.
+
+The signed bin prices come from Chafik Boukhalfa's PR795. The proof method
+builds on the PR890/PR942 owner bounds and the prior all-replica T37 theorem.
+The new right-hand side, exact attaining flow, and complete R480 owner map
+are specific to the changed seven-slot inventory. The old theorem did not
+cover this word.
+
+The T16 source-event routines are by Hao Yan (@FanPUYen). Their source notice
+is kept in `vendor/pr1074/t16/NOTICE.md` and their source headers. The derived
+independent owner checker comes from `research/complex-t21-owners` at the
+exact repository base. `INDEPENDENT-DERIVATION.patch` records its changes.
+
+The global admission code comes from the exact PR1074 package. Its sources
+and notices are retained. `CODE-DERIVATION.patch` records all changes needed
+for 37 replicas and the 1024-bit complex prefix allowance. The arithmetic
+engines and full PR589 bit supplier are unchanged and source-pinned.
+
+PR1034 proved a mixed bound for 71 older catalogue entries and excluded
+R480. PR1069 independently checked the rank-mass identity for recent claims.
+These contributions informed the scope and cost audit. Neither admits the
+new physical owner map by itself.
+
+The concurrent mutable-leaver sprint worker rebuilt the unchanged local k8
+and seven-slot chains, including their scalar and phase checks. This package
+retains that source-bound evidence. It does not use the worker's new local
+word experiments. No predecessor notice, license, or AI disclosure is replaced
+by this notice.
+
+Josie Elliston's PR1091 independently checked fifteen T16 owner maps and
+made the disjoint-pending-axis obligation explicit. The independent T37
+audit includes that check and a targeted negative control. Rohan Arun's
+PR1094 gives a later same-word T16 repack. Jeremy Kothe's PR1117 changes
+the local word; it is a concurrent comparison outside the proved inventory.
diff --git a/research/k8-x54-t37/ORDER.json b/research/k8-x54-t37/ORDER.json
new file mode 100644
index 0000000000..500a9c3738
--- /dev/null
+++ b/research/k8-x54-t37/ORDER.json
@@ -0,0 +1 @@
+[[0, 0], [0, 21], [0, 8], [0, 29], [0, 1], [0, 22], [0, 9], [0, 30], [1, 0], [1, 8], [1, 21], [0, 16], [1, 29], [0, 2], [0, 23], [0, 10], [0, 17], [0, 31], [1, 1], [1, 22], [1, 9], [1, 30], [1, 16], [2, 0], [2, 21], [2, 8], [2, 29], [0, 18], [0, 24], [0, 3], [0, 11], [0, 32], [1, 17], [1, 23], [1, 2], [1, 31], [1, 10], [2, 16], [2, 22], [2, 1], [2, 30], [2, 9], [3, 21], [0, 19], [3, 29], [3, 0], [3, 8], [0, 25], [1, 18], [0, 33], [0, 4], [1, 24], [0, 12], [2, 17], [1, 32], [1, 3], [2, 23], [1, 11], [2, 31], [3, 16], [2, 2], [3, 22], [2, 10], [3, 30], [0, 20], [4, 21], [3, 1], [3, 9], [4, 29], [1, 19], [0, 26], [4, 0], [0, 34], [4, 8], [2, 18], [1, 25], [0, 5], [1, 33], [0, 13], [2, 24], [3, 17], [2, 32], [1, 4], [1, 12], [3, 23], [4, 16], [3, 31], [2, 3], [4, 22], [2, 11], [3, 2], [4, 30], [3, 10], [5, 21], [1, 20], [5, 29], [4, 1], [4, 9], [0, 27], [2, 19], [0, 35], [5, 0], [1, 26], [5, 8], [3, 18], [1, 34], [0, 6], [2, 25], [0, 14], [2, 33], [4, 17], [1, 5], [3, 24], [1, 13], [3, 32], [5, 16], [4, 23], [2, 4], [4, 31], [2, 12], [3, 3], [5, 22], [3, 11], [5, 30], [4, 2], [0, 28], [4, 10], [2, 20], [0, 36], [5, 1], [6, 21], [5, 9], [6, 29], [3, 19], [0, 7], [1, 27], [0, 15], [1, 35], [4, 18], [2, 26], [6, 0], [6, 8], [2, 34], [5, 17], [3, 25], [1, 6], [3, 33], [1, 14], [2, 5], [4, 24], [2, 13], [4, 32], [6, 16], [5, 23], [3, 4], [5, 31], [3, 12], [4, 3], [6, 22], [4, 11], [6, 30], [5, 2], [1, 28], [5, 10], [3, 20], [1, 36], [6, 1], [7, 21], [6, 9], [7, 29], [4, 19], [1, 7], [2, 27], [1, 15], [2, 35], [5, 18], [3, 26], [7, 0], [7, 8], [3, 34], [6, 17], [4, 25], [2, 6], [4, 33], [2, 14], [3, 5], [5, 24], [3, 13], [5, 32], [7, 16], [6, 23], [4, 4], [6, 31], [4, 12], [5, 3], [7, 22], [5, 11], [7, 30], [6, 2], [2, 28], [6, 10], [4, 20], [2, 36], [7, 1], [8, 21], [7, 9], [8, 29], [5, 19], [2, 7], [3, 27], [2, 15], [3, 35], [6, 18], [4, 26], [8, 0], [8, 8], [4, 34], [7, 17], [5, 25], [3, 6], [5, 33], [3, 14], [4, 5], [6, 24], [4, 13], [6, 32], [8, 16], [7, 23], [5, 4], [7, 31], [5, 12], [6, 3], [8, 22], [6, 11], [8, 30], [7, 2], [3, 28], [7, 10], [5, 20], [3, 36], [8, 1], [4, 27], [8, 9], [4, 35], [6, 19], [3, 7], [5, 26], [3, 15], [5, 34], [7, 18], [6, 25], [4, 6], [4, 14], [6, 33], [8, 17], [7, 24], [5, 5], [7, 32], [5, 13], [6, 4], [8, 23], [6, 12], [8, 31], [7, 3], [4, 28], [7, 11], [4, 36], [8, 2], [8, 10], [5, 27], [6, 20], [5, 35], [4, 7], [6, 26], [4, 15], [7, 19], [6, 34], [5, 6], [7, 25], [5, 14], [7, 33], [8, 18], [6, 5], [8, 24], [6, 13], [8, 32], [7, 4], [5, 28], [7, 12], [8, 3], [5, 36], [8, 11], [6, 27], [5, 7], [6, 35], [5, 15], [7, 20], [7, 26], [6, 6], [7, 34], [6, 14], [8, 25], [8, 19], [8, 33], [7, 5], [7, 13], [6, 28], [8, 4], [6, 36], [8, 12], [7, 27], [6, 7], [6, 15], [7, 35], [7, 6], [8, 26], [7, 14], [8, 34], [8, 20], [8, 5], [7, 28], [8, 13], [7, 36], [7, 7], [8, 27], [7, 15], [8, 6], [8, 35], [8, 14], [8, 28], [8, 7], [8, 36], [8, 15]]
diff --git a/research/k8-x54-t37/OWNERS.json.gz b/research/k8-x54-t37/OWNERS.json.gz
new file mode 100644
index 0000000000..6dd3d937a5
Binary files /dev/null and b/research/k8-x54-t37/OWNERS.json.gz differ
diff --git a/research/k8-x54-t37/PATTERN-FLOW.json b/research/k8-x54-t37/PATTERN-FLOW.json
new file mode 100644
index 0000000000..1e60b5a70a
--- /dev/null
+++ b/research/k8-x54-t37/PATTERN-FLOW.json
@@ -0,0 +1 @@
+{"T": 37, "kind": "t37", "order": [[0, 0], [0, 21], [0, 8], [0, 29], [0, 1], [0, 22], [0, 9], [0, 30], [1, 0], [1, 8], [1, 21], [0, 16], [1, 29], [0, 2], [0, 23], [0, 10], [0, 17], [0, 31], [1, 1], [1, 22], [1, 9], [1, 30], [1, 16], [2, 0], [2, 21], [2, 8], [2, 29], [0, 18], [0, 24], [0, 3], [0, 11], [0, 32], [1, 17], [1, 23], [1, 2], [1, 31], [1, 10], [2, 16], [2, 22], [2, 1], [2, 30], [2, 9], [3, 21], [0, 19], [3, 29], [3, 0], [3, 8], [0, 25], [1, 18], [0, 33], [0, 4], [1, 24], [0, 12], [2, 17], [1, 32], [1, 3], [2, 23], [1, 11], [2, 31], [3, 16], [2, 2], [3, 22], [2, 10], [3, 30], [0, 20], [4, 21], [3, 1], [3, 9], [4, 29], [1, 19], [0, 26], [4, 0], [0, 34], [4, 8], [2, 18], [1, 25], [0, 5], [1, 33], [0, 13], [2, 24], [3, 17], [2, 32], [1, 4], [1, 12], [3, 23], [4, 16], [3, 31], [2, 3], [4, 22], [2, 11], [3, 2], [4, 30], [3, 10], [5, 21], [1, 20], [5, 29], [4, 1], [4, 9], [0, 27], [2, 19], [0, 35], [5, 0], [1, 26], [5, 8], [3, 18], [1, 34], [0, 6], [2, 25], [0, 14], [2, 33], [4, 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index 0000000000..d06537cb52
--- /dev/null
+++ b/research/k8-x54-t37/PROOF.md
@@ -0,0 +1,265 @@
+# Composition note (this package)
+
+The local word is the seven-slot k8 word plus the X54 triangle-hybrid slot (construction/x54). The slot is
+width-neutral: helper widths `{4:56,5:32,7:30,8:122,9:240}`, start/end frames and local prefixes are unchanged, so
+the capacity inventory, the signed-price dual and the attaining 37-replica packing below apply verbatim. Only the
+local paid profile changes, to `{1:2412,2:418,3:434,4:138,5:84,8:8}`. With it, the certified complex root is
+`[0.001676945247549584231285, 0.001676945247549584231286]` and both endpoints give the outer grid value
+`kappa = 0.001674137810105185`, which the attaining construction reaches. Everything below is #1129's note,
+unchanged; read its seven-slot numbers as those of that word.
+
+# The fixed R480 owner optimum
+
+This note fixes the seven-slot k8 word from Jeremy Kothe's PR1074 at
+`052afc128954f7b6a2b3c409eb4d72248e4020f2`. Its source package is
+`research/gauge44-slots-t16`. PR1018 applies the seven-slot construction,
+which credits Rohan Arun's PR987 search, to the R480 k8 leaver word.
+This note changes the owner assignment. It does not change that local word.
+
+The result is conditional on the same local supplier and physical interfaces.
+It is not a formal proof of integer multiplication, an unconditional bound,
+or a measured runtime gain. The selected result is not changed by this package.
+
+## 1. Fixed inventory
+
+Each replica has nine complete calls and 896 live data families. Each call has
+480 whole helpers. Their widths are
+
+```
+width:     4   5   7    8    9
+count:    56  32  30  122  240
+```
+
+The paid local child profile is
+
+```
+{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}.
+```
+
+Each replica has 672 bins of capacity 8 and 448 bins of each capacity 16, 32,
+and 48. Thus the helper width per call is 3730. The local paid rank mass is
+5586. The residual rank mass per replica is
+
+```
+M = 8*672 + (16+32+48)*448 - 9*3730 = 14814.
+```
+
+The complete deficit remains `73*896 - 9*5586 - 14814 = 320` per replica.
+The gain comes from the child-rank distribution. It does not come from a new
+rank deficit. PR1069 independently describes this distinction for recent claims.
+
+The inputs retain the full PR1074 SPEC and PLAN. The checker compares the
+provider width list, local profile, complete call set, and per-replica capacity
+stock. Source files and arithmetic engines have SHA256 pins. These comparisons
+bind a declared cost contract; they do not replace the local scalar proof.
+
+## 2. A necessary inequality for every positive replica count
+
+Use the signed width prices from Chafik Boukhalfa's PR795 and the retained
+PR890/PR942 proof:
+
+```
+width price at (4,5,7,8,9): (-1,-20,-8,-2,4)
+capacity bonus at (8,16,32,48): (2,4,8,-13).
+```
+
+For a residual rank `r`, let `u(r)` be the maximum capacity bonus plus signed
+width price over all legal patterns that leave `r`. The checker enumerates all
+1,163 patterns. A separate fill recurrence gives the same table. In particular,
+`u(0)=0`, `u(1)=19`, and `u(48)=-13`.
+
+For `T` replicas, let `n_r` be the number of bins with residual rank `r`. All
+helper roles occur exactly once. Therefore their total actual signed price is
+
+```
+S*T = [672*2 + 448*(4+8-13)
+       + 9*(-56-20*32-8*30-2*122+4*240)]*T = -1084*T.
+```
+
+Each bin's actual price is at most `u(r)`. Thus
+
+```
+sum r*n_r = 14814*T,
+sum u(r)*n_r >= -1084*T.
+```
+
+Eliminate `n_48` and use `u(0)=0`. With
+
+```
+v(r) = 48*u(r)+13*r,
+v(1) = 925,
+```
+
+we obtain the necessary inequality
+
+```
+sum_(0<r<48) v(r)*n_r >= 140550*T.                 (1)
+```
+
+The PR942 U8 theorem has different right-hand sides. It cannot be reused by
+keeping its U8 profile or its demand 150. Equation (1) is for this R480 inventory.
+The prior PR1034 mixed-catalogue theorem also excludes this new inventory.
+
+## 3. Supporting moment inequality
+
+Let
+
+```
+I = [0.001676905273619680861300,
+     0.001676905273619680861301],
+phi_b(r) = r*(73/r)^b,
+c_b(r) = 48*phi_b(r)-r*phi_b(48),
+lambda_b = c_b(1)/925.
+```
+
+For every `b` in `I`, both retained exact rational engines certify
+
+```
+lambda_b > 0,
+c_b(r) > lambda_b*v(r)   for every attainable 0<r<48, r != 1.
+```
+
+At rank one there is equality by definition. The certificate encloses `phi`
+over the complete interval `I`. It uses the lower endpoint for a positive
+lower bound and the upper endpoint for a positive upper bound. It reverses the
+chosen endpoint when it multiplies by a negative integer. No floating-point
+sign decision is used.
+
+Multiply (1) by `lambda_b`. The residual moment then satisfies
+
+```
+sum phi_b(r)*n_r / T
+  >= (5622/37)*phi_b(1) + (11302/37)*phi_b(48).    (2)
+```
+
+This follows by writing the left side as
+`(14814/48)*phi_b(48) + sum_(r<48) c_b(r)*n_r/(48*T)`.
+The arithmetic is `140550/925 = 5622/37` and
+`(14814-5622/37)/48 = 11302/37`.
+
+The bound permits all positive integer replica counts. It removes chronology,
+per-call matching, coordinate charts, and finite precision constraints. These
+relaxations can only lower the possible moment. The strict supporting margins
+imply that equality has no nonzero residual rank other than 1 and 48. Equality
+also requires (1) to be tight. Both normalized counts then force `37 | T`.
+This is a necessary equality condition, not a uniqueness claim for owners.
+
+## 4. An exact bin construction
+
+The following bin pattern counts attain (2) at `T=37`. The width-count vector
+uses the order `(4,5,7,8,9)`.
+
+| Capacity | Width-count vector | Number of bins | Residual rank |
+| --- | --- | ---: | ---: |
+| 8 | (0,0,0,1,0) | 24864 | 0 |
+| 16 | (0,0,0,2,0) | 3306 | 0 |
+| 16 | (0,0,1,0,1) | 9394 | 0 |
+| 16 | (2,0,0,1,0) | 3876 | 0 |
+| 32 | (0,0,2,0,2) | 298 | 0 |
+| 32 | (0,1,0,0,3) | 10656 | 0 |
+| 32 | (1,0,0,0,3) | 5622 | 1 |
+| 48 | (0,0,0,0,0) | 11302 | 48 |
+| 48 | (1,0,0,1,4) | 5274 | 0 |
+
+The checker sums every capacity and helper width. It requires exact equality
+with the full inventories, not only with total occupied width. This table
+proves attainment of the bin relaxation. The next section supplies its actual
+time and physical-family assignment.
+
+## 5. From exact pattern flow to literal owners
+
+The call order is the source-bound PR942 T37 order. Each replica retains the
+same 30 source events. A pending child can host a complete call only after its
+last physical-pair touch and before its idle event. Bridge touches are included.
+
+`PATTERN-FLOW.json` contains integer pattern counts and integer assignments of
+widths to call times. It groups the two equivalent child sides, with 224 ports
+per group. For each group and pattern, the certificate has `N` bins. It assigns
+exactly `N*n_w` width-`w` roles, and at most `N` roles at each call time. Each
+call receives the exact width inventory above. All assigned times are in the
+actual source-event window.
+
+`construct.py` converts each group and pattern to `N` literal bins. Split each
+width vertex into `n_w` vertices of degree `N`. The other vertices are call
+times, each with degree at most `N`. This is a bipartite multigraph. A matching
+can cover every width vertex and every time vertex of degree `N`: add dummy
+vertices and edges to obtain an `N`-regular bipartite graph, and take a perfect
+matching. Remove it and repeat. The implementation obtains the same covering
+matching directly with augmenting paths. It checks the degree invariant after
+each removal.
+
+Each matching names one physical bin. Thus no bin uses two helpers from one
+call. The constructor assigns the bins to literal child/port coordinates and
+assigns the local helper numbers of each width to the resulting slots. It
+sets offsets to contiguous prefixes. Its output must equal the frozen owners
+as a complete decoded JSON value. Compression-container bytes are not used
+as mathematical equality.
+
+The final map has 159,840 roles in 333 calls. Its residual profile is
+`{1:5622,48:11302}`. The independent owner audit reconstructs source-event
+windows and orthogonal 73-axis charts without importing the constructor or
+flow model. The global controller audit checks the emitted program and its
+phase projections. These audits are separate from the bin theorem.
+
+The independent audit also checks that distinct pending children on one
+physical family have disjoint axes. It checks all 2016 child/port bases.
+A control copies one axis into a second child of the same family. It must
+fail at this disjointness guard. Josie Elliston's PR1091 identified this
+explicit check in the concurrent T16 audits.
+
+
+## 6. Complete moment and outer recipe
+
+The complete T37 profile is
+
+```
+{1:808818, 2:139194, 3:143856, 4:47286,
+ 5:27306, 8:2664, 48:11302}.
+```
+
+It has 33,152 live families, rank mass 2,408,256, and deficit 11,840. Both
+rational engines accept the lower endpoint of `I` and reject the upper endpoint.
+The proper-child guard is `73^2 > 2*48^2`.
+
+Equation (2) applies throughout `I`, so it applies at the unique root of this
+profile's strictly increasing moment. Every other packing has at least that
+moment. The table attains it. This proves the optimum complex root in the bin
+relaxation. The finite owner construction attains the same profile.
+
+The unchanged PR589 bit endpoint is `0.001733427039589844234749`, with its
+exceptional-residue surcharge. It is larger than the complex endpoint. The
+retained seven-step outer recipe is monotone in this range. Each update is
+`a_next=s*(1-s+a_old)`. Both relevant partial derivatives are positive here;
+the final map in `a` is also increasing. The strict reserves remain fixed.
+Both endpoints of `I` give the same outer grid value:
+
+```
+kappa = 0.001674097969905390.
+```
+
+All 47 inequalities are checked. The next grid value is rejected. This is a
+global grid optimum for this word, whole-helper capacity inventory, and fixed
+outer recipe. It is not a ceiling for another word, helper splitting, new
+capacity stock, another outer reduction, or relaxed restoration rules.
+
+## 7. Scope of physical admission
+
+The bank envelope uses 8+8+8+8+5 lanes. Its five groups retain the inherited
+504-helper dedicated banks, which provide a conservative reserve envelope.
+The final hosted construction removes those banks. It uses the 480-helper
+local word and has 33,642 physical families. The partial group's complement
+coordinates are recomputed. They are not selected recursive children.
+
+The finite invoice charges 1024 complex prefix bits. The local prefix is 68,
+and `68+37+333+333+4=775`. The bit allowance stays 512. The independent row coefficient is 17495, below
+20161. The global audit checks 1110 source events, 666 pending windows, and
+11150 distinct orthogonal charts. The full invoice recounts
+all helper operations, wrappers, scalar work, bridges, shifts, moves, local
+adapters, recursive children, and final corrections. The seven finite bootstrap
+cutoffs use the new complex allowance. `CODE-DERIVATION.patch` records every
+change from the immutable PR1074 code. Verification executes normal source
+files; it does not patch imported modules at runtime.
+
+The all-size/compiler, common-label/mutable-source, whole-call hosting,
+precision/tape, exact-recovery, analytic-transfer, and bit H1-H5 obligations
+remain inherited. Passing finite checks does not discharge these assumptions.
diff --git a/research/k8-x54-t37/README-R480-OWNER-OPTIMUM.md b/research/k8-x54-t37/README-R480-OWNER-OPTIMUM.md
new file mode 100644
index 0000000000..4fa54b2da8
--- /dev/null
+++ b/research/k8-x54-t37/README-R480-OWNER-OPTIMUM.md
@@ -0,0 +1,101 @@
+# R480 owner optimum and an attaining construction
+
+The frozen seven-slot k8 word has a complete owner construction with
+`kappa = 0.001674097969905390`. An exact supporting inequality proves that
+no positive replica count can give a larger complex root for this word and
+its whole-helper capacity inventory. The construction attains the bound at
+37 replicas. Both endpoints of the certified root interval give the same
+maximum grid value under the fixed outer recipe.
+
+This is a conditional construction and a scoped optimum theorem. It does
+not prove the full integer-multiplication theorem or a practical speed gain.
+It does not change the selected result.
+
+Run from a checkout at the exact base, with this package added:
+
+```sh
+python3 -B research/r480-owner-optimum/check.py --work /tmp/r480-owner-check
+```
+
+Use a new output directory. No network access, solver, or third-party Python
+package is needed. The expected final line is:
+
+```text
+PASS_R480_ALL_REPLICA_OPTIMUM_AND_ATTAINING_CONSTRUCTION 0.00167409796990539
+```
+
+The check covers the 1,163-pattern dual, an independent fill recurrence,
+two rational moment engines, all 47 outer inequalities, 18 certificate CLI
+controls, exact flow-to-owner reconstruction, 159,840 literal owner roles,
+333 complete calls, actual source-event windows, orthogonal charts, the full
+finite invoice, and strict global admission. The global replay also runs
+15 controller, 7 independent owner, 69 admission, and 12 bit-supplier controls.
+The bit endpoint and its exceptional-residue surcharge are unchanged.
+
+The finite prefix bound is 775 bits. It needs the 1024-bit complex allowance.
+The physical row coefficient is 17,495, below 20,161. All seven finite
+bootstrap cutoffs use that larger complex allowance. The complete profile is
+
+```text
+{1:808818, 2:139194, 3:143856, 4:47286, 5:27306, 8:2664, 48:11302}.
+```
+
+The complex root lies in
+`[0.001676905273619680861300, 0.001676905273619680861301]`.
+The normalized residual optimum is `{1:5622/37, 48:11302/37}`.
+The complete deficit remains 320 per replica. The improvement changes the
+rank distribution, not that deficit.
+
+The exact experimental base is
+`abdc6a7002abdbcd9e21bfc5e1a795784deacfdf`. The fixed local source is PR1074
+at `052afc128954f7b6a2b3c409eb4d72248e4020f2`. `SOURCES.json` pins the proof
+inputs and rational engines. `SOURCE-FREEZE.json` pins this package's code
+and immutable data. The fresh global replay also checks the 21 inherited
+upstream pins before it reads the bank envelope.
+
+`inputs/local` contains the fixed native local artifacts. A concurrent sprint
+worker rebuilt the unchanged base, k8 cell, full local chain, seven-slot step,
+scalar replay, wrappers, and all 2,896 exact phase edges. The corresponding
+command receipts are in `evidence/local-source`. The owner check consumes this
+source-bound local admission; it does not rebuild every upstream local step.
+Use `--local PATH` to replay with a separately rebuilt local directory. The
+same semantic and artifact contracts must pass. In a sparse checkout,
+`--main PATH` may name a complete checkout with the pinned base dependencies.
+
+`PROOF.md` states the all-replica argument and the matching construction.
+`PATTERN-FLOW.json` and `OWNERS.json.gz` are exact certificates.
+`construct.py` rebuilds the owners with integer counts and bipartite matching.
+`independent_owner.py` derives windows and charts from actual source events.
+It imports no flow or constructor code. `CODE-DERIVATION.patch` and
+`INDEPENDENT-DERIVATION.patch` expose all changes to inherited admission code.
+No source patch is applied at runtime.
+
+`SEARCH.json` records the search domain and stopping rule. The full tight-face
+chronology LP reached its time limit. Restriction to the nine-pattern optimal
+basis then gave an exact integer flow. That timeout is not an impossibility
+claim. The delivered optimum follows from the exact bound and attaining map,
+not from solver optimality or a failed search.
+
+At refresh, main `ba82555c64e1879e4b7decce28186f208fcb8262` selected PR1042
+at `kappa = 0.001672188119205421`. PR1082 at
+`0c2e294ec204e83846d27344f829d15ed9ee7cc6` gave a T16 repack at
+`0.001672653061493085`. This theorem closes the fixed-word gap across all
+positive replica counts. PR1107 at
+`6123fc5d57db16aaa3e8a26b4a11a34b46c0c391` changes a rank-seven helper end
+and reports `0.001672765980186726`; its changed word is outside this theorem.
+PR1094 at `0fc329d0bec93ca7cd288eaea1295172e8789810` gives another same-word
+T16 repack at `0.001672660197076918`. PR1117 at
+`342b67f23dfa8f41a520a0d58978b2875e9eb0dd` reports
+`0.001672846995880185` with the changed rank-seven-end word. It is also
+outside this theorem. These comparisons are records of the stated heads,
+not admission of those PRs. PR1091 at
+`b4c13a228acb80f74c682b7097f0ce9bbf51bc4e` independently checked fifteen
+T16 maps. This package follows its explicit disjoint-pending-axis check and
+extends that finite check to the attaining T37 map.
+
+All-size/compiler, common-label/mutable-source, whole-call hosting,
+precision/tape, exact-recovery, analytic-transfer, and bit H1-H5 obligations
+remain inherited. A different local word, split helpers, new capacity stock,
+or another outer recipe can exceed this scoped ceiling.
+
+See `NOTICE.md` for predecessor credit, licenses, and substantial AI assistance.
diff --git a/research/k8-x54-t37/README.md b/research/k8-x54-t37/README.md
new file mode 100644
index 0000000000..190248f195
--- /dev/null
+++ b/research/k8-x54-t37/README.md
@@ -0,0 +1,88 @@
+# Eight-slot k8 word (X54 added) with the T37 owner optimum
+
+```text
+kappa = 334827562021037 / 2*10^17 = 0.001674137810105185
+```
+
+This is **+3.98402e-8 over the current best open result**, #1129/#1131 (`0.001674097969905390`: the T37 owner optimum on
+the seven-slot k8 word). It is also above every open local-word variant: #1130 (X54 and rank-seven ends with T16
+owners) is at 0.001673006105142741. The complex side binds, and the PR589 bit supplier is unchanged.
+
+## What changes
+
+The change is a composition of two width-neutral pieces that have not yet been combined.
+
+1. **Local word.** Jeremy Kothe's eighth triangle-hybrid slot **X54/E589** (#1130) is applied to the seven-slot k8
+   word `c2b29430…` (#1018/#1074). #1130 applies it to the rank-seven-ends word; here it goes onto the seven-slot word
+   directly.
+   - `construction/x54/RECIPE-X54-k8.json` keeps #1130's `RECIPE-X54-ends7.json` byte for byte in its edits and frames:
+     5 B deletes, 5 inserts, one FULL restore of holder 335 and one early restore of holder 367. Only the base and
+     result pins and the profile change.
+   - NewBArch's unchanged `build_tri.py` gives word content `512452c0…`.
+   - Local profile: `{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}` → `{1:2412, 2:418, 3:434, 4:138, 5:84, 8:8}`.
+   - Widths `{4:56, 5:32, 7:30, 8:122, 9:240}` (R=480) and the local prefixes (52/68 bits) are unchanged.
+2. **Owners.** Ali Romman's exact T37 owner optimum for this capacity inventory (#1129; same map as #1131) is used
+   unchanged: owners, order, pattern flow, 159,840 roles, idle `{1:5622, 48:11302}`.
+   - Its all-replica bound is rerun with the eight-slot local profile and still attains the ceiling, so the bound and
+     the construction agree at **0.001674137810105185**.
+   - Global profile: `333 × local + {1:5622, 48:11302}` =
+     `{1:808818, 2:139194, 3:144522, 4:45954, 5:27972, 8:2664, 48:11302}`.
+
+## Verification
+
+```sh
+# from a checkout of this branch (no network, solver or third-party package)
+python3 -B research/k8-x54-t37/check.py --work /tmp/k8-x54-check
+# PASS_K8_X54_ALL_REPLICA_OPTIMUM_AND_ATTAINING_CONSTRUCTION 0.001674137810105185
+```
+
+`check.py` runs four steps:
+
+1. The all-replica certificate (`verify.py`).
+2. 18 certificate controls.
+3. The literal owner reconstruction (`construct.py`).
+4. The strict global replay (`replay.py`): bind, emit, controller audit with 15 mutations, the full finite invoice
+   (prefix 775 < 1024, row 17,495 < 20,161), assembly with all 47 outer inequalities, 69 admission and 12 bit
+   controls, and the independent owner check.
+
+The native locals of the eight-slot word are committed in `inputs/local`. They are rebuilt from the seven-slot word by
+`construction/x54/build_x54.py`, which runs, all pinned in `X54-PINS.json`:
+
+- the unchanged builder;
+- the 10 slot controls;
+- the independent `audit_local`;
+- PR635's native chain: native, ledgers, replay, wrappers and phases.
+
+The seven-slot word itself is #1018's `research/gauge44-slots` step on #1005's leaver chain.
+
+## Changes relative to `research/r480-owner-optimum`
+
+The package is #1129's, copied with these changes:
+
+- `inputs/local`: the eight-slot locals.
+- `inputs/SPEC.json` and `inputs/PLAN.json`: the source local-profile contract.
+- `vendor/pr1074/T8/PLAN.json`: its provider identities are rebound to the eight-slot locals (11 identities: semantic
+  artifact ids, the LOCAL-CHECKS pin and both program hashes) plus the paid profile.
+- `vendor/pr1074/data/SPEC-T8.json`: plan pin, expected profile and semantic ids, re-recorded by the unchanged bind
+  code in discovery mode.
+- `CERTIFICATE.json`: the root interval `[0.001676945247549584231285, …286]` and the κ grid.
+- `controls.py`: the shifted-root and next-grid control values.
+- `replay.py` and `check.py`: the new κ constant and the final marker.
+- `data/PLAN.json` and `data/SPEC.json`: re-frozen by the package's own `replay.py --discover`.
+- `SOURCES.json` and `SOURCE-FREEZE.json`: refreshed.
+- New: `construction/x54/` and `evidence/`.
+
+`OWNERS.json.gz`, `ORDER.json`, `PATTERN-FLOW.json`, `construct.py`, `lift.py`, `verify.py`, `independent_owner.py` and
+`code/` are byte-identical to #1129. #1129's README is kept as `README-R480-OWNER-OPTIMUM.md`.
+
+## Credits
+
+- **Ali Romman** (#1129): the R480 owner theorem, the attaining T37 construction and this package's machinery.
+  **Chafik Boukhalfa** (#1131) published the same optimum; his PR795 supplied the signed prices.
+- **Jeremy Kothe**: the X54 slot recipe (#1130), the seven-slot k8 word (#1018/#1074) and the leaver chain (#1005).
+- **NewBArch**: the triangle-hybrid move and the unchanged builder and controls.
+- **Rohan Arun** (#987): the slot search used to find the k8 slots.
+- **Hao Yan**: the T16 machinery.
+- Every upstream contributor credited in the retained notices.
+
+Composition prepared by Rohan Arun with Claude (Anthropic).
diff --git a/research/k8-x54-t37/SEARCH.json b/research/k8-x54-t37/SEARCH.json
new file mode 100644
index 0000000000..677eb1e419
--- /dev/null
+++ b/research/k8-x54-t37/SEARCH.json
@@ -0,0 +1,57 @@
+{
+  "route": "Fixed R480 seven-slot k8 all-replica owner optimum",
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "source_head": "052afc128954f7b6a2b3c409eb4d72248e4020f2",
+  "candidates": [
+    "Exact signed bin dual and supporting moment inequality",
+    "Mixed T16/T21/T37 owner lifts for the fixed word",
+    "Higher-replica owner construction on the tight dual face"
+  ],
+  "choice": "Combine the first and third approaches at the least possible equality replica count T=37.",
+  "domain": {
+    "widths": [4, 5, 7, 8, 9],
+    "capacities": [8, 16, 32, 48],
+    "bin_patterns_exhausted": 1163,
+    "dual_tight_patterns": 20,
+    "constructive_basis_patterns": 9,
+    "call_order": "The frozen PR942 T37 order",
+    "physical_groups": "Replica, capacity, and exact source-event window; paired child sides have 224 ports."
+  },
+  "attempts": [
+    {
+      "method": "Continuous bin LP, then exact rational dual and moment support checks",
+      "result": "Nine-pattern optimum and equality denominator 37. Exact checks replace floating-point decisions."
+    },
+    {
+      "method": "Chronology LP with all 20 tight patterns",
+      "time_limit_seconds": 60,
+      "result": "Time limit. No infeasibility result was obtained."
+    },
+    {
+      "method": "Chronology LP restricted to the nine-pattern optimal basis",
+      "variables": 126128,
+      "constraints": 59478,
+      "matrix_nonzeros": 431038,
+      "elapsed_seconds": 20.65,
+      "result": "Feasible. The solution still had fractional entries."
+    },
+    {
+      "method": "Integer feasibility model on the same basis, all variables integral",
+      "time_limit_seconds": 180,
+      "elapsed_seconds": 177.92,
+      "result": "Feasible integer flow. All rounded entries pass the full exact integer equations and inequalities."
+    },
+    {
+      "method": "Bipartite matching decomposition of the frozen integer flow",
+      "result": "159840 literal whole-helper roles in 333 calls. Exact replay needs no optimizer."
+    }
+  ],
+  "discovery_environment": {
+    "scipy": "1.18.1",
+    "sympy": "1.14.0",
+    "threads": 1,
+    "randomness": "No custom random search or seed. The solver used its default internal settings."
+  },
+  "stopping_rule": "Stop when one full physical T37 map attains the exact bin ceiling. Do not search for further T16 increments.",
+  "coverage_limit": "Only the bin-pattern enumeration and its separate recurrence are exhaustive. Solver timeouts do not prove infeasibility. The exact certificate and owner checks establish the delivered result."
+}
diff --git a/research/k8-x54-t37/SOURCE-FREEZE.json b/research/k8-x54-t37/SOURCE-FREEZE.json
new file mode 100644
index 0000000000..5b741d686d
--- /dev/null
+++ b/research/k8-x54-t37/SOURCE-FREEZE.json
@@ -0,0 +1,78 @@
+{
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "files": {
+    "CERTIFICATE.json": "b3282207a42f79dfde750bdb70e9273e719c17094c8b94e69863c9e9e69b55e5",
+    "CODE-DERIVATION.json": "cc6b7ab7e8c9dc33be30875fe5f0f21a47f92b73f02f2ef42897a49b0b94953f",
+    "CODE-DERIVATION.patch": "1e37b85b1335595a366a4a8810b898869d9c63cc8231b5576b0fdaffd2009eef",
+    "INDEPENDENT-DERIVATION.patch": "bde2ae12f44a1d2310bb607a5ed2078cf67e58bf736b05a1b278eba772921323",
+    "NOTICE.md": "413de9d1be5bb8ec875bea552ac54b5632d6eaa2df24570274feeb53cc9d2f18",
+    "ORDER.json": "2093ca4050e1ce95621f4702bebe8b01b36773b1ecfa2c0d6275e132bd33d578",
+    "OWNERS.json.gz": "c35ac0c6f77c6b7cb32bee953770de3ef8a575aef36efc4764e0bb3325a04737",
+    "PATTERN-FLOW.json": "de533d6a4f978c2abd433a6521798ace3773ad952dce683ec5c2ecc489962643",
+    "PROOF.md": "8244024094a431025c56cc266e458fb998e30d096c998927a51fdc33c47e866e",
+    "README-R480-OWNER-OPTIMUM.md": "fbed39077a7220643feaf542f402bda7ba50a5fa3fe0b384c6cbaa26a830b8f8",
+    "README.md": "e53c2048d72208bfac020a993179f96ea620d1d8e2f79d1d72a9d9a1f4964677",
+    "SEARCH.json": "b0f24b26647971f7295ea1d6cf3f8a3752fe174b9d41e08b1dd5afceea3a40fa",
+    "SOURCES.json": "9d9fcd475f959c113619af51195327c6362a535117e8d41996ef7c01e50023a5",
+    "check.py": "ef1278d938d0923e0518666db1700675ffb758424782690df6d596f8ec33b5a2",
+    "code/assemble.py": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a",
+    "code/assembly_controls.py": "29ba6742d899d2318a96745c8ec21de06ba3968d4641c3400a15bc714e0d7f9e",
+    "code/audit_allcold.py": "a8d3c48e26957c5174ea35043545d3863a4c19c82422074ac42132b446533b4a",
+    "code/bind_providers_portable.py": "1d39bcc7b63ac158e021454beaae897d123e174360573762aecade3cd43193f6",
+    "code/bit_supplier_controls.py": "e6d33fb61a570c3f50669412acc467a3fd06ef0b806da6a75bc296c6ba2142a5",
+    "code/emit_allcold.py": "3219e0706d497a2e6b595cec0a0d5bdbfbd1d991bf70136762eada44126a9ac1",
+    "code/freeze_spec.py": "e9132a9d195c66123f2747a17f7ef404b4d1e3ef6263ab4c28c983a052cf10bd",
+    "code/generated_identity.py": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+    "code/invoice_allcold.py": "e97c74d1ccfb0b0e26260e65bb780fa0103f4c716647e238f943a2e840a1f566",
+    "code/prepare_global.py": "8c0dae301a8f34b77a5a462f840952d08ed120576212adf5051bc09bcad874dc",
+    "code/restore_parent.py": "69b7b25ff85e9b8160e233c1d415cc6a0272019e5c486dcec14cb6c349e7024d",
+    "code/witness.py": "779c5172894b992131e85be1e592ed2a1aec8c287b872ff42007d36a7291e444",
+    "construct.py": "5d06e8f5f3ed4015171d6cbfaa995eb1d1a0a14e687595910391caffcf3ca474",
+    "construction/x54/RECIPE-X54-k8.json": "03a02e49bb397d53c4702c5ea4f4af41ea3b441198ffc491d202bc0ac715cae4",
+    "construction/x54/X54-PINS.json": "40d5850e2ac5f36a2313251207c9a9f2feb42d004672ebe098f19fe7f3e07ab9",
+    "construction/x54/build_x54.py": "2118b063f84e9cf2bebb979f2ef88258dde4e6ef813a34611d6eb65a30183639",
+    "controls.py": "bf55dcea7c5dabf52bb6c562804bf570ac0fcce9fbe2dccb585e599ff1e5af7f",
+    "data/PLAN.json": "1e1b7ef0cc33e4bd70e66a40809c37f59deeca0d6e54914b87ec7195d9b47e31",
+    "data/SPEC.json": "2ada5abf34eee9a5d273fb07b11e4b6ddd55e64cb3a9e5e54bcf0b51f274488f",
+    "independent_owner.py": "bbd9c43b3db12d61a4ae1050949320cd6d7e610ef2aa9ccabd309d7b5e07ad82",
+    "inputs/PLAN.json": "b44c520e9288967e4814603fe1137ac1ec899552c657f6ba3428c941ada141fc",
+    "inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "inputs/RESULT.json": "ebf3577df9efccc213998a6cf43f25fb3cd1a26893847b68d60d276e3b76440c",
+    "inputs/SPEC.json": "b114e32f15fff8974709c040544bc653436c83cd0d83f823c7331a7c84625aae",
+    "inputs/local/CANONICAL-WORD.json.gz": "75507b67a784bd1e54e1451b6263624fe4d05bd08b850c4fb87c82776ec1909a",
+    "inputs/local/CLIFFORD-RECIPES.json": "7ed4c7e81ace3e7837067167745d2ca1bc3212079de284e76760c1c45b31d0ce",
+    "inputs/local/CLIFFORD-REVIEW.json": "e792f172a6a84c29c73d8b42b5a6705d5eed1369aec955270b83b4dca6c6fdf5",
+    "inputs/local/FULL-WORD.json.gz": "ac196f39a72ef658aeba7199947e603da730a944c11e7300d12372f2e5875dcd",
+    "inputs/local/INDEPENDENT-LOCAL-REPLAY.json": "0ac952f4900d2ef2508abd60ca4a7448b1a17b0a3f7e6fb3b4ee0c228c728766",
+    "inputs/local/LOCAL-CHECKS.json": "f04e637879fa041e363b70873a0713f7ac15336da81a49460eabaac3683c4a3e",
+    "inputs/local/LOCAL-PROGRAMS.json.gz": "43b7cd0eafaf840288ee7d1695dac5b5905033ca7f2df4bd9517e75387db5857",
+    "inputs/local/RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c",
+    "inputs/local/SCALAR-FRAME-AUDIT.json": "63c3e15b946596b1027cd793a862d153d4eb8f586b8819c527fd30031d023381",
+    "inputs/local/WRAPPER-CHECKS.json": "0ae753d6fa6e922d8b8180da602828f6cb3f444fcd124d019acee74e145c0836",
+    "lift.py": "211a73218c8923b9b71093fa6affa21a3b906c0dc12931836fbc652e477e478b",
+    "replay.py": "382c78dfbfa57bd566fbbd5d35548006ba581d633e05ddab9909e7e029b07d68",
+    "vendor/pr1074/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "vendor/pr1074/NOTICE.md": "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf",
+    "vendor/pr1074/T8/PLAN.json": "20c84a852caa664cc3283d1c4e21c2f97df9a166ccab513fb442477a618882a0",
+    "vendor/pr1074/UPSTREAM-NOTICE.md": "a75967ebc34e3bf2ff2c25c08e6c7f1a61b0c0d171cfd1b62196ae2caaf2c610",
+    "vendor/pr1074/UPSTREAM-PINS.json": "ccc37ab7fbf78947fe02c7f57ea672d2e4eae8454cb1158ed964c75bf423869b",
+    "vendor/pr1074/code/assemble.py": "15f6986a476bac76bcdc0bfcf51da115389b46f1950d2766b6822f757888b13a",
+    "vendor/pr1074/code/assembly_controls.py": "da7e981ae1b9f099d4e1524cb4f3ba1116011936ebe378692889b5dbfa99029d",
+    "vendor/pr1074/code/audit_allcold.py": "1467a2acb654e62552c69fb9a7c4c85f70a02120881d222313865058ab71a6cc",
+    "vendor/pr1074/code/bind_providers_portable.py": "1d39bcc7b63ac158e021454beaae897d123e174360573762aecade3cd43193f6",
+    "vendor/pr1074/code/bit_supplier_controls.py": "e6d33fb61a570c3f50669412acc467a3fd06ef0b806da6a75bc296c6ba2142a5",
+    "vendor/pr1074/code/emit_allcold.py": "354367e1fd6185a67b04f4268bcae4d502e47b18cb2131e247f5bcab5b3a769e",
+    "vendor/pr1074/code/freeze_spec.py": "5971eecac6d6fbcb53244b80f1b9d7232012dc32876fab511214a5addebbe6c2",
+    "vendor/pr1074/code/generated_identity.py": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+    "vendor/pr1074/code/invoice_allcold.py": "71eb57514e28ced97251e0507105f654f59885ec4d40486a780bf166098858a8",
+    "vendor/pr1074/code/prepare_global.py": "8c0dae301a8f34b77a5a462f840952d08ed120576212adf5051bc09bcad874dc",
+    "vendor/pr1074/code/restore_parent.py": "69b7b25ff85e9b8160e233c1d415cc6a0272019e5c486dcec14cb6c349e7024d",
+    "vendor/pr1074/code/witness.py": "779c5172894b992131e85be1e592ed2a1aec8c287b872ff42007d36a7291e444",
+    "vendor/pr1074/construction/leaver/PIVOT-SWAP-k8.json": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb",
+    "vendor/pr1074/data/SPEC-T8.json": "c804307a8be68e2a58b592043233f0b851fa3c50336f2e8f08b613e9eee5b132",
+    "vendor/pr1074/inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "vendor/pr1074/t16/NOTICE.md": "902370e6bfcd39dbea2ece474f15fccbcce3b8e966b2b94066bd03e5174591b5",
+    "vendor/pr1074/t16/build_parent.py": "82e274d0c7a94f9bf0468dd37f0505d0c42017559ebb4ba8c079a1f4e403d91e",
+    "verify.py": "1ecc9f9a78fc4b0c3a100ee48fef70bf0f3b2d711d9be646623ffe781c2e596c"
+  }
+}
diff --git a/research/k8-x54-t37/SOURCES.json b/research/k8-x54-t37/SOURCES.json
new file mode 100644
index 0000000000..e0d3aa03ba
--- /dev/null
+++ b/research/k8-x54-t37/SOURCES.json
@@ -0,0 +1,22 @@
+{
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "source_head": "052afc128954f7b6a2b3c409eb4d72248e4020f2",
+  "source_package": "research/gauge44-slots-t16",
+  "engine_directory": "research/complex-k492-owner-repair/vendor/multicold/engines",
+  "outer_driver": "research/complex-t21-owners/vendor/pr870/independent/price_profile_t16.py",
+  "bit_expected": "research/complex-t21-owners/vendor/pr870/inputs/PR589-EXPECTED.json",
+  "files": {
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "research/complex-t21-owners/vendor/pr870/independent/price_profile_t16.py": "53f8e62dcf27bee032c1bee0245d126a9c8a12ebcf24f6aaff65ea3122fffe29",
+    "research/complex-t21-owners/vendor/pr870/inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "research/complex-t37-owners/ALL-T-PROOF.md": "4c0c71ccd0afb850538af1b467e5208b7eb3edd0260fded84e02a8c01dfc868b",
+    "research/complex-t21-owner-bound/PROOF.md": "2aa0aa6ec1d87402138564c38749b5ca0f058c16817efdf58a2685d2d90cb417",
+    "package:inputs/SPEC.json": "b114e32f15fff8974709c040544bc653436c83cd0d83f823c7331a7c84625aae",
+    "package:inputs/PLAN.json": "b44c520e9288967e4814603fe1137ac1ec899552c657f6ba3428c941ada141fc",
+    "package:inputs/RESULT.json": "ebf3577df9efccc213998a6cf43f25fb3cd1a26893847b68d60d276e3b76440c",
+    "research/complex-t21-owners/independent_check.py": "9d8c86bf45cdaef37f223c88704055ced503ee295645611e13f3fb9059a00e55",
+    "research/complex-t37-owners/ORDER.json": "2093ca4050e1ce95621f4702bebe8b01b36773b1ecfa2c0d6275e132bd33d578"
+  }
+}
diff --git a/research/k8-x54-t37/check.py b/research/k8-x54-t37/check.py
new file mode 100644
index 0000000000..4996479e87
--- /dev/null
+++ b/research/k8-x54-t37/check.py
@@ -0,0 +1,45 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Check the exact bound and the frozen finite construction."""
+import argparse
+import json
+import os
+from pathlib import Path
+import subprocess
+import sys
+
+HERE = Path(__file__).resolve().parent
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, default=HERE.parents[1])
+    parser.add_argument('--local', type=Path, default=HERE / 'inputs/local')
+    parser.add_argument('--work', type=Path, required=True)
+    args = parser.parse_args()
+    if args.work.exists():
+        raise ValueError('Choose a new check directory')
+    if sys.flags.optimize:
+        raise ValueError('Retained checks require assertions')
+    args.work.mkdir(parents=True)
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', OPENBLAS_NUM_THREADS='1',
+               OMP_NUM_THREADS='1')
+    commands = [
+        ['verify.py', '--out', args.work / 'BOUND.json'],
+        ['controls.py', '--out', args.work / 'BOUND-CONTROLS.json'],
+        ['construct.py', '--out', args.work / 'construction'],
+        ['replay.py', '--main', args.main, '--local', args.local,
+         '--work', args.work / 'replay'],
+    ]
+    for script, *arguments in commands:
+        subprocess.run([sys.executable, '-B', str(HERE / script), *map(str, arguments)],
+                       env=env, check=True)
+    receipt = json.loads((args.work / 'replay/RESULT.json').read_text())
+    if receipt['status'] != 'PASS_R480_T37_STRICT_FINITE_CONSTRUCTION':
+        raise ValueError('Strict construction replay did not pass')
+    print('PASS_K8_X54_ALL_REPLICA_OPTIMUM_AND_ATTAINING_CONSTRUCTION',
+          receipt['kappa_decimal'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/k8-x54-t37/code/assemble.py b/research/k8-x54-t37/code/assemble.py
new file mode 100644
index 0000000000..f6cc563542
--- /dev/null
+++ b/research/k8-x54-t37/code/assemble.py
@@ -0,0 +1,241 @@
+"""Gauge44 complete global admission with the retained 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 PR589 supplier (PR555's punctured
+R439 word, v = 111, decoder constant 63, two A-section transports), shipped
+as inputs/PR589-EXPECTED.json and pinned by git blob id. Its rank-mass
+deficit is derived from the word's parameters, T(2Kv - L*cst) at nine
+stages (PR545/PR555 rank-mass identity), not hard-coded. 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,SPOT,spot_widths
+# Cited bit supplier: PR589's tune/EXPECTED.json (merged on main as research/e8-bit-p111-tuned/tune/EXPECTED.json).
+BIT_PATH=Path(__file__).resolve().parents[1]/'inputs/PR589-EXPECTED.json'
+BIT_BLOB='e293ddc557742637f9f679f083a1a282d87b1b13'
+# Nine-stage bit template (PR463/PR510 chain, 32 replicas): L stages, T replicas, K=(L-1)//2 pairs, moment width M=1+7L.
+BIT_L,BIT_T=9,32;BIT_K=(BIT_L-1)//2;BIT_M=1+7*BIT_L
+def git_blob(data):return hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()
+def load_bit(data):
+ """The pinned supplier record: its full record (word parameters) and its nine-stage price."""
+ assert git_blob(data)==BIT_BLOB,'bit supplier blob pin'
+ return json.loads(data)
+def bit_deficit(word,live):
+ """Rank-mass deficit M*live - mass = T(2Kv - L*cst) of a v-port bit word with decoder constant cst (PR545/PR555).
+ cst is the sum of the retained totals' COPY ranks and live = 2KvT data wires; both are cross-checked here, and the
+ caller checks the result against the priced profile, so neither v nor cst is free."""
+ v,cst,ranks=word['v'],word['decoder_constant'],word['copy_ranks']
+ assert type(v)is int and type(cst)is int and all(type(r)is int and 0<r<=8 for r in ranks)
+ assert len(ranks)==word['retained_totals']==BIT_L and cst==sum(ranks)
+ assert live==2*BIT_K*v*BIT_T
+ d=BIT_T*(2*BIT_K*v-BIT_L*cst);assert d>0;return d
+
+
+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
+ # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+ R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==333*R==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']==333
+ assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+ assert invoice['centres']==8
+ assert invoice['physical_stock_identity']==dict(data_and_owner_families=33152,local_helpers=R,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']==R and p['centres']==8 and p['n']==2*112+R 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*R-p['entrance_rank']-p['terminal_codimension'] and len(p['widths'])==R   # HPE: widths |final|-|start|
+  pin(K+'width_digest',digest(p['widths']));assert tuple(p['widths'][h]for h in SPOT)==spot_widths()
+  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 in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):pin(K+'artifacts.'+name,p['artifacts'][name])
+  pin(K+'artifact_semantic_sha256',p['semantic_artifact_sha256'])
+  pin(K+'complete_contract',{k:v for k,v in p.items()if k!='artifacts'})
+  assert owner['provider_artifact_semantic_sha256'][pid]==p['semantic_artifact_sha256']
+  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']==2*112+R and z['dirty_helper_columns']==R
+   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']+p.get('cold_hyperplane_ended_helpers',0);pin(K+'wrappers',z['pre_wrappers'])   # COLD-HPE
+   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']+2*112+R+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)==333
+ 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(37)}
+ 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=55832,56346,74592
+ parent_banks,rem=divmod(parent_live-2*112*4*37,9);assert rem==0 and parent_physical==parent_live+504+8+2   # five bank groups with 8,8,8,8,5 active lanes and R0=504 helpers; shared private work is restored
+ assert owner['source_idle_children_charged']==parent_idle
+ bridges,shifts=2*112*333,4*112*37;moves=2*shifts
+ nonlocal_items=(4*112*37*9+2*112*37*9+2*333*R+parent_idle+9*parent_banks+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+(333*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']==1024
+ assert invoice['row_prefix_extra']==2048
+ assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+333+333+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+2048
+ 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_record=load_bit(BIT_PATH.read_bytes())
+ bit=bit_record['nine']
+ assert 'nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline']
+ c=Q(bit['bit_lower'])
+ bit_D=bit_deficit(bit_record['word'],bit['bit']['live'])
+ 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']==11840
+ 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()}
+ assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+ bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,11840,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+1024)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+1024)
+   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,11840,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,'package:inputs/PR589-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_GAUGE44_NATIVE_EXACT_GLOBAL_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_pr635_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=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),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 R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain.')
+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/k8-x54-t37/code/assembly_controls.py b/research/k8-x54-t37/code/assembly_controls.py
new file mode 100644
index 0000000000..cc4a8edb0e
--- /dev/null
+++ b/research/k8-x54-t37/code/assembly_controls.py
@@ -0,0 +1,260 @@
+"""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 + 333 + 333 + 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) if len(PIDS)>1 else '__unregistered__'
+        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 is not c and (d['provider_id'] != P or len(PIDS)==1) 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),
+        ]
+        if len(PIDS)==1:
+            # Cross-provider substitutions require a second actual supplier.
+            # All single-provider program, phase, profile and dispatch bindings
+            # retain their direct mutations above and in the controller audit.
+            partner_only = {P+':stale_partner_program_consistent_call_hashes',
+                            P+':stale_partner_profile_consistent_child_total',
+                            P+':relocated_against_partner_same_counts',
+                            P+':compensating_false_profiles_with_'+Qp}
+            controls = [(name, fn) for name, fn in controls if name not in partner_only]
+        # 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 SPOT:
+            def cold_swap(o, i, P=P, h=h):
+                w = i['providers'][P]['widths']; j = w.index(9 if w[h] != 9 else 8); w[h], w[j] = w[j], w[h]   # never the identity
+            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/k8-x54-t37/code/audit_allcold.py b/research/k8-x54-t37/code/audit_allcold.py
new file mode 100644
index 0000000000..f4f71d0756
--- /dev/null
+++ b/research/k8-x54-t37/code/audit_allcold.py
@@ -0,0 +1,254 @@
+"""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 *
+from generated_identity import artifact_identities
+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={};artifact_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=[len(c['frames'][c['final'][2*c['v']+h]])-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths();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']
+ artifact_semantic_hashes[pid]=artifact_identities(p)
+ pin('providers.%s.artifact_semantic_sha256'%pid,artifact_semantic_hashes[pid])
+ phase_semantic_hashes[pid]=artifact_semantic_hashes[pid]['CLIFFORD-REVIEW.json']
+ for h,w in enumerate(widths):
+  assert 0<w<=c['h']
+  f=c['start'][2*c['v']+h];u=c['final'][2*c['v']+h]
+  # COLD-HPE: a cold helper (f == 0) may end below FULL too; its wrapper is the '0:U' recipe (E = bottom instance of #593)
+  if u!=1:   # HPE: wrapper for T_U T_E^-1, keyed 'E:U', rank |U|-|E|
+   a=adapters['%d:%d'%(f,u)]
+   assert a['frame']==f and a['terminal']==u and a['vectors']==c['frames'][f] and a['terminal_vectors']==c['frames'][u]
+   assert a['rank']==w==len(c['frames'][u])-len(c['frames'][f]) and a['entrance_rank']==len(c['frames'][f]) and a['terminal_rank']==len(c['frames'][u])<c['h']
+  elif w<c['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'))
+# Independently compare ordered common frames; exact local carrier names remain
+# bound to each canonical word, program, phase receipt and residual adapters.
+for p in provider_ids:
+ c=providers[p]['canonical']
+ assert len(c['centers'])==len(c['center_frames'])==8
+ assert [c['frames'][f]for f in c['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+assert required_artifacts<=set(summary['source_artifacts'])
+prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=37;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=333;HOSTED=CALLS*R
+# The selected map is an input to check, not a claim from the emitter.
+
+assert len(DISPATCH)==333 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'])==333 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))==333
+ all_local=[];perrep={r:[]for r in range(37)};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<37 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']<333 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(37)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==11840 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=333)
+
+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))
+# Single-provider dispatch still has all source/program/width binding controls.
+if len(provider_ids)==1:
+ P=provider_ids[0]
+ at_p=lambda q:next(c for c in q['calls']if c['provider_id']==P)
+ narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+ reject(P+': wrong provider at its invocation',lambda q:at_p(q).__setitem__('provider_id','__unregistered__'))
+ reject(P+': stale per-call local program hash',lambda q:at_p(q).__setitem__('local_program_sha256','0'*64))
+ reject(P+': stale serialized provider program',lambda q:q['local_providers'][P]['local_programs']['forward'].pop())
+ reject(P+': unbound residual adapter hash',lambda q:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+ reject(P+': wrong provider width registry',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,providers[P]['widths'][narrow]-1))
+ reject(P+': wrong per-call residual width',lambda q:at_p(q)['owners'][2*V+narrow][1].__setitem__(3,at_p(q)['owners'][2*V+narrow][1][3]-1))
+ reject(P+': wrong sweep provider',lambda q:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep').__setitem__('provider_id','__unregistered__'))
+ reject(P+': entering helper width silently restored to nine',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,9))
+else:
+ # 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=11840,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,provider_artifact_semantic_sha256=artifact_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=11840,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,provider_artifact_semantic_sha256=artifact_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/k8-x54-t37/code/bind_providers_portable.py b/research/k8-x54-t37/code/bind_providers_portable.py
new file mode 100644
index 0000000000..97e28da17e
--- /dev/null
+++ b/research/k8-x54-t37/code/bind_providers_portable.py
@@ -0,0 +1,67 @@
+"""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 *
+from generated_identity import artifact_identities
+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={};helpers=set()   # R: helper count per provider word; all providers must agree
+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'],len(word['centers']))==(112,9,8) and type(word['R']) is int and word['R']>0;helpers.add(word['R'])
+ assert word['ports']==desc['ports'] and word['centers']==desc['centers']
+ widths=[len(word['frames'][word['final'][r]])-len(word['frames'][word['start'][r]])for r in range(2*112,2*112+word['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths()
+ 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']
+ identities=artifact_identities(d)
+ pin('providers.%s.artifact_semantic_sha256'%pid,identities)
+ assert identities==desc['artifact_semantic_sha256']
+ for name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):
+  assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-reference artifact')
+ 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'])
+assert len(helpers)==1,'providers disagree on helper count R: %s'%sorted(helpers)
+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','runtime_source_plan_sha256'])
+(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(receipt['status'])
diff --git a/research/k8-x54-t37/code/bit_supplier_controls.py b/research/k8-x54-t37/code/bit_supplier_controls.py
new file mode 100644
index 0000000000..e86b8527b4
--- /dev/null
+++ b/research/k8-x54-t37/code/bit_supplier_controls.py
@@ -0,0 +1,111 @@
+"""Negative controls for the cited PR589 bit supplier and its derived rank-mass deficit.
+
+Apache-2.0. Each control mutates one input of the changed bit-supplier sites in assemble.py (the pinned record, the
+deficit derivation from the word's parameters, the profile/live binding, the claimed endpoint) and runs the unchanged
+assemble() on the fresh owner/invoice receipts. Every control must be rejected; the unmutated run must pass.
+`revert_hardcoded_9984` restores the PR543 constant the parent package hard-coded: with PR589's word it must fail.
+"""
+import argparse
+import copy
+import hashlib
+import json
+import os
+import tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+
+assert __debug__, 'Assertions required'
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    import assemble as A
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    args = (owner, invoice, sha(owner_path), sha(invoice_path))
+    baseline = A.assemble(*args)
+    data = A.BIT_PATH.read_bytes()
+    record = A.load_bit(data)
+    word = record['word']
+    assert A.bit_deficit(word, record['nine']['bit']['live']) == 10272 == 32 * (8 * 111 - 9 * 63)
+
+    real_load, real_deficit = A.load_bit, A.bit_deficit
+
+    def with_record(mutate):
+        def load(d):
+            r = copy.deepcopy(real_load(d)); mutate(r); return r
+        return load
+
+    def shift_profile(r):  # one rank-1 child becomes rank 2: rank mass +1, totals unchanged
+        p = r['nine']['profile']; p['1'] -= 1; p['2'] += 1; r['nine']['bit']['rank_mass'] += 1
+
+    bumped = data.replace(record['nine']['bit_lower'].encode(),
+                          str(Q(record['nine']['bit_lower']) + Q(1, 10**24)).encode(), 1)
+    assert bumped != data
+    pr543 = (source_package / 'inputs/PR543-EXPECTED.json').read_bytes()
+    controls = [
+        # deficit site: the parent's hard-coded constant, restored
+        ('revert_hardcoded_9984', dict(bit_deficit=lambda w, live: 9984)),
+        # deficit site: each word parameter perturbed alone
+        ('ports_112', dict(load_bit=with_record(lambda r: r['word'].__setitem__('v', 112)))),
+        ('decoder_constant_64_copy_ranks_unchanged', dict(load_bit=with_record(lambda r: r['word'].__setitem__('decoder_constant', 64)))),
+        # v=111, cst=64 derives 32*(888-576)=9984: consistent word, wrong for the priced profile
+        ('decoder_constant_64_with_one_copy_rank_8', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('decoder_constant', 64), r['word']['copy_ranks'].__setitem__(0, 8))))),
+        ('eight_retained_totals', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('copy_ranks', [7] * 8), r['word'].__setitem__('decoder_constant', 56))))),
+        ('live_minus_one', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('live', r['nine']['bit']['live'] - 1)))),
+        # profile binding: same totals, rank mass +1
+        ('profile_rank_mass_plus_one', dict(load_bit=with_record(shift_profile))),
+        ('profile_rank_mass_receipt_mismatch', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('rank_mass', r['nine']['bit']['rank_mass'] + 1)))),
+        # endpoint: the next 1e-24 grid point
+        ('bit_lower_next_grid', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('bit_lower', str(Q(r['nine']['bit_lower']) + Q(1, 10**24)))))),
+        ('not_nine_stage_record', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('pipeline', r['nine']['pipeline'].replace('nine-stage', 'eleven-stage'))))),
+        # pinned-input site: tampered bytes and the parent's PR543 file under the PR589 pin
+        ('tampered_bytes_next_grid', dict(read=bumped)),
+        ('pr543_file_under_pr589_pin', dict(read=pr543)),
+    ]
+    rejected = []
+    scratch = Path(tempfile.mkdtemp(prefix='bitctl-'))
+    for name, patch in controls:
+        saved_path = A.BIT_PATH
+        try:
+            if 'read' in patch:
+                tmp = scratch / (name + '.json'); tmp.write_bytes(patch['read']); A.BIT_PATH = tmp
+            A.load_bit = patch.get('load_bit', real_load)
+            A.bit_deficit = patch.get('bit_deficit', real_deficit)
+            try:
+                A.assemble(*args)
+            except (AssertionError, KeyError):
+                rejected.append(name)
+            else:
+                raise AssertionError('Invalid bit supplier accepted: ' + name)
+        finally:
+            A.load_bit, A.bit_deficit, A.BIT_PATH = real_load, real_deficit, saved_path
+            if 'read' in patch:
+                tmp.unlink()
+    scratch.rmdir()
+    assert rejected == [n for n, _ in controls]
+    again = A.assemble(*args)
+    assert again['kappa'] == baseline['kappa'] and again['bit_lower'] == baseline['bit_lower']
+    return dict(
+        status='PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS',
+        kappa=baseline['kappa_decimal'], bit_lower=baseline['bit_lower'], bit_decimal=baseline['bit_decimal'],
+        binding=baseline['binding'], bit_supplier=baseline['bit_supplier'],
+        derived_deficit=baseline['bit_supplier']['derived_deficit'],
+        rejected_controls=rejected,
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+    )
+
+
+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', newline='\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/k8-x54-t37/code/emit_allcold.py b/research/k8-x54-t37/code/emit_allcold.py
new file mode 100644
index 0000000000..7f76f14819
--- /dev/null
+++ b/research/k8-x54-t37/code/emit_allcold.py
@@ -0,0 +1,150 @@
+"""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))==333;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=37;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,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')
+ # Carrier names belong to the independently checked local program. The global
+ # controller's centre contract is the ordered eight exact common frame bases.
+ assert(pc['v'],pc['h'],pc['ports'])==(V,9,canon['ports'])
+ assert len(pc['centers'])==len(pc['center_frames'])==len(canon['centers'])==8
+ assert [pc['frames'][f]for f in pc['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+ R=pc['R'];assert type(R)is int and R>0 and all(x['R']==R for x in registry.values()),'providers disagree on helper count R'
+ 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=[len(pc['frames'][pc['final'][2*V+h]])-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)]   # HPE: residual width |final|-|start|
+ 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)
+assert len(roles)==333*R   # one whole-owner role per (call, provider helper)
+selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+assert len(selected)==333 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())==11840
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R0+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-R%d-asynchronous-whole-owner-v1'%R,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=11840,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/k8-x54-t37/code/freeze_spec.py b/research/k8-x54-t37/code/freeze_spec.py
new file mode 100644
index 0000000000..e4e72b5a07
--- /dev/null
+++ b/research/k8-x54-t37/code/freeze_spec.py
@@ -0,0 +1,29 @@
+"""Freeze independently recomputed discovery values before strict replay."""
+import argparse
+import json
+from pathlib import Path
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--spec', type=Path, required=True)
+ap.add_argument('--discovery', type=Path, required=True)
+a = ap.parse_args()
+spec = json.loads(a.spec.read_text())
+for line in (a.discovery/'WITNESS-RECORD.jsonl').read_text().splitlines():
+    key, value = json.loads(line)
+    parts = key.split('.')
+    if len(parts)>3 and parts[0]=='providers' and parts[2]=='artifacts':
+        parts = parts[:3] + ['.'.join(parts[3:])]
+    target = spec
+    for part in parts[:-1]:
+        target = target.setdefault(part, {})
+    if parts[-1] in target:
+        assert target[parts[-1]]==value, 'Conflicting independent recomputations: '+key
+    target[parts[-1]] = value
+assembly = json.loads((a.discovery/'ASSEMBLY.json').read_text())
+for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+    spec['expected'][key] = assembly[key]
+spec['expected']['assembly_controls_rejected'] = 69
+spec['expected']['provider_counts'] = {'gauge44':333}
+spec['expected']['mutations_rejected'] = 15
+a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
diff --git a/research/k8-x54-t37/code/generated_identity.py b/research/k8-x54-t37/code/generated_identity.py
new file mode 100644
index 0000000000..74a9b60479
--- /dev/null
+++ b/research/k8-x54-t37/code/generated_identity.py
@@ -0,0 +1,62 @@
+"""Proof-relevant identities for generated artifacts, independent of gzip streams.
+
+Immutable source archives retain their exact byte hashes. For freshly emitted
+artifacts, gzip identity is the exact decompressed payload and JSON identity
+retains every field. Only CLIFFORD-REVIEW's root timing field is excluded.
+Literal receipt references are checked against actual files before replacing
+the three gzip references (and the phase recipe reference) with content hashes.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import copy
+import gzip
+import hashlib
+import json
+import math
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+
+FILES=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+       'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+       'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json')
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+def json_identity(value):
+    return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode('utf-8')).hexdigest()
+
+def payload_identity(path):
+    return hashlib.sha256(gzip.decompress(Path(path).read_bytes())).hexdigest()
+
+def phase_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'CLIFFORD-REVIEW.json').read_bytes())if value is None else value)
+    assert value['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz'),'stale phase canonical word reference'
+    assert value['recipe_sha256']==sha(directory/'CLIFFORD-RECIPES.json'),'stale phase recipe reference'
+    seconds=value.pop('seconds')
+    assert type(seconds)in(int,float) and math.isfinite(seconds) and seconds>=0,'invalid phase timing metadata'
+    value['canonical_word_sha256']=payload_identity(directory/'CANONICAL-WORD.json.gz')
+    value['recipe_sha256']=json_identity(json.loads((directory/'CLIFFORD-RECIPES.json').read_bytes()))
+    return value
+
+def native_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'INDEPENDENT-LOCAL-REPLAY.json').read_bytes())if value is None else value)
+    for field,name in [('canonical_word_sha256','CANONICAL-WORD.json.gz'),('local_programs_sha256','LOCAL-PROGRAMS.json.gz')]:
+        assert value[field]==sha(directory/name),'stale native artifact reference: '+field
+        value[field]=payload_identity(directory/name)
+    return value
+
+def artifact_identities(directory):
+    directory=Path(directory)
+    result={}
+    for name in FILES:
+        path=directory/name
+        if name.endswith('.gz'):
+            result[name]=payload_identity(path)
+        else:
+            value=phase_value(directory)if name=='CLIFFORD-REVIEW.json'else native_value(directory)if name=='INDEPENDENT-LOCAL-REPLAY.json'else json.loads(path.read_bytes())
+            result[name]=json_identity(value)
+    return result
diff --git a/research/k8-x54-t37/code/invoice_allcold.py b/research/k8-x54-t37/code/invoice_allcold.py
new file mode 100644
index 0000000000..1ada7c24e8
--- /dev/null
+++ b/research/k8-x54-t37/code/invoice_allcold.py
@@ -0,0 +1,329 @@
+"""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 generated_identity import artifact_identities
+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,h)==(112,9) and type(helpers) is int and helpers>0
+    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 = [len(w['frames'][w['final'][r]])-len(w['frames'][w['start'][r]]) for r in range(2*v, 2*v+helpers)]  # HPE: |final|-|start|
+    terminal_codim = sum(h-len(w['frames'][w['final'][r]]) for r in range(2*v, 2*v+helpers))  # HPE: 0 for FULL-ended helpers
+    ends = {r: f for r, f in enumerate(w['final']) if r >= 2*v and f != 1}
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    wrapped = {**entrances, **{r: 0 for r in ends if r not in entrances}}   # COLD-HPE: cold hyperplane-ended helpers carry wrappers too
+    cold_ends = len(wrapped) - 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, *end = event
+                assert kind in wrappers and wrapped.get(register) == frame
+                assert end == ([ends[register]] if register in ends else [])  # HPE: R_{E,U}^-1 and L_{E,U}^-1 name U
+                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(wrapped)
+        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')
+    return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n,
+                entering_helpers=entering,entrance_rank=sum(len(w['frames'][f]) for f in w['start'][2*v:]),
+                terminal_codimension=terminal_codim, hyperplane_ended_helpers=len(ends),  # HPE: always reported (0 for FULL-ended words)
+                **({'cold_hyperplane_ended_helpers': cold_ends} if cold_ends else {}),  # COLD-HPE: absent without cold ends
+                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=artifact_identities(local_dir))
+
+
+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]
+    # R is read from the provider words (all must agree); the parent dedicated-bank
+    # envelope keeps its own helper count R0 from the parent split-centres word.
+    assert len({p['helpers'] for p in providers.values()})==1,'providers disagree on helper count R'
+    v,h,m,centres=112,9,73,8
+    helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+    assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+    parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+    stages,replicas,blocks_per_stream=9,37,4
+    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+parent_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']==11840
+    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=1024
+    if retained_invoice is not None:
+        previous=read(retained_invoice)
+        assert previous['compiler']==compiler and previous['charged_prefix_bits']==512
+        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. The fixed provider uses 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 333 invocation and 333 bridge sweeps and take the maximum local scalar/Horner prefix over both orientations of the fixed provider. 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/k8-x54-t37/code/prepare_global.py b/research/k8-x54-t37/code/prepare_global.py
new file mode 100644
index 0000000000..655c9470f6
--- /dev/null
+++ b/research/k8-x54-t37/code/prepare_global.py
@@ -0,0 +1,124 @@
+"""Bind a frozen explicit owner map to exact native local artifacts.
+
+This preparer nominates a witness. The separate serialized controller audit,
+finite invoice, two exact moment engines and strict pinned replay admit it.
+Apache-2.0; prepared with OpenAI assistance. See NOTICE.md.
+"""
+import argparse
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+from generated_identity import artifact_identities, FILES
+
+assert __debug__, 'Assertions required'
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--parent', type=Path, required=True)
+ap.add_argument('--owners', type=Path, required=True)
+ap.add_argument('--local', type=Path, required=True)
+ap.add_argument('--data', type=Path, required=True)
+args = ap.parse_args()
+args.data.mkdir(parents=True, exist_ok=True)
+parent_path = args.parent / 'data/PLAN.json'
+assert sha(parent_path) == '258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda'
+plan = read(parent_path)
+word = read(args.local / 'CANONICAL-WORD.json.gz')
+checks = read(args.local / 'LOCAL-CHECKS.json')
+assert (word['v'], word['h'], word['R']) == (112, 9, 492)
+widths = [len(word['frames'][word['final'][224+h]]) -
+          len(word['frames'][word['start'][224+h]]) for h in range(492)]
+profile = {int(k): v for k, v in word['local_profile'].items()}
+assert profile == {1: 2514, 2: 404, 3: 448, 4: 160, 5: 56, 8: 8}
+assert Counter(widths) == {4: 52, 5: 48, 7: 34, 8: 114, 9: 244}
+assert sum(widths) == 3794
+owners = read(args.owners)
+assert len(owners) == 72 * 492
+order = [tuple(x) for x in plan['order']]
+times = {x: i for i, x in enumerate(order)}
+used, call_helpers, call_families = defaultdict(set), defaultdict(set), defaultdict(set)
+for z in owners:
+    key = (z['stage'], z['replica'])
+    h, i, rep, port = z['helper'], z['child'], z['owner_replica'], z['port']
+    assert key in times and 0 <= h < 492 and 0 <= rep < 8 and 0 <= port < 112
+    assert z['time'] == times[key] and h not in call_helpers[key]
+    assert z['family'] not in call_families[key]
+    call_helpers[key].add(h)
+    call_families[key].add(z['family'])
+    cap, allowed = plan['windows'][f'{rep},{i}']
+    assert z['time'] in allowed and z['width'] == widths[h]
+    assert z['copy'] == rep * 112 + port
+    assert z['family'] == rep * 896 + (2*plan['pairs'][str(i)] + plan['sides'][str(i)])*112 + port
+    assert 0 <= z['offset'] and z['offset'] + z['width'] <= cap
+    cells = set(range(z['offset'], z['offset'] + z['width']))
+    group = (i, rep, port)
+    assert not used[group] & cells
+    used[group].update(cells)
+assert set(call_helpers) == set(order)
+assert all(hs == set(range(492)) for hs in call_helpers.values())
+idle = Counter()
+for key, (cap, _) in plan['windows'].items():
+    rep, i = map(int, key.split(','))
+    for port in range(112):
+        cells = used[i, rep, port]
+        assert cells == set(range(len(cells)))
+        left = cap - len(cells)
+        if left:
+            idle[left] += 1
+global_profile = Counter({r: 72*n for r, n in profile.items()}) + idle
+assert sum(r*n for r, n in global_profile.items()) == 520704
+assert 73*7168 - sum(r*n for r, n in global_profile.items()) == 2560
+pid = 'gauge44'
+for c in plan['provider_calls']:
+    c['provider'] = pid
+    c['local_program_sha256'] = checks[c['orientation']]['sha256']
+for c in plan['per_call_widths']:
+    c['widths'] = widths
+artifacts = {name: sha(args.local / name) for name in FILES}
+identities = artifact_identities(args.local)
+plan['provider_registry'] = {pid: dict(
+    directory='providers/' + pid, artifact_sha256=artifacts,
+    ports=word['ports'], centers=word['centers'], widths=widths,
+    actual_paid_profile=word['local_profile'],
+    orientation_program_sha256={k: v['sha256'] for k, v in checks.items()},
+    artifact_semantic_sha256=identities)}
+plan.update(status='FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION',
+            mode='gauge44-all72', profile=dict(sorted(global_profile.items())),
+            solver_status='deterministic-capacity-matching', gap=None,
+            source_plan_sha256=sha(parent_path),
+            source_owners_sha256=sha(args.parent / 'data/OWNERS.json.gz'),
+            assignment_sha256=sha(args.owners))
+target_owners = args.data / 'OWNERS.json.gz'
+if args.owners.resolve() != target_owners.resolve():
+    shutil.copyfile(args.owners, target_owners)
+dump(args.data / 'PLAN.json', plan)
+spec = dict(schema='witness-spec/1', name='gauge44-all72',
+            data=dict(plan_sha256=sha(args.data / 'PLAN.json'), owners_sha256=sha(target_owners)),
+            dispatch=[[s, r, pid] for s in range(9) for r in range(8)],
+            call_order=plan['order'], width_spot_helpers=[264, 276, 288, 300],
+            providers={pid: {}}, expected=dict(gain_baseline_kappa='0.001636241501576388'))
+dump(args.data / 'SPEC.json', spec)
+dump(args.data / 'PREPARATION.json', dict(
+    status='PASS_EXPLICIT_MAP_AND_FRESH_PROVIDER_NOMINATION',
+    parent_plan_sha256=sha(parent_path), source_owners_sha256=sha(args.owners),
+    global_profile=dict(sorted(global_profile.items())), idle_profile=dict(sorted(idle.items())),
+    roles=len(owners), rank_mass=520704, deficit=2560,
+    remaining='Independent emitted-controller audit, fresh finite invoice, exact moments and outer assembly.'))
+print('Prepared all72 gauge44 candidate:', dict(sorted(global_profile.items())))
diff --git a/research/k8-x54-t37/code/restore_parent.py b/research/k8-x54-t37/code/restore_parent.py
new file mode 100644
index 0000000000..21135f898a
--- /dev/null
+++ b/research/k8-x54-t37/code/restore_parent.py
@@ -0,0 +1,67 @@
+"""Materialize the omitted generated PR558 parent, then require its reviewed hash.
+
+The integrated review contains the native inputs and INTEGRATION.json but
+omits GLOBAL-TEMPLATE.json.gz. This is only the deterministic template
+binding from the inherited prepare_supplier_base.py; no old circuit or
+phase calculation is rerun. The whole exact payload must match the review.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source',type=Path,required=True)
+ap.add_argument('--baseline',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+assert not a.out.exists()
+base=a.out/'complex-global/base'
+shutil.copytree(a.baseline/'complex-global/base',base)
+d=base/'split-centres'
+parent=a.source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz'
+old=read(parent);can=read(d/'CANONICAL-WORD.json.gz')
+checks=read(d/'LOCAL-CHECKS.json');programs=read(d/'LOCAL-PROGRAMS.json.gz')
+v,h,r=can['v'],can['h'],can['R'];c=len(can['centers']);m,t,l,k=73,8,9,4
+assert(v,h,r,c)==(112,9,504,8)
+widths=[h-len(can['frames'][f])for f in can['start'][2*v:]]
+data=2*k*t*v;live=data+l*r;physical=live+r+c+2
+word=copy.deepcopy(old)
+word.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=live,physical=physical,local_programs=programs)
+word['private_namespace']={'centers':[live,live+c],'reserved_tableau':[live+c,live+c+r],'coefficient':[physical-2,physical]}
+for call in word['calls']:
+ s,rep=call['stage'],call['replica'];owners=copy.deepcopy(call['owners'][:2*v])
+ for helper,w in enumerate(widths):
+  route=[2,rep]if w==9 else[2,rep*w,w,list(range(t*w,t*w+9-w))]
+  owners.append([data+s*r+helper,route])
+ call['owners']=owners;call['local_program_sha256']=checks[call['orientation']]['sha256']
+children=[]
+for s in range(l):
+ for helper,w in enumerate(widths):
+  axes=list(range(t*w,m))
+  children.append(dict(family=data+s*r+helper,rank=len(axes),axis_indices=axes,orthogonal_axes=[1<<j for j in axes]))
+word['bank_padding']={'families':list(range(data,live)),'children':children,
+ 'semantics':'Each listed complement frame is applied once after the eight disjoint residual blocks of that dedicated bank. The final hosted derivative has empty families and children.'}
+word['cover_final_correction'].update(families=[0,live],charged_calls_per_cover=live)
+for i,e in enumerate(word['execution_schedule']):
+ if e['kind']=='bank_padding_cover_sweep':word['execution_schedule'][i]={'kind':'bank_padding_cover_sweep','families':[data,live],'children_source':'bank_padding.children'}
+ elif e['kind']=='translate_every_live_family':e.update(word['cover_final_correction'])
+word['exact_data_phase_recipe_sha256']=sha(base/'work/complex-nine-native/DATA-PHASES.json')
+word['exact_local_clifford_recipe_sha256']=sha(d/'CLIFFORD-RECIPES.json')
+word['residual_adapter_sha256']=sha(d/'RESIDUAL-ADAPTERS.json')
+word['supplier_substitution']={'parent_template_sha256':sha(parent),
+ 'old_canonical_word_sha256':sha(a.baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz'),
+ 'new_canonical_word_sha256':sha(d/'CANONICAL-WORD.json.gz'),
+ 'exact_same_ports':True,'data_contract':'The same ordered 112 data ports and both complete-invocation identity-shear orientations feed the unchanged nine-stage controller. No old local program or helper profile is reused.'}
+word['route_semantics']['helper']='Dedicated family DATA+stage*R+helper; one helper per bank per complete invocation. Width-nine route[2,replica] uses axes9*replica..9*replica+8. Width-w entering route[2,w*replica,w,spectators] uses the disjoint residual block and paid normalization wrappers; spectator axes start at8*w, beyond all residual blocks.'
+raw=json.dumps(word,sort_keys=True,separators=(',',':')).encode()
+expected=read(d/'INTEGRATION.json')['global_template_sha256']
+assert hashlib.sha256(raw).hexdigest()==expected=='7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3'
+(d/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+print('PASS_EXACT_REVIEWED_PARENT_TEMPLATE_RESTORED',expected)
diff --git a/research/k8-x54-t37/code/witness.py b/research/k8-x54-t37/code/witness.py
new file mode 100644
index 0000000000..c5c7fbc114
--- /dev/null
+++ b/research/k8-x54-t37/code/witness.py
@@ -0,0 +1,55 @@
+"""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']]
+# width-8 spot helpers: PR558's helpers 270, 282, 294, 306, or their images under a K-triangle word's 504 -> R helper map
+# (verify.py checks the spec value against the constructor's HELPER-MAP.json)
+SPOT=tuple(SPEC.get('width_spot_helpers',(270,282,294,306)))
+# A pivot swap moves a kernel family's pivot role p -> x; the old pivot p becomes an ordinary cold helper and its width
+# goes 8 -> 9 (construction/layers, PR641 PROOF-NOTE-PIVOT). Expected spot widths are derived from the package's pinned
+# pivot-swap recipe (path and sha256 in the spec), not from free data: 9 at a swapped-out pivot, 8 otherwise.
+_PKG=Path(os.environ['WITNESS_SPEC']).resolve().parents[1]
+def _old_pivots():
+ ps=SPEC.get('pivot_swap')
+ if not ps:return frozenset()
+ raw=(_PKG/ps['recipe']).read_bytes();import hashlib
+ assert hashlib.sha256(raw).hexdigest()==ps['sha256'],'pivot-swap recipe pin'
+ return frozenset(s['pivot']for s in json.loads(raw)['swaps'])
+OLD_PIVOTS=_old_pivots()
+def spot_widths(v=112):
+ """Expected residual widths at the spot helpers (helper indices) of the gauge44 provider."""
+ return tuple(9 if 2*v+h in OLD_PIVOTS else 8 for h in SPOT)
+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:
+  if os.environ.get('WITNESS_RECORD'):   # discovery bookkeeping only: append (key, value) for the spec writer
+   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))
+  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/k8-x54-t37/construct.py b/research/k8-x54-t37/construct.py
new file mode 100644
index 0000000000..04e2a22e24
--- /dev/null
+++ b/research/k8-x54-t37/construct.py
@@ -0,0 +1,108 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Rebuild literal owners from the exact pattern-flow certificate."""
+import argparse,json,gzip,hashlib
+from collections import Counter,defaultdict
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--out',type=Path,required=True)
+args=parser.parse_args()
+if not __debug__:raise ValueError('Construction checks require assertions')
+if args.out.exists():raise ValueError('Choose a new construction directory')
+D=json.loads((HERE/'PATTERN-FLOW.json').read_text())
+assert D['T']==37 and D['order']==json.loads((HERE/'ORDER.json').read_text())
+S=json.loads((HERE/'inputs/SPEC.json').read_text())
+P=json.loads((HERE/'inputs/PLAN.json').read_text())
+widths=S['providers']['gauge44']['complete_contract']['widths'];ws=(4,5,7,8,9)
+xs={};ys=defaultdict(Counter)
+for entry,n in D['entries']:
+ assert type(n) is int and n>0
+ if entry[0]=='x':_,g,p=entry;xs[g,p]=n
+ else:_,g,p,t,w=entry;ys[g,p][t,w]+=n
+assign=defaultdict(list);global_count=Counter();idle=Counter();offsets=defaultdict(int)
+for gi,(r,cap,ts,children) in enumerate(D['groups']):
+ port_index=0
+ for pi,pat in enumerate(D['patterns'][str(cap)]):
+  N=xs.get((gi,pi),0)
+  if not N:continue
+  v=ys[gi,pi]
+  assert all(t in ts for t,w in v)
+  assert Counter({w:sum(n for (t,ww),n in v.items() if w==ww) for w,num in enumerate(pat) if num})==Counter({w:N*num for w,num in enumerate(pat) if num})
+  assert all(sum(n for (tt,w),n in v.items() if tt==t)<=N for t in ts)
+  slot_width=[w for w,n in enumerate(pat) for _ in range(n)]
+  graph=[Counter() for _ in slot_width]
+  # Split each width vertex into vertices of degree N.
+  for w in set(slot_width):
+   slots=[s for s,ww in enumerate(slot_width) if ww==w];j=0;used=0
+   for (t,ww),n in sorted(v.items()):
+    if ww!=w:continue
+    while n:
+     count=min(n,N-used);graph[slots[j]][t]+=count;used+=count;n-=count
+     if used==N:used=0;j+=1
+   assert j==len(slots) and used==0
+  assert all(sum(a.values())==N for a in graph)
+  for remaining in range(N,0,-1):
+   degree=Counter()
+   for adj in graph:degree.update(adj)
+   assert max(degree.values(),default=0)<=remaining
+   required=sorted(t for t,n in degree.items() if n==remaining)
+   st={};tt={}
+   def match_time(t,seen):
+    for s,adj in enumerate(graph):
+     if adj[t]==0 or s in seen:continue
+     seen.add(s)
+     if s not in st or match_time(st[s],seen):
+      st[s]=t;tt[t]=s;return True
+    return False
+   for t in required:assert match_time(t,set())
+   def match_slot(s,seen):
+    for t,n in sorted(graph[s].items()):
+     if not n or t in seen:continue
+     seen.add(t)
+     if t not in tt or match_slot(tt[t],seen):
+      tt[t]=s;st[s]=t;return True
+    return False
+   for s in range(len(graph)):
+    if s not in st:assert match_slot(s,set())
+   assert len(st)==len(tt)==len(graph) and all(t in tt for t in required)
+   child=children[port_index//112];port=port_index%112;port_index+=1
+   offset=0
+   for s,t in sorted(st.items(),key=lambda it:(it[1],it[0])):
+    w=ws[slot_width[s]];graph[s][t]-=1
+    assign[t,w].append((r,child,port,offset))
+    offset+=w;global_count[w]+=1
+   assert offset<=cap
+   idle[cap-offset]+=1
+  assert all(not any(adj.values()) for adj in graph)
+ assert port_index==112*len(children)
+roles=[]
+for t,(stage,replica) in enumerate(D['order']):
+ for h,w in enumerate(widths):
+  owner,child,port,offset=assign[t,w].pop()
+  family=896*owner+112*(2*P['pairs'][str(child)]+P['sides'][str(child)])+port
+  roles.append(dict(time=t,stage=stage,replica=replica,helper=h,width=w,owner_replica=owner,child=child,port=port,offset=offset,copy=112*owner+port,family=family))
+assert not any(assign.values());assert len(roles)==37*9*480
+print('literal roles',len(roles),'idle',dict(sorted(idle.items())))
+# Separate direct check from the aggregate model.
+used=defaultdict(set);seen=defaultdict(set);coverage=defaultdict(set)
+windows={(r,ch):(cap,set(ts)) for r,cap,ts,chs in D['groups'] for ch in chs}
+for z in roles:
+ t=z['time'];key=z['owner_replica'],z['child'];cap,ts=windows[key]
+ assert t in ts and z['family'] not in seen[t];seen[t].add(z['family'])
+ g=key+(z['port'],);cells=set(range(z['offset'],z['offset']+z['width']))
+ assert not cells&used[g] and all(0<=x<cap for x in cells);used[g]|=cells;coverage[t].add(z['helper'])
+for t,hh in coverage.items():assert hh==set(range(480))
+left=Counter()
+for key,(cap,ts) in windows.items():
+ for port in range(112):
+  cell=used[key+(port,)];assert cell==set(range(len(cell)));left[cap-len(cell)]+=1
+assert left==idle
+raw=json.dumps(roles,sort_keys=True,separators=(',',':')).encode()
+frozen=json.loads(gzip.decompress((HERE/'OWNERS.json.gz').read_bytes()))
+assert roles==frozen, 'Frozen owner map differs from exact decomposition'
+out=args.out;out.mkdir(parents=True)
+(out/'OWNERS.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+(out/'ORDER.json').write_text(json.dumps(D['order'])+'\n')
+(out/'GEOMETRY-CHECK.json').write_text(json.dumps({'roles':len(roles),'idle':dict(sorted(idle.items())),'owner_content_sha256':hashlib.sha256(raw).hexdigest(),'status':'PASS_LITERAL_WHOLE_HELPER_GEOMETRY'},indent=2)+'\n')
+print('PASS_LITERAL_WHOLE_HELPER_GEOMETRY',hashlib.sha256(raw).hexdigest())
diff --git a/research/k8-x54-t37/construction/x54/RECIPE-X54-k8.json b/research/k8-x54-t37/construction/x54/RECIPE-X54-k8.json
new file mode 100644
index 0000000000..c1f1e7fe16
--- /dev/null
+++ b/research/k8-x54-t37/construction/x54/RECIPE-X54-k8.json
@@ -0,0 +1,163 @@
+{
+ "base_sha256": "c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8",
+ "B_delete": [
+  44,
+  922,
+  933,
+  1196,
+  1212
+ ],
+ "B_insert": [
+  [
+   44,
+   [
+    "add",
+    219,
+    589,
+    -1,
+    1,
+    [
+     30
+    ]
+   ]
+  ],
+  [
+   898,
+   [
+    "add",
+    367,
+    589,
+    1,
+    1,
+    [
+     288,
+     166,
+     96,
+     20,
+     10,
+     1
+    ]
+   ]
+  ],
+  [
+   898,
+   [
+    "add",
+    335,
+    54,
+    1,
+    1,
+    [
+     267,
+     138,
+     75,
+     42,
+     25,
+     7
+    ]
+   ]
+  ],
+  [
+   1196,
+   [
+    "add",
+    219,
+    589,
+    1,
+    1,
+    [
+     256,
+     134,
+     64,
+     32,
+     20,
+     10,
+     1
+    ]
+   ]
+  ],
+  [
+   1212,
+   [
+    "add",
+    155,
+    54,
+    1,
+    1,
+    [
+     257,
+     128,
+     65,
+     32,
+     19,
+     10,
+     7
+    ]
+   ]
+  ]
+ ],
+ "B_frames": {},
+ "tail_insert": [
+  [
+   0,
+   [
+    "add",
+    367,
+    589,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ]
+ ],
+ "cleanup_prepend": [
+  [
+   "add",
+   335,
+   54,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ]
+ ],
+ "local_profile": {
+  "1": 2412,
+  "2": 418,
+  "3": 434,
+  "4": 138,
+  "5": 84,
+  "8": 8
+ },
+ "expect_sha256": "512452c0aa64e35c98c5af35d250f103e28e48d8404fdc25a6bb15113ebfb300",
+ "variants": [
+  {
+   "X": 54,
+   "E": 589,
+   "hold": [
+    335,
+    367
+   ]
+  }
+ ],
+ "source": "Eighth triangle-hybrid slot X54/E589 (holders 335, 367) from jeremykothe2 #1130 (RECIPE-X54-ends7.json), with identical edits and frames, rebased onto the seven-slot k8 word c2b29430 (no rank-seven ends).",
+ "note": "early-cleanup gate frames in cleanup are kept as in base (package T-frame convention)"
+}
\ No newline at end of file
diff --git a/research/k8-x54-t37/construction/x54/X54-PINS.json b/research/k8-x54-t37/construction/x54/X54-PINS.json
new file mode 100644
index 0000000000..0c8cf0ff51
--- /dev/null
+++ b/research/k8-x54-t37/construction/x54/X54-PINS.json
@@ -0,0 +1,30 @@
+{
+ "base_content_sha256": "c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8",
+ "word_content_sha256": "512452c0aa64e35c98c5af35d250f103e28e48d8404fdc25a6bb15113ebfb300",
+ "controls": [
+  "C0_identity",
+  "donation_after",
+  "donation_after@54",
+  "drop_preread",
+  "drop_preread@54",
+  "drop_restore",
+  "drop_restore@54",
+  "recipe",
+  "restore_full",
+  "restore_full@54"
+ ],
+ "canonical_sha256": "c1900aa7398e34916fe5b57553ca7d1cea6283143be6bb4ccf39321a84263a6c",
+ "program_sha256": {
+  "forward": "00a232a940f27da7842c9efa49e8eca3c7a399edde920b2c742006f8f4938dad",
+  "backward": "d93c027a832200728ff23f420042d43a9cb0016a41e995ee12538776ab3704b7"
+ },
+ "clifford_recipes_sha256": "7ed4c7e81ace3e7837067167745d2ca1bc3212079de284e76760c1c45b31d0ce",
+ "local_profile": {
+  "1": 2412,
+  "2": 418,
+  "3": 434,
+  "4": 138,
+  "5": 84,
+  "8": 8
+ }
+}
\ No newline at end of file
diff --git a/research/k8-x54-t37/construction/x54/build_x54.py b/research/k8-x54-t37/construction/x54/build_x54.py
new file mode 100644
index 0000000000..4dc5d99f5b
--- /dev/null
+++ b/research/k8-x54-t37/construction/x54/build_x54.py
@@ -0,0 +1,45 @@
+#!/usr/bin/env python3
+"""Rebuild the eight-slot k8 word (seven-slot k8 word + X54 slot) and its native locals.
+
+Input: the seven-slot k8 word (content c2b29430..., research/gauge44-slots RECIPE-SLOTS-k8.json on #1005's db2c7cfb).
+Steps (each checked): build_tri.py (NewBArch, unchanged) applies RECIPE-X54-k8.json (jeremykothe2's #1130 X54 recipe,
+identical edits and frames, rebased onto the seven-slot word); run_controls.py (10 outcomes); independent audit_local;
+PR635 native chain (native, ledgers, local-replay, wrappers, phases). Pins: X54-PINS.json.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+def csha(p): return hashlib.sha256(gzip.decompress(Path(p).read_bytes())).hexdigest()
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True); ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--seven-slot-word', type=Path, required=True); ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args(); out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    pins = json.loads((HERE/'X54-PINS.json').read_text()); rec = HERE/'RECIPE-X54-k8.json'
+    main = a.main.resolve(); src = main/'research/complex-k492-owner-repair/vendor/multicold'
+    up = a.pr635.resolve()/'research/complex-571-cold14-st2'; base = src/'vendor/pr558'; par = base/'vendor/pr552'
+    barch = main/'research/complex-t21-owners/vendor/pr870/construction/barch'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0', MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    def run(label, script, *args, portable=True):
+        cmd = [sys.executable, '-B'] + ([str(src/'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out/(label+'.log')).open('w') as f: rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        assert rc == 0, label; print('PASS', label, flush=True)
+    assert csha(a.seven_slot_word) == pins['base_content_sha256'], 'seven-slot base word'
+    word = out/'FULL-WORD.json.gz'
+    run('x54', barch/'build_tri.py', a.seven_slot_word, rec, word, portable=False)
+    assert csha(word) == pins['word_content_sha256']
+    run('x54-controls', barch/'run_controls.py', a.seven_slot_word, rec, main/'research/complex-t21-owners/vendor/pr870/independent/audit_local.py', out/'controls', portable=False)
+    res = json.loads((out/'controls/controls.json').read_text()); assert sorted(res) == sorted(pins['controls']) and all(x['ok'] for x in res.values())
+    run('audit-local', main/'research/complex-t21-owners/vendor/pr870/independent/audit_local.py', '--word', word, '--main', main, '--output', out/'AUDIT-LOCAL.json', portable=False)
+    local = out/'local'; routing = par/'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    run('native', up/'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert csha(local/'CANONICAL-WORD.json.gz') == pins['canonical_sha256']
+    run('ledgers', up/'code/hpe_emit_local.py', local)
+    run('local-replay', up/'code/hpe_audit_local.py', local)
+    run('wrappers', up/'code/hpe_adapters_local.py', local/'CANONICAL-WORD.json.gz', local/'RESIDUAL-ADAPTERS.json', local/'WRAPPER-CHECKS.json')
+    checks = json.loads((local/'LOCAL-CHECKS.json').read_text())
+    assert {o: checks[o]['sha256'] for o in ('forward', 'backward')} == pins['program_sha256']
+    run('phases', base/'code/phases_full.py', local, par/'complex-global/vendor531/vendor/clifford')
+    assert hashlib.sha256((local/'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256']
+    print('DONE', local, flush=True)
+if __name__ == '__main__': main()
diff --git a/research/k8-x54-t37/controls.py b/research/k8-x54-t37/controls.py
new file mode 100644
index 0000000000..e89ac44128
--- /dev/null
+++ b/research/k8-x54-t37/controls.py
@@ -0,0 +1,71 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Run certificate controls through the public command-line checker."""
+import argparse
+import copy
+import json
+from pathlib import Path
+import subprocess
+import sys
+import tempfile
+
+HERE = Path(__file__).resolve().parent
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    if args.out.exists():
+        raise ValueError('Choose a new output file')
+    certificate = json.loads((HERE / 'CERTIFICATE.json').read_text())
+    cases = [
+        ('boolean_width_price', lambda d: d['width_prices'].__setitem__('4', True), 'integer width prices'),
+        ('float_width_price', lambda d: d['width_prices'].__setitem__('4', -1.0), 'integer width prices'),
+        ('boolean_capacity_bonus', lambda d: d['capacity_bonuses'].__setitem__('8', True), 'integer capacity bonuses'),
+        ('float_capacity_bonus', lambda d: d['capacity_bonuses'].__setitem__('8', 2.0), 'integer capacity bonuses'),
+        ('boolean_row_capacity', lambda d: d['packing'][0].__setitem__('capacity', True), 'integer packing capacity'),
+        ('float_row_capacity', lambda d: d['packing'][0].__setitem__('capacity', 8.0), 'integer packing capacity'),
+        ('boolean_bin_count', lambda d: d['packing'][0].__setitem__('bins', True), 'positive packing multiplicity'),
+        ('float_width_count', lambda d: d['packing'][0]['width_counts'].__setitem__(3, 1.0), 'integer packing vector'),
+        ('missing_bin', lambda d: d['packing'][0].__setitem__('bins', 24863), 'complete bin stock'),
+        ('missing_width_four', lambda d: d['packing'][3]['width_counts'].__setitem__(0, 1), 'complete helper inventory'),
+        ('nonintegral_replica_count', lambda d: d.__setitem__('replicas', 16), 'integral residual counts'),
+        ('negative_bin_count', lambda d: d['packing'][0].__setitem__('bins', -1), 'positive packing multiplicity'),
+        ('false_zero_price', lambda d: d['capacity_bonuses'].__setitem__('8', 3), 'zero and maximum residual'),
+        ('wrong_root_interval', lambda d: d.__setitem__('root_interval', ['0.001676945247549584231286', '0.001676945247549584231287']), 'two exact root signs: lower'),
+        ('next_outer_grid', lambda d: d.__setitem__('kappa_grid', '0.001674137810105186'), 'same outer grid cell'),
+        ('float_root', lambda d: d['root_interval'].__setitem__(0, 0.0016769452475495842), 'rational root strings'),
+    ]
+    outcomes = []
+    with tempfile.TemporaryDirectory(prefix='r480-owner-controls-') as tmp:
+        directory = Path(tmp)
+        for name, change, reason in cases:
+            mutated = copy.deepcopy(certificate)
+            change(mutated)
+            path, result = directory / (name+'.json'), directory / (name+'-output.json')
+            path.write_text(json.dumps(mutated)+'\n')
+            command = [sys.executable, '-B', str(HERE / 'verify.py'), '--certificate', str(path), '--out', str(result)]
+            process = subprocess.run(command, capture_output=True, text=True)
+            if process.returncode == 0 or ('ValueError: '+reason) not in process.stderr or result.exists():
+                raise ValueError('Wrong rejection for '+name+': '+process.stdout+process.stderr)
+            outcomes.append(dict(name=name, rejected_by=reason, output_created=False))
+        old = directory / 'retained.json'
+        old.write_text('retain exact bytes\n')
+        command = [sys.executable, '-B', str(HERE / 'verify.py'), '--out', str(old)]
+        process = subprocess.run(command, capture_output=True, text=True)
+        if process.returncode == 0 or old.read_text() != 'retain exact bytes\n':
+            raise ValueError('Output preservation control failed')
+        outcomes.append(dict(name='output_preservation', rejected_by='Choose a new output file', retained_bytes=True))
+        optimized = directory / 'optimized.json'
+        process = subprocess.run([sys.executable, '-O', '-B', str(HERE / 'verify.py'), '--out', str(optimized)], capture_output=True, text=True)
+        if process.returncode == 0 or 'Retained outer assertions require Python without -O' not in process.stderr or optimized.exists():
+            raise ValueError('Optimization guard failed')
+        outcomes.append(dict(name='optimization_guard', rejected_by='Retained outer assertions require Python without -O'))
+    result = dict(status='PASS_R480_OWNER_CERTIFICATE_CONTROLS', count=len(outcomes), cases=outcomes)
+    args.out.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], 'cases='+str(result['count']))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/k8-x54-t37/data/PLAN.json b/research/k8-x54-t37/data/PLAN.json
new file mode 100644
index 0000000000..f33e648fc5
--- /dev/null
+++ b/research/k8-x54-t37/data/PLAN.json
@@ -0,0 +1,233067 @@
+{
+  "status": "FROZEN_EXPLICIT_R480_T37_OWNER_NOMINATION",
+  "mode": "seven-slot-k8-all-replica-optimum",
+  "K": 4,
+  "T": 37,
+  "M": 73,
+  "L": 9,
+  "live": 33152,
+  "deficit": 11840,
+  "profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 144522,
+    "4": 45954,
+    "5": 27972,
+    "8": 2664,
+    "48": 11302
+  },
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diff --git a/research/k8-x54-t37/data/SPEC.json b/research/k8-x54-t37/data/SPEC.json
new file mode 100644
index 0000000000..15c3572aa9
--- /dev/null
+++ b/research/k8-x54-t37/data/SPEC.json
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+          "prefix_l1": "14824960514781440791821/64",
+          "coefficient_work_primitive_count": 98373
+        }
+      },
+      "wrappers": 240
+    }
+  },
+  "expected": {
+    "gain_baseline_kappa": "0.001636241501576388",
+    "hosted_residuals": 159840,
+    "rank_mass": 2408256,
+    "actual_73column_sigmas": 11150,
+    "cross_replica_helper_roles": 151156,
+    "idle_remainders": 16924,
+    "idle_remainder_profile": {
+      "1": 5622,
+      "48": 11302
+    },
+    "global_profile": {
+      "1": 808818,
+      "2": 139194,
+      "3": 144522,
+      "4": 45954,
+      "5": 27972,
+      "8": 2664,
+      "48": 11302
+    },
+    "live": 33152,
+    "physical": 33642,
+    "conservative_kappa_decimal": "0.001674137807251909",
+    "kappa_decimal": "0.001674137810105185",
+    "complex_lower": "335389049509916846257/200000000000000000000000",
+    "conservative_complex_lower": "67077809787469242059/40000000000000000000000",
+    "kappa": "334827562021037/200000000000000000",
+    "assembly_controls_rejected": 69,
+    "provider_counts": {
+      "gauge44": 333
+    },
+    "mutations_rejected": 15
+  },
+  "pivot_swap": {
+    "recipe": "construction/leaver/PIVOT-SWAP-k8.json",
+    "sha256": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb"
+  }
+}
diff --git a/research/k8-x54-t37/evidence/ADMISSION-CONTROLS.json b/research/k8-x54-t37/evidence/ADMISSION-CONTROLS.json
new file mode 100644
index 0000000000..3e1de0e531
--- /dev/null
+++ b/research/k8-x54-t37/evidence/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "167409796990539/100000000000000000",
+  "input_sha256": {
+    "owner_audit": "ed4074eafe47ffd95a272436e3d4f654e4066dc57d12e77cf4be62e970f6c671",
+    "fresh_invoice": "a56e07538d1fff4af1d172ce81f0bf1d6b6ae3e4f1bd3401d3c2c530f641ba6b",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_258",
+    "gauge44:cold_helper_width_swap_270",
+    "gauge44:cold_helper_width_swap_282",
+    "gauge44:cold_helper_width_swap_294",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "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."
+}
diff --git a/research/k8-x54-t37/evidence/ASSEMBLY.json b/research/k8-x54-t37/evidence/ASSEMBLY.json
new file mode 100644
index 0000000000..0e696d96ee
--- /dev/null
+++ b/research/k8-x54-t37/evidence/ASSEMBLY.json
@@ -0,0 +1,344 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "167409796990539/100000000000000000",
+  "kappa_decimal": "0.00167409796990539",
+  "complex_lower": "16769052736196808613/10000000000000000000000",
+  "complex_decimal": "0.0016769052736196808613",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "gain_over_pr635_percent": "2.313623526388391711421361679688421607983496591569222376409213845570493",
+  "complex_profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664,
+    "48": 11302
+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  },
+  "conservative_complex_lower": "1676905270756896217493/1000000000000000000000000",
+  "conservative_complex_decimal": "0.001676905270756896217493",
+  "conservative_kappa": "1674097967052183/1000000000000000000",
+  "conservative_kappa_decimal": "0.001674097967052183",
+  "conservative_moments": [
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "1676905270756896217493/1000000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-9016630032146056312229461271793500241892699/6739986666787659948666753771754907668409286105635143120275902562304",
+        "-18033260064292112624458922543587000483785397/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "-13377816215429592073693/10000000000000000000000000000000000000000000000",
+        "-13377806215429592073551/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "838452635378448108747/500000000000000000000000",
+      "accept": false,
+      "mercator": [
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+        "42829816297972688627190483264457374488549991/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
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+        "3971615946232462784957/2500000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
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+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Conditional R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain."
+}
diff --git a/research/k8-x54-t37/evidence/AXIS-CLI-CONTROL.json b/research/k8-x54-t37/evidence/AXIS-CLI-CONTROL.json
new file mode 100644
index 0000000000..4d667945ea
--- /dev/null
+++ b/research/k8-x54-t37/evidence/AXIS-CLI-CONTROL.json
@@ -0,0 +1,25 @@
+{
+  "command": [
+    "/opt/homebrew/opt/python@3.14/bin/python3.14",
+    "-B",
+    "/tmp/k9-owner-package/independent_owner.py",
+    "--baseline-parent",
+    "/tmp/k9-owner-strict1/replay/global8/base/split-centres/GLOBAL-TEMPLATE.json.gz",
+    "--owners",
+    "/tmp/k9-owner-package/OWNERS.json.gz",
+    "--word",
+    "/tmp/k9-owner-package/inputs/local/CANONICAL-WORD.json.gz",
+    "--out",
+    "/tmp/k9-owner-bad-phase-result.json",
+    "--replicas",
+    "37",
+    "--expected-idle",
+    "{\"1\":5622,\"48\":11302}",
+    "--phases",
+    "/tmp/k9-owner-bad-phases.json"
+  ],
+  "exit_code": 1,
+  "reason": "overlapping pending children on one family",
+  "output_created": false,
+  "status": "PASS_ACTUAL_CLI_PENDING_AXIS_REJECTION"
+}
diff --git a/research/k8-x54-t37/evidence/BIT-CONTROLS.json b/research/k8-x54-t37/evidence/BIT-CONTROLS.json
new file mode 100644
index 0000000000..42f029308f
--- /dev/null
+++ b/research/k8-x54-t37/evidence/BIT-CONTROLS.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS",
+  "kappa": "0.00167409796990539",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "derived_deficit": 10272,
+  "rejected_controls": [
+    "revert_hardcoded_9984",
+    "ports_112",
+    "decoder_constant_64_copy_ranks_unchanged",
+    "decoder_constant_64_with_one_copy_rank_8",
+    "eight_retained_totals",
+    "live_minus_one",
+    "profile_rank_mass_plus_one",
+    "profile_rank_mass_receipt_mismatch",
+    "bit_lower_next_grid",
+    "not_nine_stage_record",
+    "tampered_bytes_next_grid",
+    "pr543_file_under_pr589_pin"
+  ],
+  "assembler_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a"
+}
diff --git a/research/k8-x54-t37/evidence/BOUND-CONTROLS.json b/research/k8-x54-t37/evidence/BOUND-CONTROLS.json
new file mode 100644
index 0000000000..d9d490bb71
--- /dev/null
+++ b/research/k8-x54-t37/evidence/BOUND-CONTROLS.json
@@ -0,0 +1,95 @@
+{
+  "status": "PASS_R480_OWNER_CERTIFICATE_CONTROLS",
+  "count": 18,
+  "cases": [
+    {
+      "name": "boolean_width_price",
+      "rejected_by": "integer width prices",
+      "output_created": false
+    },
+    {
+      "name": "float_width_price",
+      "rejected_by": "integer width prices",
+      "output_created": false
+    },
+    {
+      "name": "boolean_capacity_bonus",
+      "rejected_by": "integer capacity bonuses",
+      "output_created": false
+    },
+    {
+      "name": "float_capacity_bonus",
+      "rejected_by": "integer capacity bonuses",
+      "output_created": false
+    },
+    {
+      "name": "boolean_row_capacity",
+      "rejected_by": "integer packing capacity",
+      "output_created": false
+    },
+    {
+      "name": "float_row_capacity",
+      "rejected_by": "integer packing capacity",
+      "output_created": false
+    },
+    {
+      "name": "boolean_bin_count",
+      "rejected_by": "positive packing multiplicity",
+      "output_created": false
+    },
+    {
+      "name": "float_width_count",
+      "rejected_by": "integer packing vector",
+      "output_created": false
+    },
+    {
+      "name": "missing_bin",
+      "rejected_by": "complete bin stock",
+      "output_created": false
+    },
+    {
+      "name": "missing_width_four",
+      "rejected_by": "complete helper inventory",
+      "output_created": false
+    },
+    {
+      "name": "nonintegral_replica_count",
+      "rejected_by": "integral residual counts",
+      "output_created": false
+    },
+    {
+      "name": "negative_bin_count",
+      "rejected_by": "positive packing multiplicity",
+      "output_created": false
+    },
+    {
+      "name": "false_zero_price",
+      "rejected_by": "zero and maximum residual",
+      "output_created": false
+    },
+    {
+      "name": "wrong_root_interval",
+      "rejected_by": "two exact root signs: lower",
+      "output_created": false
+    },
+    {
+      "name": "next_outer_grid",
+      "rejected_by": "same outer grid cell",
+      "output_created": false
+    },
+    {
+      "name": "float_root",
+      "rejected_by": "rational root strings",
+      "output_created": false
+    },
+    {
+      "name": "output_preservation",
+      "rejected_by": "Choose a new output file",
+      "retained_bytes": true
+    },
+    {
+      "name": "optimization_guard",
+      "rejected_by": "Retained outer assertions require Python without -O"
+    }
+  ]
+}
diff --git a/research/k8-x54-t37/evidence/BOUND.json b/research/k8-x54-t37/evidence/BOUND.json
new file mode 100644
index 0000000000..5b7fb9d029
--- /dev/null
+++ b/research/k8-x54-t37/evidence/BOUND.json
@@ -0,0 +1,302 @@
+{
+  "status": "PASS_R480_ALL_REPLICA_BIN_OPTIMUM",
+  "scope": "Exact owner bin relaxation. Time windows, per-call family matching, charts, local admission and finite invoices are separate.",
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "source_head": "052afc128954f7b6a2b3c409eb4d72248e4020f2",
+  "inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 432,
+    "4": 142,
+    "5": 82,
+    "8": 8
+  },
+  "capacity_stock": {
+    "16": 448,
+    "8": 672,
+    "32": 448,
+    "48": 448
+  },
+  "bin_patterns": 1163,
+  "upper_price_by_residual": {
+    "8": 2,
+    "0": 0,
+    "1": 19,
+    "3": 7,
+    "4": 1,
+    "16": 4,
+    "7": 8,
+    "9": -4,
+    "2": 13,
+    "11": 9,
+    "6": 14,
+    "12": 3,
+    "5": 20,
+    "32": 8,
+    "23": 12,
+    "14": 16,
+    "24": 6,
+    "15": 10,
+    "25": 0,
+    "17": -2,
+    "18": -8,
+    "10": 15,
+    "27": -12,
+    "19": 11,
+    "20": 5,
+    "13": -3,
+    "22": -7,
+    "28": 7,
+    "21": -1,
+    "48": -13,
+    "39": -9,
+    "30": -5,
+    "40": -15,
+    "31": -11,
+    "41": -21,
+    "33": -23,
+    "34": -29,
+    "26": -6,
+    "43": -33,
+    "35": -10,
+    "36": -16,
+    "29": -24,
+    "38": -53,
+    "44": -14,
+    "37": -22
+  },
+  "idle_mass_per_replica": 14814,
+  "signed_price_per_replica": -1084,
+  "credit_per_replica": 140550,
+  "rank_one_credit": 925,
+  "normalized_idle": {
+    "1": "5622/37",
+    "48": "11302/37"
+  },
+  "minimum_equality_replicas": 37,
+  "packing_replicas": 37,
+  "packing_idle": {
+    "1": 5622,
+    "48": 11302
+  },
+  "profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664,
+    "48": 11302
+  },
+  "live": 33152,
+  "deficit": 11840,
+  "root_interval": [
+    "16769052736196808613/10000000000000000000000",
+    "1676905273619680861301/1000000000000000000000000"
+  ],
+  "two_engine_signs": {
+    "lower": {
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+      ],
+      "atanh": [
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+        "-1299429/1000000000000000000000000000000"
+      ]
+    },
+    "upper": {
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+        "43863783899943171831995157596908580818041755/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "atanh": [
+        "813499/500000000000000000000000000000",
+        "1626999/1000000000000000000000000000000"
+      ]
+    }
+  },
+  "support_over_root_interval": {
+    "mercator": {
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+  "headroom_over_pr1074": "289350197273/200000000000000000",
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+    "research/complex-t21-owner-bound/PROOF.md": "2aa0aa6ec1d87402138564c38749b5ca0f058c16817efdf58a2685d2d90cb417",
+    "package:inputs/SPEC.json": "7f5f710df21fe48079b4c79727953ff41cd8bec688592578554109ebf6b6d929",
+    "package:inputs/PLAN.json": "68c110602df12bd7de3749514224021ef1ef0ebcf072d7c727f9b66099fbebb1",
+    "package:inputs/RESULT.json": "ebf3577df9efccc213998a6cf43f25fb3cd1a26893847b68d60d276e3b76440c",
+    "research/complex-t21-owners/independent_check.py": "9d8c86bf45cdaef37f223c88704055ced503ee295645611e13f3fb9059a00e55",
+    "research/complex-t37-owners/ORDER.json": "2093ca4050e1ce95621f4702bebe8b01b36773b1ecfa2c0d6275e132bd33d578"
+  }
+}
diff --git a/research/k8-x54-t37/evidence/CONSTRUCTION.json b/research/k8-x54-t37/evidence/CONSTRUCTION.json
new file mode 100644
index 0000000000..a4f3de140d
--- /dev/null
+++ b/research/k8-x54-t37/evidence/CONSTRUCTION.json
@@ -0,0 +1,10 @@
+{
+  "roles": 159840,
+  "idle": {
+    "0": 57668,
+    "1": 5622,
+    "48": 11302
+  },
+  "owner_content_sha256": "592dd6d5c3dc29a33472f75425f9652c73993a8e38bdc17c7372b321aaeefa03",
+  "status": "PASS_LITERAL_WHOLE_HELPER_GEOMETRY"
+}
diff --git a/research/k8-x54-t37/evidence/CONTROLLER-AUDIT.json b/research/k8-x54-t37/evidence/CONTROLLER-AUDIT.json
new file mode 100644
index 0000000000..6145d9aa5d
--- /dev/null
+++ b/research/k8-x54-t37/evidence/CONTROLLER-AUDIT.json
@@ -0,0 +1,74 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "aac9224bbdf8f198c7873c0b2042caee9043ffae594f0a1835896d5ed43920f4",
+  "complex_template_sha256": "aac9224bbdf8f198c7873c0b2042caee9043ffae594f0a1835896d5ed43920f4",
+  "complex_live": 33152,
+  "complex_profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664,
+    "48": 11302
+  },
+  "complex_hosted_residuals": 159840,
+  "physical": 33642,
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "entering_helper_roles": 79920,
+  "cross_replica_helper_roles": 151156,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 159840,
+  "complete_invocations": 333,
+  "actual_orthogonal_73column_maps": 11150,
+  "actual_sigma_stream_sha256": "1e243d977e2e67af21554555dbc0dee5a92e8745a5361c7df3e007f5a963af33",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 16924,
+  "mutations_rejected": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong provider width registry",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "mutation_controls_run": true,
+  "provider_phase_semantic_sha256": {
+    "gauge44": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+      "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3",
+      "LOCAL-CHECKS.json": "18f09b79835aa352f04d27041d86d1338c5ad0094b888588c1c05af2dc399ffd",
+      "INDEPENDENT-LOCAL-REPLAY.json": "2d4680965c62db1fde1236c4857b19bf7bc97af58805e6b4109afbc452f0fdd8",
+      "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+      "CLIFFORD-REVIEW.json": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+      "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+    }
+  },
+  "widths_by_provider": {
+    "gauge44": {
+      "4": 56,
+      "5": 32,
+      "7": 30,
+      "8": 122,
+      "9": 240
+    }
+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "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."
+}
diff --git a/research/k8-x54-t37/evidence/INDEPENDENT-OWNER.json b/research/k8-x54-t37/evidence/INDEPENDENT-OWNER.json
new file mode 100644
index 0000000000..19bb5f3f4b
--- /dev/null
+++ b/research/k8-x54-t37/evidence/INDEPENDENT-OWNER.json
@@ -0,0 +1,119 @@
+{
+  "status": "PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW",
+  "roles": 159840,
+  "calls": 333,
+  "source_events_per_replica": 30,
+  "expanded_replica_events": 1110,
+  "bridge_events": 333,
+  "literal_windows": 666,
+  "checked_whole_helper_widths": 159840,
+  "checked_busy_family_windows": 159840,
+  "orthogonal_port_bases": 112,
+  "actual_73_axis_charts": 11150,
+  "checked_slice_prefixes": 74592,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 432,
+    "4": 142,
+    "5": 82,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "idle": {
+    "1": 5622,
+    "48": 11302
+  },
+  "profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664,
+    "48": 11302
+  },
+  "live": 33152,
+  "physical": 33642,
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "namespace": {
+    "data": [
+      0,
+      33152
+    ],
+    "centres": [
+      33152,
+      33160
+    ],
+    "tableau": [
+      33160,
+      33640
+    ],
+    "coefficient": [
+      33640,
+      33642
+    ]
+  },
+  "local_prefix_bits": 68,
+  "local_prefix_from_native_receipt": true,
+  "local_profile_recounted": true,
+  "prefix_formula": {
+    "local_scalar": 68,
+    "input_l2": 37,
+    "invocations": 333,
+    "bridges": 333,
+    "margin": 4
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+  "prefix_bits": 775,
+  "charged_prefix_bits": 1024,
+  "physical_stock_bits": 2643,
+  "physical_row_coefficient": 17495,
+  "row_limit": 20161,
+  "scope": "Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.",
+  "disjoint_pending_child_axis_checks": 2016,
+  "controls_rejected": [
+    {
+      "name": "private_namespace_collision",
+      "reason": "private-namespace collision"
+    },
+    {
+      "name": "copy_replica_alias",
+      "reason": "role invocation time"
+    },
+    {
+      "name": "missing_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "split_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "truncated_helper_width",
+      "reason": "whole-helper residual width"
+    },
+    {
+      "name": "cross_idle_boundary",
+      "reason": "strict bridge-aware idle window"
+    },
+    {
+      "name": "cross_child_pending_axis_alias",
+      "reason": "overlapping pending children on one family"
+    }
+  ],
+  "input_sha256": {
+    "/private/tmp/k9-owner-parent-check/replay/global8/base/split-centres/GLOBAL-TEMPLATE.json.gz": "ab8448de2036a23d9b55a196a8846512dc24fdf09855c1e0f0caa5b7a6965f7b",
+    "/private/tmp/k9-owner-parent-check/replay/global8/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "/private/tmp/k9-owner-parent-check/replay/global8/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "/Users/aliromman/.codex/worktrees/kappa9-lane03/IntegerMultiplicationBounds/research/r480-owner-optimum/inputs/local/CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+    "/Users/aliromman/.codex/worktrees/kappa9-lane03/IntegerMultiplicationBounds/research/r480-owner-optimum/inputs/local/INDEPENDENT-LOCAL-REPLAY.json": "13dd18297162569532983db1a2ab67926b064330cd7edd3587e7b546b2dedf17",
+    "/Users/aliromman/.codex/worktrees/kappa9-lane03/IntegerMultiplicationBounds/research/r480-owner-optimum/OWNERS.json.gz": "c35ac0c6f77c6b7cb32bee953770de3ef8a575aef36efc4764e0bb3325a04737"
+  }
+}
diff --git a/research/k8-x54-t37/evidence/OVERLAP.json b/research/k8-x54-t37/evidence/OVERLAP.json
new file mode 100644
index 0000000000..50f5ad8cab
--- /dev/null
+++ b/research/k8-x54-t37/evidence/OVERLAP.json
@@ -0,0 +1,43 @@
+{
+  "at_utc": "2026-10-13T18:41:00Z",
+  "scope": "Exact heads read before local handoff. Reported PR values are comparisons, not an independent admission of those PRs.",
+  "selected_main": {
+    "commit": "ba82555c64e1879e4b7decce28186f208fcb8262",
+    "selected_pr": 1042,
+    "kappa": "0.001672188119205421"
+  },
+  "same_word": [
+    {
+      "pr": 1082,
+      "head": "0c2e294ec204e83846d27344f829d15ed9ee7cc6",
+      "kappa": "0.001672653061493085"
+    },
+    {
+      "pr": 1094,
+      "head": "0fc329d0bec93ca7cd288eaea1295172e8789810",
+      "kappa": "0.001672660197076918"
+    }
+  ],
+  "changed_word": [
+    {
+      "pr": 1107,
+      "head": "6123fc5d57db16aaa3e8a26b4a11a34b46c0c391",
+      "kappa": "0.001672765980186726"
+    },
+    {
+      "pr": 1117,
+      "head": "342b67f23dfa8f41a520a0d58978b2875e9eb0dd",
+      "kappa": "0.001672846995880185"
+    },
+    {
+      "pr": 1121,
+      "head": "61e816c29165a94f6cfc57d9e195063a5b027bc2",
+      "kappa": "0.001672965558289236"
+    }
+  ],
+  "independent_audit": {
+    "pr": 1091,
+    "head": "b4c13a228acb80f74c682b7097f0ce9bbf51bc4e"
+  },
+  "distinct_contribution": "All positive replica counts for the fixed R480 seven-slot k8 inventory; exact integral T37 attainment, actual windows/charts and full finite admission. Changed-word PRs are outside the theorem."
+}
diff --git a/research/k8-x54-t37/evidence/PREFIX-AND-INVOICE.json b/research/k8-x54-t37/evidence/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..1d68c15e2f
--- /dev/null
+++ b/research/k8-x54-t37/evidence/PREFIX-AND-INVOICE.json
@@ -0,0 +1,5649 @@
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+      "provider_id": "gauge44",
+      "orientation": "forward",
+      "program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8",
+      "events": 24767,
+      "macros": 19693,
+      "real_component_primitives": 198766,
+      "coefficient_work_primitive_count": 98333,
+      "entering_helpers": 192,
+      "entrance_rank": 384,
+      "pre_wrappers": 240,
+      "post_wrappers": 240
+    }
+  ],
+  "selected_local_paid_profile": {
+    "1": 803196,
+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664
+  },
+  "selected_real_component_primitives": 66196182,
+  "selected_coefficient_work_primitive_count": 32749625,
+  "selected_scalar_macros": 6557769,
+  "global_prefix_bits": 775,
+  "charged_prefix_bits": 1024,
+  "complete_invocation_sweeps": 333,
+  "bridge_sweeps": 333,
+  "row_prefix_extra": 2048,
+  "helpers": 480,
+  "centres": 8,
+  "live": 33152,
+  "physical": 33642,
+  "physical_stock_identity": {
+    "data_and_owner_families": 33152,
+    "local_helpers": 480,
+    "private_centres": 8,
+    "coefficient_work": 2
+  },
+  "local_adapters": 387056,
+  "local_primitive_bound": 10038040553630,
+  "wrapper_elementary_factors_charged": 23016960,
+  "factors_per_wrapper": 144,
+  "compiler": 25934336,
+  "unhosted_pervertex": 8300227458717966,
+  "hosted_rebased_pervertex": 8300227457219526,
+  "conservative_pervertex_used": 11178174448442534,
+  "retained_prior_overcharge": {
+    "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+    "previous_pervertex_allowance": 2877946989724568,
+    "added_complete_new_pervertex": 8300227458717966,
+    "policy": "Retain old allowance and add entire fresh mixed recount."
+  },
+  "finite": {
+    "physical_stock_bits": 2643,
+    "router_bits": 7991,
+    "literal_bits": 35286,
+    "physical_row_coefficient": 17495,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. The fixed provider uses 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."
+}
diff --git a/research/k8-x54-t37/evidence/STRICT-REPLAY.json b/research/k8-x54-t37/evidence/STRICT-REPLAY.json
new file mode 100644
index 0000000000..dcdf30a995
--- /dev/null
+++ b/research/k8-x54-t37/evidence/STRICT-REPLAY.json
@@ -0,0 +1,91 @@
+{
+  "status": "PASS_R480_T37_STRICT_FINITE_CONSTRUCTION",
+  "kappa": "167409796990539/100000000000000000",
+  "kappa_decimal": "0.00167409796990539",
+  "roles": 159840,
+  "calls": 333,
+  "prefix_bits": 775,
+  "charged_prefix_bits": 1024,
+  "physical_row_coefficient": 17495,
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 1.718,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind8",
+      "seconds": 0.408,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "lift",
+      "seconds": 4.799,
+      "exit_code": 0,
+      "log_sha256": "c8f864806d6a40d8899bcf4e4f94d8914bc1e7d67b77b30af71e38c9784c6e36"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.614,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 18.002,
+      "exit_code": 0,
+      "log_sha256": "62dd713211fe1fb69d0b36a8c350a41a12f23139dc53a09ec1ca6e95a96adcc4"
+    },
+    {
+      "name": "audit",
+      "seconds": 54.656,
+      "exit_code": 0,
+      "log_sha256": "50cb933ed29b9d894ada2f8343b16b8e3fc6ee676e1e4414a0c8f47a4f308f32"
+    },
+    {
+      "name": "invoice",
+      "seconds": 2.028,
+      "exit_code": 0,
+      "log_sha256": "7a24483ea6432bc7616837eba11ae00c0ecffa307a98aff58237db8b0c443188"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.519,
+      "exit_code": 0,
+      "log_sha256": "7032142fbd0dd614840f381755a7e2dcf39933c10a5ab68c836e432f39ce6ad7"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.775,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    },
+    {
+      "name": "bit-controls",
+      "seconds": 1.065,
+      "exit_code": 0,
+      "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+    },
+    {
+      "name": "independent-owner",
+      "seconds": 2.724,
+      "exit_code": 0,
+      "log_sha256": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e"
+    }
+  ],
+  "local_input_sha256": {
+    "CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+    "RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c",
+    "LOCAL-PROGRAMS.json.gz": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+    "LOCAL-CHECKS.json": "2b8b1891a736598010232bfb26abc31973b265a53a2009a3fcfd9138b5ecadb4",
+    "CLIFFORD-REVIEW.json": "dd57b86b730923b19f64e5d09d8885149366db636607dcd5e2acf9a56d11e72b",
+    "INDEPENDENT-LOCAL-REPLAY.json": "13dd18297162569532983db1a2ab67926b064330cd7edd3587e7b546b2dedf17",
+    "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+    "FULL-WORD.json.gz": "49596aa4ed4fd36cd4582fd0e8ddeb09fd80370a7d8aea1ede52a135b536d289",
+    "SCALAR-FRAME-AUDIT.json": "2861f75f7667b10ed7235ab4d932da4797f7e7e4a26d4bc467110114bab77eec",
+    "WRAPPER-CHECKS.json": "0ae753d6fa6e922d8b8180da602828f6cb3f444fcd124d019acee74e145c0836"
+  },
+  "scope": "Finite owner, controller, chart, invoice and assembly replay. Local scalar and phase replay and inherited all-size obligations are recorded separately."
+}
diff --git a/research/k8-x54-t37/evidence/VALIDATION.json b/research/k8-x54-t37/evidence/VALIDATION.json
new file mode 100644
index 0000000000..3cc9897aea
--- /dev/null
+++ b/research/k8-x54-t37/evidence/VALIDATION.json
@@ -0,0 +1,48 @@
+{
+  "status": "PASS_FOCUSED_FINITE_AND_EXACT_BOUND_CHECKS",
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "python": "3.14.7 (main, Aug  5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]",
+  "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O",
+  "one_command": [
+    "python3",
+    "-B",
+    "research/r480-owner-optimum/check.py",
+    "--work",
+    "/tmp/r480-owner-check"
+  ],
+  "executed_check_work": "/tmp/k9-owner-strict1",
+  "exact_bound_patterns": 1163,
+  "certificate_cli_controls": 18,
+  "literal_roles": 159840,
+  "controller_mutations": 15,
+  "independent_owner_controls": 7,
+  "pending_child_port_basis_checks": 2016,
+  "admission_controls": 69,
+  "bit_supplier_controls": 12,
+  "outer_constraints": 47,
+  "charged_complex_prefix_bits": 1024,
+  "actual_prefix_bits": 775,
+  "physical_row_coefficient": 17495,
+  "kappa": "167409796990539/100000000000000000",
+  "post_strict_change": "The independent checker added a disjoint-pending-axis guard and its seventh control. Targeted and actual-CLI checks passed. The coordinator then reran the complete public check with the final code and inputs; every stage passed.",
+  "derived_code_reproduction": "All six source-to-derived edit lists reproduce their target byte for byte.",
+  "syntax_check": "Every packaged Python file parsed.",
+  "shared_baseline_make_verify": {
+    "status": "RUNNING_AT_HANDOFF",
+    "log": "work/nine-pr-sprint-20261013/baseline-verification/make-verify.log",
+    "scope": "Unchanged exact base; run once by the sprint coordinator."
+  },
+  "limits": [
+    "The local source chain was rebuilt by the concurrent sprint worker. The one-command owner replay consumes its source-bound artifacts.",
+    "The cited PR589 bit circuit is not rebuilt here; its full profile and exceptional-residue surcharge are repriced.",
+    "All inherited asymptotic obligations remain conditional.",
+    "No selected-result pointer was changed."
+  ],
+  "independent_full_replay": {
+    "status": "PASS_R480_ALL_REPLICA_OPTIMUM_AND_ATTAINING_CONSTRUCTION",
+    "work": "/tmp/k9-owner-parent-check",
+    "reviewer": "Separate coordinator agent",
+    "source_freeze_sha256": "2780bd3f6ffa6584ae92993a7fe7223f01002860ae4bb6c52c9fc5203f08b025",
+    "scope": "The coordinator read PROOF.md, README.md, all derived-code changes and the pending-axis guard. It separately ran the complete public check with the final code and inputs."
+  }
+}
diff --git a/research/k8-x54-t37/evidence/k8-x54/ADMISSION-CONTROLS.json b/research/k8-x54-t37/evidence/k8-x54/ADMISSION-CONTROLS.json
new file mode 100644
index 0000000000..e08a887f8e
--- /dev/null
+++ b/research/k8-x54-t37/evidence/k8-x54/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "334827562021037/200000000000000000",
+  "input_sha256": {
+    "owner_audit": "ee982a1a8c061ee47b8971ea5c4ffab13004fb2c4c8839cbebacd4e64bd8128e",
+    "fresh_invoice": "5d794b616c6727d04eb67b27c8f18e1a26a0aad6669fccfb02c77cb67ff307e5",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_258",
+    "gauge44:cold_helper_width_swap_270",
+    "gauge44:cold_helper_width_swap_282",
+    "gauge44:cold_helper_width_swap_294",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "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."
+}
diff --git a/research/k8-x54-t37/evidence/k8-x54/ASSEMBLY.json b/research/k8-x54-t37/evidence/k8-x54/ASSEMBLY.json
new file mode 100644
index 0000000000..da4786ac7f
--- /dev/null
+++ b/research/k8-x54-t37/evidence/k8-x54/ASSEMBLY.json
@@ -0,0 +1,344 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "334827562021037/200000000000000000",
+  "kappa_decimal": "0.001674137810105185",
+  "complex_lower": "335389049509916846257/200000000000000000000000",
+  "complex_decimal": "0.001676945247549584231285",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "gain_over_pr635_percent": "2.316058386997697681813762422454733413369253685330477757402717648319912",
+  "complex_profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 144522,
+    "4": 45954,
+    "5": 27972,
+    "8": 2664,
+    "48": 11302
+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  },
+  "conservative_complex_lower": "67077809787469242059/40000000000000000000000",
+  "conservative_complex_decimal": "0.001676945244686731051475",
+  "conservative_kappa": "1674137807251909/1000000000000000000",
+  "conservative_kappa_decimal": "0.001674137807251909",
+  "conservative_moments": [
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "67077809787469242059/40000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-3923963144167127670257399657795535331055501/1684996666696914987166688442938726917102321526408785780068975640576",
+        "-31391705153337021362059197262364282648444007/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "-23287662347916708475121/10000000000000000000000000000000000000000000000",
+        "-23287652347916708474979/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "419236311171682762869/250000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "8055525445929792250146147392939614534293397/13479973333575319897333507543509815336818572211270286240551805124608",
+        "4027762722964896125073073696469807267146699/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "1195183530488546959981/2000000000000000000000000000000000000000000000",
+        "5975927652442734800047/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "conservative_bootstrap": [
+    {
+      "exponent": "2678716151167151581447577783800994407170381361662480472294520237518190755455349024065440519/1600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "4396240331618100912417933086614094059936278337519527705479762481809244544650975934559481/1600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "4768476137395"
+    },
+    {
+      "exponent": "107324200769778043014724034267392774428454893493012625978136488386387804445578194680989335662770796871612977338001041207539332687122411379/64000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "294890172744279675794408111565620757812106987374021863511613612195554421805319010664337229203128387022661998958792460667312877588621/64000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1695672000438747067"
+    },
+    {
+      "exponent": "4292979806617444576241254389915478276772129045869128498274221411339829774301288243354120949779334906140322786435764587289787227275398332649335388323324123676386247181082310626473010639/2560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "19780586915534738757104695325196379178130871501725778588660170225698711756645879050220665093859677213564235412710212772724601667350664611676675876323613752818917689373526989361/2560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "602981634011669460350886"
+    },
+    {
+      "exponent": "171719193054594421224434983755734666669033730447086922544137149100057347730006892340511589599698802995966588537971756172759983157252588088851826700865447241409725584720378325799077106256668024382338438907241150821086900686826734299/102400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "1326838446604742125072277409706598512913077455862850899942652269993107659488410400301197004033411462028243827240016842747411911148173299134552758590274415279621674200922893743331975617661561092758849178913099313173265701/102400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "214420507539964408145238243249"
+    },
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+    "dimension_above_kappa": "255570702016627306506675677389161435215028786617993716146232668492040859190415626728206323559568766900760002758587203090697836297825495480277853496558082761707037554884885574260605228045395472218597942662500362658971959055014675583554449067515898482831564136178784456878503491133003413693813142901308369025866013226306857082892259730364321957653031777384867598316620586891853242012998532518388799140194562551810188561363/256429297983372693563193315648321864294280915088161061074048191259754805123668978372063240684569227469147732361085975994869188092397366124027559288062073855943577235482782966284308116961955976682358065906356602665631705512905144589725265717779389436232396389975469526739222922649671918626550437882349283017108289525453332706227727354759091693388065559168858391375938602240803512540445260085628270424960200000000000000000"
+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Conditional R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain."
+}
diff --git a/research/k8-x54-t37/evidence/k8-x54/BIT-CONTROLS.json b/research/k8-x54-t37/evidence/k8-x54/BIT-CONTROLS.json
new file mode 100644
index 0000000000..1edf7099f0
--- /dev/null
+++ b/research/k8-x54-t37/evidence/k8-x54/BIT-CONTROLS.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS",
+  "kappa": "0.001674137810105185",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "derived_deficit": 10272,
+  "rejected_controls": [
+    "revert_hardcoded_9984",
+    "ports_112",
+    "decoder_constant_64_copy_ranks_unchanged",
+    "decoder_constant_64_with_one_copy_rank_8",
+    "eight_retained_totals",
+    "live_minus_one",
+    "profile_rank_mass_plus_one",
+    "profile_rank_mass_receipt_mismatch",
+    "bit_lower_next_grid",
+    "not_nine_stage_record",
+    "tampered_bytes_next_grid",
+    "pr543_file_under_pr589_pin"
+  ],
+  "assembler_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a"
+}
diff --git a/research/k8-x54-t37/evidence/k8-x54/BOUND-CONTROLS.json b/research/k8-x54-t37/evidence/k8-x54/BOUND-CONTROLS.json
new file mode 100644
index 0000000000..d9d490bb71
--- /dev/null
+++ b/research/k8-x54-t37/evidence/k8-x54/BOUND-CONTROLS.json
@@ -0,0 +1,95 @@
+{
+  "status": "PASS_R480_OWNER_CERTIFICATE_CONTROLS",
+  "count": 18,
+  "cases": [
+    {
+      "name": "boolean_width_price",
+      "rejected_by": "integer width prices",
+      "output_created": false
+    },
+    {
+      "name": "float_width_price",
+      "rejected_by": "integer width prices",
+      "output_created": false
+    },
+    {
+      "name": "boolean_capacity_bonus",
+      "rejected_by": "integer capacity bonuses",
+      "output_created": false
+    },
+    {
+      "name": "float_capacity_bonus",
+      "rejected_by": "integer capacity bonuses",
+      "output_created": false
+    },
+    {
+      "name": "boolean_row_capacity",
+      "rejected_by": "integer packing capacity",
+      "output_created": false
+    },
+    {
+      "name": "float_row_capacity",
+      "rejected_by": "integer packing capacity",
+      "output_created": false
+    },
+    {
+      "name": "boolean_bin_count",
+      "rejected_by": "positive packing multiplicity",
+      "output_created": false
+    },
+    {
+      "name": "float_width_count",
+      "rejected_by": "integer packing vector",
+      "output_created": false
+    },
+    {
+      "name": "missing_bin",
+      "rejected_by": "complete bin stock",
+      "output_created": false
+    },
+    {
+      "name": "missing_width_four",
+      "rejected_by": "complete helper inventory",
+      "output_created": false
+    },
+    {
+      "name": "nonintegral_replica_count",
+      "rejected_by": "integral residual counts",
+      "output_created": false
+    },
+    {
+      "name": "negative_bin_count",
+      "rejected_by": "positive packing multiplicity",
+      "output_created": false
+    },
+    {
+      "name": "false_zero_price",
+      "rejected_by": "zero and maximum residual",
+      "output_created": false
+    },
+    {
+      "name": "wrong_root_interval",
+      "rejected_by": "two exact root signs: lower",
+      "output_created": false
+    },
+    {
+      "name": "next_outer_grid",
+      "rejected_by": "same outer grid cell",
+      "output_created": false
+    },
+    {
+      "name": "float_root",
+      "rejected_by": "rational root strings",
+      "output_created": false
+    },
+    {
+      "name": "output_preservation",
+      "rejected_by": "Choose a new output file",
+      "retained_bytes": true
+    },
+    {
+      "name": "optimization_guard",
+      "rejected_by": "Retained outer assertions require Python without -O"
+    }
+  ]
+}
diff --git a/research/k8-x54-t37/evidence/k8-x54/BOUND.json b/research/k8-x54-t37/evidence/k8-x54/BOUND.json
new file mode 100644
index 0000000000..826f137bc8
--- /dev/null
+++ b/research/k8-x54-t37/evidence/k8-x54/BOUND.json
@@ -0,0 +1,302 @@
+{
+  "status": "PASS_R480_ALL_REPLICA_BIN_OPTIMUM",
+  "scope": "Exact owner bin relaxation. Time windows, per-call family matching, charts, local admission and finite invoices are separate.",
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "source_head": "052afc128954f7b6a2b3c409eb4d72248e4020f2",
+  "inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 434,
+    "4": 138,
+    "5": 84,
+    "8": 8
+  },
+  "capacity_stock": {
+    "16": 448,
+    "8": 672,
+    "32": 448,
+    "48": 448
+  },
+  "bin_patterns": 1163,
+  "upper_price_by_residual": {
+    "8": 2,
+    "0": 0,
+    "1": 19,
+    "3": 7,
+    "4": 1,
+    "16": 4,
+    "7": 8,
+    "9": -4,
+    "2": 13,
+    "11": 9,
+    "6": 14,
+    "12": 3,
+    "5": 20,
+    "32": 8,
+    "23": 12,
+    "14": 16,
+    "24": 6,
+    "15": 10,
+    "25": 0,
+    "17": -2,
+    "18": -8,
+    "10": 15,
+    "27": -12,
+    "19": 11,
+    "20": 5,
+    "13": -3,
+    "22": -7,
+    "28": 7,
+    "21": -1,
+    "48": -13,
+    "39": -9,
+    "30": -5,
+    "40": -15,
+    "31": -11,
+    "41": -21,
+    "33": -23,
+    "34": -29,
+    "26": -6,
+    "43": -33,
+    "35": -10,
+    "36": -16,
+    "29": -24,
+    "38": -53,
+    "44": -14,
+    "37": -22
+  },
+  "idle_mass_per_replica": 14814,
+  "signed_price_per_replica": -1084,
+  "credit_per_replica": 140550,
+  "rank_one_credit": 925,
+  "normalized_idle": {
+    "1": "5622/37",
+    "48": "11302/37"
+  },
+  "minimum_equality_replicas": 37,
+  "packing_replicas": 37,
+  "packing_idle": {
+    "1": 5622,
+    "48": 11302
+  },
+  "profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 144522,
+    "4": 45954,
+    "5": 27972,
+    "8": 2664,
+    "48": 11302
+  },
+  "live": 33152,
+  "deficit": 11840,
+  "root_interval": [
+    "335389049509916846257/200000000000000000000000",
+    "838472623774792115643/500000000000000000000000"
+  ],
+  "two_engine_signs": {
+    "lower": {
+      "mercator": [
+        "-10100309075574269736392011350601680454704255/6739986666787659948666753771754907668409286105635143120275902562304",
+        "-20200618151148539472784022701203360909408509/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "atanh": [
+        "-749283/500000000000000000000000000000",
+        "-299713/200000000000000000000000000000"
+      ]
+    },
+    "upper": {
+      "mercator": [
+        "4811653112011405163816071374960398688226443/3369993333393829974333376885877453834204643052817571560137951281152",
+        "19246612448045620655264285499841594752905773/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "atanh": [
+        "1427793/1000000000000000000000000000000",
+        "713897/500000000000000000000000000000"
+      ]
+    }
+  },
+  "support_over_root_interval": {
+    "mercator": {
+      "multiplier_interval": [
+        "105426712199221647429280215393872592446087476154734984006557868491/311724383338929272625837361943664479663929482385625369312760493506560",
+        "527133560996108237146784527752180526467562115902159603805113074189/1558621916694646363129186809718322398319647411928126846563802467532800"
+      ],
+      "strict_margins": {
+        "2": "9149668937299812218776188637468870677093909903287592477023101983189/31172438333892927262583736194366447966392948238562536931276049350656",
+        "3": "33961067531904272498391196493638181591387429954395883896714414461915/62344876667785854525167472388732895932785896477125073862552098701312",
+        "4": "5988901429325663433428312850736464985218858229720028012122300964337/7793109583473231815645934048591611991598237059640634232819012337664",
+        "5": "35286862551835581894651963230195249928072370172795312882201814791421/62344876667785854525167472388732895932785896477125073862552098701312",
+        "6": "11737896455637197518821223254536099812412938593948631120405762906185/15586219166946463631291868097183223983196474119281268465638024675328",
+        "7": "57773878390984812446885120337373097557276935353441982487498643404245/62344876667785854525167472388732895932785896477125073862552098701312",
+        "8": "8484397038610907524995731268656978569532208420055557741141243533919/7793109583473231815645934048591611991598237059640634232819012337664",
+        "9": "77346254865846107953108740854183609993799263652168089831893639516761/62344876667785854525167472388732895932785896477125073862552098701312",
+        "10": "15238786923324096954220910837672630374880224069561943191047552462381/15586219166946463631291868097183223983196474119281268465638024675328",
+        "11": "34681470960456420648195851388007309653952656870122833811654061714675/31172438333892927262583736194366447966392948238562536931276049350656",
+        "12": "19328301709295522103323219608118194213810826082604598756461278411789/15586219166946463631291868097183223983196474119281268465638024675328",
+        "13": "84844224002931861326124842120502711351372488870689487383765908506457/62344876667785854525167472388732895932785896477125073862552098701312",
+        "14": "16671487735765530528926326783956311818549898022141861185656176799785/15586219166946463631291868097183223983196474119281268465638024675328",
+        "15": "73470937480649734040523964766121973194408843793466815702299042987897/62344876667785854525167472388732895932785896477125073862552098701312",
+        "16": "4995049489177738880746764643968413796339613857800584746157387028007/3896554791736615907822967024295805995799118529820317116409506168832",
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+      "controls_rejected": [
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+        "zero_beta",
+        "unit_beta"
+      ]
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+  "headroom_over_pr1074": "18582389827/12500000000000000",
+  "source_sha256": {
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+    "research/complex-t21-owners/vendor/pr870/independent/price_profile_t16.py": "53f8e62dcf27bee032c1bee0245d126a9c8a12ebcf24f6aaff65ea3122fffe29",
+    "research/complex-t21-owners/vendor/pr870/inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "research/complex-t37-owners/ALL-T-PROOF.md": "4c0c71ccd0afb850538af1b467e5208b7eb3edd0260fded84e02a8c01dfc868b",
+    "research/complex-t21-owner-bound/PROOF.md": "2aa0aa6ec1d87402138564c38749b5ca0f058c16817efdf58a2685d2d90cb417",
+    "package:inputs/SPEC.json": "b114e32f15fff8974709c040544bc653436c83cd0d83f823c7331a7c84625aae",
+    "package:inputs/PLAN.json": "b44c520e9288967e4814603fe1137ac1ec899552c657f6ba3428c941ada141fc",
+    "package:inputs/RESULT.json": "ebf3577df9efccc213998a6cf43f25fb3cd1a26893847b68d60d276e3b76440c",
+    "research/complex-t21-owners/independent_check.py": "9d8c86bf45cdaef37f223c88704055ced503ee295645611e13f3fb9059a00e55",
+    "research/complex-t37-owners/ORDER.json": "2093ca4050e1ce95621f4702bebe8b01b36773b1ecfa2c0d6275e132bd33d578"
+  }
+}
diff --git a/research/k8-x54-t37/evidence/k8-x54/GEOMETRY-CHECK.json b/research/k8-x54-t37/evidence/k8-x54/GEOMETRY-CHECK.json
new file mode 100644
index 0000000000..a4f3de140d
--- /dev/null
+++ b/research/k8-x54-t37/evidence/k8-x54/GEOMETRY-CHECK.json
@@ -0,0 +1,10 @@
+{
+  "roles": 159840,
+  "idle": {
+    "0": 57668,
+    "1": 5622,
+    "48": 11302
+  },
+  "owner_content_sha256": "592dd6d5c3dc29a33472f75425f9652c73993a8e38bdc17c7372b321aaeefa03",
+  "status": "PASS_LITERAL_WHOLE_HELPER_GEOMETRY"
+}
diff --git a/research/k8-x54-t37/evidence/k8-x54/INDEPENDENT-OWNER.json b/research/k8-x54-t37/evidence/k8-x54/INDEPENDENT-OWNER.json
new file mode 100644
index 0000000000..1e5cca63eb
--- /dev/null
+++ b/research/k8-x54-t37/evidence/k8-x54/INDEPENDENT-OWNER.json
@@ -0,0 +1,119 @@
+{
+  "status": "PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW",
+  "roles": 159840,
+  "calls": 333,
+  "source_events_per_replica": 30,
+  "expanded_replica_events": 1110,
+  "bridge_events": 333,
+  "literal_windows": 666,
+  "checked_whole_helper_widths": 159840,
+  "checked_busy_family_windows": 159840,
+  "orthogonal_port_bases": 112,
+  "actual_73_axis_charts": 11150,
+  "checked_slice_prefixes": 74592,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 434,
+    "4": 138,
+    "5": 84,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "idle": {
+    "1": 5622,
+    "48": 11302
+  },
+  "profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 144522,
+    "4": 45954,
+    "5": 27972,
+    "8": 2664,
+    "48": 11302
+  },
+  "live": 33152,
+  "physical": 33642,
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "namespace": {
+    "data": [
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+      33152
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+    "centres": [
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+      33160
+    ],
+    "tableau": [
+      33160,
+      33640
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+    "coefficient": [
+      33640,
+      33642
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+  },
+  "local_prefix_bits": 68,
+  "local_prefix_from_native_receipt": true,
+  "local_profile_recounted": true,
+  "prefix_formula": {
+    "local_scalar": 68,
+    "input_l2": 37,
+    "invocations": 333,
+    "bridges": 333,
+    "margin": 4
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+  "prefix_bits": 775,
+  "charged_prefix_bits": 1024,
+  "physical_stock_bits": 2643,
+  "physical_row_coefficient": 17495,
+  "row_limit": 20161,
+  "scope": "Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.",
+  "disjoint_pending_child_axis_checks": 2016,
+  "controls_rejected": [
+    {
+      "name": "private_namespace_collision",
+      "reason": "private-namespace collision"
+    },
+    {
+      "name": "copy_replica_alias",
+      "reason": "role invocation time"
+    },
+    {
+      "name": "missing_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "split_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "truncated_helper_width",
+      "reason": "whole-helper residual width"
+    },
+    {
+      "name": "cross_idle_boundary",
+      "reason": "strict bridge-aware idle window"
+    },
+    {
+      "name": "cross_child_pending_axis_alias",
+      "reason": "overlapping pending children on one family"
+    }
+  ],
+  "input_sha256": {
+    "/tmp/k8/check1/replay/global8/base/split-centres/GLOBAL-TEMPLATE.json.gz": "ab8448de2036a23d9b55a196a8846512dc24fdf09855c1e0f0caa5b7a6965f7b",
+    "/tmp/k8/check1/replay/global8/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "/tmp/k8/check1/replay/global8/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "/tmp/wx54/research/k8-x54-t37/inputs/local/CANONICAL-WORD.json.gz": "75507b67a784bd1e54e1451b6263624fe4d05bd08b850c4fb87c82776ec1909a",
+    "/tmp/wx54/research/k8-x54-t37/inputs/local/INDEPENDENT-LOCAL-REPLAY.json": "0ac952f4900d2ef2508abd60ca4a7448b1a17b0a3f7e6fb3b4ee0c228c728766",
+    "/tmp/wx54/research/k8-x54-t37/OWNERS.json.gz": "c35ac0c6f77c6b7cb32bee953770de3ef8a575aef36efc4764e0bb3325a04737"
+  }
+}
diff --git a/research/k8-x54-t37/evidence/k8-x54/REPLAY-RESULT.json b/research/k8-x54-t37/evidence/k8-x54/REPLAY-RESULT.json
new file mode 100644
index 0000000000..83cedbe45b
--- /dev/null
+++ b/research/k8-x54-t37/evidence/k8-x54/REPLAY-RESULT.json
@@ -0,0 +1,91 @@
+{
+  "status": "PASS_R480_T37_STRICT_FINITE_CONSTRUCTION",
+  "kappa": "334827562021037/200000000000000000",
+  "kappa_decimal": "0.001674137810105185",
+  "roles": 159840,
+  "calls": 333,
+  "prefix_bits": 775,
+  "charged_prefix_bits": 1024,
+  "physical_row_coefficient": 17495,
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 2.73,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind8",
+      "seconds": 0.762,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "lift",
+      "seconds": 8.239,
+      "exit_code": 0,
+      "log_sha256": "c8f864806d6a40d8899bcf4e4f94d8914bc1e7d67b77b30af71e38c9784c6e36"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.791,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 26.885,
+      "exit_code": 0,
+      "log_sha256": "31f8b554a565dc7a0fd79c010d63b3e1724920b14af734a41b7b1e8441239a99"
+    },
+    {
+      "name": "audit",
+      "seconds": 97.524,
+      "exit_code": 0,
+      "log_sha256": "67d7b7eec622c4395e5d2817287c2be64426a5da345749707348cea6036e4c30"
+    },
+    {
+      "name": "invoice",
+      "seconds": 3.058,
+      "exit_code": 0,
+      "log_sha256": "19571dcad21b6e4ad414138545569eece71c693db6fc515ca7c9c485226d25ca"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.673,
+      "exit_code": 0,
+      "log_sha256": "87831bcc550f83013fb5b289fd4f20997448a54e02b009d103ff83e9bccd6a0a"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 1.052,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    },
+    {
+      "name": "bit-controls",
+      "seconds": 1.387,
+      "exit_code": 0,
+      "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+    },
+    {
+      "name": "independent-owner",
+      "seconds": 3.469,
+      "exit_code": 0,
+      "log_sha256": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e"
+    }
+  ],
+  "local_input_sha256": {
+    "SCALAR-FRAME-AUDIT.json": "63c3e15b946596b1027cd793a862d153d4eb8f586b8819c527fd30031d023381",
+    "RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c",
+    "CLIFFORD-RECIPES.json": "7ed4c7e81ace3e7837067167745d2ca1bc3212079de284e76760c1c45b31d0ce",
+    "WRAPPER-CHECKS.json": "0ae753d6fa6e922d8b8180da602828f6cb3f444fcd124d019acee74e145c0836",
+    "LOCAL-PROGRAMS.json.gz": "43b7cd0eafaf840288ee7d1695dac5b5905033ca7f2df4bd9517e75387db5857",
+    "CLIFFORD-REVIEW.json": "e792f172a6a84c29c73d8b42b5a6705d5eed1369aec955270b83b4dca6c6fdf5",
+    "CANONICAL-WORD.json.gz": "75507b67a784bd1e54e1451b6263624fe4d05bd08b850c4fb87c82776ec1909a",
+    "LOCAL-CHECKS.json": "f04e637879fa041e363b70873a0713f7ac15336da81a49460eabaac3683c4a3e",
+    "FULL-WORD.json.gz": "ac196f39a72ef658aeba7199947e603da730a944c11e7300d12372f2e5875dcd",
+    "INDEPENDENT-LOCAL-REPLAY.json": "0ac952f4900d2ef2508abd60ca4a7448b1a17b0a3f7e6fb3b4ee0c228c728766"
+  },
+  "scope": "Finite owner, controller, chart, invoice and assembly replay. Local scalar and phase replay and inherited all-size obligations are recorded separately."
+}
diff --git a/research/k8-x54-t37/evidence/k8-x54/STAGES.json b/research/k8-x54-t37/evidence/k8-x54/STAGES.json
new file mode 100644
index 0000000000..67b2d2aec2
--- /dev/null
+++ b/research/k8-x54-t37/evidence/k8-x54/STAGES.json
@@ -0,0 +1,68 @@
+[
+  {
+    "name": "restore-parent",
+    "seconds": 2.73,
+    "exit_code": 0,
+    "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+  },
+  {
+    "name": "bind8",
+    "seconds": 0.762,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "lift",
+    "seconds": 8.239,
+    "exit_code": 0,
+    "log_sha256": "c8f864806d6a40d8899bcf4e4f94d8914bc1e7d67b77b30af71e38c9784c6e36"
+  },
+  {
+    "name": "bind",
+    "seconds": 0.791,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "emit",
+    "seconds": 26.885,
+    "exit_code": 0,
+    "log_sha256": "31f8b554a565dc7a0fd79c010d63b3e1724920b14af734a41b7b1e8441239a99"
+  },
+  {
+    "name": "audit",
+    "seconds": 97.524,
+    "exit_code": 0,
+    "log_sha256": "67d7b7eec622c4395e5d2817287c2be64426a5da345749707348cea6036e4c30"
+  },
+  {
+    "name": "invoice",
+    "seconds": 3.058,
+    "exit_code": 0,
+    "log_sha256": "19571dcad21b6e4ad414138545569eece71c693db6fc515ca7c9c485226d25ca"
+  },
+  {
+    "name": "assembly",
+    "seconds": 0.673,
+    "exit_code": 0,
+    "log_sha256": "87831bcc550f83013fb5b289fd4f20997448a54e02b009d103ff83e9bccd6a0a"
+  },
+  {
+    "name": "admission-controls",
+    "seconds": 1.052,
+    "exit_code": 0,
+    "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+  },
+  {
+    "name": "bit-controls",
+    "seconds": 1.387,
+    "exit_code": 0,
+    "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+  },
+  {
+    "name": "independent-owner",
+    "seconds": 3.469,
+    "exit_code": 0,
+    "log_sha256": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e"
+  }
+]
diff --git a/research/k8-x54-t37/evidence/local-source/BASE-STEPS.json b/research/k8-x54-t37/evidence/local-source/BASE-STEPS.json
new file mode 100644
index 0000000000..8d74a9b9a9
--- /dev/null
+++ b/research/k8-x54-t37/evidence/local-source/BASE-STEPS.json
@@ -0,0 +1,37 @@
+[
+  {
+    "step": "shadow-early",
+    "exit_code": 0,
+    "seconds": 0.312
+  },
+  {
+    "step": "shadow-prefix",
+    "exit_code": 0,
+    "seconds": 0.472
+  },
+  {
+    "step": "gauge-forward",
+    "exit_code": 0,
+    "seconds": 0.45
+  },
+  {
+    "step": "port0",
+    "exit_code": 0,
+    "seconds": 0.346
+  },
+  {
+    "step": "port1",
+    "exit_code": 0,
+    "seconds": 0.356
+  },
+  {
+    "step": "port2",
+    "exit_code": 0,
+    "seconds": 0.354
+  },
+  {
+    "step": "port3",
+    "exit_code": 0,
+    "seconds": 0.442
+  }
+]
diff --git a/research/k8-x54-t37/evidence/local-source/CELL-STEPS.json b/research/k8-x54-t37/evidence/local-source/CELL-STEPS.json
new file mode 100644
index 0000000000..5fdf17814b
--- /dev/null
+++ b/research/k8-x54-t37/evidence/local-source/CELL-STEPS.json
@@ -0,0 +1,32 @@
+[
+  {
+    "step": "gauge-forward",
+    "exit_code": 0,
+    "seconds": 0.395
+  },
+  {
+    "step": "port0",
+    "exit_code": 0,
+    "seconds": 0.374
+  },
+  {
+    "step": "port1",
+    "exit_code": 0,
+    "seconds": 0.482
+  },
+  {
+    "step": "port2",
+    "exit_code": 0,
+    "seconds": 0.517
+  },
+  {
+    "step": "port3",
+    "exit_code": 0,
+    "seconds": 0.442
+  },
+  {
+    "step": "cold44",
+    "exit_code": 0,
+    "seconds": 2.81
+  }
+]
diff --git a/research/k8-x54-t37/evidence/local-source/CHAIN-STEPS.json b/research/k8-x54-t37/evidence/local-source/CHAIN-STEPS.json
new file mode 100644
index 0000000000..bf5c0e6f62
--- /dev/null
+++ b/research/k8-x54-t37/evidence/local-source/CHAIN-STEPS.json
@@ -0,0 +1,107 @@
+[
+  {
+    "step": "pivot-swap",
+    "exit_code": 0,
+    "seconds": 10.172
+  },
+  {
+    "step": "cold44-exact",
+    "exit_code": 0,
+    "seconds": 2.01
+  },
+  {
+    "step": "lec-p6n",
+    "exit_code": 0,
+    "seconds": 117.763
+  },
+  {
+    "step": "promotion",
+    "exit_code": 0,
+    "seconds": 0.264
+  },
+  {
+    "step": "promo-controls",
+    "exit_code": 0,
+    "seconds": 7.186
+  },
+  {
+    "step": "lec-promo",
+    "exit_code": 0,
+    "seconds": 81.834
+  },
+  {
+    "step": "jx",
+    "exit_code": 0,
+    "seconds": 0.174
+  },
+  {
+    "step": "jx-control-C0_identity",
+    "exit_code": 0,
+    "seconds": 0.127
+  },
+  {
+    "step": "jx-control-C1_741_only",
+    "exit_code": 0,
+    "seconds": 0.128
+  },
+  {
+    "step": "jx-control-N3_plain_join_moved_reads",
+    "exit_code": 0,
+    "seconds": 0.133
+  },
+  {
+    "step": "lec-jx",
+    "exit_code": 0,
+    "seconds": 105.512
+  },
+  {
+    "step": "hybrids",
+    "exit_code": 0,
+    "seconds": 0.105
+  },
+  {
+    "step": "hybrid-controls",
+    "exit_code": 0,
+    "seconds": 13.119
+  },
+  {
+    "step": "lec-hyb",
+    "exit_code": 0,
+    "seconds": 88.857
+  },
+  {
+    "step": "frames",
+    "exit_code": 0,
+    "seconds": 0.521
+  },
+  {
+    "step": "lec-frames",
+    "exit_code": 0,
+    "seconds": 90.473
+  },
+  {
+    "step": "native",
+    "exit_code": 0,
+    "seconds": 1.243
+  },
+  {
+    "step": "ledgers",
+    "exit_code": 0,
+    "seconds": 0.822
+  },
+  {
+    "step": "local-replay",
+    "exit_code": 0,
+    "seconds": 5.213
+  },
+  {
+    "step": "wrappers",
+    "exit_code": 0,
+    "seconds": 2.337
+  },
+  {
+    "step": "phases",
+    "exit_code": 0,
+    "seconds": 191.38
+  }
+]
diff --git a/research/k8-x54-t37/evidence/local-source/NATIVE-REPLAY-NOTES.txt b/research/k8-x54-t37/evidence/local-source/NATIVE-REPLAY-NOTES.txt
new file mode 100644
index 0000000000..1b0738f3b8
--- /dev/null
+++ b/research/k8-x54-t37/evidence/local-source/NATIVE-REPLAY-NOTES.txt
@@ -0,0 +1,7 @@
+Base main: abdc6a7002abdbcd9e21bfc5e1a795784deacfdf, shared lane01.
+Sources: PR1074 052afc128954f7b6a2b3c409eb4d72248e4020f2 (gauge44-leaver8 and gauge44-slots); PR635 a6895a69f8ad98ab45777b03e9e6f48888c39f6f (complex-571-cold14-st2).
+Base scalar driver: /tmp/k9-leaver-base/STEPS.json
+Cell scalar driver: /tmp/k9-leaver-cell/STEPS.json
+Full unchanged k8 chain driver: /tmp/k9-leaver-chain/STEPS.json. All 21 steps including phases passed.
+Slot scalar/native/ledger/endpoint/wrapper command receipt: /tmp/k9-leaver-slots/STEPS.json. All word, canonical and forward/backward pins matched SLOT-PINS-k8.json.
+Slot phase replay: phases.log (PASS exact local phases; 2896 edges; 339.109 seconds; recipe SHA256 d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731). Source-specific slot controls remain separate from these native checks.
diff --git a/research/k8-x54-t37/evidence/local-source/SLOTS-STEPS.json b/research/k8-x54-t37/evidence/local-source/SLOTS-STEPS.json
new file mode 100644
index 0000000000..582d5773e5
--- /dev/null
+++ b/research/k8-x54-t37/evidence/local-source/SLOTS-STEPS.json
@@ -0,0 +1,84 @@
+[
+  {
+    "step": "slots",
+    "command": [
+      "python3",
+      "-B",
+      "/tmp/k9-leaver-sources/research/gauge44-leaver8/construction/barch/build_tri.py",
+      "/tmp/k9-leaver-chain/frames/FULL-WORD.json.gz",
+      "/tmp/k9-leaver-sources/research/gauge44-slots/construction/slots/RECIPE-SLOTS-k8.json",
+      "/tmp/k9-leaver-slots/FULL-WORD.json.gz"
+    ],
+    "exit_code": 0,
+    "seconds": 0.14077299972996116
+  },
+  {
+    "step": "native",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/tmp/k9-leaver-sources/research/complex-571-cold14-st2/code/hpe_audit_and_transport.py",
+      "--raw",
+      "/tmp/k9-leaver-slots/FULL-WORD.json.gz",
+      "--routing",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz",
+      "--out",
+      "/tmp/k9-leaver-slots/local"
+    ],
+    "exit_code": 0,
+    "seconds": 1.8713445831090212
+  },
+  {
+    "step": "ledgers",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/tmp/k9-leaver-sources/research/complex-571-cold14-st2/code/hpe_emit_local.py",
+      "/tmp/k9-leaver-slots/local"
+    ],
+    "exit_code": 0,
+    "seconds": 1.0618331669829786
+  },
+  {
+    "step": "local-replay",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/tmp/k9-leaver-sources/research/complex-571-cold14-st2/code/hpe_audit_local.py",
+      "/tmp/k9-leaver-slots/local"
+    ],
+    "exit_code": 0,
+    "seconds": 6.432917749974877
+  },
+  {
+    "step": "wrappers",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/tmp/k9-leaver-sources/research/complex-571-cold14-st2/code/hpe_adapters_local.py",
+      "/tmp/k9-leaver-slots/local/CANONICAL-WORD.json.gz",
+      "/tmp/k9-leaver-slots/local/RESIDUAL-ADAPTERS.json",
+      "/tmp/k9-leaver-slots/local/WRAPPER-CHECKS.json"
+    ],
+    "exit_code": 0,
+    "seconds": 2.5233489158563316
+  },
+  {
+    "step": "exact-phases",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/code/phases_full.py",
+      "/tmp/k9-leaver-slots/local",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/vendor/clifford"
+    ],
+    "exit_code": 0,
+    "seconds": 339.10877466667444,
+    "clifford_recipes_sha256": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731"
+  }
+]
diff --git a/research/k8-x54-t37/evidence/x54/LOCAL-AUDIT-X54.json b/research/k8-x54-t37/evidence/x54/LOCAL-AUDIT-X54.json
new file mode 100644
index 0000000000..dd86ea0ef4
--- /dev/null
+++ b/research/k8-x54-t37/evidence/x54/LOCAL-AUDIT-X54.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "k8x54final.json.gz",
+  "content_sha256": "512452c0aa64e35c98c5af35d250f103e28e48d8404fdc25a6bb15113ebfb300",
+  "compressed_sha256": "ac196f39a72ef658aeba7199947e603da730a944c11e7300d12372f2e5875dcd",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 480,
+  "entering": 192,
+  "lowends": 78,
+  "coldends": 48,
+  "compensation_gates": 7208,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 434,
+    "4": 138,
+    "5": 84,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "checked_columns": 704,
+  "elapsed_seconds": 1.7009585930009052,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/k8-x54-t37/evidence/x54/X54-CONTROLS.json b/research/k8-x54-t37/evidence/x54/X54-CONTROLS.json
new file mode 100644
index 0000000000..c7f50fb84c
--- /dev/null
+++ b/research/k8-x54-t37/evidence/x54/X54-CONTROLS.json
@@ -0,0 +1,78 @@
+{
+ "C0_identity": {
+  "ok": true,
+  "out": "{\"control\": null, \"sha256\": \"c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8\"}"
+ },
+ "recipe": {
+  "ok": true,
+  "build": {
+   "control": null,
+   "sha256": "512452c0aa64e35c98c5af35d250f103e28e48d8404fdc25a6bb15113ebfb300"
+  },
+  "audit_tail": "}"
+ },
+ "drop_restore": {
+  "ok": true,
+  "build": {
+   "control": "drop_restore",
+   "sha256": "112f940250f0839cb0f42f3f512d4365d781c869a4aa7e1c95b2a38679eab6cd"
+  },
+  "audit_tail": "RuntimeError: all-column endpoint failure (False, [108, 111, 328, 334, 335, 511, 519])"
+ },
+ "restore_full": {
+  "ok": true,
+  "build": {
+   "control": "restore_full",
+   "sha256": "647a0a2a49a5e69e3d9cb2bdc9931571493e1370f8e6c92e76af7e58cbb2820e"
+  },
+  "audit_tail": "RuntimeError: all-column endpoint failure (False, [44, 47, 359, 360, 366, 367, 519, 543])"
+ },
+ "drop_preread": {
+  "ok": true,
+  "build": {
+   "control": "drop_preread",
+   "sha256": "e8f0f1dd052d4decd001e5883c2096a92ce569fec7aa2b8ec13a3371c8017251"
+  },
+  "audit_tail": "RuntimeError: nonzero entrance response"
+ },
+ "donation_after": {
+  "ok": true,
+  "build": {
+   "control": "donation_after",
+   "sha256": "4de2815e97657c1e3f5f36cb335499df8d879a5ef845d5054a412daf6c8600a8"
+  },
+  "audit_tail": "RuntimeError: nonzero entrance response"
+ },
+ "drop_restore@54": {
+  "ok": true,
+  "build": {
+   "control": "drop_restore@54",
+   "sha256": "112f940250f0839cb0f42f3f512d4365d781c869a4aa7e1c95b2a38679eab6cd"
+  },
+  "audit_tail": "RuntimeError: all-column endpoint failure (False, [108, 111, 328, 334, 335, 511, 519])"
+ },
+ "restore_full@54": {
+  "ok": true,
+  "build": {
+   "control": "restore_full@54",
+   "sha256": "647a0a2a49a5e69e3d9cb2bdc9931571493e1370f8e6c92e76af7e58cbb2820e"
+  },
+  "audit_tail": "RuntimeError: all-column endpoint failure (False, [44, 47, 359, 360, 366, 367, 519, 543])"
+ },
+ "drop_preread@54": {
+  "ok": true,
+  "build": {
+   "control": "drop_preread@54",
+   "sha256": "e8f0f1dd052d4decd001e5883c2096a92ce569fec7aa2b8ec13a3371c8017251"
+  },
+  "audit_tail": "RuntimeError: nonzero entrance response"
+ },
+ "donation_after@54": {
+  "ok": true,
+  "build": {
+   "control": "donation_after@54",
+   "sha256": "4de2815e97657c1e3f5f36cb335499df8d879a5ef845d5054a412daf6c8600a8"
+  },
+  "audit_tail": "RuntimeError: nonzero entrance response"
+ }
+}
\ No newline at end of file
diff --git a/research/k8-x54-t37/independent_owner.py b/research/k8-x54-t37/independent_owner.py
new file mode 100644
index 0000000000..bf2de9be49
--- /dev/null
+++ b/research/k8-x54-t37/independent_owner.py
@@ -0,0 +1,343 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Prepared for haoyan with substantial OpenAI Codex assistance.
+"""Independent source-event, owner, chart, and finite-reserve audit.
+
+This derivative fixes the R480 seven-slot k8 word and 37 replicas. It charges
+1024 complex prefix bits and checks disjoint pending children on each family.
+The source is Hao Yan's variable-replica checker at the pinned repository base.
+SOURCES.json and INDEPENDENT-DERIVATION.patch identify that source and all edits.
+
+Inputs are read-only. No owner constructor or controller auditor is imported.
+--word is the canonical local supplier JSON.gz, with a hash-bound native
+INDEPENDENT-LOCAL-REPLAY.json beside it (override with --local-replay).
+--baseline-parent is the original eight-replica GLOBAL-TEMPLATE.json.gz.
+Its sibling CANONICAL-WORD.json.gz supplies the ports and centre frames.
+DATA-PHASES.json defaults to ../work/complex-nine-native/DATA-PHASES.json
+(override with --phases). The checker recounts local widths and paid ranks.
+--out names a JSON receipt. Checks remain enabled under python -O.
+"""
+import argparse
+import copy
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+
+V, H, M, T, R = 112, 9, 73, 37, 480
+EXPECTED_IDLE = None
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+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 basis(vectors):
+    pivots = {}
+    for x in vectors:
+        require(type(x) is int and 0 <= x < 1 << H, 'invalid local frame vector')
+        while x:
+            bit = x.bit_length() - 1
+            if bit in pivots:
+                x ^= pivots[bit]
+            else:
+                pivots[bit] = x
+                break
+    for bit in sorted(pivots):
+        for upper in pivots:
+            if upper > bit and pivots[upper] >> bit & 1:
+                pivots[upper] ^= pivots[bit]
+    return tuple(pivots[bit] for bit in sorted(pivots, reverse=True))
+
+
+def local_inventory(word, replay):
+    require((word['v'], word['h'], word['R']) == (V, H, R), 'local supplier dimensions')
+    frames = [basis(frame) for frame in word['frames']]
+    n = 2 * V + R
+    require(len(word['start']) == len(word['final']) == n, 'local frame vector lengths')
+    current = [frames[f] for f in word['start']]
+    paid = Counter()
+
+    def climb(register, frame):
+        require(basis(current[register] + frame) == frame, 'nonmonotone local frame')
+        jump = len(frame) - len(current[register])
+        if jump:
+            paid[jump] += 1
+        current[register] = frame
+
+    require(not word['target_levels'], 'this audit requires the current zero-level centre interface')
+    for section in ('A', 'B', 'tail'):
+        if section == 'B':
+            require(all(current[t] == () for t in range(V, 2 * V)), 'target centre level')
+            for q, frame_id in zip(word['centers'], word['center_frames']):
+                require(current[q] == frames[frame_id], 'centre carrier frame')
+                paid[len(frames[frame_id])] += 1
+        for gate in word[section]:
+            registers = gate[1:3] if gate[0] == 'add' else gate[1:2]
+            require(gate[0] in ('add', 'scale'), 'unknown scalar gate')
+            for register in registers:
+                climb(register, frames[gate[-1]])
+    for register, frame_id in enumerate(word['final']):
+        climb(register, frames[frame_id])
+    require(dict(paid) == {int(r): count for r, count in word['local_profile'].items()}, 'local paid-profile recount')
+    for orientation in ('forward', 'backward'):
+        require(dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}, 'local replay profile binding')
+    widths = [len(frames[word['final'][q]]) - len(frames[word['start'][q]]) for q in range(2 * V, n)]
+    require(Counter(widths) == {4: 56, 5: 32, 7: 30, 8: 122, 9: 240}, 'current supplier width inventory')
+    return widths, paid
+
+
+def make_context(parent, phases, ports, word, replay, roles):
+    widths, paid = local_inventory(word, replay)
+    require(len(parent['calls']) == 72 and {(c['stage'], c['replica']) for c in parent['calls']} == {(s, r) for s in range(9) for r in range(8)}, 'original eight-replica baseline calls')
+    require(len(roles) == 9 * T * R, 'complete helper role count')
+    address = {}
+    for role in roles:
+        key = (role['stage'], role['replica'])
+        time = role['time']
+        require(time not in address or address[time] == key, 'inconsistent invocation time address')
+        address[time] = key
+    require(set(address) == set(range(9 * T)), 'contiguous invocation times')
+    order = [address[t] for t in range(9 * T)]
+    require(set(order) == {(s, r) for s in range(9) for r in range(T)}, 'stage/replica inventory')
+    # Arbitrary interleaving: the exact per-replica projection is checked below.
+    rank = {child['child']: child['rank'] for child in parent['idle_children']}
+    source = parent['execution_schedule']
+    blocks, stage = {}, None
+    for index, event in enumerate(source):
+        if event['kind'] in ('bank_padding_cover_sweep', 'translate_every_live_family'):
+            continue
+        if event['kind'] == 'local_cover_sweep':
+            stage = event['stage']
+            blocks[stage] = []
+        require(stage is not None, 'source event before first invocation')
+        blocks[stage].append((index, event))
+    require(set(blocks) == set(range(9)), 'source stage inventory')
+    events = [(index, event, replica, time) for time, (stage, replica) in enumerate(order) for index, event in blocks[stage]]
+    projections = defaultdict(list)
+    for index, event, replica, time in events:
+        projections[replica].append(index)
+    require(set(projections) == set(range(T)) and all(p == list(range(30)) for p in projections.values()), 'per-replica source-event projection')
+    stage_pair = {e['stage']: e['pair'] for e in parent['recipe'] if e['kind'] == 'local'}
+    last, windows, callpos, child_pair, side = {}, {}, {}, {}, {}
+    bridges = 0
+    for position, (_, event, replica, _) in enumerate(events):
+        kind = event['kind']
+        if kind == 'local_cover_sweep':
+            stage = event['stage']
+            callpos[stage, replica] = position
+            last[replica, stage_pair[stage]] = position
+        elif kind == 'bridge':
+            last[replica, event['src']] = last[replica, event['dst']] = position
+            bridges += 1
+        elif kind == 'idle_cover_sweep':
+            for sd, child in enumerate(event['child_indices']):
+                if child in rank:
+                    windows[replica, child] = (last.get((replica, event['pair']), -1), position)
+                    child_pair[child], side[child] = event['pair'], sd
+    require(len(windows) == T * len(rank), 'actual window inventory')
+    require(len(ports) == V, 'port count')
+    bases = []
+    for q in ports:
+        zero = next(i for i in range(H) if not (q >> i & 1))
+        correction = q ^ (1 << zero)
+        axes = list(range(H))
+        axes[0], axes[zero] = axes[zero], axes[0]
+        frame = [(1 << i) ^ (correction if correction >> i & 1 else 0) for i in axes] + [1 << i for i in range(H, M)]
+        require(all((x & y).bit_count() % 2 == int(i == j) for i, x in enumerate(frame) for j, y in enumerate(frame)), 'nonorthogonal owner basis')
+        bases.append(frame)
+    return dict(widths=widths, paid=paid, order=order, at={key:t for t,key in enumerate(order)}, rank=rank,
+                windows=windows, callpos=callpos, child_pair=child_pair, side=side, stage_pair=stage_pair,
+                bases=bases, phases=phases, bridges=bridges, event_count=len(events), replay=replay)
+
+
+def check_pending_axes(context):
+    checked = 0
+    for port, frame in enumerate(context['bases']):
+        used = defaultdict(set)
+        for child, rank in context['rank'].items():
+            axes = list(map(int, context['phases']['recipes'][port]['idle_children'][child]['orthogonal_axes']))
+            require(len(axes) == rank and len(set(axes)) == rank and set(axes) <= set(frame),
+                    'pending child orthogonal basis')
+            family = context['child_pair'][child], context['side'][child]
+            require(not used[family] & set(axes), 'overlapping pending children on one family')
+            used[family].update(axes)
+            checked += 1
+    return checked
+
+
+def check_roles(context, roles):
+    c = context
+    live, physical = T * 8 * V, T * 8 * V + 8 + R + 2
+    require(len(roles) == 9 * T * R, 'complete helper role count')
+    helpers, families, used = defaultdict(set), defaultdict(set), defaultdict(set)
+    charts, chart_cache = set(), {}
+    for z in roles:
+        s, r, helper = z['stage'], z['replica'], z['helper']
+        owner, child, port = z['owner_replica'], z['child'], z['port']
+        offset, width, family = z['offset'], z['width'], z['family']
+        call = (s, r)
+        require(call in c['at'] and 0 <= helper < R and 0 <= owner < T and 0 <= port < V, 'role coordinates')
+        require(z['time'] == c['at'][call], 'role invocation time')
+        require(width == c['widths'][helper], 'whole-helper residual width')
+        require(0 <= family < live, 'private-namespace collision')
+        require(child in c['rank'], 'unknown idle child')
+        require(z['copy'] == V * owner + port and family == owner * 896 + (2 * c['child_pair'][child] + c['side'][child]) * V + port, 'physical family identity')
+        lo, hi = c['windows'][owner, child]
+        require(lo < c['callpos'][call] < hi, 'strict bridge-aware idle window')
+        require(family // 224 != r * 4 + c['stage_pair'][s], 'helper aliases active data pair')
+        require(helper not in helpers[call] and family not in families[call], 'duplicate helper or family within whole invocation')
+        helpers[call].add(helper)
+        families[call].add(family)
+        cells = set(range(offset, offset + width))
+        bin_key = (owner, child, port)
+        require(offset >= 0 and offset + width <= c['rank'][child] and not used[bin_key] & cells, 'overlapping or out-of-capacity slice')
+        used[bin_key].update(cells)
+        chart_key = (port, child, offset, width)
+        if chart_key not in chart_cache:
+            frame = c['bases'][port]
+            pending = list(map(int, c['phases']['recipes'][port]['idle_children'][child]['orthogonal_axes']))
+            require(len(pending) == c['rank'][child], 'phase child rank')
+            occupied = [frame.index(x) for x in pending[offset:offset + width]]
+            spectators = [i for i in range(M) if i not in occupied][:H - width]
+            permutation = occupied + spectators + [i for i in range(M) if i not in occupied and i not in spectators]
+            require(len(occupied) == width and len(set(occupied + spectators)) == H and sorted(permutation) == list(range(M)), 'residual/spectator permutation')
+            require([frame[i] for i in permutation[:width]] == pending[offset:offset + width], 'pending-axis binding')
+            chart_cache[chart_key] = tuple(frame[i] for i in permutation)
+        charts.add(chart_cache[chart_key])
+    require(set(helpers) == set(c['order']) and all(h == set(range(R)) for h in helpers.values()), 'complete per-call helper inventory')
+    idle = Counter()
+    for owner, child in c['windows']:
+        for port in range(V):
+            cells = used[owner, child, port]
+            require(cells == set(range(len(cells))), 'gap in pending prefix')
+            left = c['rank'][child] - len(cells)
+            if left:
+                idle[left] += 1
+    require(dict(idle) == EXPECTED_IDLE, 'nominated idle profile')
+    profile = Counter({rank: 9 * T * count for rank, count in c['paid'].items()})
+    profile.update(idle)
+    mass = sum(rank * count for rank, count in profile.items())
+    require(M * live - mass == 320*T, 'replica-scaled rank deficit')
+    require(c['bridges'] == 9*T, 'actual bridge count')
+    localbits = max(x['prefix_bits_upper'] for x in c['replay']['local'].values())
+    prefix = localbits + (M + 1) // 2 + len(c['order']) + c['bridges'] + 4
+    group = 2 ** (36 * 36)
+    for i in range(1, 37):
+        group *= 2 ** (2 * i) - 1
+    stock = group * physical
+    row = 2 * stock.bit_length() + 9909 + 252 + 2 * 1024
+    require(prefix < 1024, 'prefix reserve')
+    require(row < 20161 and M * M > 2 * max(profile) ** 2, 'row or halving reserve')
+    return dict(status='PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW', roles=len(roles), calls=len(c['order']),
+                source_events_per_replica=30, expanded_replica_events=c['event_count'], bridge_events=c['bridges'],
+                literal_windows=len(c['windows']), checked_whole_helper_widths=len(roles), checked_busy_family_windows=len(roles),
+                orthogonal_port_bases=len(c['bases']), actual_73_axis_charts=len(charts), checked_slice_prefixes=len(c['windows']) * V,
+                local_profile=dict(sorted(c['paid'].items())), width_inventory=dict(sorted(Counter(c['widths']).items())),
+                idle=dict(sorted(idle.items())), profile=dict(sorted(profile.items())), live=live, physical=physical,
+                rank_mass=mass, deficit=320*T, namespace={'data':[0,live], 'centres':[live,live+8], 'tableau':[live+8,live+8+R], 'coefficient':[live+8+R,physical]},
+                local_prefix_bits=localbits, local_prefix_from_native_receipt=True, local_profile_recounted=True,
+                prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], margin=4),
+                prefix_bits=prefix, charged_prefix_bits=1024, physical_stock_bits=stock.bit_length(),
+                physical_row_coefficient=row, row_limit=20161,
+                scope='Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.')
+
+
+def controls(context, roles):
+    candidates = []
+    first = roles[0]
+    bad = dict(first, family=896*T)
+    candidates.append(('private_namespace_collision', [bad] + roles[1:], 'private-namespace collision'))
+    index = next(i for i, z in enumerate(roles) if z['replica'] >= 1)
+    bad = dict(roles[index], replica=roles[index]['replica'] - 1)
+    candidates.append(('copy_replica_alias', [bad] + roles[:index] + roles[index+1:], 'role invocation time'))
+    candidates.append(('missing_whole_helper', roles[1:], 'complete helper role count'))
+    split = dict(first, width=first['width'] - 1)
+    fragment = dict(first, offset=first['offset'] + first['width'] - 1, width=1)
+    candidates.append(('split_whole_helper', [split, fragment] + roles[1:], 'complete helper role count'))
+    candidates.append(('truncated_helper_width', [split] + roles[1:], 'whole-helper residual width'))
+    # Keep the family and chart valid, but move one complete role past its
+    # actual idle event. Freeze the original invocation order for controls.
+    crossing = None
+    for index, z in enumerate(roles):
+        lo, hi = context['windows'][z['owner_replica'], z['child']]
+        later = next((key for key in context['order'] if context['callpos'][key] >= hi), None)
+        if later is not None:
+            crossing = [dict(z, stage=later[0], replica=later[1], time=context['at'][later])] + roles[:index] + roles[index+1:]
+            break
+    require(crossing is not None, 'no idle-boundary control could be constructed')
+    candidates.append(('cross_idle_boundary', crossing, 'strict bridge-aware idle window'))
+    rejected = []
+    for name, bad, expected in candidates:
+        try:
+            check_roles(context, bad)
+        except ValueError as exc:
+            require(str(exc) == expected, 'control rejected at unexpected predicate: ' + name)
+            rejected.append(dict(name=name, reason=str(exc)))
+        else:
+            raise ValueError('accepted negative control: ' + name)
+    bad = dict(context, phases=copy.deepcopy(context['phases']))
+    pair = next((a, b) for a in context['rank'] for b in context['rank']
+                if a < b and (context['child_pair'][a], context['side'][a]) ==
+                (context['child_pair'][b], context['side'][b]))
+    children = bad['phases']['recipes'][0]['idle_children']
+    children[pair[1]]['orthogonal_axes'][0] = children[pair[0]]['orthogonal_axes'][0]
+    try:
+        check_pending_axes(bad)
+    except ValueError as exc:
+        require(str(exc) == 'overlapping pending children on one family',
+                'pending-axis control rejected at unexpected predicate')
+        rejected.append(dict(name='cross_child_pending_axis_alias', reason=str(exc)))
+    else:
+        raise ValueError('accepted negative control: cross_child_pending_axis_alias')
+    return rejected
+
+
+def main():
+    global T, EXPECTED_IDLE
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--baseline-parent', type=Path, required=True)
+    parser.add_argument('--owners', type=Path, required=True)
+    parser.add_argument('--word', type=Path, required=True)
+    parser.add_argument('--phases', type=Path)
+    parser.add_argument('--local-replay', type=Path)
+    parser.add_argument('--out', type=Path, required=True)
+    parser.add_argument("--replicas", type=int, required=True)
+    parser.add_argument("--expected-idle", required=True)
+    args = parser.parse_args()
+    T = args.replicas
+    require(T == 37, "replica range")
+    EXPECTED_IDLE = {int(k): v for k,v in json.loads(args.expected_idle).items()}
+    phases_path = args.phases or args.baseline_parent.parent.parent / 'work/complex-nine-native/DATA-PHASES.json'
+    canonical_path = args.baseline_parent.parent / 'CANONICAL-WORD.json.gz'
+    replay_path = args.local_replay or args.word.parent / 'INDEPENDENT-LOCAL-REPLAY.json'
+    parent, phases, canonical, word, replay, roles = map(read, (args.baseline_parent, phases_path, canonical_path, args.word, replay_path, args.owners))
+    require(replay['status'] == 'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY', 'local replay status')
+    require(replay['canonical_word_sha256'] == filehash(args.word), 'local word/replay hash binding')
+    require(set(replay['local']) == {'forward', 'backward'}, 'both native prefix orientations')
+    require(word['ports'] == canonical['ports'], 'local/controller port interface')
+    require(len(word['center_frames']) == len(canonical['center_frames']) == 8, 'eight centre interfaces')
+    require([basis(word['frames'][f]) for f in word['center_frames']] == [basis(canonical['frames'][f]) for f in canonical['center_frames']], 'ordered centre-frame interface')
+    context = make_context(parent, phases, canonical['ports'], word, replay, roles)
+    pending = check_pending_axes(context)
+    receipt = check_roles(context, roles)
+    receipt['disjoint_pending_child_axis_checks'] = pending
+    receipt['controls_rejected'] = controls(context, roles)
+    receipt['input_sha256'] = {str(path): filehash(path) for path in (args.baseline_parent, phases_path, canonical_path, args.word, replay_path, args.owners)}
+    args.out.write_text(json.dumps(receipt, indent=2) + '\n', encoding='utf-8')
+    print(receipt['status'], 'roles=' + str(receipt['roles']), 'controls=' + str(len(receipt['controls_rejected'])))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/k8-x54-t37/inputs/PLAN.json b/research/k8-x54-t37/inputs/PLAN.json
new file mode 100644
index 0000000000..b0463a14ae
--- /dev/null
+++ b/research/k8-x54-t37/inputs/PLAN.json
@@ -0,0 +1,85660 @@
+{
+  "status": "FROZEN_EXPLICIT_T16_TWO_BANK_DIRECT_SUM_OWNER_NOMINATION",
+  "mode": "gauge44-all144-t16-idle-concentration",
+  "K": 4,
+  "T": 16,
+  "M": 73,
+  "L": 9,
+  "live": 14336,
+  "deficit": 5120,
+  "profile": {
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+    "2": 60193,
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+      "actual_paid_profile": {
+        "1": 2412,
+        "2": 418,
+        "3": 434,
+        "4": 138,
+        "5": 84,
+        "8": 8
+      },
+      "orientation_program_sha256": {
+        "forward": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8",
+        "backward": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+      },
+      "artifact_semantic_sha256": {
+        "CANONICAL-WORD.json.gz": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+        "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3",
+        "LOCAL-CHECKS.json": "18f09b79835aa352f04d27041d86d1338c5ad0094b888588c1c05af2dc399ffd",
+        "INDEPENDENT-LOCAL-REPLAY.json": "2d4680965c62db1fde1236c4857b19bf7bc97af58805e6b4109afbc452f0fdd8",
+        "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+        "CLIFFORD-REVIEW.json": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+        "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+      }
+    }
+  },
+  "source_plan_sha256": "1dec4ca3af6d45d82286005cae4c5e56e7253adefb117d797da55c55c891af08",
+  "assignment_sha256": "2e1252f4e459bb957160e36715b212f3670d50979666d8496b99f39a50142271",
+  "source_owners_sha256": "32ca30cd1c652ef6ad43657273a08a157e1df3545e759ab36306a0d0b516fb4a",
+  "assignment_content_sha256": "64e0efcfbdd6e5dc0951afd915311f21a6a83f4d7702c68d353a09c36dd5b787",
+  "replica_lift": {
+    "groups": 2,
+    "source_replicas": 8,
+    "replicas": 16,
+    "parent_template_content_sha256": "8904bbbf46dfbf1c6df0e43479a23913fc59a410e879188112e88f16c850ede8",
+    "owners_file_sha256": "2e1252f4e459bb957160e36715b212f3670d50979666d8496b99f39a50142271",
+    "window_semantics": "strict physical source-event touch intervals, including bridges",
+    "schedule_content_sha256": "ef9b70f30251e90ca15f54e7802cedf9b2d23bdc150e8f2bc18c916d0f2f2312"
+  }
+}
diff --git a/research/k8-x54-t37/inputs/PR589-EXPECTED.json b/research/k8-x54-t37/inputs/PR589-EXPECTED.json
new file mode 100644
index 0000000000..e293ddc557
--- /dev/null
+++ b/research/k8-x54-t37/inputs/PR589-EXPECTED.json
@@ -0,0 +1,222 @@
+{
+ "word": {
+  "file": "tune/bitE8mut-p111-tuned.json.gz",
+  "file_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f",
+  "content_sha256": "5642fd0e35a1acc11acff8d0c08350c1617e95f310d4d35ad63a651f9eeeba0b",
+  "v": 111,
+  "R": 439,
+  "punctured": [
+   10,
+   15,
+   51,
+   53,
+   56,
+   66,
+   72,
+   89,
+   111
+  ],
+  "retained_totals": 9,
+  "copy_ranks": [
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7
+  ],
+  "decoder_constant": 63,
+  "gates": {
+   "D": 111,
+   "A": 2075,
+   "B": 712,
+   "C": 2574
+  },
+  "local_histogram": {
+   "1": 1323,
+   "2": 1342,
+   "3": 79,
+   "4": 44,
+   "5": 102,
+   "6": 11,
+   "7": 19
+  },
+  "legality": {
+   "records": 27234,
+   "common_frame_ADDs": 24305,
+   "rank_mass": 5129
+  },
+  "five_stage_columns": 883,
+  "five_stage_payload_bits": 93,
+  "nine_stage_columns": 1327,
+  "nine_stage_payload_bits": 93,
+  "eleven_stage_columns": 1549,
+  "eleven_stage_payload_bits": 93,
+  "base_content_sha256": "d0df3c89ae84989f4045ba1681a5e2e9fcdfa38ed0301c8abf5185537155cbe3"
+ },
+ "interface": {
+  "hypotheses": {
+   "H1_no_target_feeds_z": true,
+   "H2_D_frame0_targets_from_helpers": true,
+   "H3_A_z_only_scatter_targets_B_split": true,
+   "H4_C_literal_reverse_at_full": true,
+   "H5_V_identity": true
+  },
+  "conclusion": {
+   "U_block_form": true,
+   "J_identity": true,
+   "K_equals_D": true,
+   "C_is_U_inverse": true
+  },
+  "interleaving": {
+   "z_gates_A": 2075,
+   "source_writes_A": 0,
+   "z_gates_B": 499,
+   "source_writes_B": 483,
+   "helper_writes_B": 16,
+   "sources_rewritten_B": 108,
+   "B_z_write_frame_dims": {
+    "4": 388,
+    "6": 111
+   },
+   "B_z_operand_kinds": {
+    "helper<-helper": 3,
+    "helper<-source": 13,
+    "source<-helper": 108,
+    "source<-source": 375
+   },
+   "B_z_operand_kinds_by_dim": {
+    "dim4:helper<-source": 13,
+    "dim4:source<-source": 375,
+    "dim6:helper<-helper": 3,
+    "dim6:source<-helper": 108
+   },
+   "B_z_writes_after_a_target_read_of_the_same_register": 454,
+   "B_target_reads_of_registers_rewritten_earlier_in_B": 111,
+   "target_reads_of_targets": 0,
+   "cleanup_gates": 2574
+  }
+ },
+ "nine": {
+  "pipeline": "PR #510 (PR #463 nine-stage template, 32 replicas, PR #442 hosting, PR #493 outer assembly), parameterised for v <= 120 by code/adapt9p.py",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_lower_decimal": "0.001733427039589844234749",
+  "profile": {
+   "1": 381024,
+   "2": 400416,
+   "3": 22752,
+   "4": 26880,
+   "5": 29376,
+   "6": 17376,
+   "7": 26784,
+   "42": 288
+  },
+  "bit": {
+   "live": 28416,
+   "physical": 28425,
+   "maxchild": 42,
+   "rank_mass": 1808352,
+   "hosted_residuals": 126432,
+   "bank_assignments": 0,
+   "prefix_bits": 177,
+   "charged_prefix_bits": 192,
+   "coefficient_bits": 177,
+   "two_level_coefficient_bits": 393,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "eleven": {
+  "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting), parameterised by PR #545's code/adapt.py",
+  "bit_lower": "855475950388791987811/500000000000000000000000",
+  "bit_lower_decimal": "0.001710951900777583975622",
+  "profile": {
+   "1": 116424,
+   "2": 121648,
+   "3": 6952,
+   "4": 7424,
+   "5": 8976,
+   "6": 4520,
+   "7": 8776,
+   "56": 2600
+  },
+  "bit": {
+   "live": 8880,
+   "physical": 8889,
+   "maxchild": 56,
+   "rank_mass": 689304,
+   "hosted_residuals": 38632,
+   "prefix_bits": 4304,
+   "charged_prefix_bits": 4352,
+   "coefficient_bits": 4304,
+   "three_level_coefficient_bits": 12966,
+   "charged_three_level_coefficient_bits": 12992,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "793b6f40c9aa4b8db57fec0ac0973e16884dae28707e482ee8f7a2349a5d5a4b",
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "base": {
+  "nine_bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "nine_bit_lower_decimal": "0.001733052823330162099157",
+  "eleven_bit_lower": "427652201524503168379/250000000000000000000000",
+  "eleven_bit_lower_decimal": "0.001710608806098012673516",
+  "note": "PR #555's EXPECTED.json (untuned word); the tune/ pipeline is the same, with the same frozen hosting selections"
+ }
+}
diff --git a/research/k8-x54-t37/inputs/RESULT.json b/research/k8-x54-t37/inputs/RESULT.json
new file mode 100644
index 0000000000..c34aef055f
--- /dev/null
+++ b/research/k8-x54-t37/inputs/RESULT.json
@@ -0,0 +1,109 @@
+{
+  "status": "PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY",
+  "kappa": "66906048756761/40000000000000000",
+  "kappa_decimal": "0.001672651218919025",
+  "conservative_kappa_decimal": "0.001672651216067113",
+  "complex_lower": "67018146741598030641/40000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "complex_profile": {
+    "1": 349602,
+    "2": 60193,
+    "3": 62592,
+    "4": 20448,
+    "5": 11808,
+    "7": 4,
+    "8": 1152,
+    "48": 4866
+  },
+  "idle_remainder_profile": {
+    "1": 2274,
+    "2": 1,
+    "3": 384,
+    "7": 4,
+    "48": 4866
+  },
+  "complete_invocations": 144,
+  "roles": 69120,
+  "prefix_bits": 397,
+  "charged_prefix_bits": 512,
+  "physical_row_coefficient": 16469,
+  "retained_row_coefficient": 20161,
+  "actual_73_axis_charts": 10200,
+  "controls": {
+    "admission": 69,
+    "bit_supplier": 12,
+    "independent_t16": 6,
+    "controller_mutations": 15
+  },
+  "t8_kappa": "167166528321877/100000000000000000",
+  "spec_sha256": "7f5f710df21fe48079b4c79727953ff41cd8bec688592578554109ebf6b6d929",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 3.719,
+      "exit_code": 0,
+      "log_sha256": "3aea2a4b68e7aaeadd9ffef649be0d25e2dff1535d9a61bffeaf6d92e55ba6a8"
+    },
+    {
+      "name": "bind8",
+      "seconds": 0.922,
+      "exit_code": 0,
+      "log_sha256": "78a081673d6b4fde10a86e6f767d53648b868d1f0cac2441d12951434ad7341b"
+    },
+    {
+      "name": "lift16",
+      "seconds": 4.437,
+      "exit_code": 0,
+      "log_sha256": "f38fc6d2a39b8779e04f7c787c4d668c2f9e359a1de069b63a6c177a9ca9b2bc"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.734,
+      "exit_code": 0,
+      "log_sha256": "78a081673d6b4fde10a86e6f767d53648b868d1f0cac2441d12951434ad7341b"
+    },
+    {
+      "name": "emit",
+      "seconds": 10.468,
+      "exit_code": 0,
+      "log_sha256": "67bc257d4a163312137b43eef4270bffca031b565e7221e96c476216ee007565"
+    },
+    {
+      "name": "audit",
+      "seconds": 59.969,
+      "exit_code": 0,
+      "log_sha256": "089b0fa21e04d000d0601c61895aa5adfeacdc9fcd192ea1ef859ad48ef8f1cd"
+    },
+    {
+      "name": "invoice",
+      "seconds": 3.343,
+      "exit_code": 0,
+      "log_sha256": "caa1229b78eca961462d35e8ee458be536111111a985294a153e4dd74b9171a8"
+    },
+    {
+      "name": "assembly",
+      "seconds": 1.156,
+      "exit_code": 0,
+      "log_sha256": "eee609c93b4647fc340f4041ba763ced4d2df47cb94dd3d7ed83ceb3005b56ce"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 1.391,
+      "exit_code": 0,
+      "log_sha256": "34527ddfe1e53bec71dc5759eb9a26417be6d4e93e76cbf80575d9bafebd876b"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 1.703,
+      "exit_code": 0,
+      "log_sha256": "c648542cd6dddbb154af7d02a41aaed1025603d9a4ab54f7c249d2b683e22249"
+    },
+    {
+      "name": "independent-t16",
+      "seconds": 3.062,
+      "exit_code": 0,
+      "log_sha256": "d2c13b333d463a5c2de42078e9c47a89209075e1d1beac24cf3fc1f573f18c05"
+    }
+  ],
+  "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. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. 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."
+}
diff --git a/research/k8-x54-t37/inputs/SPEC.json b/research/k8-x54-t37/inputs/SPEC.json
new file mode 100644
index 0000000000..0dd69ec585
--- /dev/null
+++ b/research/k8-x54-t37/inputs/SPEC.json
@@ -0,0 +1,1973 @@
+{
+  "schema": "witness-spec/1",
+  "name": "gauge44-t16-two-bank",
+  "data": {
+    "plan_sha256": "68c110602df12bd7de3749514224021ef1ef0ebcf072d7c727f9b66099fbebb1",
+    "owners_sha256": "2e1252f4e459bb957160e36715b212f3670d50979666d8496b99f39a50142271"
+  },
+  "dispatch": [
+    [
+      0,
+      0,
+      "gauge44"
+    ],
+    [
+      0,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      1,
+      "gauge44"
+    ],
+    [
+      0,
+      9,
+      "gauge44"
+    ],
+    [
+      1,
+      0,
+      "gauge44"
+    ],
+    [
+      1,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      2,
+      "gauge44"
+    ],
+    [
+      0,
+      10,
+      "gauge44"
+    ],
+    [
+      1,
+      1,
+      "gauge44"
+    ],
+    [
+      1,
+      9,
+      "gauge44"
+    ],
+    [
+      2,
+      0,
+      "gauge44"
+    ],
+    [
+      2,
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diff --git a/research/k8-x54-t37/inputs/local/CANONICAL-WORD.json.gz b/research/k8-x54-t37/inputs/local/CANONICAL-WORD.json.gz
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index 0000000000..4dd73325af
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diff --git a/research/k8-x54-t37/inputs/local/CLIFFORD-RECIPES.json b/research/k8-x54-t37/inputs/local/CLIFFORD-RECIPES.json
new file mode 100644
index 0000000000..eab7072831
--- /dev/null
+++ b/research/k8-x54-t37/inputs/local/CLIFFORD-RECIPES.json
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diff --git a/research/k8-x54-t37/inputs/local/CLIFFORD-REVIEW.json b/research/k8-x54-t37/inputs/local/CLIFFORD-REVIEW.json
new file mode 100644
index 0000000000..1bb5dda929
--- /dev/null
+++ b/research/k8-x54-t37/inputs/local/CLIFFORD-REVIEW.json
@@ -0,0 +1,19 @@
+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
+  "canonical_word_sha256": "75507b67a784bd1e54e1451b6263624fe4d05bd08b850c4fb87c82776ec1909a",
+  "frames": 1004,
+  "directed_edges": 2896,
+  "ranks": {
+    "1": 1928,
+    "2": 380,
+    "3": 410,
+    "8": 16,
+    "4": 120,
+    "5": 42
+  },
+  "endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "7ed4c7e81ace3e7837067167745d2ca1bc3212079de284e76760c1c45b31d0ce",
+  "seconds": 291.1772421120004,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations."
+}
diff --git a/research/k8-x54-t37/inputs/local/FULL-WORD.json.gz b/research/k8-x54-t37/inputs/local/FULL-WORD.json.gz
new file mode 100644
index 0000000000..fd3903d17b
Binary files /dev/null and b/research/k8-x54-t37/inputs/local/FULL-WORD.json.gz differ
diff --git a/research/k8-x54-t37/inputs/local/INDEPENDENT-LOCAL-REPLAY.json b/research/k8-x54-t37/inputs/local/INDEPENDENT-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..02016b45a3
--- /dev/null
+++ b/research/k8-x54-t37/inputs/local/INDEPENDENT-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "75507b67a784bd1e54e1451b6263624fe4d05bd08b850c4fb87c82776ec1909a",
+  "local_programs_sha256": "43b7cd0eafaf840288ee7d1695dac5b5905033ca7f2df4bd9517e75387db5857",
+  "v": 112,
+  "helpers": 480,
+  "local": {
+    "forward": {
+      "all_exact_columns": 704,
+      "prefix_l1_upper": "2765345371136269591/1024",
+      "prefix_bits_upper": 52,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    },
+    "backward": {
+      "all_exact_columns": 704,
+      "prefix_l1_upper": "14824960514781440791821/64",
+      "prefix_bits_upper": 68,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    }
+  },
+  "paid_profiles": {
+    "forward": {
+      "1": 2412,
+      "4": 138,
+      "8": 8,
+      "3": 434,
+      "2": 418,
+      "5": 84
+    },
+    "backward": {
+      "1": 2412,
+      "4": 138,
+      "8": 8,
+      "3": 434,
+      "2": 418,
+      "5": 84
+    }
+  },
+  "entering_helpers": 192,
+  "cold_hyperplane_ended_helpers": 48,
+  "negative_controls_rejected": [
+    "wrong_scale",
+    "missing_center",
+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "hpe_pre_wrapper_resolved_to_full_recipe",
+    "hpe_post_wrapper_without_terminal_frame",
+    "hpe_post_wrapper_wrong_terminal_frame",
+    "hpe_tail_gate_at_full_frame",
+    "hpe_tail_climb_dropped",
+    "hpe_helper_exit_adapter_to_full",
+    "hpe_tail_gate_moved_into_full_cleanup",
+    "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+    "cold_hpe_pre_wrapper_dropped",
+    "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+    "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+    "cold_hpe_wrapper_with_nonzero_entrance",
+    "cold_hpe_post_wrapper_wrong_terminal_frame",
+    "cold_hpe_premix_gate_before_pre_wrapper"
+  ],
+  "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate."
+}
diff --git a/research/k8-x54-t37/inputs/local/LOCAL-CHECKS.json b/research/k8-x54-t37/inputs/local/LOCAL-CHECKS.json
new file mode 100644
index 0000000000..a7a9214248
--- /dev/null
+++ b/research/k8-x54-t37/inputs/local/LOCAL-CHECKS.json
@@ -0,0 +1,36 @@
+{
+  "forward": {
+    "sha256": "00a232a940f27da7842c9efa49e8eca3c7a399edde920b2c742006f8f4938dad",
+    "events": 24769,
+    "scalar_macros": 19695,
+    "real_component_primitive_bound": 198782,
+    "paid_profile": {
+      "1": 2412,
+      "2": 418,
+      "3": 434,
+      "4": 138,
+      "5": 84,
+      "8": 8
+    },
+    "all_columns": 704,
+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  },
+  "backward": {
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+  "seconds": 2.7339988719995745,
+  "scope": "Fresh exact forward and inverse-transpose scalar replay on every arbitrary input; all native frame chains and dyadic primitives. Phase lowering, wrappers, global owners and global assembly are separate.",
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+  ],
+  "early_cleanup_gates": 117,
+  "cold_hyperplane_ended_helpers": [
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+  ],
+  "refactored_cleanup_gates": 6798,
+  "refactored_cleanup": {
+    "cold_low_frame_ended_helpers": [
+      273,
+      275,
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+      282,
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+    ],
+    "construction": "; G44Stack premix-only factored entering ends 554,555,566,567 (start frame [24]); G44Stack premix-only factored entering ends 586,588,531,543 (start frame [30]); CarrierBypass premix-only factored cold ends 513,574,575,573,581,582; CarrierBypass premix-only factored cold ends 572,583,580,512; CarrierBypass premix-only factored cold ends 500,501,311,498,510,327",
+    "entering_low_frame_ended_helpers": [
+      531,
+      543,
+      554,
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+      567,
+      586,
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+    ],
+    "exact_non_target_isolation_checked": true,
+    "forward_absorption_A_indices": [],
+    "forward_absorptions": 0,
+    "high_inverse": "dyadic_sparse_Gauss_Jordan",
+    "kind": "source_branch_gauge_and_retired_completion_cold44",
+    "lower_frame_gates": 81,
+    "new_cold_ends": 32,
+    "premix_gates": 1190,
+    "premix_target_writes": 0
+  }
+}
diff --git a/research/k8-x54-t37/inputs/local/WRAPPER-CHECKS.json b/research/k8-x54-t37/inputs/local/WRAPPER-CHECKS.json
new file mode 100644
index 0000000000..8b07253ef3
--- /dev/null
+++ b/research/k8-x54-t37/inputs/local/WRAPPER-CHECKS.json
@@ -0,0 +1,396 @@
+{
+ "status": "PASS_RESIDUAL_WRAPPERS_ARE_EXACT",
+ "frames": 22,
+ "hyperplane_end_pairs": [
+  {
+   "frame": 0,
+   "terminal": 124,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 153,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
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+   "terminal": 182,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
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+   "terminal": 211,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
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+   "terminal": 240,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
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+   "terminal": 269,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
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+   "terminal": 298,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 327,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 1000,
+   "entrance_rank": 0,
+   "terminal_rank": 8,
+   "residual_width": 8
+  },
+  {
+   "frame": 0,
+   "terminal": 1001,
+   "entrance_rank": 0,
+   "terminal_rank": 8,
+   "residual_width": 8
+  },
+  {
+   "frame": 0,
+   "terminal": 1002,
+   "entrance_rank": 0,
+   "terminal_rank": 8,
+   "residual_width": 8
+  },
+  {
+   "frame": 0,
+   "terminal": 1003,
+   "entrance_rank": 0,
+   "terminal_rank": 8,
+   "residual_width": 8
+  },
+  {
+   "frame": 2,
+   "terminal": 999,
+   "entrance_rank": 1,
+   "terminal_rank": 8,
+   "residual_width": 7
+  },
+  {
+   "frame": 3,
+   "terminal": 998,
+   "entrance_rank": 1,
+   "terminal_rank": 8,
+   "residual_width": 7
+  }
+ ],
+ "cold_hyperplane_end_pairs": 12,
+ "wrappers_reject": [
+  "wrong global phase",
+  "wrong translation",
+  "wrong quadratic form",
+  "sides swapped",
+  "wrong width",
+  "hpe: U-wrapper decoded against a FULL ending",
+  "hpe: width misreported as 9 - dim E",
+  "hpe: wrong terminal hyperplane",
+  "hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}",
+  "hpe: wrong global phase",
+  "cold hpe: identity pre wrapper instead of R_{0,U}",
+  "cold hpe: identity post wrapper instead of L_{0,U}",
+  "cold hpe: no wrappers (cold FULL convention L = R = I)",
+  "cold hpe: U-wrapper decoded against a FULL ending",
+  "cold hpe: width misreported as 9",
+  "cold hpe: wrong terminal hyperplane",
+  "cold hpe: wrong global phase"
+ ],
+ "all_even_weight": false,
+ "all_totally_isotropic": false,
+ "detail": [
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+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
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+   "totally_isotropic": false
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+   "totally_isotropic": false
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+  }
+ ]
+}
diff --git a/research/k8-x54-t37/lift.py b/research/k8-x54-t37/lift.py
new file mode 100644
index 0000000000..7864acbe03
--- /dev/null
+++ b/research/k8-x54-t37/lift.py
@@ -0,0 +1,178 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Build the fixed T37 bank envelope and its source-event windows."""
+import argparse
+import copy
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import importlib.util
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+
+
+def need(ok, reason):
+    if not ok:
+        raise ValueError(reason)
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+
+def canonical(value):
+    return json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+
+
+def identity(value):
+    return hashlib.sha256(canonical(value)).hexdigest()
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def write_gzip(path, value):
+    raw = bytearray(gzip.compress(canonical(value), mtime=0))
+    raw[9] = 255
+    path.write_bytes(raw)
+
+
+def lift(source):
+    need((source['live'], source['physical']) == (11704, 12218), 'T8 source stock')
+    data0, bank0, data, live = 7168, 4536, 33152, 55832
+    groups = (8, 8, 8, 8, 5)
+    target = copy.deepcopy(source)
+    target['calls'] = []
+    for call in source['calls']:
+        for group, lanes in enumerate(groups):
+            if call['replica'] >= lanes:
+                continue
+            new = copy.deepcopy(call)
+            new['replica'] += 8*group
+            new['owners'] = [[family+data0*group if family < data0 else
+                              data+group*bank0+family-data0, route]
+                             for family, route in new['owners']]
+            target['calls'].append(new)
+    for child in target['idle_children']:
+        need(child['replicas'] == 8, 'T8 idle multiplicity')
+        child['replicas'] = 37
+    for event in target['execution_schedule']:
+        if 'replicas' in event:
+            need(event['replicas'] == list(range(8)), 'T8 sweep multiplicity')
+            event['replicas'] = list(range(37))
+        if event['kind'] == 'bank_padding_cover_sweep':
+            event['families'] = [data, live]
+        elif event['kind'] == 'translate_every_live_family':
+            event.update(families=[0, live], charged_calls_per_cover=live)
+    target['bank_padding']['families'], target['bank_padding']['children'] = [], []
+    for group, lanes in enumerate(groups):
+        for child in source['bank_padding']['children']:
+            new = copy.deepcopy(child)
+            new['family'] = data+group*bank0+child['family']-data0
+            width, remainder = divmod(73-child['rank'], 8)
+            need(remainder == 0 and 1 <= width <= 9, 'dedicated bank width')
+            need(child['axis_indices'] == list(range(8*width, 73)), 'original complement indices')
+            need(list(map(int, child['orthogonal_axes'])) ==
+                 [1 << i for i in child['axis_indices']], 'original complement axes')
+            new.update(axis_indices=list(range(lanes*width, 73)), rank=73-lanes*width)
+            new['orthogonal_axes'] = [1 << i for i in new['axis_indices']]
+            target['bank_padding']['children'].append(new)
+            target['bank_padding']['families'].append(new['family'])
+    target['bank_padding']['semantics'] = (
+        'Each complement follows the complete calls in its bank group. '
+        'Final hosting removes all dedicated banks and their padding children.')
+    target['cover_final_correction'].update(families=[0, live], charged_calls_per_cover=live)
+    target['private_namespace'] = {key: [live+x-source['live'] for x in interval]
+                                  for key, interval in source['private_namespace'].items()}
+    target.update(live=live, physical=live+514, version='r480-t37-bank-envelope-v1')
+    target['route_semantics']['helper'] = (
+        'The bank group is replica//8. Each local lane is replica%8. '
+        'Residual and spectator routes retain their source coordinates.')
+    target['replica_lift'] = dict(groups=list(groups), replicas=37, data_stock=data,
+                                 bank_stock=22680, source_template_content_sha256=identity(source),
+                                 phase_recipe_unchanged=True)
+    return target
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--base', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    need(not args.out.exists(), 'Choose a new lift directory')
+    original = read(HERE / 'vendor/pr1074/T8/PLAN.json')
+    owner_path = HERE / 'OWNERS.json.gz'
+    owners, order = read(owner_path), read(HERE / 'ORDER.json')
+    source = read(args.base / 'split-centres/GLOBAL-TEMPLATE.json.gz')
+    need(source['exact_data_phase_recipe_sha256'] ==
+         sha(args.base / 'work/complex-nine-native/DATA-PHASES.json'), 'data phase binding')
+    module_path = HERE / 'vendor/pr1074/t16/build_parent.py'
+    spec = importlib.util.spec_from_file_location('source_windows', module_path)
+    windows_module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(windows_module)
+    need(windows_module.actual_windows(source, original['order'])[0] == original['windows'],
+         'T8 source window replay')
+    parent = lift(source)
+    windows, schedule = windows_module.actual_windows(parent, order)
+    used = defaultdict(set)
+    at = {tuple(key): time for time, key in enumerate(order)}
+    need(len(at) == 333 and len(owners) == 159840, 'complete call and helper inventory')
+    for role in owners:
+        need(role['time'] == at[role['stage'], role['replica']], 'role call time')
+        capacity, times = windows[f"{role['owner_replica']},{role['child']}"]
+        need(role['time'] in times, 'source-event window')
+        group = role['owner_replica'], role['child'], role['port']
+        cells = set(range(role['offset'], role['offset']+role['width']))
+        need(not (used[group] & cells) and max(cells) < capacity, 'whole-helper capacity')
+        used[group].update(cells)
+    idle = Counter()
+    for key, (capacity, _) in windows.items():
+        replica, child = map(int, key.split(','))
+        for port in range(112):
+            cells = used[replica, child, port]
+            need(cells == set(range(len(cells))), 'pending prefix')
+            if len(cells) < capacity:
+                idle[capacity-len(cells)] += 1
+    need(idle == {1: 5622, 48: 11302}, 'attaining idle profile')
+    local = {int(r): n for r, n in original['provider_registry']['gauge44']['actual_paid_profile'].items()}
+    profile = Counter({r: 333*n for r, n in local.items()})
+    profile.update(idle)
+    plan = copy.deepcopy(original)
+    plan.update(T=37, live=33152, deficit=11840, order=order, windows=windows,
+                profile={str(r): n for r, n in sorted(profile.items())},
+                status='FROZEN_EXPLICIT_R480_T37_OWNER_NOMINATION',
+                mode='seven-slot-k8-all-replica-optimum',
+                solver_status='Frozen exact pattern flow and bipartite matching decomposition', gap=None)
+    for field in ('provider_calls', 'per_call_widths'):
+        bycall = {(c['stage'], c['replica']): c for c in original[field]}
+        plan[field] = []
+        for time, (stage, replica) in enumerate(order):
+            call = copy.deepcopy(bycall[stage, replica % 8])
+            call['replica'] = replica
+            if 'time' in call:
+                call['time'] = time
+            plan[field].append(call)
+    plan['assignment_sha256'] = sha(owner_path)
+    plan['assignment_content_sha256'] = identity(owners)
+    plan['replica_lift'] = dict(groups=[8, 8, 8, 8, 5], source_replicas=8, replicas=37,
+                               parent_template_content_sha256=identity(parent),
+                               owners_file_sha256=sha(owner_path), schedule_content_sha256=identity(schedule),
+                               window_semantics='Strict physical source-event intervals, including bridges')
+    need(sum(r*n for r, n in profile.items()) == 73*33152-11840, 'T37 rank mass')
+    args.out.mkdir(parents=True)
+    write_gzip(args.out / 'GLOBAL-TEMPLATE.json.gz', parent)
+    (args.out / 'PLAN.json').write_text(json.dumps(plan, indent=2)+'\n')
+    receipt = dict(status='PASS_R480_T37_BANK_LIFT_AND_WINDOWS', calls=333, roles=159840,
+                   parent_live=55832, parent_physical=56346, bank_groups=[8,8,8,8,5],
+                   idle=dict(sorted(idle.items())), literal_windows=len(windows),
+                   parent_content_sha256=identity(parent), schedule_content_sha256=identity(schedule))
+    (args.out / 'PARENT-LIFT.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(receipt['status'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/k8-x54-t37/replay.py b/research/k8-x54-t37/replay.py
new file mode 100644
index 0000000000..f28222c5d7
--- /dev/null
+++ b/research/k8-x54-t37/replay.py
@@ -0,0 +1,154 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Replay the fixed R480 T37 owner construction and its full finite invoice."""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import time
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def read(path):
+    return json.loads(path.read_text())
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def main():
+    need(not sys.flags.optimize, 'Retained checks require assertions')
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, default=ROOT)
+    parser.add_argument('--local', type=Path, default=HERE / 'inputs/local')
+    parser.add_argument('--work', type=Path, required=True)
+    parser.add_argument('--discover', action='store_true')
+    args = parser.parse_args()
+    main, local, work = args.main.resolve(), args.local.resolve(), args.work.resolve()
+    need(not work.exists(), 'Choose a new replay directory')
+    for relative, expected in read(HERE / 'SOURCE-FREEZE.json')['files'].items():
+        need(sha(HERE / relative) == expected, 'Package source changed: ' + relative)
+    upstream = main / 'research/complex-k492-owner-repair/vendor/multicold'
+    baseline = main / 'research/community-k492-audit/pr622/replay/baseline558'
+    source1074 = HERE / 'vendor/pr1074'
+    for relative, expected in read(source1074 / 'UPSTREAM-PINS.json').items():
+        need(sha(main / relative) == expected, 'Upstream dependency changed: ' + relative)
+    need(local.is_dir(), 'Native local directory is missing')
+    work.mkdir(parents=True)
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1',
+               PYTHONINTMAXSTRDIGITS='0', OPENBLAS_NUM_THREADS='1', OMP_NUM_THREADS='1',
+               MULTICOLD_SOURCE=str(upstream), GAIN_PR564_SOURCE=str(upstream))
+    for key in ('PYTHONOPTIMIZE', 'WITNESS_DISCOVER', 'WITNESS_RECORD', 'WITNESS_SPEC'):
+        env.pop(key, None)
+    stages = []
+
+    def run(name, script, *arguments, spec=None, discover=False):
+        started = time.monotonic()
+        command = [sys.executable, '-B', str(upstream / 'code/run_portable.py'),
+                   str(script), *map(str, arguments)]
+        childenv = dict(env)
+        if spec:
+            childenv['WITNESS_SPEC'] = str(spec)
+        if discover:
+            childenv.update(WITNESS_DISCOVER='1', WITNESS_RECORD=str(work / 'WITNESS-RECORD.jsonl'))
+        log = work / (name + '.log')
+        with log.open('w') as output:
+            result = subprocess.run(command, env=childenv, stdout=output, stderr=subprocess.STDOUT)
+        stages.append(dict(name=name, seconds=round(time.monotonic()-started, 3),
+                           exit_code=result.returncode, log_sha256=sha(log)))
+        (work / 'STAGES.json').write_text(json.dumps(stages, indent=2)+'\n')
+        need(result.returncode == 0, name + ' failed:\n' + log.read_text()[-6000:])
+        print('PASS', name, stages[-1]['seconds'], flush=True)
+
+    spec8 = source1074 / 'data/SPEC-T8.json'
+    run('restore-parent', source1074 / 'code/restore_parent.py', '--source', upstream,
+        '--baseline', baseline, '--out', work / 'parent558')
+    run('bind8', source1074 / 'code/bind_providers_portable.py', '--baseline', work / 'parent558',
+        '--provider', 'gauge44='+str(local), '--plan', source1074 / 'T8/PLAN.json',
+        '--out', work / 'global8', spec=spec8)
+    run('lift', HERE / 'lift.py', '--base', work / 'global8/base', '--out', work / 'lift')
+    plan = work / 'lift/PLAN.json'
+    if not args.discover:
+        need(read(plan) == read(HERE / 'data/PLAN.json'), 'Frozen T37 plan differs')
+    runtime = work / 'runtime'
+    (runtime / 'data').mkdir(parents=True)
+    shutil.copytree(source1074 / 'construction', runtime / 'construction')
+    specpath = runtime / 'data/SPEC.json'
+    if args.discover:
+        spec = read(spec8)
+        spec['name'] = 'r480-k8-x54-t37-owner-optimum'
+        spec['call_order'] = read(HERE / 'ORDER.json')
+        spec['dispatch'] = [[s, r, 'gauge44'] for s, r in spec['call_order']]
+        spec['providers'] = {}
+        spec['expected'] = {'gain_baseline_kappa': spec['expected']['gain_baseline_kappa']}
+        spec['data'] = dict(plan_sha256=sha(plan), owners_sha256=sha(HERE / 'OWNERS.json.gz'))
+        specpath.write_text(json.dumps(spec, indent=2)+'\n')
+    else:
+        shutil.copyfile(HERE / 'data/SPEC.json', specpath)
+    parent = work / 'parent37'
+    shutil.copytree(work / 'parent558', parent)
+    shutil.copyfile(work / 'lift/GLOBAL-TEMPLATE.json.gz',
+                    parent / 'complex-global/base/split-centres/GLOBAL-TEMPLATE.json.gz')
+    code, global_ = HERE / 'code', work / 'global'
+    def stage(name, script, *arguments):
+        run(name, code / script, *arguments, spec=specpath, discover=args.discover)
+    stage('bind', 'bind_providers_portable.py', '--baseline', parent, '--provider',
+          'gauge44='+str(local), '--plan', plan, '--out', global_)
+    stage('emit', 'emit_allcold.py', '--base', global_ / 'base', '--owners', HERE / 'OWNERS.json.gz',
+          '--plan', global_ / 'PLAN.json', '--out', global_ / 'hosted')
+    stage('audit', 'audit_allcold.py', global_ / 'base', global_ / 'hosted',
+          global_ / 'audit/ASYNC-AUDIT.json', '--mutation-controls')
+    retained = upstream / 'vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json'
+    stage('invoice', 'invoice_allcold.py', '--base', global_ / 'base', '--hosted', global_ / 'hosted',
+          '--audit', global_ / 'audit', '--out', global_ / 'audit', '--retained-invoice', retained)
+    stage('assembly', 'assemble.py', upstream, global_, work / 'ASSEMBLY.json')
+    if args.discover:
+        run('freeze', code / 'freeze_spec.py', '--spec', specpath, '--discovery', work)
+    else:
+        for name, script, filename in [('admission-controls', 'assembly_controls.py', 'ADMISSION-CONTROLS.json'),
+                                        ('bit-controls', 'bit_supplier_controls.py', 'BIT-CONTROLS.json')]:
+            stage(name, script, '--source-package', upstream, '--owner', global_ / 'audit/OWNERS-AND-PROFILE.json',
+                  '--invoice', global_ / 'audit/PREFIX-AND-INVOICE.json', '--out', work / filename)
+    run('independent-owner', HERE / 'independent_owner.py', '--baseline-parent',
+        work / 'global8/base/split-centres/GLOBAL-TEMPLATE.json.gz', '--owners', HERE / 'OWNERS.json.gz',
+        '--word', local / 'CANONICAL-WORD.json.gz', '--out', work / 'INDEPENDENT-OWNER.json',
+        '--replicas', 37, '--expected-idle', '{"1":5622,"48":11302}')
+    assembly = read(work / 'ASSEMBLY.json')
+    owner = read(work / 'INDEPENDENT-OWNER.json')
+    invoice = read(global_ / 'audit/PREFIX-AND-INVOICE.json')
+    need(owner['profile'] == assembly['complex_profile'], 'Independent complete profile')
+    need(owner['prefix_bits'] == invoice['global_prefix_bits'] < 1024, 'Independent prefix bound')
+    need(owner['physical_row_coefficient'] == invoice['finite']['physical_row_coefficient'] < 20161,
+         'Independent physical row bound')
+    need(owner['roles'] == 159840 and owner['calls'] == 333 and owner['deficit'] == 11840,
+         'Complete fixed construction')
+    need(assembly['kappa_decimal'] == '0.001674137810105185', 'Attained bound')
+    if not args.discover:
+        admission, bit = read(work / 'ADMISSION-CONTROLS.json'), read(work / 'BIT-CONTROLS.json')
+        need(len(admission['rejected_controls']) == 69 and not admission['discovery_accepted_controls'],
+             'Complete strict admission controls')
+        need(len(bit['rejected_controls']) == 12, 'Complete bit controls')
+    receipt = dict(status='DISCOVERY_R480_T37' if args.discover else 'PASS_R480_T37_STRICT_FINITE_CONSTRUCTION',
+                   kappa=assembly['kappa'], kappa_decimal=assembly['kappa_decimal'],
+                   roles=159840, calls=333, prefix_bits=owner['prefix_bits'], charged_prefix_bits=1024,
+                   physical_row_coefficient=owner['physical_row_coefficient'],
+                   stages=stages, local_input_sha256={p.name: sha(p) for p in local.iterdir() if p.is_file()},
+                   scope='Finite owner, controller, chart, invoice and assembly replay. Local scalar and phase replay and inherited all-size obligations are recorded separately.')
+    (work / 'RESULT.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(receipt['status'], receipt['kappa_decimal'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/k8-x54-t37/vendor/pr1074/LICENSE b/research/k8-x54-t37/vendor/pr1074/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
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+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
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+   6. Trademarks. This License does not grant permission to use the trade
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+      origin of the Work and reproducing the content of the NOTICE file.
+
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+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
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+
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+
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+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
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+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
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+   limitations under the License.
diff --git a/research/k8-x54-t37/vendor/pr1074/NOTICE.md b/research/k8-x54-t37/vendor/pr1074/NOTICE.md
new file mode 100644
index 0000000000..30d0c8cd3c
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/NOTICE.md
@@ -0,0 +1,24 @@
+# Gauge44 attribution and scope
+
+New contributions by icekylinx, with OpenAI GPT-6 Astra assistance.
+Local review and packaging used OpenAI Codex. Apache-2.0 applies;
+the license is included. The full original PR635 notice is preserved as
+UPSTREAM-NOTICE.md and construction/UPSTREAM-NOTICE.md.
+
+The new contribution is the changed source-branch gauge and retired-row
+completion, source-carried coordinate totals, exact 44-cold-end realization,
+and explicit all72 whole-family assignment using concave capacity matching
+with integer majorization certificates. The center-carrier generalization
+retains the exact ordered common frames and complete native local contract.
+Independent local, price, interface and owner fixed-point checks are included.
+
+The construction retains the credited PR635 K-triangle and porting machinery,
+earlier joint-prefix/HPE/frame ancestry and icekylinx's prior factory work.
+#645 used the same cited PR543 bit supplier as PR635. This package (research/gauge44-leaver8) cites the merged PR589 bit supplier instead, with a derived rank-mass deficit (PROOF-NOTE-BIT.md); #645's retained PR543-based evidence is historical. It builds #645's word without K-triangles (PartialK) and stacks earlier community jp8 layers on it (G44Stack), adds the p6n ends (NoTriReopen), entrance promotions (BlockInvert) a read-set exchange (BRoute), chafreaky's #741 frames, JointXF's joint exchange, NewBArch's triangle-hybrid B rewrite and LeaverSAT's eight k8 leaver cells (with LeaverSAT2's frame re-optimisation); see README. All-size, realization,
+hosting, precision/tape, analytic-transfer and bit H1-H5 assumptions remain
+conditional. No upstream license, credit, source pin or AI disclosure is
+replaced by this notice.
+
+PR641 and PR642 were checked as concurrent reported frontier comparisons.
+Their endpoints and owner maps are not included here. See CONSTRUCTION.md,
+hosting/PROOF.md, independent/ and README.md for the exact contribution scope.
diff --git a/research/k8-x54-t37/vendor/pr1074/T8/PLAN.json b/research/k8-x54-t37/vendor/pr1074/T8/PLAN.json
new file mode 100644
index 0000000000..073daeb4c0
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/T8/PLAN.json
@@ -0,0 +1,40249 @@
+{
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+      },
+      "orientation_program_sha256": {
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+        "backward": "d93c027a832200728ff23f420042d43a9cb0016a41e995ee12538776ab3704b7"
+      },
+      "artifact_semantic_sha256": {
+        "CANONICAL-WORD.json.gz": "c1900aa7398e34916fe5b57553ca7d1cea6283143be6bb4ccf39321a84263a6c",
+        "LOCAL-PROGRAMS.json.gz": "7e326f73db4037580b298ecb59e6357f286c4ba048f3a05077388b43c68fcaff",
+        "LOCAL-CHECKS.json": "6ff1d2b4e60002bfa7051fd7adb8db3d41ed8312ca959b2710ec41a7718b9712",
+        "INDEPENDENT-LOCAL-REPLAY.json": "58531ad056cd658f0d77480879b4fd5d33cbd865d32dc1a216e041c32a4c8aa2",
+        "CLIFFORD-RECIPES.json": "7ed4c7e81ace3e7837067167745d2ca1bc3212079de284e76760c1c45b31d0ce",
+        "CLIFFORD-REVIEW.json": "9c2f14d22422ec61a77786cd2b007d779aac5d2b93d3e2edb95d9790a62c448c",
+        "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+      }
+    }
+  },
+  "source_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "assignment_sha256": "32ca30cd1c652ef6ad43657273a08a157e1df3545e759ab36306a0d0b516fb4a",
+  "source_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add"
+}
diff --git a/research/k8-x54-t37/vendor/pr1074/UPSTREAM-NOTICE.md b/research/k8-x54-t37/vendor/pr1074/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/k8-x54-t37/vendor/pr1074/UPSTREAM-PINS.json b/research/k8-x54-t37/vendor/pr1074/UPSTREAM-PINS.json
new file mode 100644
index 0000000000..68486b84e3
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/UPSTREAM-PINS.json
@@ -0,0 +1,23 @@
+{
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-RECIPES.json": "534ace870cabe515987e00f50f71550030965006ea18978e0924590ac6944345",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-REVIEW.json": "ee9b86428278392d2c933f76d60e51f5af90d4ab67e4d3937ed2fa416e7755ab",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-LOCAL-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INTEGRATION.json": "5c14538134dfffbc58fa4b4d2f26b270ec5f56d17d4bf23752c82964f45171db",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-CHECKS.json": "79177449e404403964ce1b2f4a9a8bd49e1916daba3123d7fd7f5cfd1f1ac0ea",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-PROGRAMS.json.gz": "99a18eede965accf65943e490b8d2b2ffb9f1c9bc6babdb825413a80cbea2cde",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/RESIDUAL-ADAPTERS.json": "baafef737acc16dafbe1150896feb16744f3d669fa123bb2bff19ecc4e71b275",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/SCALAR-FRAME-AUDIT.json": "73b3601a6239502475a272ea0c46945fd42034486aaf43e66a212eb4f012ca44",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/WRAPPER-CHECKS.json": "9a09146e686c4f535b04fdef3753fe01dad8f5e8881a69408a91394acb5b48f5",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "research/complex-k492-owner-repair/vendor/multicold/inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py": "f5eae94aca965d0008bc07cff8245ccb7509042ccad457d3bcb7d51c1e9409f0"
+}
diff --git a/research/k8-x54-t37/vendor/pr1074/code/assemble.py b/research/k8-x54-t37/vendor/pr1074/code/assemble.py
new file mode 100644
index 0000000000..581dd9cb29
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/assemble.py
@@ -0,0 +1,241 @@
+"""Gauge44 complete global admission with the retained 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 PR589 supplier (PR555's punctured
+R439 word, v = 111, decoder constant 63, two A-section transports), shipped
+as inputs/PR589-EXPECTED.json and pinned by git blob id. Its rank-mass
+deficit is derived from the word's parameters, T(2Kv - L*cst) at nine
+stages (PR545/PR555 rank-mass identity), not hard-coded. 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,SPOT,spot_widths
+# Cited bit supplier: PR589's tune/EXPECTED.json (merged on main as research/e8-bit-p111-tuned/tune/EXPECTED.json).
+BIT_PATH=Path(__file__).resolve().parents[1]/'inputs/PR589-EXPECTED.json'
+BIT_BLOB='e293ddc557742637f9f679f083a1a282d87b1b13'
+# Nine-stage bit template (PR463/PR510 chain, 32 replicas): L stages, T replicas, K=(L-1)//2 pairs, moment width M=1+7L.
+BIT_L,BIT_T=9,32;BIT_K=(BIT_L-1)//2;BIT_M=1+7*BIT_L
+def git_blob(data):return hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()
+def load_bit(data):
+ """The pinned supplier record: its full record (word parameters) and its nine-stage price."""
+ assert git_blob(data)==BIT_BLOB,'bit supplier blob pin'
+ return json.loads(data)
+def bit_deficit(word,live):
+ """Rank-mass deficit M*live - mass = T(2Kv - L*cst) of a v-port bit word with decoder constant cst (PR545/PR555).
+ cst is the sum of the retained totals' COPY ranks and live = 2KvT data wires; both are cross-checked here, and the
+ caller checks the result against the priced profile, so neither v nor cst is free."""
+ v,cst,ranks=word['v'],word['decoder_constant'],word['copy_ranks']
+ assert type(v)is int and type(cst)is int and all(type(r)is int and 0<r<=8 for r in ranks)
+ assert len(ranks)==word['retained_totals']==BIT_L and cst==sum(ranks)
+ assert live==2*BIT_K*v*BIT_T
+ d=BIT_T*(2*BIT_K*v-BIT_L*cst);assert d>0;return d
+
+
+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
+ # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+ R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==144*R==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']==144
+ assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+ assert invoice['centres']==8
+ assert invoice['physical_stock_identity']==dict(data_and_owner_families=14336,local_helpers=R,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']==R and p['centres']==8 and p['n']==2*112+R 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*R-p['entrance_rank']-p['terminal_codimension'] and len(p['widths'])==R   # HPE: widths |final|-|start|
+  pin(K+'width_digest',digest(p['widths']));assert tuple(p['widths'][h]for h in SPOT)==spot_widths()
+  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 in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):pin(K+'artifacts.'+name,p['artifacts'][name])
+  pin(K+'artifact_semantic_sha256',p['semantic_artifact_sha256'])
+  pin(K+'complete_contract',{k:v for k,v in p.items()if k!='artifacts'})
+  assert owner['provider_artifact_semantic_sha256'][pid]==p['semantic_artifact_sha256']
+  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']==2*112+R and z['dirty_helper_columns']==R
+   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']+p.get('cold_hyperplane_ended_helpers',0);pin(K+'wrappers',z['pre_wrappers'])   # COLD-HPE
+   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']+2*112+R+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)==144
+ 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(16)}
+ 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=23408,23922,32256
+ parent_banks,rem=divmod(parent_live-2*112*4*16,9);assert rem==0 and parent_physical==parent_live+504+8+2   # two independent bank groups, each with R0=504 helpers; restored private workspace is shared
+ assert owner['source_idle_children_charged']==parent_idle
+ bridges,shifts=2*112*144,4*112*16;moves=2*shifts
+ nonlocal_items=(4*112*16*9+2*112*16*9+2*144*R+parent_idle+9*parent_banks+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+(144*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+144+144+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_record=load_bit(BIT_PATH.read_bytes())
+ bit=bit_record['nine']
+ assert 'nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline']
+ c=Q(bit['bit_lower'])
+ bit_D=bit_deficit(bit_record['word'],bit['bit']['live'])
+ 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']==5120
+ 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()}
+ assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+ bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,5120,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,5120,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,'package:inputs/PR589-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_GAUGE44_NATIVE_EXACT_GLOBAL_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_pr635_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=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),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. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. 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/k8-x54-t37/vendor/pr1074/code/assembly_controls.py b/research/k8-x54-t37/vendor/pr1074/code/assembly_controls.py
new file mode 100644
index 0000000000..096ba9cdfe
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/assembly_controls.py
@@ -0,0 +1,260 @@
+"""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 + 144 + 144 + 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) if len(PIDS)>1 else '__unregistered__'
+        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 is not c and (d['provider_id'] != P or len(PIDS)==1) 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),
+        ]
+        if len(PIDS)==1:
+            # Cross-provider substitutions require a second actual supplier.
+            # All single-provider program, phase, profile and dispatch bindings
+            # retain their direct mutations above and in the controller audit.
+            partner_only = {P+':stale_partner_program_consistent_call_hashes',
+                            P+':stale_partner_profile_consistent_child_total',
+                            P+':relocated_against_partner_same_counts',
+                            P+':compensating_false_profiles_with_'+Qp}
+            controls = [(name, fn) for name, fn in controls if name not in partner_only]
+        # 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 SPOT:
+            def cold_swap(o, i, P=P, h=h):
+                w = i['providers'][P]['widths']; j = w.index(9 if w[h] != 9 else 8); w[h], w[j] = w[j], w[h]   # never the identity
+            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/k8-x54-t37/vendor/pr1074/code/audit_allcold.py b/research/k8-x54-t37/vendor/pr1074/code/audit_allcold.py
new file mode 100644
index 0000000000..923bf7b675
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/audit_allcold.py
@@ -0,0 +1,254 @@
+"""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 *
+from generated_identity import artifact_identities
+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={};artifact_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=[len(c['frames'][c['final'][2*c['v']+h]])-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths();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']
+ artifact_semantic_hashes[pid]=artifact_identities(p)
+ pin('providers.%s.artifact_semantic_sha256'%pid,artifact_semantic_hashes[pid])
+ phase_semantic_hashes[pid]=artifact_semantic_hashes[pid]['CLIFFORD-REVIEW.json']
+ for h,w in enumerate(widths):
+  assert 0<w<=c['h']
+  f=c['start'][2*c['v']+h];u=c['final'][2*c['v']+h]
+  # COLD-HPE: a cold helper (f == 0) may end below FULL too; its wrapper is the '0:U' recipe (E = bottom instance of #593)
+  if u!=1:   # HPE: wrapper for T_U T_E^-1, keyed 'E:U', rank |U|-|E|
+   a=adapters['%d:%d'%(f,u)]
+   assert a['frame']==f and a['terminal']==u and a['vectors']==c['frames'][f] and a['terminal_vectors']==c['frames'][u]
+   assert a['rank']==w==len(c['frames'][u])-len(c['frames'][f]) and a['entrance_rank']==len(c['frames'][f]) and a['terminal_rank']==len(c['frames'][u])<c['h']
+  elif w<c['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'))
+# Independently compare ordered common frames; exact local carrier names remain
+# bound to each canonical word, program, phase receipt and residual adapters.
+for p in provider_ids:
+ c=providers[p]['canonical']
+ assert len(c['centers'])==len(c['center_frames'])==8
+ assert [c['frames'][f]for f in c['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+assert required_artifacts<=set(summary['source_artifacts'])
+prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=16;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=144;HOSTED=CALLS*R
+# The selected map is an input to check, not a claim from the emitter.
+
+assert len(DISPATCH)==144 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'])==144 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))==144
+ all_local=[];perrep={r:[]for r in range(16)};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<16 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']<144 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(16)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==5120 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=144)
+
+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))
+# Single-provider dispatch still has all source/program/width binding controls.
+if len(provider_ids)==1:
+ P=provider_ids[0]
+ at_p=lambda q:next(c for c in q['calls']if c['provider_id']==P)
+ narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+ reject(P+': wrong provider at its invocation',lambda q:at_p(q).__setitem__('provider_id','__unregistered__'))
+ reject(P+': stale per-call local program hash',lambda q:at_p(q).__setitem__('local_program_sha256','0'*64))
+ reject(P+': stale serialized provider program',lambda q:q['local_providers'][P]['local_programs']['forward'].pop())
+ reject(P+': unbound residual adapter hash',lambda q:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+ reject(P+': wrong provider width registry',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,providers[P]['widths'][narrow]-1))
+ reject(P+': wrong per-call residual width',lambda q:at_p(q)['owners'][2*V+narrow][1].__setitem__(3,at_p(q)['owners'][2*V+narrow][1][3]-1))
+ reject(P+': wrong sweep provider',lambda q:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep').__setitem__('provider_id','__unregistered__'))
+ reject(P+': entering helper width silently restored to nine',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,9))
+else:
+ # 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=5120,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,provider_artifact_semantic_sha256=artifact_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=5120,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,provider_artifact_semantic_sha256=artifact_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/k8-x54-t37/vendor/pr1074/code/bind_providers_portable.py b/research/k8-x54-t37/vendor/pr1074/code/bind_providers_portable.py
new file mode 100644
index 0000000000..97e28da17e
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/bind_providers_portable.py
@@ -0,0 +1,67 @@
+"""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 *
+from generated_identity import artifact_identities
+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={};helpers=set()   # R: helper count per provider word; all providers must agree
+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'],len(word['centers']))==(112,9,8) and type(word['R']) is int and word['R']>0;helpers.add(word['R'])
+ assert word['ports']==desc['ports'] and word['centers']==desc['centers']
+ widths=[len(word['frames'][word['final'][r]])-len(word['frames'][word['start'][r]])for r in range(2*112,2*112+word['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths()
+ 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']
+ identities=artifact_identities(d)
+ pin('providers.%s.artifact_semantic_sha256'%pid,identities)
+ assert identities==desc['artifact_semantic_sha256']
+ for name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):
+  assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-reference artifact')
+ 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'])
+assert len(helpers)==1,'providers disagree on helper count R: %s'%sorted(helpers)
+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','runtime_source_plan_sha256'])
+(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(receipt['status'])
diff --git a/research/k8-x54-t37/vendor/pr1074/code/bit_supplier_controls.py b/research/k8-x54-t37/vendor/pr1074/code/bit_supplier_controls.py
new file mode 100644
index 0000000000..e86b8527b4
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/bit_supplier_controls.py
@@ -0,0 +1,111 @@
+"""Negative controls for the cited PR589 bit supplier and its derived rank-mass deficit.
+
+Apache-2.0. Each control mutates one input of the changed bit-supplier sites in assemble.py (the pinned record, the
+deficit derivation from the word's parameters, the profile/live binding, the claimed endpoint) and runs the unchanged
+assemble() on the fresh owner/invoice receipts. Every control must be rejected; the unmutated run must pass.
+`revert_hardcoded_9984` restores the PR543 constant the parent package hard-coded: with PR589's word it must fail.
+"""
+import argparse
+import copy
+import hashlib
+import json
+import os
+import tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+
+assert __debug__, 'Assertions required'
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    import assemble as A
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    args = (owner, invoice, sha(owner_path), sha(invoice_path))
+    baseline = A.assemble(*args)
+    data = A.BIT_PATH.read_bytes()
+    record = A.load_bit(data)
+    word = record['word']
+    assert A.bit_deficit(word, record['nine']['bit']['live']) == 10272 == 32 * (8 * 111 - 9 * 63)
+
+    real_load, real_deficit = A.load_bit, A.bit_deficit
+
+    def with_record(mutate):
+        def load(d):
+            r = copy.deepcopy(real_load(d)); mutate(r); return r
+        return load
+
+    def shift_profile(r):  # one rank-1 child becomes rank 2: rank mass +1, totals unchanged
+        p = r['nine']['profile']; p['1'] -= 1; p['2'] += 1; r['nine']['bit']['rank_mass'] += 1
+
+    bumped = data.replace(record['nine']['bit_lower'].encode(),
+                          str(Q(record['nine']['bit_lower']) + Q(1, 10**24)).encode(), 1)
+    assert bumped != data
+    pr543 = (source_package / 'inputs/PR543-EXPECTED.json').read_bytes()
+    controls = [
+        # deficit site: the parent's hard-coded constant, restored
+        ('revert_hardcoded_9984', dict(bit_deficit=lambda w, live: 9984)),
+        # deficit site: each word parameter perturbed alone
+        ('ports_112', dict(load_bit=with_record(lambda r: r['word'].__setitem__('v', 112)))),
+        ('decoder_constant_64_copy_ranks_unchanged', dict(load_bit=with_record(lambda r: r['word'].__setitem__('decoder_constant', 64)))),
+        # v=111, cst=64 derives 32*(888-576)=9984: consistent word, wrong for the priced profile
+        ('decoder_constant_64_with_one_copy_rank_8', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('decoder_constant', 64), r['word']['copy_ranks'].__setitem__(0, 8))))),
+        ('eight_retained_totals', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('copy_ranks', [7] * 8), r['word'].__setitem__('decoder_constant', 56))))),
+        ('live_minus_one', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('live', r['nine']['bit']['live'] - 1)))),
+        # profile binding: same totals, rank mass +1
+        ('profile_rank_mass_plus_one', dict(load_bit=with_record(shift_profile))),
+        ('profile_rank_mass_receipt_mismatch', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('rank_mass', r['nine']['bit']['rank_mass'] + 1)))),
+        # endpoint: the next 1e-24 grid point
+        ('bit_lower_next_grid', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('bit_lower', str(Q(r['nine']['bit_lower']) + Q(1, 10**24)))))),
+        ('not_nine_stage_record', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('pipeline', r['nine']['pipeline'].replace('nine-stage', 'eleven-stage'))))),
+        # pinned-input site: tampered bytes and the parent's PR543 file under the PR589 pin
+        ('tampered_bytes_next_grid', dict(read=bumped)),
+        ('pr543_file_under_pr589_pin', dict(read=pr543)),
+    ]
+    rejected = []
+    scratch = Path(tempfile.mkdtemp(prefix='bitctl-'))
+    for name, patch in controls:
+        saved_path = A.BIT_PATH
+        try:
+            if 'read' in patch:
+                tmp = scratch / (name + '.json'); tmp.write_bytes(patch['read']); A.BIT_PATH = tmp
+            A.load_bit = patch.get('load_bit', real_load)
+            A.bit_deficit = patch.get('bit_deficit', real_deficit)
+            try:
+                A.assemble(*args)
+            except (AssertionError, KeyError):
+                rejected.append(name)
+            else:
+                raise AssertionError('Invalid bit supplier accepted: ' + name)
+        finally:
+            A.load_bit, A.bit_deficit, A.BIT_PATH = real_load, real_deficit, saved_path
+            if 'read' in patch:
+                tmp.unlink()
+    scratch.rmdir()
+    assert rejected == [n for n, _ in controls]
+    again = A.assemble(*args)
+    assert again['kappa'] == baseline['kappa'] and again['bit_lower'] == baseline['bit_lower']
+    return dict(
+        status='PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS',
+        kappa=baseline['kappa_decimal'], bit_lower=baseline['bit_lower'], bit_decimal=baseline['bit_decimal'],
+        binding=baseline['binding'], bit_supplier=baseline['bit_supplier'],
+        derived_deficit=baseline['bit_supplier']['derived_deficit'],
+        rejected_controls=rejected,
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+    )
+
+
+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', newline='\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/k8-x54-t37/vendor/pr1074/code/emit_allcold.py b/research/k8-x54-t37/vendor/pr1074/code/emit_allcold.py
new file mode 100644
index 0000000000..28a08a79da
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/emit_allcold.py
@@ -0,0 +1,150 @@
+"""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))==144;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=16;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,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')
+ # Carrier names belong to the independently checked local program. The global
+ # controller's centre contract is the ordered eight exact common frame bases.
+ assert(pc['v'],pc['h'],pc['ports'])==(V,9,canon['ports'])
+ assert len(pc['centers'])==len(pc['center_frames'])==len(canon['centers'])==8
+ assert [pc['frames'][f]for f in pc['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+ R=pc['R'];assert type(R)is int and R>0 and all(x['R']==R for x in registry.values()),'providers disagree on helper count R'
+ 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=[len(pc['frames'][pc['final'][2*V+h]])-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)]   # HPE: residual width |final|-|start|
+ 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)
+assert len(roles)==144*R   # one whole-owner role per (call, provider helper)
+selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+assert len(selected)==144 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())==5120
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R0+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-R%d-asynchronous-whole-owner-v1'%R,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=5120,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/k8-x54-t37/vendor/pr1074/code/freeze_spec.py b/research/k8-x54-t37/vendor/pr1074/code/freeze_spec.py
new file mode 100644
index 0000000000..4fe3b88915
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/freeze_spec.py
@@ -0,0 +1,29 @@
+"""Freeze independently recomputed discovery values before strict replay."""
+import argparse
+import json
+from pathlib import Path
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--spec', type=Path, required=True)
+ap.add_argument('--discovery', type=Path, required=True)
+a = ap.parse_args()
+spec = json.loads(a.spec.read_text())
+for line in (a.discovery/'WITNESS-RECORD.jsonl').read_text().splitlines():
+    key, value = json.loads(line)
+    parts = key.split('.')
+    if len(parts)>3 and parts[0]=='providers' and parts[2]=='artifacts':
+        parts = parts[:3] + ['.'.join(parts[3:])]
+    target = spec
+    for part in parts[:-1]:
+        target = target.setdefault(part, {})
+    if parts[-1] in target:
+        assert target[parts[-1]]==value, 'Conflicting independent recomputations: '+key
+    target[parts[-1]] = value
+assembly = json.loads((a.discovery/'ASSEMBLY.json').read_text())
+for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+    spec['expected'][key] = assembly[key]
+spec['expected']['assembly_controls_rejected'] = 69
+spec['expected']['provider_counts'] = {'gauge44':144}
+spec['expected']['mutations_rejected'] = 15
+a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
diff --git a/research/k8-x54-t37/vendor/pr1074/code/generated_identity.py b/research/k8-x54-t37/vendor/pr1074/code/generated_identity.py
new file mode 100644
index 0000000000..74a9b60479
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/generated_identity.py
@@ -0,0 +1,62 @@
+"""Proof-relevant identities for generated artifacts, independent of gzip streams.
+
+Immutable source archives retain their exact byte hashes. For freshly emitted
+artifacts, gzip identity is the exact decompressed payload and JSON identity
+retains every field. Only CLIFFORD-REVIEW's root timing field is excluded.
+Literal receipt references are checked against actual files before replacing
+the three gzip references (and the phase recipe reference) with content hashes.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import copy
+import gzip
+import hashlib
+import json
+import math
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+
+FILES=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+       'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+       'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json')
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+def json_identity(value):
+    return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode('utf-8')).hexdigest()
+
+def payload_identity(path):
+    return hashlib.sha256(gzip.decompress(Path(path).read_bytes())).hexdigest()
+
+def phase_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'CLIFFORD-REVIEW.json').read_bytes())if value is None else value)
+    assert value['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz'),'stale phase canonical word reference'
+    assert value['recipe_sha256']==sha(directory/'CLIFFORD-RECIPES.json'),'stale phase recipe reference'
+    seconds=value.pop('seconds')
+    assert type(seconds)in(int,float) and math.isfinite(seconds) and seconds>=0,'invalid phase timing metadata'
+    value['canonical_word_sha256']=payload_identity(directory/'CANONICAL-WORD.json.gz')
+    value['recipe_sha256']=json_identity(json.loads((directory/'CLIFFORD-RECIPES.json').read_bytes()))
+    return value
+
+def native_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'INDEPENDENT-LOCAL-REPLAY.json').read_bytes())if value is None else value)
+    for field,name in [('canonical_word_sha256','CANONICAL-WORD.json.gz'),('local_programs_sha256','LOCAL-PROGRAMS.json.gz')]:
+        assert value[field]==sha(directory/name),'stale native artifact reference: '+field
+        value[field]=payload_identity(directory/name)
+    return value
+
+def artifact_identities(directory):
+    directory=Path(directory)
+    result={}
+    for name in FILES:
+        path=directory/name
+        if name.endswith('.gz'):
+            result[name]=payload_identity(path)
+        else:
+            value=phase_value(directory)if name=='CLIFFORD-REVIEW.json'else native_value(directory)if name=='INDEPENDENT-LOCAL-REPLAY.json'else json.loads(path.read_bytes())
+            result[name]=json_identity(value)
+    return result
diff --git a/research/k8-x54-t37/vendor/pr1074/code/invoice_allcold.py b/research/k8-x54-t37/vendor/pr1074/code/invoice_allcold.py
new file mode 100644
index 0000000000..d1dd221291
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/invoice_allcold.py
@@ -0,0 +1,329 @@
+"""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 generated_identity import artifact_identities
+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,h)==(112,9) and type(helpers) is int and helpers>0
+    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 = [len(w['frames'][w['final'][r]])-len(w['frames'][w['start'][r]]) for r in range(2*v, 2*v+helpers)]  # HPE: |final|-|start|
+    terminal_codim = sum(h-len(w['frames'][w['final'][r]]) for r in range(2*v, 2*v+helpers))  # HPE: 0 for FULL-ended helpers
+    ends = {r: f for r, f in enumerate(w['final']) if r >= 2*v and f != 1}
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    wrapped = {**entrances, **{r: 0 for r in ends if r not in entrances}}   # COLD-HPE: cold hyperplane-ended helpers carry wrappers too
+    cold_ends = len(wrapped) - 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, *end = event
+                assert kind in wrappers and wrapped.get(register) == frame
+                assert end == ([ends[register]] if register in ends else [])  # HPE: R_{E,U}^-1 and L_{E,U}^-1 name U
+                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(wrapped)
+        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')
+    return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n,
+                entering_helpers=entering,entrance_rank=sum(len(w['frames'][f]) for f in w['start'][2*v:]),
+                terminal_codimension=terminal_codim, hyperplane_ended_helpers=len(ends),  # HPE: always reported (0 for FULL-ended words)
+                **({'cold_hyperplane_ended_helpers': cold_ends} if cold_ends else {}),  # COLD-HPE: absent without cold ends
+                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=artifact_identities(local_dir))
+
+
+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]
+    # R is read from the provider words (all must agree); the parent dedicated-bank
+    # envelope keeps its own helper count R0 from the parent split-centres word.
+    assert len({p['helpers'] for p in providers.values()})==1,'providers disagree on helper count R'
+    v,h,m,centres=112,9,73,8
+    helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+    assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+    parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+    stages,replicas,blocks_per_stream=9,16,4
+    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+parent_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']==5120
+    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 144 invocation and 144 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/k8-x54-t37/vendor/pr1074/code/prepare_global.py b/research/k8-x54-t37/vendor/pr1074/code/prepare_global.py
new file mode 100644
index 0000000000..655c9470f6
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/prepare_global.py
@@ -0,0 +1,124 @@
+"""Bind a frozen explicit owner map to exact native local artifacts.
+
+This preparer nominates a witness. The separate serialized controller audit,
+finite invoice, two exact moment engines and strict pinned replay admit it.
+Apache-2.0; prepared with OpenAI assistance. See NOTICE.md.
+"""
+import argparse
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+from generated_identity import artifact_identities, FILES
+
+assert __debug__, 'Assertions required'
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--parent', type=Path, required=True)
+ap.add_argument('--owners', type=Path, required=True)
+ap.add_argument('--local', type=Path, required=True)
+ap.add_argument('--data', type=Path, required=True)
+args = ap.parse_args()
+args.data.mkdir(parents=True, exist_ok=True)
+parent_path = args.parent / 'data/PLAN.json'
+assert sha(parent_path) == '258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda'
+plan = read(parent_path)
+word = read(args.local / 'CANONICAL-WORD.json.gz')
+checks = read(args.local / 'LOCAL-CHECKS.json')
+assert (word['v'], word['h'], word['R']) == (112, 9, 492)
+widths = [len(word['frames'][word['final'][224+h]]) -
+          len(word['frames'][word['start'][224+h]]) for h in range(492)]
+profile = {int(k): v for k, v in word['local_profile'].items()}
+assert profile == {1: 2514, 2: 404, 3: 448, 4: 160, 5: 56, 8: 8}
+assert Counter(widths) == {4: 52, 5: 48, 7: 34, 8: 114, 9: 244}
+assert sum(widths) == 3794
+owners = read(args.owners)
+assert len(owners) == 72 * 492
+order = [tuple(x) for x in plan['order']]
+times = {x: i for i, x in enumerate(order)}
+used, call_helpers, call_families = defaultdict(set), defaultdict(set), defaultdict(set)
+for z in owners:
+    key = (z['stage'], z['replica'])
+    h, i, rep, port = z['helper'], z['child'], z['owner_replica'], z['port']
+    assert key in times and 0 <= h < 492 and 0 <= rep < 8 and 0 <= port < 112
+    assert z['time'] == times[key] and h not in call_helpers[key]
+    assert z['family'] not in call_families[key]
+    call_helpers[key].add(h)
+    call_families[key].add(z['family'])
+    cap, allowed = plan['windows'][f'{rep},{i}']
+    assert z['time'] in allowed and z['width'] == widths[h]
+    assert z['copy'] == rep * 112 + port
+    assert z['family'] == rep * 896 + (2*plan['pairs'][str(i)] + plan['sides'][str(i)])*112 + port
+    assert 0 <= z['offset'] and z['offset'] + z['width'] <= cap
+    cells = set(range(z['offset'], z['offset'] + z['width']))
+    group = (i, rep, port)
+    assert not used[group] & cells
+    used[group].update(cells)
+assert set(call_helpers) == set(order)
+assert all(hs == set(range(492)) for hs in call_helpers.values())
+idle = Counter()
+for key, (cap, _) in plan['windows'].items():
+    rep, i = map(int, key.split(','))
+    for port in range(112):
+        cells = used[i, rep, port]
+        assert cells == set(range(len(cells)))
+        left = cap - len(cells)
+        if left:
+            idle[left] += 1
+global_profile = Counter({r: 72*n for r, n in profile.items()}) + idle
+assert sum(r*n for r, n in global_profile.items()) == 520704
+assert 73*7168 - sum(r*n for r, n in global_profile.items()) == 2560
+pid = 'gauge44'
+for c in plan['provider_calls']:
+    c['provider'] = pid
+    c['local_program_sha256'] = checks[c['orientation']]['sha256']
+for c in plan['per_call_widths']:
+    c['widths'] = widths
+artifacts = {name: sha(args.local / name) for name in FILES}
+identities = artifact_identities(args.local)
+plan['provider_registry'] = {pid: dict(
+    directory='providers/' + pid, artifact_sha256=artifacts,
+    ports=word['ports'], centers=word['centers'], widths=widths,
+    actual_paid_profile=word['local_profile'],
+    orientation_program_sha256={k: v['sha256'] for k, v in checks.items()},
+    artifact_semantic_sha256=identities)}
+plan.update(status='FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION',
+            mode='gauge44-all72', profile=dict(sorted(global_profile.items())),
+            solver_status='deterministic-capacity-matching', gap=None,
+            source_plan_sha256=sha(parent_path),
+            source_owners_sha256=sha(args.parent / 'data/OWNERS.json.gz'),
+            assignment_sha256=sha(args.owners))
+target_owners = args.data / 'OWNERS.json.gz'
+if args.owners.resolve() != target_owners.resolve():
+    shutil.copyfile(args.owners, target_owners)
+dump(args.data / 'PLAN.json', plan)
+spec = dict(schema='witness-spec/1', name='gauge44-all72',
+            data=dict(plan_sha256=sha(args.data / 'PLAN.json'), owners_sha256=sha(target_owners)),
+            dispatch=[[s, r, pid] for s in range(9) for r in range(8)],
+            call_order=plan['order'], width_spot_helpers=[264, 276, 288, 300],
+            providers={pid: {}}, expected=dict(gain_baseline_kappa='0.001636241501576388'))
+dump(args.data / 'SPEC.json', spec)
+dump(args.data / 'PREPARATION.json', dict(
+    status='PASS_EXPLICIT_MAP_AND_FRESH_PROVIDER_NOMINATION',
+    parent_plan_sha256=sha(parent_path), source_owners_sha256=sha(args.owners),
+    global_profile=dict(sorted(global_profile.items())), idle_profile=dict(sorted(idle.items())),
+    roles=len(owners), rank_mass=520704, deficit=2560,
+    remaining='Independent emitted-controller audit, fresh finite invoice, exact moments and outer assembly.'))
+print('Prepared all72 gauge44 candidate:', dict(sorted(global_profile.items())))
diff --git a/research/k8-x54-t37/vendor/pr1074/code/restore_parent.py b/research/k8-x54-t37/vendor/pr1074/code/restore_parent.py
new file mode 100644
index 0000000000..21135f898a
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/restore_parent.py
@@ -0,0 +1,67 @@
+"""Materialize the omitted generated PR558 parent, then require its reviewed hash.
+
+The integrated review contains the native inputs and INTEGRATION.json but
+omits GLOBAL-TEMPLATE.json.gz. This is only the deterministic template
+binding from the inherited prepare_supplier_base.py; no old circuit or
+phase calculation is rerun. The whole exact payload must match the review.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source',type=Path,required=True)
+ap.add_argument('--baseline',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+assert not a.out.exists()
+base=a.out/'complex-global/base'
+shutil.copytree(a.baseline/'complex-global/base',base)
+d=base/'split-centres'
+parent=a.source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz'
+old=read(parent);can=read(d/'CANONICAL-WORD.json.gz')
+checks=read(d/'LOCAL-CHECKS.json');programs=read(d/'LOCAL-PROGRAMS.json.gz')
+v,h,r=can['v'],can['h'],can['R'];c=len(can['centers']);m,t,l,k=73,8,9,4
+assert(v,h,r,c)==(112,9,504,8)
+widths=[h-len(can['frames'][f])for f in can['start'][2*v:]]
+data=2*k*t*v;live=data+l*r;physical=live+r+c+2
+word=copy.deepcopy(old)
+word.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=live,physical=physical,local_programs=programs)
+word['private_namespace']={'centers':[live,live+c],'reserved_tableau':[live+c,live+c+r],'coefficient':[physical-2,physical]}
+for call in word['calls']:
+ s,rep=call['stage'],call['replica'];owners=copy.deepcopy(call['owners'][:2*v])
+ for helper,w in enumerate(widths):
+  route=[2,rep]if w==9 else[2,rep*w,w,list(range(t*w,t*w+9-w))]
+  owners.append([data+s*r+helper,route])
+ call['owners']=owners;call['local_program_sha256']=checks[call['orientation']]['sha256']
+children=[]
+for s in range(l):
+ for helper,w in enumerate(widths):
+  axes=list(range(t*w,m))
+  children.append(dict(family=data+s*r+helper,rank=len(axes),axis_indices=axes,orthogonal_axes=[1<<j for j in axes]))
+word['bank_padding']={'families':list(range(data,live)),'children':children,
+ 'semantics':'Each listed complement frame is applied once after the eight disjoint residual blocks of that dedicated bank. The final hosted derivative has empty families and children.'}
+word['cover_final_correction'].update(families=[0,live],charged_calls_per_cover=live)
+for i,e in enumerate(word['execution_schedule']):
+ if e['kind']=='bank_padding_cover_sweep':word['execution_schedule'][i]={'kind':'bank_padding_cover_sweep','families':[data,live],'children_source':'bank_padding.children'}
+ elif e['kind']=='translate_every_live_family':e.update(word['cover_final_correction'])
+word['exact_data_phase_recipe_sha256']=sha(base/'work/complex-nine-native/DATA-PHASES.json')
+word['exact_local_clifford_recipe_sha256']=sha(d/'CLIFFORD-RECIPES.json')
+word['residual_adapter_sha256']=sha(d/'RESIDUAL-ADAPTERS.json')
+word['supplier_substitution']={'parent_template_sha256':sha(parent),
+ 'old_canonical_word_sha256':sha(a.baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz'),
+ 'new_canonical_word_sha256':sha(d/'CANONICAL-WORD.json.gz'),
+ 'exact_same_ports':True,'data_contract':'The same ordered 112 data ports and both complete-invocation identity-shear orientations feed the unchanged nine-stage controller. No old local program or helper profile is reused.'}
+word['route_semantics']['helper']='Dedicated family DATA+stage*R+helper; one helper per bank per complete invocation. Width-nine route[2,replica] uses axes9*replica..9*replica+8. Width-w entering route[2,w*replica,w,spectators] uses the disjoint residual block and paid normalization wrappers; spectator axes start at8*w, beyond all residual blocks.'
+raw=json.dumps(word,sort_keys=True,separators=(',',':')).encode()
+expected=read(d/'INTEGRATION.json')['global_template_sha256']
+assert hashlib.sha256(raw).hexdigest()==expected=='7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3'
+(d/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+print('PASS_EXACT_REVIEWED_PARENT_TEMPLATE_RESTORED',expected)
diff --git a/research/k8-x54-t37/vendor/pr1074/code/witness.py b/research/k8-x54-t37/vendor/pr1074/code/witness.py
new file mode 100644
index 0000000000..c5c7fbc114
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/code/witness.py
@@ -0,0 +1,55 @@
+"""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']]
+# width-8 spot helpers: PR558's helpers 270, 282, 294, 306, or their images under a K-triangle word's 504 -> R helper map
+# (verify.py checks the spec value against the constructor's HELPER-MAP.json)
+SPOT=tuple(SPEC.get('width_spot_helpers',(270,282,294,306)))
+# A pivot swap moves a kernel family's pivot role p -> x; the old pivot p becomes an ordinary cold helper and its width
+# goes 8 -> 9 (construction/layers, PR641 PROOF-NOTE-PIVOT). Expected spot widths are derived from the package's pinned
+# pivot-swap recipe (path and sha256 in the spec), not from free data: 9 at a swapped-out pivot, 8 otherwise.
+_PKG=Path(os.environ['WITNESS_SPEC']).resolve().parents[1]
+def _old_pivots():
+ ps=SPEC.get('pivot_swap')
+ if not ps:return frozenset()
+ raw=(_PKG/ps['recipe']).read_bytes();import hashlib
+ assert hashlib.sha256(raw).hexdigest()==ps['sha256'],'pivot-swap recipe pin'
+ return frozenset(s['pivot']for s in json.loads(raw)['swaps'])
+OLD_PIVOTS=_old_pivots()
+def spot_widths(v=112):
+ """Expected residual widths at the spot helpers (helper indices) of the gauge44 provider."""
+ return tuple(9 if 2*v+h in OLD_PIVOTS else 8 for h in SPOT)
+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:
+  if os.environ.get('WITNESS_RECORD'):   # discovery bookkeeping only: append (key, value) for the spec writer
+   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))
+  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/k8-x54-t37/vendor/pr1074/construction/leaver/PIVOT-SWAP-k8.json b/research/k8-x54-t37/vendor/pr1074/construction/leaver/PIVOT-SWAP-k8.json
new file mode 100644
index 0000000000..7a8edeb1e4
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/construction/leaver/PIVOT-SWAP-k8.json
@@ -0,0 +1 @@
+{"input_content_sha256": "00aeefe0c778ff64125628d7c869ae1aa27db60911f0289a2d4283af5cff85d2", "output_content_sha256": "377ab10c2bf6173498c8af15f8654060331ec9ee232e58cc75956dc015b23685", "swaps": [{"pivot": 482, "new_pivot": 554, "entrance": [24], "gates": [{"part": "B", "index": 331, "before": ["add", 554, 482, -1, 1, [24]], "after": ["add", 482, 554, -1, 1, [24]]}, {"part": "B", "index": 332, "before": ["add", 616, 482, 2, 1, [24]], "after": ["add", 616, 554, -2, 1, [24]]}, {"part": "B", "index": 333, "before": ["add", 618, 482, -2, 1, [24]], "after": ["add", 618, 554, 2, 1, [24]]}, {"part": "B", "index": 334, "before": ["add", 664, 482, 1, 1, [24]], "after": ["add", 664, 554, -1, 1, [24]]}, {"part": "B", "index": 335, "before": ["add", 666, 482, -1, 1, [24]], "after": ["add", 666, 554, 1, 1, [24]]}]}, {"pivot": 483, "new_pivot": 555, "entrance": [24], "gates": [{"part": "B", "index": 468, "before": ["add", 123, 483, 1, 1, [24]], "after": ["add", 123, 555, -1, 1, [24]]}, {"part": "B", "index": 504, "before": ["add", 187, 483, -1, 1, [24]], "after": ["add", 187, 555, 1, 1, [24]]}, {"part": "B", "index": 734, "before": ["add", 555, 483, -1, 1, [24]], "after": ["add", 483, 555, -1, 1, [24]]}]}, {"pivot": 494, "new_pivot": 566, "entrance": [24], "gates": [{"part": "B", "index": 128, "before": ["add", 628, 494, 2, 1, [24]], "after": ["add", 628, 566, -2, 1, [24]]}, {"part": "B", "index": 130, "before": ["add", 628, 494, -2, 1, [24]], "after": ["add", 628, 566, 2, 1, [24]]}, {"part": "B", "index": 230, "before": ["add", 676, 494, -2, 1, [24]], "after": ["add", 676, 566, 2, 1, [24]]}, {"part": "B", "index": 232, "before": ["add", 676, 494, 2, 1, [24]], "after": ["add", 676, 566, -2, 1, [24]]}, {"part": "B", "index": 750, "before": ["add", 566, 494, -1, 1, [24]], "after": ["add", 494, 566, -1, 1, [24]]}]}, {"pivot": 495, "new_pivot": 567, "entrance": [24], "gates": [{"part": "B", "index": 49, "before": ["add", 211, 495, -1, 1, [24]], "after": ["add", 211, 567, 1, 1, [24]]}, {"part": "B", "index": 477, "before": ["add", 147, 495, 1, 1, [24]], "after": ["add", 147, 567, -1, 1, [24]]}, {"part": "B", "index": 752, "before": ["add", 567, 495, -1, 1, [24]], "after": ["add", 495, 567, -1, 1, [24]]}]}, {"pivot": 507, "new_pivot": 531, "entrance": [30], "gates": [{"part": "B", "index": 459, "before": ["add", 115, 507, -1, 1, [30]], "after": ["add", 115, 531, 1, 1, [30]]}, {"part": "B", "index": 495, "before": ["add", 179, 507, 1, 1, [30]], "after": ["add", 179, 531, -1, 1, [30]]}, {"part": "B", "index": 770, "before": ["add", 531, 507, -1, 1, [30]], "after": ["add", 507, 531, -1, 1, [30]]}]}, {"pivot": 519, "new_pivot": 543, "entrance": [30], "gates": [{"part": "B", "index": 486, "before": ["add", 155, 519, -1, 1, [30]], "after": ["add", 155, 543, 1, 1, [30]]}, {"part": "B", "index": 521, "before": ["add", 219, 519, 1, 1, [30]], "after": ["add", 219, 543, -1, 1, [30]]}, {"part": "B", "index": 788, "before": ["add", 543, 519, -1, 1, [30]], "after": ["add", 519, 543, -1, 1, [30]]}]}]}
\ No newline at end of file
diff --git a/research/k8-x54-t37/vendor/pr1074/data/SPEC-T8.json b/research/k8-x54-t37/vendor/pr1074/data/SPEC-T8.json
new file mode 100644
index 0000000000..5c3e90593d
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/data/SPEC-T8.json
@@ -0,0 +1,1327 @@
+{
+  "schema": "witness-spec/1",
+  "name": "gauge44-all72",
+  "data": {
+    "plan_sha256": "20c84a852caa664cc3283d1c4e21c2f97df9a166ccab513fb442477a618882a0",
+    "owners_sha256": "32ca30cd1c652ef6ad43657273a08a157e1df3545e759ab36306a0d0b516fb4a"
+  },
+  "dispatch": [
+    [
+      0,
+      0,
+      "gauge44"
+    ],
+    [
+      0,
+      1,
+      "gauge44"
+    ],
+    [
+      0,
+      2,
+      "gauge44"
+    ],
+    [
+      0,
+      3,
+      "gauge44"
+    ],
+    [
+      0,
+      4,
+      "gauge44"
+    ],
+    [
+      0,
+      5,
+      "gauge44"
+    ],
+    [
+      0,
+      6,
+      "gauge44"
+    ],
+    [
+      0,
+      7,
+      "gauge44"
+    ],
+    [
+      1,
+      0,
+      "gauge44"
+    ],
+    [
+      1,
+      1,
+      "gauge44"
+    ],
+    [
+      1,
+      2,
+      "gauge44"
+    ],
+    [
+      1,
+      3,
+      "gauge44"
+    ],
+    [
+      1,
+      4,
+      "gauge44"
+    ],
+    [
+      1,
+      5,
+      "gauge44"
+    ],
+    [
+      1,
+      6,
+      "gauge44"
+    ],
+    [
+      1,
+      7,
+      "gauge44"
+    ],
+    [
+      2,
+      0,
+      "gauge44"
+    ],
+    [
+      2,
+      1,
+      "gauge44"
+    ],
+    [
+      2,
+      2,
+      "gauge44"
+    ],
+    [
+      2,
+      3,
+      "gauge44"
+    ],
+    [
+      2,
+      4,
+      "gauge44"
+    ],
+    [
+      2,
+      5,
+      "gauge44"
+    ],
+    [
+      2,
+      6,
+      "gauge44"
+    ],
+    [
+      2,
+      7,
+      "gauge44"
+    ],
+    [
+      3,
+      0,
+      "gauge44"
+    ],
+    [
+      3,
+      1,
+      "gauge44"
+    ],
+    [
+      3,
+      2,
+      "gauge44"
+    ],
+    [
+      3,
+      3,
+      "gauge44"
+    ],
+    [
+      3,
+      4,
+      "gauge44"
+    ],
+    [
+      3,
+      5,
+      "gauge44"
+    ],
+    [
+      3,
+      6,
+      "gauge44"
+    ],
+    [
+      3,
+      7,
+      "gauge44"
+    ],
+    [
+      4,
+      0,
+      "gauge44"
+    ],
+    [
+      4,
+      1,
+      "gauge44"
+    ],
+    [
+      4,
+      2,
+      "gauge44"
+    ],
+    [
+      4,
+      3,
+      "gauge44"
+    ],
+    [
+      4,
+      4,
+      "gauge44"
+    ],
+    [
+      4,
+      5,
+      "gauge44"
+    ],
+    [
+      4,
+      6,
+      "gauge44"
+    ],
+    [
+      4,
+      7,
+      "gauge44"
+    ],
+    [
+      5,
+      0,
+      "gauge44"
+    ],
+    [
+      5,
+      1,
+      "gauge44"
+    ],
+    [
+      5,
+      2,
+      "gauge44"
+    ],
+    [
+      5,
+      3,
+      "gauge44"
+    ],
+    [
+      5,
+      4,
+      "gauge44"
+    ],
+    [
+      5,
+      5,
+      "gauge44"
+    ],
+    [
+      5,
+      6,
+      "gauge44"
+    ],
+    [
+      5,
+      7,
+      "gauge44"
+    ],
+    [
+      6,
+      0,
+      "gauge44"
+    ],
+    [
+      6,
+      1,
+      "gauge44"
+    ],
+    [
+      6,
+      2,
+      "gauge44"
+    ],
+    [
+      6,
+      3,
+      "gauge44"
+    ],
+    [
+      6,
+      4,
+      "gauge44"
+    ],
+    [
+      6,
+      5,
+      "gauge44"
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diff --git a/research/k8-x54-t37/vendor/pr1074/inputs/PR589-EXPECTED.json b/research/k8-x54-t37/vendor/pr1074/inputs/PR589-EXPECTED.json
new file mode 100644
index 0000000000..e293ddc557
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/inputs/PR589-EXPECTED.json
@@ -0,0 +1,222 @@
+{
+ "word": {
+  "file": "tune/bitE8mut-p111-tuned.json.gz",
+  "file_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f",
+  "content_sha256": "5642fd0e35a1acc11acff8d0c08350c1617e95f310d4d35ad63a651f9eeeba0b",
+  "v": 111,
+  "R": 439,
+  "punctured": [
+   10,
+   15,
+   51,
+   53,
+   56,
+   66,
+   72,
+   89,
+   111
+  ],
+  "retained_totals": 9,
+  "copy_ranks": [
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7
+  ],
+  "decoder_constant": 63,
+  "gates": {
+   "D": 111,
+   "A": 2075,
+   "B": 712,
+   "C": 2574
+  },
+  "local_histogram": {
+   "1": 1323,
+   "2": 1342,
+   "3": 79,
+   "4": 44,
+   "5": 102,
+   "6": 11,
+   "7": 19
+  },
+  "legality": {
+   "records": 27234,
+   "common_frame_ADDs": 24305,
+   "rank_mass": 5129
+  },
+  "five_stage_columns": 883,
+  "five_stage_payload_bits": 93,
+  "nine_stage_columns": 1327,
+  "nine_stage_payload_bits": 93,
+  "eleven_stage_columns": 1549,
+  "eleven_stage_payload_bits": 93,
+  "base_content_sha256": "d0df3c89ae84989f4045ba1681a5e2e9fcdfa38ed0301c8abf5185537155cbe3"
+ },
+ "interface": {
+  "hypotheses": {
+   "H1_no_target_feeds_z": true,
+   "H2_D_frame0_targets_from_helpers": true,
+   "H3_A_z_only_scatter_targets_B_split": true,
+   "H4_C_literal_reverse_at_full": true,
+   "H5_V_identity": true
+  },
+  "conclusion": {
+   "U_block_form": true,
+   "J_identity": true,
+   "K_equals_D": true,
+   "C_is_U_inverse": true
+  },
+  "interleaving": {
+   "z_gates_A": 2075,
+   "source_writes_A": 0,
+   "z_gates_B": 499,
+   "source_writes_B": 483,
+   "helper_writes_B": 16,
+   "sources_rewritten_B": 108,
+   "B_z_write_frame_dims": {
+    "4": 388,
+    "6": 111
+   },
+   "B_z_operand_kinds": {
+    "helper<-helper": 3,
+    "helper<-source": 13,
+    "source<-helper": 108,
+    "source<-source": 375
+   },
+   "B_z_operand_kinds_by_dim": {
+    "dim4:helper<-source": 13,
+    "dim4:source<-source": 375,
+    "dim6:helper<-helper": 3,
+    "dim6:source<-helper": 108
+   },
+   "B_z_writes_after_a_target_read_of_the_same_register": 454,
+   "B_target_reads_of_registers_rewritten_earlier_in_B": 111,
+   "target_reads_of_targets": 0,
+   "cleanup_gates": 2574
+  }
+ },
+ "nine": {
+  "pipeline": "PR #510 (PR #463 nine-stage template, 32 replicas, PR #442 hosting, PR #493 outer assembly), parameterised for v <= 120 by code/adapt9p.py",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_lower_decimal": "0.001733427039589844234749",
+  "profile": {
+   "1": 381024,
+   "2": 400416,
+   "3": 22752,
+   "4": 26880,
+   "5": 29376,
+   "6": 17376,
+   "7": 26784,
+   "42": 288
+  },
+  "bit": {
+   "live": 28416,
+   "physical": 28425,
+   "maxchild": 42,
+   "rank_mass": 1808352,
+   "hosted_residuals": 126432,
+   "bank_assignments": 0,
+   "prefix_bits": 177,
+   "charged_prefix_bits": 192,
+   "coefficient_bits": 177,
+   "two_level_coefficient_bits": 393,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "eleven": {
+  "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting), parameterised by PR #545's code/adapt.py",
+  "bit_lower": "855475950388791987811/500000000000000000000000",
+  "bit_lower_decimal": "0.001710951900777583975622",
+  "profile": {
+   "1": 116424,
+   "2": 121648,
+   "3": 6952,
+   "4": 7424,
+   "5": 8976,
+   "6": 4520,
+   "7": 8776,
+   "56": 2600
+  },
+  "bit": {
+   "live": 8880,
+   "physical": 8889,
+   "maxchild": 56,
+   "rank_mass": 689304,
+   "hosted_residuals": 38632,
+   "prefix_bits": 4304,
+   "charged_prefix_bits": 4352,
+   "coefficient_bits": 4304,
+   "three_level_coefficient_bits": 12966,
+   "charged_three_level_coefficient_bits": 12992,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "793b6f40c9aa4b8db57fec0ac0973e16884dae28707e482ee8f7a2349a5d5a4b",
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "base": {
+  "nine_bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "nine_bit_lower_decimal": "0.001733052823330162099157",
+  "eleven_bit_lower": "427652201524503168379/250000000000000000000000",
+  "eleven_bit_lower_decimal": "0.001710608806098012673516",
+  "note": "PR #555's EXPECTED.json (untuned word); the tune/ pipeline is the same, with the same frozen hosting selections"
+ }
+}
diff --git a/research/k8-x54-t37/vendor/pr1074/t16/NOTICE.md b/research/k8-x54-t37/vendor/pr1074/t16/NOTICE.md
new file mode 100644
index 0000000000..403f4afffb
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/t16/NOTICE.md
@@ -0,0 +1,39 @@
+# Attribution and license
+
+Apache-2.0. New construction and integration: Hao Yan (@FanPUYen), 2026.
+Prepared with substantial OpenAI Codex assistance, including separately tasked
+AI agents for owner construction, independent mathematical/code checking and
+native verification. These are not claims of independent human peer review.
+
+The exact local supplier is Jeremy Kothe's accepted PR799 X4 word, layered on
+Chafik Boukhalfa's PR741 frame changes and PR685 owner construction. Chafik's
+PR795 fixed-inventory optimality result motivated changing the replica count.
+The original owner bytes, scalar program, local frame and width inventory,
+native phase and wrapper implementations retain their existing authorship.
+
+Credit icekylinx for the source gauge and supplier/admission pipeline;
+DreamingOfClouds for the PR589 bit transport and inherited cold-end work;
+eumemic for the PR555 bit supplier and earlier supplier work; Rohan Arun for
+the native exact-complex recurrence correction; Jeremy Diviney, jaymosley07,
+and the other retained owner/allocation contributors; and the complete
+PR514/PR484/PR507/PR558 controller, physical hosting and verification lineage.
+This list is cumulative credit, not approval of every claim in those PRs.
+
+All original notices and licenses remain in the referenced source packages:
+
+- `research/gauge44-frames-x/{NOTICE,UPSTREAM-NOTICE}.md`
+- `research/complex-sw4-frame8/PROVENANCE.md`
+- `research/e8-bit-p111-tuned/tune/README.md`
+- the repository `CONTRIBUTORS.md` and source-package licenses.
+
+The verifier copies pinned global source files into an external replay
+directory and applies an explicit checked edit list. Original attribution
+comments are preserved in those generated derivatives. No original source
+file or historical certificate is rewritten.
+
+The optional ancestry-reuse coverage guard addresses the omission issue
+identified by Lucas (@ljste) in PR838 and the related PR847 integration by
+Chinmay (@chinmayarvind23). Its fixed inventories were read from the accepted
+PR741 source; no pending implementation is imported. Charles Bethin's
+concurrent PR850 strengthens the fixed-inventory owner-profile theorem and
+was checked for overlap before publication; that inventory is changed here.
diff --git a/research/k8-x54-t37/vendor/pr1074/t16/build_parent.py b/research/k8-x54-t37/vendor/pr1074/t16/build_parent.py
new file mode 100644
index 0000000000..bd9e28bd2d
--- /dev/null
+++ b/research/k8-x54-t37/vendor/pr1074/t16/build_parent.py
@@ -0,0 +1,281 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Copyright (c) 2026 Hao Yan (@FanPUYen)
+"""Lift the PR741 controller and PR799 provider plan to sixteen replicas.
+
+Authored with OpenAI Codex assistance. Precursor credit: the PR514/PR484/PR507
+controller lineage, PR558/PR589 admission, Chafik Boukhalfa's PR741 frames
+and owner map, and Jeremy Kothe's PR799 paired-read-exchange provider.
+This script changes only the global replica namespace and the nominated owner
+map; it reuses the exact local programs and exact data-phase recipes.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from collections import Counter
+from pathlib import Path
+
+SOURCE_PLAN_SHA256 = '5f40e7ccfca61f298539b4f41286d2a9d62caf947057f9cec82aa53f73f707fd'
+SOURCE_OWNERS_SHA256 = '99d1c4caf85855c353d30f122d9efbd9e51562914facded13027f347b18a6082'
+
+
+def require(condition, reason):
+    if not condition:
+        raise ValueError(reason)
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def canonical(value):
+    return json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+
+
+def portable_gzip(raw):
+    compressed = bytearray(gzip.compress(raw, mtime=0))
+    compressed[9] = 255  # RFC1952 OS=unknown, independent of zlib/Python platform.
+    return bytes(compressed)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def content_sha(value):
+    return hashlib.sha256(canonical(value)).hexdigest()
+
+
+def lift_parent(source, copies=2):
+    """A direct sum of bank/data stocks; erased private streams are shared.
+
+    copies=1 is deliberately the identity, byte-for-byte after canonicalization.
+    The helper routes retain replica lanes 0..7 in each *separate* bank group.
+    No axis index is inferred from the new global replica label 8..15.
+    """
+    require(type(copies) is int and copies in (1, 2), 'only identity or T16 lift')
+    t = copy.deepcopy(source)
+    if copies == 1:
+        return t
+    require(source['m'] == 73, 'source dimension')
+    require(len(source['calls']) == 72, 'source calls')
+    data = 8*8*112
+    bank_stock = source['live'] - data
+    private_stock = source['physical'] - source['live']
+    require((bank_stock, private_stock) == (9*504, 504+8+2), 'source namespace')
+    require({(c['stage'], c['replica']) for c in source['calls']} ==
+            {(s, r) for s in range(9) for r in range(8)}, 'source coverage')
+    new_data = copies*data
+    new_live = copies*source['live']
+    new_physical = new_live + private_stock
+    t['calls'] = []
+    for c in source['calls']:
+        for group in range(copies):
+            new = copy.deepcopy(c)
+            new['replica'] = c['replica'] + 8*group
+            owners = []
+            for family, route in c['owners']:
+                require(0 <= family < source['live'], 'owner outside live stock')
+                mapped = (family + data*group if family < data else
+                          new_data + group*bank_stock + family - data)
+                owners.append([mapped, copy.deepcopy(route)])
+            new['owners'] = owners
+            t['calls'].append(new)
+    # Every data/idle recipe is a portwise direct sum, hence only multiplicity
+    # changes. Its local axis labels and exact phase words stay unchanged.
+    for child in t['idle_children']:
+        require(child['replicas'] == 8, 'source idle multiplicity')
+        child['replicas'] *= copies
+    for event in t['execution_schedule']:
+        if 'replicas' in event:
+            require(event['replicas'] == list(range(8)), 'source sweep replicas')
+            event['replicas'] = list(range(8*copies))
+        if event['kind'] == 'bank_padding_cover_sweep':
+            event['families'] = [new_data, new_live]
+        elif event['kind'] == 'translate_every_live_family':
+            event['families'] = [0, new_live]
+            event['charged_calls_per_cover'] = new_live
+    t['bank_padding']['families'] = []
+    t['bank_padding']['children'] = []
+    for group in range(copies):
+        for family in source['bank_padding']['families']:
+            t['bank_padding']['families'].append(new_data + group*bank_stock + family - data)
+        for child in source['bank_padding']['children']:
+            new = copy.deepcopy(child)
+            new['family'] = new_data + group*bank_stock + child['family'] - data
+            t['bank_padding']['children'].append(new)
+    t['cover_final_correction'].update(families=[0, new_live], charged_calls_per_cover=new_live)
+    t['private_namespace'] = {
+        key: [new_live + x - source['live'] for x in interval]
+        for key, interval in source['private_namespace'].items()
+    }
+    t.update(live=new_live, physical=new_physical,
+             version='t16-direct-sum-two-bank-groups-parent-v1')
+    t['route_semantics']['helper'] = (
+        'Two independent groups of nine dedicated banks. Group floor(replica/8) '
+        'selects the bank namespace; the stored original helper route retains '
+        'lane replica%8. All original residual/spectator axes are unchanged.')
+    t['loop_order'] = (
+        'For each recipe phase: the explicit calls order, then every cover class d; '
+        'each local invocation completes before the next. Each original replica '
+        'has a disjoint data and bank namespace in its group; private erased '
+        'streams are reused between completed calls.')
+    t['replica_lift'] = dict(
+        source_template_content_sha256=content_sha(source), groups=copies,
+        source_replicas=8, replicas=8*copies, data_stock=new_data,
+        bank_stock=copies*bank_stock, banks_per_stage=copies*504,
+        private_helpers=504, local_programs_content_sha256=content_sha(source['local_programs']),
+        construction='direct sum of data and dedicated banks; share only restored private streams',
+        phase_recipe_unchanged=True)
+    # Source data and helper owner routes are preserved literally in each copy.
+    for c in t['calls']:
+        group, replica = divmod(c['replica'], 8)
+        old = next(z for z in source['calls'] if (z['stage'], z['replica']) == (c['stage'], replica))
+        require([r for f, r in c['owners']] == [r for f, r in old['owners']], 'route changed')
+        require(c['window'] == old['window'], 'local window changed')
+        require(len({f for f, r in c['owners']}) == len(c['owners']), 'per-call owner alias')
+    require(t['local_programs'] == source['local_programs'], 'program changed')
+    require(t['recipe'] == source['recipe'], 'data recipe changed')
+    require(len(t['bank_padding']['children']) == copies*bank_stock, 'bank padding count')
+    require(t['physical'] == t['live']+514, 'private namespace size')
+    return t
+
+
+def expanded_schedule(parent, order):
+    blocks = {}
+    globals_ = []
+    stage = None
+    for index, event in enumerate(parent['execution_schedule']):
+        if event['kind'] in ('bank_padding_cover_sweep', 'translate_every_live_family'):
+            globals_.append((index, event))
+            continue
+        if event['kind'] == 'local_cover_sweep':
+            stage = event['stage']
+            blocks[stage] = []
+        require(stage is not None, 'event precedes first stage')
+        blocks[stage].append((index, event))
+    schedule = []
+    for time, (stage, replica) in enumerate(order):
+        for index, event in blocks[stage]:
+            new = copy.deepcopy(event)
+            new.update(source_event=index, replica=replica, replicas=[replica], time=time)
+            schedule.append(new)
+    for index, event in globals_:
+        schedule.append(dict(event, source_event=index))
+    return schedule
+
+
+def actual_windows(parent, order):
+    ranks = {c['child']: c['rank'] for c in parent['idle_children']}
+    stage_pair = {e['stage']: e['pair'] for e in parent['recipe'] if e['kind'] == 'local'}
+    last, intervals, callpos, perrep = {}, {}, {}, {}
+    schedule = expanded_schedule(parent, order)
+    for pos, event in enumerate(schedule):
+        if 'replica' not in event:
+            continue
+        replica = event['replica']
+        perrep.setdefault(replica, []).append(event['source_event'])
+        if event['kind'] == 'local_cover_sweep':
+            last[replica, stage_pair[event['stage']]] = pos
+            callpos[event['time']] = pos
+        elif event['kind'] == 'bridge':
+            last[replica, event['src']] = last[replica, event['dst']] = pos
+        elif event['kind'] == 'idle_cover_sweep':
+            for child in event['child_indices']:
+                if child in ranks:
+                    intervals[replica, child] = (last.get((replica, event['pair']), -1), pos)
+    require(all(events == list(range(30)) for events in perrep.values()), 'per-replica projection')
+    require([e['source_event'] for e in schedule if 'replica' not in e] == [30, 31], 'global tail')
+    require(set(callpos) == set(range(len(order))), 'complete schedule')
+    windows = {f'{replica},{child}': [ranks[child], [time for time, pos in sorted(callpos.items()) if start < pos < stop]]
+               for (replica, child), (start, stop) in intervals.items()}
+    return windows, schedule
+
+
+def lift_plan(source, parent, owners, source_plan_sha, source_owners_sha, owners_sha):
+    p = copy.deepcopy(source)
+    require(source['T'] == 8 and len(source['order']) == 72, 'source plan dimensions')
+    order = [[stage, replica + 8*group] for stage, replica in source['order'] for group in range(2)]
+    windows, schedule = actual_windows(parent, order)
+    # These windows are recomputed from actual source-event touches, not copied
+    # from the old nomination. Their T8 restriction must recover the old plan.
+    rank = Counter({int(k): 2*v for k, v in source['profile'].items()})
+    rank.update({48: 1, 44: -1, 3: -2, 2: 1})
+    rank = +rank
+    p.update(status='FROZEN_EXPLICIT_T16_TWO_BANK_DIRECT_SUM_OWNER_NOMINATION',
+             mode='gauge44-all144-t16-idle-concentration', T=16, live=14336,
+             deficit=5120, profile=dict(sorted(rank.items())), order=order, windows=windows,
+             solver_status='explicit two-role augmenting path and two-bin recombination', gap=None,
+             source_plan_sha256=source_plan_sha, source_owners_sha256=source_owners_sha,
+             assignment_sha256=owners_sha, assignment_content_sha256=content_sha(owners))
+    for field in ('provider_calls', 'per_call_widths'):
+        p[field] = []
+        for old in source[field]:
+            for group in range(2):
+                new = copy.deepcopy(old)
+                new['replica'] += 8*group
+                if 'time' in new:
+                    new['time'] = 2*old['time']+group
+                p[field].append(new)
+    at = {tuple(x): i for i, x in enumerate(order)}
+    for field in ('provider_calls', 'per_call_widths'):
+        p[field].sort(key=lambda c: at[c['stage'], c['replica']])
+    p['replica_lift'] = dict(groups=2, source_replicas=8, replicas=16,
+                             parent_template_content_sha256=content_sha(parent), owners_file_sha256=owners_sha,
+                             window_semantics='strict physical source-event touch intervals, including bridges',
+                             schedule_content_sha256=content_sha(schedule))
+    require(len(owners) == 144*504, 'owner role count')
+    for role in owners:
+        require(role['time'] == at[role['stage'], role['replica']], 'role call time')
+        require(role['time'] in windows[f"{role['owner_replica']},{role['child']}"][1],
+                'owner outside actual source-event window')
+    require(sum(int(k)*v for k,v in p['profile'].items()) == 73*p['live']-p['deficit'], 'rank mass')
+    return p, schedule
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--base', type=Path, required=True)
+    parser.add_argument('--source-plan', type=Path, required=True)
+    parser.add_argument('--source-owners', type=Path, required=True)
+    parser.add_argument('--owners', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    require(not args.out.exists(), 'output directory already exists')
+    require(sha(args.source_plan) == SOURCE_PLAN_SHA256, 'source plan byte pin')
+    require(sha(args.source_owners) == SOURCE_OWNERS_SHA256, 'source owners byte pin')
+    source_path = args.base/'split-centres/GLOBAL-TEMPLATE.json.gz'
+    source = read(source_path)
+    original_plan = read(args.source_plan)
+    require(lift_parent(source, 1) == source, 'T8 identity control')
+    require(actual_windows(source, original_plan['order'])[0] == original_plan['windows'], 'T8 source-window replay')
+    require(source['exact_data_phase_recipe_sha256'] == sha(args.base/'work/complex-nine-native/DATA-PHASES.json'), 'source exact data-phase binding')
+    parent = lift_parent(source)
+    owners = read(args.owners)
+    plan, schedule = lift_plan(original_plan, parent, owners, sha(args.source_plan), sha(args.source_owners), sha(args.owners))
+    args.out.mkdir(parents=True)
+    (args.out/'GLOBAL-TEMPLATE.json.gz').write_bytes(portable_gzip(canonical(parent)))
+    (args.out/'PLAN.json').write_bytes((json.dumps(plan, indent=2)+'\n').encode('utf-8'))
+    receipt = dict(status='PASS_T16_DIRECT_SUM_PARENT_AND_LITERAL_SOURCE_WINDOWS',
+                   source_template_file_sha256=sha(source_path), source_template_content_sha256=content_sha(source),
+                   source_plan_sha256=sha(args.source_plan), source_owners_sha256=sha(args.source_owners),
+                   owners_sha256=sha(args.owners),
+                   parent_template_file_sha256=sha(args.out/'GLOBAL-TEMPLATE.json.gz'),
+                   parent_template_content_sha256=content_sha(parent), plan_sha256=sha(args.out/'PLAN.json'),
+                   T8_identity_control=True, T8_source_window_identity=True,
+                   local_programs_identical=True, exact_data_phases_identical=True,
+                   parent_live=parent['live'], parent_physical=parent['physical'],
+                   bank_stock=9072, banks_per_stage=1008, private_helpers=504,
+                   source_idle_children_charged=sum(c['replicas'] for c in parent['idle_children']),
+                   events=len(schedule), replica_source_events=30, global_source_events=[30,31],
+                   calls=len(plan['order']), roles=len(owners), actual_window_membership_checked=len(owners),
+                   scope='Legal direct-sum parent namespace and actual source-event windows; full global emitter, geometry, finite invoice, and recurrence admission remain separate checks.')
+    (args.out/'PARENT-LIFT-RECEIPT.json').write_bytes((json.dumps(receipt, indent=2)+'\n').encode('utf-8'))
+    print(json.dumps(receipt, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/k8-x54-t37/verify.py b/research/k8-x54-t37/verify.py
new file mode 100644
index 0000000000..877a0c73e0
--- /dev/null
+++ b/research/k8-x54-t37/verify.py
@@ -0,0 +1,228 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Check the fixed R480 owner bound with exact rational arithmetic."""
+import argparse
+from collections import Counter
+from fractions import Fraction as Q
+import hashlib
+import importlib.util
+import itertools
+import json
+from pathlib import Path
+import sys
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+
+
+def need(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def read(path):
+    return json.loads(path.read_text())
+
+
+def digest(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def source_contract():
+    pins = read(HERE / 'SOURCES.json')
+    for relative, expected in pins['files'].items():
+        path = HERE / relative[8:] if relative.startswith('package:') else ROOT / relative
+        need(digest(path) == expected, 'source drift: ' + relative)
+    spec, plan = read(HERE / 'inputs/SPEC.json'), read(HERE / 'inputs/PLAN.json')
+    provider = spec['providers']['gauge44']
+    local = {int(r): n for r, n in provider['expected_profile'].items()}
+    widths = {int(w): n for w, n in provider['inventory'].items()}
+    registry = plan['provider_registry']['gauge44']
+    need(Counter(registry['widths']) == widths, 'source width contract')
+    need({int(r): n for r, n in registry['actual_paid_profile'].items()} == local,
+         'source paid profile contract')
+    T = plan['T']
+    need(len(plan['order']) == 9*T and set(map(tuple, plan['order'])) ==
+         set(itertools.product(range(9), range(T))), 'source call coverage')
+    byrep = {r: Counter() for r in range(T)}
+    for key, (capacity, times) in plan['windows'].items():
+        replica, child = map(int, key.split(','))
+        byrep[replica][capacity] += 112
+    need(all(stock == byrep[0] for stock in byrep.values()), 'replica capacity contract')
+    need(plan['M'] == 73 and plan['live'] == 896*T, 'source stock contract')
+    engine = ROOT / pins['engine_directory']
+    modules = [load(engine / (name + '.py'), 'r480_' + name)
+               for name in ('moment', 'base_two_moment', 'outer')]
+    driver = load(ROOT / pins['outer_driver'], 'r480_outer_driver')
+    return local, widths, byrep[0], modules, driver, pins
+
+
+def enumerate_bins(widths, prices, bonuses):
+    upper, patterns = {}, []
+    for capacity, bonus in sorted(bonuses.items()):
+        for counts in itertools.product(*(range(capacity//w+1) for w in widths)):
+            used = sum(w*n for w, n in zip(widths, counts))
+            if used > capacity:
+                continue
+            residual = capacity - used
+            value = bonus + sum(p*n for p, n in zip(prices, counts))
+            upper[residual] = max(upper.get(residual, -10**9), value)
+            patterns.append((capacity, counts, residual, value))
+    # This recurrence uses ordered fills, without a count-vector product.
+    second = {}
+    for capacity, bonus in sorted(bonuses.items()):
+        best = {0: 0}
+        for used in range(capacity+1):
+            if used not in best:
+                continue
+            for width, price in zip(widths, prices):
+                if used+width <= capacity:
+                    best[used+width] = max(best.get(used+width, -10**9), best[used]+price)
+        for used, value in best.items():
+            r = capacity-used
+            second[r] = max(second.get(r, -10**9), bonus+value)
+    need(upper == second, 'independent bin recurrence')
+    return upper, patterns
+
+
+def phi(engine, kind, rank, endpoint):
+    if kind == 'mercator':
+        a, b = engine.logarithm(Q(73, rank))
+        lo, hi = engine.exponential(endpoint*a, endpoint*b)
+    else:
+        a, b = engine.log_bounds(Q(73, rank))
+        lo, hi = engine.exp_bounds(endpoint*a)[0], engine.exp_bounds(endpoint*b)[1]
+    return rank*lo, rank*hi
+
+
+def supporting_certificate(engine, kind, upper, lower, higher):
+    # Enclose all exponents in the root interval, not only one grid point.
+    values = {r: (phi(engine, kind, r, lower)[0], phi(engine, kind, r, higher)[1])
+              for r in upper if r}
+    cost = {r: (48*lo-r*values[48][1], 48*hi-r*values[48][0])
+            for r, (lo, hi) in values.items() if r < 48}
+    credit = {r: 48*upper[r]-r*upper[48] for r in cost}
+    need(credit[1] > 0 and cost[1][0] > 0, 'positive rank-one multiplier')
+    margins = {}
+    for rank, (lo, hi) in cost.items():
+        if rank == 1:
+            continue
+        coefficient = credit[rank]
+        rhs = coefficient*cost[1][1 if coefficient >= 0 else 0]/credit[1]
+        margins[rank] = lo-rhs
+        need(margins[rank] > 0, 'strict rank support: ' + str(rank))
+    return {'multiplier_interval': [str(x/credit[1]) for x in cost[1]],
+            'strict_margins': {r: str(x) for r, x in sorted(margins.items())},
+            'minimum_strict_margin': str(min(margins.values()))}
+
+
+def check(certificate):
+    need(not sys.flags.optimize, 'Retained outer assertions require Python without -O')
+    local, inventory, stock, (M, B, A), outer, pins = source_contract()
+    widths = tuple(sorted(inventory))
+    need(set(certificate['width_prices']) == set(map(str, widths)), 'width price keys')
+    need(all(type(n) is int for n in certificate['width_prices'].values()), 'integer width prices')
+    need(all(type(n) is int for n in certificate['capacity_bonuses'].values()), 'integer capacity bonuses')
+    need(set(certificate['capacity_bonuses']) == set(map(str, stock)), 'capacity price keys')
+    prices = tuple(certificate['width_prices'][str(w)] for w in widths)
+    bonuses = {int(c): x for c, x in certificate['capacity_bonuses'].items()}
+    need(set(bonuses) == set(stock), 'capacity price coverage')
+    upper, patterns = enumerate_bins(widths, prices, bonuses)
+    need(upper[0] == 0 and max(upper) == 48, 'zero and maximum residual')
+    mass = sum(c*n for c, n in stock.items())-9*sum(w*n for w, n in inventory.items())
+    signed = sum(stock[c]*bonuses[c] for c in stock)+9*sum(inventory[w]*p for w, p in zip(widths, prices))
+    credit = 48*signed-upper[48]*mass
+    unit = 48*upper[1]-upper[48]
+    need(credit > 0 and unit > 0, 'positive credit demand')
+    formal = {1: Q(credit, unit)}
+    formal[48] = (mass-formal[1])/48
+    T = certificate['replicas']
+    need(type(T) is int and T > 0, 'positive integral replicas')
+    need(all((n*T).denominator == 1 for n in formal.values()), 'integral residual counts')
+    idle = Counter({r: int(n*T) for r, n in formal.items()})
+    counts, bins, actual_idle = Counter(), Counter(), Counter()
+    for row in certificate['packing']:
+        capacity, vector, multiplicity = row['capacity'], row['width_counts'], row['bins']
+        need(type(capacity) is int, 'integer packing capacity')
+        need(type(multiplicity) is int and multiplicity > 0, 'positive packing multiplicity')
+        need(len(vector) == len(widths) and all(type(n) is int and n >= 0 for n in vector),
+             'integer packing vector')
+        used = sum(w*n for w, n in zip(widths, vector))
+        need(capacity in stock and used <= capacity, 'whole-helper capacity')
+        bins[capacity] += multiplicity
+        counts.update({w: multiplicity*n for w, n in zip(widths, vector)})
+        if capacity > used:
+            actual_idle[capacity-used] += multiplicity
+    need(bins == Counter({c: n*T for c, n in stock.items()}), 'complete bin stock')
+    need(counts == Counter({w: 9*T*n for w, n in inventory.items()}), 'complete helper inventory')
+    need(actual_idle == idle, 'attaining residual profile')
+    profile = Counter({r: 9*T*n for r, n in local.items()})
+    profile.update(idle)
+    live = 896*T
+    need(73*live-sum(r*n for r, n in profile.items()) == 320*T, 'complete rank deficit')
+    need(73**2 > 2*max(profile)**2, 'proper-child halving guard')
+    need(len(certificate['root_interval']) == 2 and all(type(x) is str for x in certificate['root_interval']), 'rational root strings')
+    need(type(certificate['kappa_grid']) is str, 'rational kappa string')
+    lower, higher = map(Q, certificate['root_interval'])
+    need(higher-lower == Q(1, 10**24), 'root interval width')
+    signs = {}
+    for name, endpoint in [('lower', lower), ('upper', higher)]:
+        first, second = M.moment(profile, 73, live, endpoint), B.moment(73, live, list(profile.items()), endpoint)
+        need((first[1] < 1 and second[1] < 1) if name == 'lower' else
+             (first[0] > 1 and second[0] > 1), 'two exact root signs: ' + name)
+        signs[name] = {'mercator': [str(x-1) for x in first],
+                       'atanh': [str(x-1) for x in second]}
+    supports = {kind: supporting_certificate(engine, kind, upper, lower, higher)
+                for kind, engine in [('mercator', M), ('atanh', B)]}
+    result1074 = read(HERE / 'inputs/RESULT.json')
+    bit_record = read(ROOT / pins['bit_expected'])
+    bit = bit_record['nine']
+    c = Q(bit['bit_lower'])
+    need(c == Q(result1074['bit_lower']), 'unchanged bit endpoint')
+    bit_histogram = {int(r): n for r, n in bit['profile'].items()}
+    bit_deficit = outer.pr589_deficit(bit_record['word'], bit['bit']['live'])
+    bit_checks = outer.moment_checks(M, B, bit_histogram, 64, bit['bit']['live'], c, bit_deficit, True)
+    prices = {key: outer.outer47(c, b, A) for key, b in [('lower', lower), ('upper', higher)]}
+    need(all(Q(p['kappa']) == Q(certificate['kappa_grid']) for p in prices.values()), 'same outer grid cell')
+    minT = 1
+    import math
+    for n in formal.values():
+        minT = math.lcm(minT, n.denominator)
+    return {'status': 'PASS_R480_ALL_REPLICA_BIN_OPTIMUM',
+            'scope': 'Exact owner bin relaxation. Time windows, per-call family matching, charts, local admission and finite invoices are separate.',
+            'base': pins['base'], 'source_head': pins['source_head'],
+            'inventory': inventory, 'local_profile': local, 'capacity_stock': stock,
+            'bin_patterns': len(patterns), 'upper_price_by_residual': upper,
+            'idle_mass_per_replica': mass, 'signed_price_per_replica': signed,
+            'credit_per_replica': credit, 'rank_one_credit': unit,
+            'normalized_idle': {r: str(n) for r, n in formal.items()},
+            'minimum_equality_replicas': minT, 'packing_replicas': T,
+            'packing_idle': dict(sorted(idle.items())), 'profile': dict(sorted(profile.items())),
+            'live': live, 'deficit': 320*T, 'root_interval': [str(lower), str(higher)],
+            'two_engine_signs': signs, 'support_over_root_interval': supports,
+            'bit_moments_with_surcharge': bit_checks, 'outer': prices, 'kappa_grid_ceiling': certificate['kappa_grid'],
+            'headroom_over_pr1074': str(Q(certificate['kappa_grid'])-Q(result1074['kappa'])),
+            'source_sha256': pins['files']}
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--certificate', type=Path, default=HERE / 'CERTIFICATE.json')
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    need(not args.out.exists(), 'Choose a new output file')
+    result = check(read(args.certificate))
+    args.out.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], 'patterns='+str(result['bin_patterns']),
+          'kappa_grid_ceiling='+str(Q(result['kappa_grid_ceiling'])))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/r480-owner-optimum/CERTIFICATE.json b/research/r480-owner-optimum/CERTIFICATE.json
new file mode 100644
index 0000000000..00e921bdf2
--- /dev/null
+++ b/research/r480-owner-optimum/CERTIFICATE.json
@@ -0,0 +1,122 @@
+{
+  "replicas": 37,
+  "width_prices": {
+    "4": -1,
+    "5": -20,
+    "7": -8,
+    "8": -2,
+    "9": 4
+  },
+  "capacity_bonuses": {
+    "8": 2,
+    "16": 4,
+    "32": 8,
+    "48": -13
+  },
+  "packing": [
+    {
+      "capacity": 8,
+      "width_counts": [
+        0,
+        0,
+        0,
+        1,
+        0
+      ],
+      "bins": 24864
+    },
+    {
+      "capacity": 16,
+      "width_counts": [
+        0,
+        0,
+        0,
+        2,
+        0
+      ],
+      "bins": 3306
+    },
+    {
+      "capacity": 16,
+      "width_counts": [
+        0,
+        0,
+        1,
+        0,
+        1
+      ],
+      "bins": 9394
+    },
+    {
+      "capacity": 16,
+      "width_counts": [
+        2,
+        0,
+        0,
+        1,
+        0
+      ],
+      "bins": 3876
+    },
+    {
+      "capacity": 32,
+      "width_counts": [
+        0,
+        0,
+        2,
+        0,
+        2
+      ],
+      "bins": 298
+    },
+    {
+      "capacity": 32,
+      "width_counts": [
+        0,
+        1,
+        0,
+        0,
+        3
+      ],
+      "bins": 10656
+    },
+    {
+      "capacity": 32,
+      "width_counts": [
+        1,
+        0,
+        0,
+        0,
+        3
+      ],
+      "bins": 5622
+    },
+    {
+      "capacity": 48,
+      "width_counts": [
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "bins": 11302
+    },
+    {
+      "capacity": 48,
+      "width_counts": [
+        1,
+        0,
+        0,
+        1,
+        4
+      ],
+      "bins": 5274
+    }
+  ],
+  "root_interval": [
+    "0.001676905273619680861300",
+    "0.001676905273619680861301"
+  ],
+  "kappa_grid": "0.001674097969905390"
+}
diff --git a/research/r480-owner-optimum/CODE-DERIVATION.json b/research/r480-owner-optimum/CODE-DERIVATION.json
new file mode 100644
index 0000000000..510d91eb86
--- /dev/null
+++ b/research/r480-owner-optimum/CODE-DERIVATION.json
@@ -0,0 +1,218 @@
+{
+  "emit_allcold.py": {
+    "source_sha256": "354367e1fd6185a67b04f4268bcae4d502e47b18cb2131e247f5bcab5b3a769e",
+    "derived_sha256": "3219e0706d497a2e6b595cec0a0d5bdbfbd1d991bf70136762eada44126a9ac1",
+    "edits": [
+      {
+        "before": "==144",
+        "after": "==333",
+        "count": 3
+      },
+      {
+        "before": "T=16;",
+        "after": "T=37;",
+        "count": 1
+      },
+      {
+        "before": "==5120",
+        "after": "==11840",
+        "count": 1
+      },
+      {
+        "before": "deficit=5120",
+        "after": "deficit=11840",
+        "count": 1
+      }
+    ]
+  },
+  "audit_allcold.py": {
+    "source_sha256": "1467a2acb654e62552c69fb9a7c4c85f70a02120881d222313865058ab71a6cc",
+    "derived_sha256": "a8d3c48e26957c5174ea35043545d3863a4c19c82422074ac42132b446533b4a",
+    "edits": [
+      {
+        "before": "T=16;",
+        "after": "T=37;",
+        "count": 1
+      },
+      {
+        "before": "144",
+        "after": "333",
+        "count": 6
+      },
+      {
+        "before": "range(16)",
+        "after": "range(37)",
+        "count": 2
+      },
+      {
+        "before": "r<16",
+        "after": "r<37",
+        "count": 1
+      },
+      {
+        "before": "5120",
+        "after": "11840",
+        "count": 3
+      }
+    ]
+  },
+  "assemble.py": {
+    "source_sha256": "15f6986a476bac76bcdc0bfcf51da115389b46f1950d2766b6822f757888b13a",
+    "derived_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a",
+    "edits": [
+      {
+        "before": "==144*R",
+        "after": "==333*R",
+        "count": 1
+      },
+      {
+        "before": "invoice['bridge_sweeps']==144",
+        "after": "invoice['bridge_sweeps']==333",
+        "count": 1
+      },
+      {
+        "before": "data_and_owner_families=14336",
+        "after": "data_and_owner_families=33152",
+        "count": 1
+      },
+      {
+        "before": "len(calls)==144",
+        "after": "len(calls)==333",
+        "count": 1
+      },
+      {
+        "before": "range(16)",
+        "after": "range(37)",
+        "count": 1
+      },
+      {
+        "before": "parent_live,parent_physical,parent_idle=23408,23922,32256",
+        "after": "parent_live,parent_physical,parent_idle=55832,56346,74592",
+        "count": 1
+      },
+      {
+        "before": "2*112*4*16",
+        "after": "2*112*4*37",
+        "count": 1
+      },
+      {
+        "before": "2*112*144,4*112*16",
+        "after": "2*112*333,4*112*37",
+        "count": 1
+      },
+      {
+        "before": "4*112*16*9+2*112*16*9+2*144*R",
+        "after": "4*112*37*9+2*112*37*9+2*333*R",
+        "count": 1
+      },
+      {
+        "before": "(144*invoice['local_adapters']",
+        "after": "(333*invoice['local_adapters']",
+        "count": 1
+      },
+      {
+        "before": "invoice['charged_prefix_bits']==512",
+        "after": "invoice['charged_prefix_bits']==1024",
+        "count": 1
+      },
+      {
+        "before": "invoice['row_prefix_extra']==1024",
+        "after": "invoice['row_prefix_extra']==2048",
+        "count": 1
+      },
+      {
+        "before": "+37+144+144+4",
+        "after": "+37+333+333+4",
+        "count": 1
+      },
+      {
+        "before": "+9909+252+1024",
+        "after": "+9909+252+2048",
+        "count": 1
+      },
+      {
+        "before": "5120",
+        "after": "11840",
+        "count": 3
+      },
+      {
+        "before": "(4+512)",
+        "after": "(4+1024)",
+        "count": 2
+      },
+      {
+        "before": "two independent bank groups, each with R0=504 helpers; restored private workspace is shared",
+        "after": "five bank groups with 8,8,8,8,5 active lanes and R0=504 helpers; shared private work is restored",
+        "count": 1
+      },
+      {
+        "before": "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. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. 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.",
+        "after": "Conditional R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain.",
+        "count": 1
+      }
+    ]
+  },
+  "assembly_controls.py": {
+    "source_sha256": "da7e981ae1b9f099d4e1524cb4f3ba1116011936ebe378692889b5dbfa99029d",
+    "derived_sha256": "29ba6742d899d2318a96745c8ec21de06ba3968d4641c3400a15bc714e0d7f9e",
+    "edits": [
+      {
+        "before": "1 + 37 + 144 + 144 + 4",
+        "after": "1 + 37 + 333 + 333 + 4",
+        "count": 1
+      }
+    ]
+  },
+  "freeze_spec.py": {
+    "source_sha256": "5971eecac6d6fbcb53244b80f1b9d7232012dc32876fab511214a5addebbe6c2",
+    "derived_sha256": "e9132a9d195c66123f2747a17f7ef404b4d1e3ef6263ab4c28c983a052cf10bd",
+    "edits": [
+      {
+        "before": "{'gauge44':144}",
+        "after": "{'gauge44':333}",
+        "count": 1
+      }
+    ]
+  },
+  "invoice_allcold.py": {
+    "source_sha256": "71eb57514e28ced97251e0507105f654f59885ec4d40486a780bf166098858a8",
+    "derived_sha256": "e97c74d1ccfb0b0e26260e65bb780fa0103f4c716647e238f943a2e840a1f566",
+    "edits": [
+      {
+        "before": "stages,replicas,blocks_per_stream=9,16,4",
+        "after": "stages,replicas,blocks_per_stream=9,37,4",
+        "count": 1
+      },
+      {
+        "before": "==5120",
+        "after": "==11840",
+        "count": 1
+      },
+      {
+        "before": "payload=512",
+        "after": "payload=1024",
+        "count": 1
+      },
+      {
+        "before": "previous['charged_prefix_bits']==payload",
+        "after": "previous['charged_prefix_bits']==512",
+        "count": 1
+      },
+      {
+        "before": "all 144 invocation and 144 bridge sweeps",
+        "after": "all 333 invocation and 333 bridge sweeps",
+        "count": 1
+      },
+      {
+        "before": "All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission.",
+        "after": "The fixed provider uses fresh hash-bound independent all-column/frame/phase/normalization admission.",
+        "count": 1
+      },
+      {
+        "before": "take maximum local scalar/Horner prefix over all three providers and orientations.",
+        "after": "take the maximum local scalar/Horner prefix over both orientations of the fixed provider.",
+        "count": 1
+      }
+    ]
+  }
+}
diff --git a/research/r480-owner-optimum/CODE-DERIVATION.patch b/research/r480-owner-optimum/CODE-DERIVATION.patch
new file mode 100644
index 0000000000..3089adb97c
--- /dev/null
+++ b/research/r480-owner-optimum/CODE-DERIVATION.patch
@@ -0,0 +1,309 @@
+--- pr1074/code/emit_allcold.py
++++ r480-owner-optimum/code/emit_allcold.py
+@@ -24,8 +24,8 @@
+ 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))==144;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=16;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
++call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==333;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=37;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+ assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,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')
+@@ -49,9 +49,9 @@
+   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)
+-assert len(roles)==144*R   # one whole-owner role per (call, provider helper)
++assert len(roles)==333*R   # one whole-owner role per (call, provider helper)
+ selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+-assert len(selected)==144 and set(selected)==set(call_order)
++assert len(selected)==333 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():
+@@ -92,7 +92,7 @@
+   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())==5120
++assert M*DATA-sum(r*n for r,n in paid.items())==11840
+ C=len(canon['centers']);physical=DATA+C+R+2
+ assert parent['physical']-parent['live']==C+R0+2
+ # Local circuits, exact phase recipes, normalized wrappers and data routes stay
+@@ -140,7 +140,7 @@
+  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=5120,maxchild=max(paid),
++ rank_mass=sum(r*n for r,n in paid.items()),deficit=11840,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),
+--- pr1074/code/audit_allcold.py
++++ r480-owner-optimum/code/audit_allcold.py
+@@ -77,10 +77,10 @@
+ parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+ assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+ assert required_artifacts<=set(summary['source_artifacts'])
+-prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=16;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=144;HOSTED=CALLS*R
++prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=37;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=333;HOSTED=CALLS*R
+ # The selected map is an input to check, not a claim from the emitter.
+ 
+-assert len(DISPATCH)==144 and Counter(DISPATCH.values())==COUNTS
++assert len(DISPATCH)==333 and Counter(DISPATCH.values())==COUNTS
+ expected_provider=lambda stage,replica:DISPATCH[stage,replica]
+ 
+ def orthobasis(port):
+@@ -93,23 +93,23 @@
+  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'])==144 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
++ assert len(t['calls'])==333 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))==144
+- all_local=[];perrep={r:[]for r in range(16)};globals_=[]
++ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==333
++ all_local=[];perrep={r:[]for r in range(37)};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<16 and j<30;perrep[r].append(j)
++   r=e['replica'];assert 0<=r<37 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']<144 and order[e['time']][1]==r
++   assert 0<=e['time']<333 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:
+@@ -164,7 +164,7 @@
+    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(16)for h in range(R)}
++ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(37)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']:
+@@ -179,8 +179,8 @@
+    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==5120 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=144)
++ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==11840 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=333)
+ 
+ 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())
+@@ -228,11 +228,11 @@
+   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=5120,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,provider_artifact_semantic_sha256=artifact_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=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=11840,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,provider_artifact_semantic_sha256=artifact_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=5120,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,provider_artifact_semantic_sha256=artifact_semantic_hashes,controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
++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=11840,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,provider_artifact_semantic_sha256=artifact_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,
+--- pr1074/code/assemble.py
++++ r480-owner-optimum/code/assemble.py
+@@ -63,14 +63,14 @@
+  assert owner['all_live_owners_per_call_distinct'] is True
+  # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+  R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+- assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==144*R==pin('expected.hosted_residuals',owner['hosted_residuals'])
++ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==333*R==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']==144
++ assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==333
+  assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+  assert invoice['centres']==8
+- assert invoice['physical_stock_identity']==dict(data_and_owner_families=14336,local_helpers=R,private_centres=8,coefficient_work=2)
++ assert invoice['physical_stock_identity']==dict(data_and_owner_families=33152,local_helpers=R,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():
+@@ -106,9 +106,9 @@
+   assert p['compiler']==64*74**3
+   assert p['local_adapters']==16*(max(z['macros']for z in p['local'].values())+p['children']+2*112+R+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)==144
++ calls=invoice['selected_calls'];assert len(calls)==333
+  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(16)}
++ assert {(c['stage'],c['replica']) for c in calls}=={(s,r) for s in range(9) for r in range(37)}
+  for c in calls:
+   pid=DISPATCH[c['stage'],c['replica']]
+   assert c['provider_id']==pid
+@@ -138,13 +138,13 @@
+  # 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=23408,23922,32256
+- parent_banks,rem=divmod(parent_live-2*112*4*16,9);assert rem==0 and parent_physical==parent_live+504+8+2   # two independent bank groups, each with R0=504 helpers; restored private workspace is shared
++ parent_live,parent_physical,parent_idle=55832,56346,74592
++ parent_banks,rem=divmod(parent_live-2*112*4*37,9);assert rem==0 and parent_physical==parent_live+504+8+2   # five bank groups with 8,8,8,8,5 active lanes and R0=504 helpers; shared private work is restored
+  assert owner['source_idle_children_charged']==parent_idle
+- bridges,shifts=2*112*144,4*112*16;moves=2*shifts
+- nonlocal_items=(4*112*16*9+2*112*16*9+2*144*R+parent_idle+9*parent_banks+bridges+shifts+moves+parent_live+parent_physical+invoice['wrapper_elementary_factors_charged'])
++ bridges,shifts=2*112*333,4*112*37;moves=2*shifts
++ nonlocal_items=(4*112*37*9+2*112*37*9+2*333*R+parent_idle+9*parent_banks+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+(144*invoice['local_adapters']+outside)*invoice['compiler']+64*parent_physical)
++ pervertex=(invoice['selected_real_component_primitives']+bridges+shifts+moves+parent_live+(333*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)
+@@ -160,9 +160,9 @@
+  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+144+144+4
++ assert 0<invoice['global_prefix_bits']<=invoice['charged_prefix_bits']==1024
++ assert invoice['row_prefix_extra']==2048
++ assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+333+333+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']
+@@ -170,7 +170,7 @@
+  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['physical_row_coefficient']==2*stock.bit_length()+9909+252+2048
+  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())
+@@ -185,7 +185,7 @@
+  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']==5120
++ pin('expected.live',owner['live']);pin('expected.physical',owner['physical']);assert owner['deficit']==11840
+  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
+@@ -200,14 +200,14 @@
+  bitH={int(r):n for r,n in bit['profile'].items()}
+  assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+  bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+- conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,5120,True)
++ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,11840,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)
++   ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+1024)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+1024)
+    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)}}
+@@ -222,7 +222,7 @@
+  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,5120,False)
++ native_moments=check_moment('complex',H,73,owner['live'],b,11840,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
+@@ -231,7 +231,7 @@
+  moments=bit_moments+native_moments
+  input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'package:inputs/PR589-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_GAUGE44_NATIVE_EXACT_GLOBAL_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_pr635_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=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),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. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. 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.')
++ return dict(status='PASS_GAUGE44_NATIVE_EXACT_GLOBAL_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_pr635_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=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),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 R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain.')
+ if __name__=='__main__':
+  import sys
+  package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists()
+--- pr1074/code/assembly_controls.py
++++ r480-owner-optimum/code/assembly_controls.py
+@@ -58,7 +58,7 @@
+         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 + 144 + 144 + 4
++        i['global_prefix_bits'] = 1 + 37 + 333 + 333 + 4
+ 
+     def reordered_calls(o, i):
+         i['selected_calls'][0], i['selected_calls'][1] = i['selected_calls'][1], i['selected_calls'][0]
+--- pr1074/code/freeze_spec.py
++++ r480-owner-optimum/code/freeze_spec.py
+@@ -23,7 +23,7 @@
+ for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+     spec['expected'][key] = assembly[key]
+ spec['expected']['assembly_controls_rejected'] = 69
+-spec['expected']['provider_counts'] = {'gauge44':144}
++spec['expected']['provider_counts'] = {'gauge44':333}
+ spec['expected']['mutations_rejected'] = 15
+ a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+ print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
+--- pr1074/code/invoice_allcold.py
++++ r480-owner-optimum/code/invoice_allcold.py
+@@ -195,7 +195,7 @@
+     helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+     assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+     parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+-    stages,replicas,blocks_per_stream=9,16,4
++    stages,replicas,blocks_per_stream=9,37,4
+     call_count=len(template['calls'])
+     assert call_count==stages*replicas==control['complete_invocations']
+     assert control['one_owner_per_complete_invocation']
+@@ -250,7 +250,7 @@
+         +(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']==5120
++    assert m*live-mass==owners['deficit']==11840
+     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']
+@@ -260,10 +260,10 @@
+     # 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
++    used=max(rebased,parent_pervertex); retained=None; payload=1024
+     if retained_invoice is not None:
+         previous=read(retained_invoice)
+-        assert previous['compiler']==compiler and previous['charged_prefix_bits']==payload
++        assert previous['compiler']==compiler and previous['charged_prefix_bits']==512
+         previous_bound=previous['conservative_pervertex_used']
+         used=max(used,previous_bound+parent_pervertex)
+         retained=dict(sha256=filehash(retained_invoice),previous_pervertex_allowance=previous_bound,
+@@ -307,13 +307,13 @@
+                     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.')
++        scope='Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. The fixed provider uses 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 144 invocation and 144 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.')
++        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 333 invocation and 333 bridge sweeps and take the maximum local scalar/Horner prefix over both orientations of the fixed provider. 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')
diff --git a/research/r480-owner-optimum/INDEPENDENT-DERIVATION.patch b/research/r480-owner-optimum/INDEPENDENT-DERIVATION.patch
new file mode 100644
index 0000000000..3e8d9fed4e
--- /dev/null
+++ b/research/r480-owner-optimum/INDEPENDENT-DERIVATION.patch
@@ -0,0 +1,137 @@
+--- base/research/complex-t21-owners/independent_check.py
++++ r480-owner-optimum/independent_owner.py
+@@ -1,30 +1,31 @@
+ #!/usr/bin/env python3
+ # SPDX-License-Identifier: Apache-2.0
+ # Prepared for haoyan with substantial OpenAI Codex assistance.
+-"""Independent variable-replica event, whole-helper, chart and finite-reserve audit.
++"""Independent source-event, owner, chart, and finite-reserve audit.
++
++This derivative fixes the R480 seven-slot k8 word and 37 replicas. It charges
++1024 complex prefix bits and checks disjoint pending children on each family.
++The source is Hao Yan's variable-replica checker at the pinned repository base.
++SOURCES.json and INDEPENDENT-DERIVATION.patch identify that source and all edits.
+ 
+ Inputs are read-only. No owner constructor or controller auditor is imported.
+---word is the canonical local supplier JSON.gz, with frame IDs and a native
+-INDEPENDENT-LOCAL-REPLAY.json alongside it (override with --local-replay).
++--word is the canonical local supplier JSON.gz, with a hash-bound native
++INDEPENDENT-LOCAL-REPLAY.json beside it (override with --local-replay).
+ --baseline-parent is the original eight-replica GLOBAL-TEMPLATE.json.gz.
+-Parameterized from Hao Yan's PR858 checker; the original source is vendored.
+-Only replica cardinalities, the nominated idle profile, and the two-copy
+-interleaving restriction change. Exact per-replica source projections remain.
+-Its sibling CANONICAL-WORD.json.gz supplies ports; DATA-PHASES.json defaults
+-to ../work/complex-nine-native/DATA-PHASES.json (override with --phases).
+-The PR741 and PR799/X4 suppliers share this width/owner interface. Their
+-local paid profiles and prefix exponents are read and recounted from the
+-provided canonical word and hash-bound native replay, never fixed to PR741.
++Its sibling CANONICAL-WORD.json.gz supplies the ports and centre frames.
++DATA-PHASES.json defaults to ../work/complex-nine-native/DATA-PHASES.json
++(override with --phases). The checker recounts local widths and paid ranks.
+ --out names a JSON receipt. Checks remain enabled under python -O.
+ """
+ import argparse
++import copy
+ from collections import Counter, defaultdict
+ import gzip
+ import hashlib
+ import json
+ from pathlib import Path
+ 
+-V, H, M, T, R = 112, 9, 73, 21, 504
++V, H, M, T, R = 112, 9, 73, 37, 480
+ EXPECTED_IDLE = None
+ 
+ 
+@@ -93,7 +94,7 @@
+     for orientation in ('forward', 'backward'):
+         require(dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}, 'local replay profile binding')
+     widths = [len(frames[word['final'][q]]) - len(frames[word['start'][q]]) for q in range(2 * V, n)]
+-    require(Counter(widths) == {4: 80, 5: 32, 7: 54, 8: 122, 9: 216}, 'current supplier width inventory')
++    require(Counter(widths) == {4: 56, 5: 32, 7: 30, 8: 122, 9: 240}, 'current supplier width inventory')
+     return widths, paid
+ 
+ 
+@@ -161,6 +162,21 @@
+                 bases=bases, phases=phases, bridges=bridges, event_count=len(events), replay=replay)
+ 
+ 
++def check_pending_axes(context):
++    checked = 0
++    for port, frame in enumerate(context['bases']):
++        used = defaultdict(set)
++        for child, rank in context['rank'].items():
++            axes = list(map(int, context['phases']['recipes'][port]['idle_children'][child]['orthogonal_axes']))
++            require(len(axes) == rank and len(set(axes)) == rank and set(axes) <= set(frame),
++                    'pending child orthogonal basis')
++            family = context['child_pair'][child], context['side'][child]
++            require(not used[family] & set(axes), 'overlapping pending children on one family')
++            used[family].update(axes)
++            checked += 1
++    return checked
++
++
+ def check_roles(context, roles):
+     c = context
+     live, physical = T * 8 * V, T * 8 * V + 8 + R + 2
+@@ -221,8 +237,8 @@
+     for i in range(1, 37):
+         group *= 2 ** (2 * i) - 1
+     stock = group * physical
+-    row = 2 * stock.bit_length() + 9909 + 252 + 2 * 512
+-    require(prefix < 512, 'prefix reserve')
++    row = 2 * stock.bit_length() + 9909 + 252 + 2 * 1024
++    require(prefix < 1024, 'prefix reserve')
+     require(row < 20161 and M * M > 2 * max(profile) ** 2, 'row or halving reserve')
+     return dict(status='PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW', roles=len(roles), calls=len(c['order']),
+                 source_events_per_replica=30, expanded_replica_events=c['event_count'], bridge_events=c['bridges'],
+@@ -233,7 +249,7 @@
+                 rank_mass=mass, deficit=320*T, namespace={'data':[0,live], 'centres':[live,live+8], 'tableau':[live+8,live+8+R], 'coefficient':[live+8+R,physical]},
+                 local_prefix_bits=localbits, local_prefix_from_native_receipt=True, local_profile_recounted=True,
+                 prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], margin=4),
+-                prefix_bits=prefix, charged_prefix_bits=512, physical_stock_bits=stock.bit_length(),
++                prefix_bits=prefix, charged_prefix_bits=1024, physical_stock_bits=stock.bit_length(),
+                 physical_row_coefficient=row, row_limit=20161,
+                 scope='Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.')
+ 
+@@ -271,6 +287,20 @@
+             rejected.append(dict(name=name, reason=str(exc)))
+         else:
+             raise ValueError('accepted negative control: ' + name)
++    bad = dict(context, phases=copy.deepcopy(context['phases']))
++    pair = next((a, b) for a in context['rank'] for b in context['rank']
++                if a < b and (context['child_pair'][a], context['side'][a]) ==
++                (context['child_pair'][b], context['side'][b]))
++    children = bad['phases']['recipes'][0]['idle_children']
++    children[pair[1]]['orthogonal_axes'][0] = children[pair[0]]['orthogonal_axes'][0]
++    try:
++        check_pending_axes(bad)
++    except ValueError as exc:
++        require(str(exc) == 'overlapping pending children on one family',
++                'pending-axis control rejected at unexpected predicate')
++        rejected.append(dict(name='cross_child_pending_axis_alias', reason=str(exc)))
++    else:
++        raise ValueError('accepted negative control: cross_child_pending_axis_alias')
+     return rejected
+ 
+ 
+@@ -287,7 +317,7 @@
+     parser.add_argument("--expected-idle", required=True)
+     args = parser.parse_args()
+     T = args.replicas
+-    require(1 <= T <= 22, "replica range")
++    require(T == 37, "replica range")
+     EXPECTED_IDLE = {int(k): v for k,v in json.loads(args.expected_idle).items()}
+     phases_path = args.phases or args.baseline_parent.parent.parent / 'work/complex-nine-native/DATA-PHASES.json'
+     canonical_path = args.baseline_parent.parent / 'CANONICAL-WORD.json.gz'
+@@ -300,7 +330,9 @@
+     require(len(word['center_frames']) == len(canonical['center_frames']) == 8, 'eight centre interfaces')
+     require([basis(word['frames'][f]) for f in word['center_frames']] == [basis(canonical['frames'][f]) for f in canonical['center_frames']], 'ordered centre-frame interface')
+     context = make_context(parent, phases, canonical['ports'], word, replay, roles)
++    pending = check_pending_axes(context)
+     receipt = check_roles(context, roles)
++    receipt['disjoint_pending_child_axis_checks'] = pending
+     receipt['controls_rejected'] = controls(context, roles)
+     receipt['input_sha256'] = {str(path): filehash(path) for path in (args.baseline_parent, phases_path, canonical_path, args.word, replay_path, args.owners)}
+     args.out.write_text(json.dumps(receipt, indent=2) + '\n', encoding='utf-8')
diff --git a/research/r480-owner-optimum/NOTICE.md b/research/r480-owner-optimum/NOTICE.md
new file mode 100644
index 0000000000..1e3b40de32
--- /dev/null
+++ b/research/r480-owner-optimum/NOTICE.md
@@ -0,0 +1,45 @@
+# Attribution and license
+
+New owner theorem, exact flow construction, checker, and package by
+Ali Romman <226877337+aliromman@users.noreply.github.com>, with substantial
+OpenAI Codex assistance. New work is under Apache-2.0.
+
+The fixed local supplier is Jeremy Kothe's seven-slot k8 word in PR1074,
+commit `052afc128954f7b6a2b3c409eb4d72248e4020f2`. The seven-slot step comes
+from PR1018 and credits Rohan Arun's PR987 search. The earlier local word and
+its scalar, frame, phase, and source-access construction retain all notices
+in `vendor/pr1074/NOTICE.md` and `vendor/pr1074/UPSTREAM-NOTICE.md`.
+This package does not claim authorship of those local changes.
+
+The signed bin prices come from Chafik Boukhalfa's PR795. The proof method
+builds on the PR890/PR942 owner bounds and the prior all-replica T37 theorem.
+The new right-hand side, exact attaining flow, and complete R480 owner map
+are specific to the changed seven-slot inventory. The old theorem did not
+cover this word.
+
+The T16 source-event routines are by Hao Yan (@FanPUYen). Their source notice
+is kept in `vendor/pr1074/t16/NOTICE.md` and their source headers. The derived
+independent owner checker comes from `research/complex-t21-owners` at the
+exact repository base. `INDEPENDENT-DERIVATION.patch` records its changes.
+
+The global admission code comes from the exact PR1074 package. Its sources
+and notices are retained. `CODE-DERIVATION.patch` records all changes needed
+for 37 replicas and the 1024-bit complex prefix allowance. The arithmetic
+engines and full PR589 bit supplier are unchanged and source-pinned.
+
+PR1034 proved a mixed bound for 71 older catalogue entries and excluded
+R480. PR1069 independently checked the rank-mass identity for recent claims.
+These contributions informed the scope and cost audit. Neither admits the
+new physical owner map by itself.
+
+The concurrent mutable-leaver sprint worker rebuilt the unchanged local k8
+and seven-slot chains, including their scalar and phase checks. This package
+retains that source-bound evidence. It does not use the worker's new local
+word experiments. No predecessor notice, license, or AI disclosure is replaced
+by this notice.
+
+Josie Elliston's PR1091 independently checked fifteen T16 owner maps and
+made the disjoint-pending-axis obligation explicit. The independent T37
+audit includes that check and a targeted negative control. Rohan Arun's
+PR1094 gives a later same-word T16 repack. Jeremy Kothe's PR1117 changes
+the local word; it is a concurrent comparison outside the proved inventory.
diff --git a/research/r480-owner-optimum/ORDER.json b/research/r480-owner-optimum/ORDER.json
new file mode 100644
index 0000000000..500a9c3738
--- /dev/null
+++ b/research/r480-owner-optimum/ORDER.json
@@ -0,0 +1 @@
+[[0, 0], [0, 21], [0, 8], [0, 29], [0, 1], [0, 22], [0, 9], [0, 30], [1, 0], [1, 8], [1, 21], [0, 16], [1, 29], [0, 2], [0, 23], [0, 10], [0, 17], [0, 31], [1, 1], [1, 22], [1, 9], [1, 30], [1, 16], [2, 0], [2, 21], [2, 8], [2, 29], [0, 18], [0, 24], [0, 3], [0, 11], [0, 32], [1, 17], [1, 23], [1, 2], [1, 31], [1, 10], [2, 16], [2, 22], [2, 1], [2, 30], [2, 9], [3, 21], [0, 19], [3, 29], [3, 0], [3, 8], [0, 25], [1, 18], [0, 33], [0, 4], [1, 24], [0, 12], [2, 17], [1, 32], [1, 3], [2, 23], [1, 11], [2, 31], [3, 16], [2, 2], [3, 22], [2, 10], [3, 30], [0, 20], [4, 21], [3, 1], [3, 9], [4, 29], [1, 19], [0, 26], [4, 0], [0, 34], [4, 8], [2, 18], [1, 25], [0, 5], [1, 33], [0, 13], [2, 24], [3, 17], [2, 32], [1, 4], [1, 12], [3, 23], [4, 16], [3, 31], [2, 3], [4, 22], [2, 11], [3, 2], [4, 30], [3, 10], [5, 21], [1, 20], [5, 29], [4, 1], [4, 9], [0, 27], [2, 19], [0, 35], [5, 0], [1, 26], [5, 8], [3, 18], [1, 34], [0, 6], [2, 25], [0, 14], [2, 33], [4, 17], [1, 5], [3, 24], [1, 13], [3, 32], [5, 16], [4, 23], [2, 4], [4, 31], [2, 12], [3, 3], [5, 22], [3, 11], [5, 30], [4, 2], [0, 28], [4, 10], [2, 20], [0, 36], [5, 1], [6, 21], [5, 9], [6, 29], [3, 19], [0, 7], [1, 27], [0, 15], [1, 35], [4, 18], [2, 26], [6, 0], [6, 8], [2, 34], [5, 17], [3, 25], [1, 6], [3, 33], [1, 14], [2, 5], [4, 24], [2, 13], [4, 32], [6, 16], [5, 23], [3, 4], [5, 31], [3, 12], [4, 3], [6, 22], [4, 11], [6, 30], [5, 2], [1, 28], [5, 10], [3, 20], [1, 36], [6, 1], [7, 21], [6, 9], [7, 29], [4, 19], [1, 7], [2, 27], [1, 15], [2, 35], [5, 18], [3, 26], [7, 0], [7, 8], [3, 34], [6, 17], [4, 25], [2, 6], [4, 33], [2, 14], [3, 5], [5, 24], [3, 13], [5, 32], [7, 16], [6, 23], [4, 4], [6, 31], [4, 12], [5, 3], [7, 22], [5, 11], [7, 30], [6, 2], [2, 28], [6, 10], [4, 20], [2, 36], [7, 1], [8, 21], [7, 9], [8, 29], [5, 19], [2, 7], [3, 27], [2, 15], [3, 35], [6, 18], [4, 26], [8, 0], [8, 8], [4, 34], [7, 17], [5, 25], [3, 6], [5, 33], [3, 14], [4, 5], [6, 24], [4, 13], [6, 32], [8, 16], [7, 23], [5, 4], [7, 31], [5, 12], [6, 3], [8, 22], [6, 11], [8, 30], [7, 2], [3, 28], [7, 10], [5, 20], [3, 36], [8, 1], [4, 27], [8, 9], [4, 35], [6, 19], [3, 7], [5, 26], [3, 15], [5, 34], [7, 18], [6, 25], [4, 6], [4, 14], [6, 33], [8, 17], [7, 24], [5, 5], [7, 32], [5, 13], [6, 4], [8, 23], [6, 12], [8, 31], [7, 3], [4, 28], [7, 11], [4, 36], [8, 2], [8, 10], [5, 27], [6, 20], [5, 35], [4, 7], [6, 26], [4, 15], [7, 19], [6, 34], [5, 6], [7, 25], [5, 14], [7, 33], [8, 18], [6, 5], [8, 24], [6, 13], [8, 32], [7, 4], [5, 28], [7, 12], [8, 3], [5, 36], [8, 11], [6, 27], [5, 7], [6, 35], [5, 15], [7, 20], [7, 26], [6, 6], [7, 34], [6, 14], [8, 25], [8, 19], [8, 33], [7, 5], [7, 13], [6, 28], [8, 4], [6, 36], [8, 12], [7, 27], [6, 7], [6, 15], [7, 35], [7, 6], [8, 26], [7, 14], [8, 34], [8, 20], [8, 5], [7, 28], [8, 13], [7, 36], [7, 7], [8, 27], [7, 15], [8, 6], [8, 35], [8, 14], [8, 28], [8, 7], [8, 36], [8, 15]]
diff --git a/research/r480-owner-optimum/OWNERS.json.gz b/research/r480-owner-optimum/OWNERS.json.gz
new file mode 100644
index 0000000000..6dd3d937a5
Binary files /dev/null and b/research/r480-owner-optimum/OWNERS.json.gz differ
diff --git a/research/r480-owner-optimum/PATTERN-FLOW.json b/research/r480-owner-optimum/PATTERN-FLOW.json
new file mode 100644
index 0000000000..1e60b5a70a
--- /dev/null
+++ b/research/r480-owner-optimum/PATTERN-FLOW.json
@@ -0,0 +1 @@
+{"T": 37, "kind": "t37", "order": [[0, 0], [0, 21], [0, 8], [0, 29], [0, 1], [0, 22], [0, 9], [0, 30], [1, 0], [1, 8], [1, 21], [0, 16], [1, 29], [0, 2], [0, 23], [0, 10], [0, 17], [0, 31], [1, 1], [1, 22], [1, 9], [1, 30], [1, 16], [2, 0], [2, 21], [2, 8], [2, 29], [0, 18], [0, 24], [0, 3], [0, 11], [0, 32], [1, 17], [1, 23], [1, 2], [1, 31], [1, 10], [2, 16], [2, 22], [2, 1], [2, 30], [2, 9], [3, 21], [0, 19], [3, 29], [3, 0], [3, 8], [0, 25], [1, 18], [0, 33], [0, 4], [1, 24], [0, 12], [2, 17], [1, 32], [1, 3], [2, 23], [1, 11], [2, 31], [3, 16], [2, 2], [3, 22], [2, 10], [3, 30], [0, 20], [4, 21], [3, 1], [3, 9], [4, 29], [1, 19], [0, 26], [4, 0], [0, 34], [4, 8], [2, 18], [1, 25], [0, 5], [1, 33], [0, 13], [2, 24], [3, 17], [2, 32], [1, 4], [1, 12], [3, 23], [4, 16], [3, 31], [2, 3], [4, 22], [2, 11], [3, 2], [4, 30], [3, 10], [5, 21], [1, 20], [5, 29], [4, 1], [4, 9], [0, 27], [2, 19], [0, 35], [5, 0], [1, 26], [5, 8], [3, 18], [1, 34], [0, 6], [2, 25], [0, 14], [2, 33], [4, 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318, 1, 319, 0], 14], [["y", 318, 1, 319, 3], 70], [["y", 318, 1, 328, 3], 11], [["x", 319, 3], 224], [["y", 319, 3, 260, 1], 32], [["y", 319, 3, 262, 4], 224], [["y", 319, 3, 282, 4], 38], [["y", 319, 3, 284, 1], 32], [["y", 319, 3, 295, 4], 38], [["y", 319, 3, 298, 1], 32], [["y", 319, 3, 303, 1], 19], [["y", 319, 3, 305, 1], 31], [["y", 319, 3, 306, 1], 14], [["y", 319, 3, 313, 4], 224], [["y", 319, 3, 316, 1], 32], [["y", 319, 3, 324, 1], 32], [["y", 319, 3, 324, 4], 148], [["x", 320, 0], 214], [["y", 320, 0, 304, 3], 52], [["y", 320, 0, 305, 3], 122], [["y", 320, 0, 322, 3], 60], [["y", 320, 0, 323, 3], 21], [["y", 320, 0, 325, 3], 122], [["y", 320, 0, 326, 3], 51], [["x", 320, 2], 10], [["y", 320, 2, 323, 0], 10], [["y", 320, 2, 325, 0], 10], [["y", 320, 2, 328, 3], 10], [["x", 321, 0], 64], [["x", 321, 1], 160], [["y", 321, 1, 227, 3], 12], [["y", 321, 1, 233, 4], 72], [["y", 321, 1, 242, 3], 6], [["y", 321, 1, 250, 4], 84], [["y", 321, 1, 283, 0], 8], [["y", 321, 1, 283, 4], 125], [["y", 321, 1, 289, 0], 56], [["y", 321, 1, 292, 4], 74], [["y", 321, 1, 307, 3], 6], [["y", 321, 1, 309, 4], 77], [["y", 321, 1, 313, 0], 56], [["y", 321, 1, 318, 3], 1], [["y", 321, 1, 319, 3], 51], [["y", 321, 1, 321, 3], 84], [["y", 321, 1, 321, 4], 66], [["y", 321, 1, 323, 0], 37], [["y", 321, 1, 327, 4], 5], [["y", 321, 1, 328, 0], 3], [["y", 321, 1, 329, 4], 137], [["x", 322, 3], 224], [["y", 322, 3, 271, 1], 32], [["y", 322, 3, 289, 1], 12], [["y", 322, 3, 290, 1], 15], [["y", 322, 3, 290, 4], 209], [["y", 322, 3, 305, 1], 1], [["y", 322, 3, 305, 4], 223], [["y", 322, 3, 308, 1], 32], [["y", 322, 3, 310, 1], 10], [["y", 322, 3, 310, 4], 53], [["y", 322, 3, 315, 1], 32], [["y", 322, 3, 322, 4], 171], [["y", 322, 3, 325, 1], 32], [["y", 322, 3, 326, 1], 31], [["y", 322, 3, 326, 4], 16], [["y", 322, 3, 329, 1], 27], [["x", 323, 1], 168], [["y", 323, 1, 312, 2], 30], [["y", 323, 1, 314, 2], 18], [["y", 323, 1, 320, 2], 30], [["y", 323, 1, 324, 2], 30], [["y", 323, 1, 325, 4], 16], [["y", 323, 1, 328, 2], 30], [["y", 323, 1, 328, 4], 131], [["y", 323, 1, 329, 2], 30], [["y", 323, 1, 329, 4], 21], [["x", 323, 2], 56], [["y", 323, 2, 307, 0], 56], [["y", 323, 2, 309, 3], 35], [["y", 323, 2, 312, 0], 7], [["y", 323, 2, 320, 3], 20], [["y", 323, 2, 321, 3], 1], [["y", 323, 2, 329, 0], 49], [["x", 324, 1], 224], [["y", 324, 1, 228, 4], 34], [["y", 324, 1, 242, 0], 56], [["y", 324, 1, 247, 0], 43], [["y", 324, 1, 247, 4], 181], [["y", 324, 1, 256, 4], 16], [["y", 324, 1, 261, 0], 42], [["y", 324, 1, 261, 4], 16], [["y", 324, 1, 270, 0], 40], [["y", 324, 1, 270, 4], 184], [["y", 324, 1, 272, 4], 224], [["y", 324, 1, 274, 0], 31], [["y", 324, 1, 274, 4], 193], [["y", 324, 1, 276, 0], 11], [["y", 324, 1, 304, 4], 48], [["y", 324, 1, 310, 3], 102], [["y", 324, 1, 317, 0], 1], [["y", 324, 1, 329, 3], 122], [["x", 325, 3], 103], [["y", 325, 3, 281, 1], 32], [["y", 325, 3, 301, 4], 103], [["y", 325, 3, 304, 1], 7], [["y", 325, 3, 307, 4], 24], [["y", 325, 3, 311, 1], 32], [["y", 325, 3, 321, 4], 8], [["y", 325, 3, 322, 1], 32], [["y", 325, 3, 324, 4], 92], [["y", 325, 3, 329, 4], 82], [["x", 325, 4], 121], [["y", 325, 4, 275, 4], 121], [["y", 325, 4, 277, 0], 56], [["y", 325, 4, 306, 0], 9], [["y", 325, 4, 312, 4], 1], [["y", 325, 4, 314, 4], 10], [["y", 325, 4, 318, 4], 62], [["y", 325, 4, 322, 0], 56], [["y", 325, 4, 327, 4], 121], [["y", 325, 4, 330, 4], 48], [["x", 326, 0], 155], [["y", 326, 0, 327, 3], 122], [["y", 326, 0, 328, 3], 66], [["y", 326, 0, 330, 3], 122], [["x", 326, 1], 69], [["y", 326, 1, 316, 2], 30], [["y", 326, 1, 318, 2], 15], [["y", 326, 1, 322, 4], 69], [["y", 326, 1, 330, 2], 24], [["x", 327, 0], 68], [["x", 327, 1], 156], [["y", 327, 1, 234, 4], 156], [["y", 327, 1, 251, 0], 24], [["y", 327, 1, 278, 4], 156], [["y", 327, 1, 283, 4], 43], [["y", 327, 1, 299, 4], 16], [["y", 327, 1, 316, 0], 56], [["y", 327, 1, 323, 4], 58], [["y", 327, 1, 326, 4], 1], [["y", 327, 1, 327, 4], 114], [["y", 327, 1, 328, 0], 52], [["y", 327, 1, 328, 3], 34], [["y", 327, 1, 328, 4], 70], [["y", 327, 1, 331, 0], 24], [["y", 327, 1, 331, 3], 122], [["y", 327, 1, 331, 4], 10], [["x", 328, 2], 90], [["y", 328, 2, 268, 2], 30], [["y", 328, 2, 270, 2], 30], [["y", 328, 2, 271, 2], 30], [["y", 328, 2, 272, 2], 30], [["y", 328, 2, 272, 4], 2], [["y", 328, 2, 275, 2], 30], [["y", 328, 2, 279, 4], 10], [["y", 328, 2, 282, 4], 74], [["y", 328, 2, 283, 2], 30], [["y", 328, 2, 325, 4], 6], [["y", 328, 2, 331, 4], 88], [["x", 328, 3], 71], [["y", 328, 3, 292, 1], 32], [["y", 328, 3, 299, 1], 1], [["y", 328, 3, 305, 4], 17], [["y", 328, 3, 306, 4], 43], [["y", 328, 3, 316, 4], 29], [["y", 328, 3, 321, 1], 1], [["y", 328, 3, 321, 4], 70], [["y", 328, 3, 328, 1], 32], [["y", 328, 3, 328, 4], 39], [["y", 328, 3, 329, 1], 5], [["y", 328, 3, 331, 4], 15], [["x", 328, 4], 63], [["y", 328, 4, 286, 4], 23], [["y", 328, 4, 292, 0], 56], [["y", 328, 4, 304, 4], 40], [["y", 328, 4, 323, 4], 63], [["y", 328, 4, 329, 0], 7], [["y", 328, 4, 331, 4], 63], [["x", 329, 1], 224], [["y", 329, 1, 309, 2], 30], [["y", 329, 1, 314, 2], 12], [["y", 329, 1, 317, 2], 30], [["y", 329, 1, 319, 2], 30], [["y", 329, 1, 320, 4], 224], [["y", 329, 1, 321, 2], 30], [["y", 329, 1, 323, 2], 30], [["y", 329, 1, 326, 2], 30], [["y", 329, 1, 327, 2], 25], [["y", 329, 1, 330, 2], 6], [["y", 329, 1, 331, 2], 1], [["x", 330, 1], 224], [["y", 330, 1, 215, 4], 20], [["y", 330, 1, 217, 0], 55], [["y", 330, 1, 233, 3], 9], [["y", 330, 1, 237, 4], 5], [["y", 330, 1, 241, 4], 224], [["y", 330, 1, 250, 0], 3], [["y", 330, 1, 251, 0], 5], [["y", 330, 1, 258, 0], 56], [["y", 330, 1, 262, 4], 16], [["y", 330, 1, 268, 4], 21], [["y", 330, 1, 306, 4], 197], [["y", 330, 1, 312, 0], 48], [["y", 330, 1, 312, 3], 41], [["y", 330, 1, 312, 4], 135], [["y", 330, 1, 313, 3], 52], [["y", 330, 1, 316, 4], 6], [["y", 330, 1, 317, 4], 224], [["y", 330, 1, 326, 0], 56], [["y", 330, 1, 328, 0], 1], [["y", 330, 1, 332, 3], 122], [["y", 330, 1, 332, 4], 48], [["x", 331, 3], 224], [["y", 331, 3, 277, 1], 32], [["y", 331, 3, 285, 4], 224], [["y", 331, 3, 304, 1], 1], [["y", 331, 3, 317, 1], 32], [["y", 331, 3, 321, 1], 31], [["y", 331, 3, 327, 1], 32], [["y", 331, 3, 330, 1], 32], [["y", 331, 3, 330, 4], 192], [["y", 331, 3, 331, 1], 32], [["y", 331, 3, 331, 4], 64], [["y", 331, 3, 332, 1], 32], [["y", 331, 3, 332, 4], 192], [["x", 332, 1], 96], [["y", 332, 1, 313, 2], 7], [["y", 332, 1, 321, 4], 96], [["y", 332, 1, 325, 2], 30], [["y", 332, 1, 331, 2], 29], [["y", 332, 1, 332, 2], 30], [["x", 332, 2], 128], [["y", 332, 2, 321, 0], 56], [["y", 332, 2, 321, 3], 26], [["y", 332, 2, 323, 3], 101], [["y", 332, 2, 327, 0], 56], [["y", 332, 2, 328, 3], 1], [["y", 332, 2, 330, 0], 56], [["y", 332, 2, 331, 0], 32], [["y", 332, 2, 332, 0], 56]]}
\ No newline at end of file
diff --git a/research/r480-owner-optimum/PROOF.md b/research/r480-owner-optimum/PROOF.md
new file mode 100644
index 0000000000..5eed050bdc
--- /dev/null
+++ b/research/r480-owner-optimum/PROOF.md
@@ -0,0 +1,255 @@
+# The fixed R480 owner optimum
+
+This note fixes the seven-slot k8 word from Jeremy Kothe's PR1074 at
+`052afc128954f7b6a2b3c409eb4d72248e4020f2`. Its source package is
+`research/gauge44-slots-t16`. PR1018 applies the seven-slot construction,
+which credits Rohan Arun's PR987 search, to the R480 k8 leaver word.
+This note changes the owner assignment. It does not change that local word.
+
+The result is conditional on the same local supplier and physical interfaces.
+It is not a formal proof of integer multiplication, an unconditional bound,
+or a measured runtime gain. The selected result is not changed by this package.
+
+## 1. Fixed inventory
+
+Each replica has nine complete calls and 896 live data families. Each call has
+480 whole helpers. Their widths are
+
+```
+width:     4   5   7    8    9
+count:    56  32  30  122  240
+```
+
+The paid local child profile is
+
+```
+{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}.
+```
+
+Each replica has 672 bins of capacity 8 and 448 bins of each capacity 16, 32,
+and 48. Thus the helper width per call is 3730. The local paid rank mass is
+5586. The residual rank mass per replica is
+
+```
+M = 8*672 + (16+32+48)*448 - 9*3730 = 14814.
+```
+
+The complete deficit remains `73*896 - 9*5586 - 14814 = 320` per replica.
+The gain comes from the child-rank distribution. It does not come from a new
+rank deficit. PR1069 independently describes this distinction for recent claims.
+
+The inputs retain the full PR1074 SPEC and PLAN. The checker compares the
+provider width list, local profile, complete call set, and per-replica capacity
+stock. Source files and arithmetic engines have SHA256 pins. These comparisons
+bind a declared cost contract; they do not replace the local scalar proof.
+
+## 2. A necessary inequality for every positive replica count
+
+Use the signed width prices from Chafik Boukhalfa's PR795 and the retained
+PR890/PR942 proof:
+
+```
+width price at (4,5,7,8,9): (-1,-20,-8,-2,4)
+capacity bonus at (8,16,32,48): (2,4,8,-13).
+```
+
+For a residual rank `r`, let `u(r)` be the maximum capacity bonus plus signed
+width price over all legal patterns that leave `r`. The checker enumerates all
+1,163 patterns. A separate fill recurrence gives the same table. In particular,
+`u(0)=0`, `u(1)=19`, and `u(48)=-13`.
+
+For `T` replicas, let `n_r` be the number of bins with residual rank `r`. All
+helper roles occur exactly once. Therefore their total actual signed price is
+
+```
+S*T = [672*2 + 448*(4+8-13)
+       + 9*(-56-20*32-8*30-2*122+4*240)]*T = -1084*T.
+```
+
+Each bin's actual price is at most `u(r)`. Thus
+
+```
+sum r*n_r = 14814*T,
+sum u(r)*n_r >= -1084*T.
+```
+
+Eliminate `n_48` and use `u(0)=0`. With
+
+```
+v(r) = 48*u(r)+13*r,
+v(1) = 925,
+```
+
+we obtain the necessary inequality
+
+```
+sum_(0<r<48) v(r)*n_r >= 140550*T.                 (1)
+```
+
+The PR942 U8 theorem has different right-hand sides. It cannot be reused by
+keeping its U8 profile or its demand 150. Equation (1) is for this R480 inventory.
+The prior PR1034 mixed-catalogue theorem also excludes this new inventory.
+
+## 3. Supporting moment inequality
+
+Let
+
+```
+I = [0.001676905273619680861300,
+     0.001676905273619680861301],
+phi_b(r) = r*(73/r)^b,
+c_b(r) = 48*phi_b(r)-r*phi_b(48),
+lambda_b = c_b(1)/925.
+```
+
+For every `b` in `I`, both retained exact rational engines certify
+
+```
+lambda_b > 0,
+c_b(r) > lambda_b*v(r)   for every attainable 0<r<48, r != 1.
+```
+
+At rank one there is equality by definition. The certificate encloses `phi`
+over the complete interval `I`. It uses the lower endpoint for a positive
+lower bound and the upper endpoint for a positive upper bound. It reverses the
+chosen endpoint when it multiplies by a negative integer. No floating-point
+sign decision is used.
+
+Multiply (1) by `lambda_b`. The residual moment then satisfies
+
+```
+sum phi_b(r)*n_r / T
+  >= (5622/37)*phi_b(1) + (11302/37)*phi_b(48).    (2)
+```
+
+This follows by writing the left side as
+`(14814/48)*phi_b(48) + sum_(r<48) c_b(r)*n_r/(48*T)`.
+The arithmetic is `140550/925 = 5622/37` and
+`(14814-5622/37)/48 = 11302/37`.
+
+The bound permits all positive integer replica counts. It removes chronology,
+per-call matching, coordinate charts, and finite precision constraints. These
+relaxations can only lower the possible moment. The strict supporting margins
+imply that equality has no nonzero residual rank other than 1 and 48. Equality
+also requires (1) to be tight. Both normalized counts then force `37 | T`.
+This is a necessary equality condition, not a uniqueness claim for owners.
+
+## 4. An exact bin construction
+
+The following bin pattern counts attain (2) at `T=37`. The width-count vector
+uses the order `(4,5,7,8,9)`.
+
+| Capacity | Width-count vector | Number of bins | Residual rank |
+| --- | --- | ---: | ---: |
+| 8 | (0,0,0,1,0) | 24864 | 0 |
+| 16 | (0,0,0,2,0) | 3306 | 0 |
+| 16 | (0,0,1,0,1) | 9394 | 0 |
+| 16 | (2,0,0,1,0) | 3876 | 0 |
+| 32 | (0,0,2,0,2) | 298 | 0 |
+| 32 | (0,1,0,0,3) | 10656 | 0 |
+| 32 | (1,0,0,0,3) | 5622 | 1 |
+| 48 | (0,0,0,0,0) | 11302 | 48 |
+| 48 | (1,0,0,1,4) | 5274 | 0 |
+
+The checker sums every capacity and helper width. It requires exact equality
+with the full inventories, not only with total occupied width. This table
+proves attainment of the bin relaxation. The next section supplies its actual
+time and physical-family assignment.
+
+## 5. From exact pattern flow to literal owners
+
+The call order is the source-bound PR942 T37 order. Each replica retains the
+same 30 source events. A pending child can host a complete call only after its
+last physical-pair touch and before its idle event. Bridge touches are included.
+
+`PATTERN-FLOW.json` contains integer pattern counts and integer assignments of
+widths to call times. It groups the two equivalent child sides, with 224 ports
+per group. For each group and pattern, the certificate has `N` bins. It assigns
+exactly `N*n_w` width-`w` roles, and at most `N` roles at each call time. Each
+call receives the exact width inventory above. All assigned times are in the
+actual source-event window.
+
+`construct.py` converts each group and pattern to `N` literal bins. Split each
+width vertex into `n_w` vertices of degree `N`. The other vertices are call
+times, each with degree at most `N`. This is a bipartite multigraph. A matching
+can cover every width vertex and every time vertex of degree `N`: add dummy
+vertices and edges to obtain an `N`-regular bipartite graph, and take a perfect
+matching. Remove it and repeat. The implementation obtains the same covering
+matching directly with augmenting paths. It checks the degree invariant after
+each removal.
+
+Each matching names one physical bin. Thus no bin uses two helpers from one
+call. The constructor assigns the bins to literal child/port coordinates and
+assigns the local helper numbers of each width to the resulting slots. It
+sets offsets to contiguous prefixes. Its output must equal the frozen owners
+as a complete decoded JSON value. Compression-container bytes are not used
+as mathematical equality.
+
+The final map has 159,840 roles in 333 calls. Its residual profile is
+`{1:5622,48:11302}`. The independent owner audit reconstructs source-event
+windows and orthogonal 73-axis charts without importing the constructor or
+flow model. The global controller audit checks the emitted program and its
+phase projections. These audits are separate from the bin theorem.
+
+The independent audit also checks that distinct pending children on one
+physical family have disjoint axes. It checks all 2016 child/port bases.
+A control copies one axis into a second child of the same family. It must
+fail at this disjointness guard. Josie Elliston's PR1091 identified this
+explicit check in the concurrent T16 audits.
+
+
+## 6. Complete moment and outer recipe
+
+The complete T37 profile is
+
+```
+{1:808818, 2:139194, 3:143856, 4:47286,
+ 5:27306, 8:2664, 48:11302}.
+```
+
+It has 33,152 live families, rank mass 2,408,256, and deficit 11,840. Both
+rational engines accept the lower endpoint of `I` and reject the upper endpoint.
+The proper-child guard is `73^2 > 2*48^2`.
+
+Equation (2) applies throughout `I`, so it applies at the unique root of this
+profile's strictly increasing moment. Every other packing has at least that
+moment. The table attains it. This proves the optimum complex root in the bin
+relaxation. The finite owner construction attains the same profile.
+
+The unchanged PR589 bit endpoint is `0.001733427039589844234749`, with its
+exceptional-residue surcharge. It is larger than the complex endpoint. The
+retained seven-step outer recipe is monotone in this range. Each update is
+`a_next=s*(1-s+a_old)`. Both relevant partial derivatives are positive here;
+the final map in `a` is also increasing. The strict reserves remain fixed.
+Both endpoints of `I` give the same outer grid value:
+
+```
+kappa = 0.001674097969905390.
+```
+
+All 47 inequalities are checked. The next grid value is rejected. This is a
+global grid optimum for this word, whole-helper capacity inventory, and fixed
+outer recipe. It is not a ceiling for another word, helper splitting, new
+capacity stock, another outer reduction, or relaxed restoration rules.
+
+## 7. Scope of physical admission
+
+The bank envelope uses 8+8+8+8+5 lanes. Its five groups retain the inherited
+504-helper dedicated banks, which provide a conservative reserve envelope.
+The final hosted construction removes those banks. It uses the 480-helper
+local word and has 33,642 physical families. The partial group's complement
+coordinates are recomputed. They are not selected recursive children.
+
+The finite invoice charges 1024 complex prefix bits. The local prefix is 68,
+and `68+37+333+333+4=775`. The bit allowance stays 512. The independent row coefficient is 17495, below
+20161. The global audit checks 1110 source events, 666 pending windows, and
+11150 distinct orthogonal charts. The full invoice recounts
+all helper operations, wrappers, scalar work, bridges, shifts, moves, local
+adapters, recursive children, and final corrections. The seven finite bootstrap
+cutoffs use the new complex allowance. `CODE-DERIVATION.patch` records every
+change from the immutable PR1074 code. Verification executes normal source
+files; it does not patch imported modules at runtime.
+
+The all-size/compiler, common-label/mutable-source, whole-call hosting,
+precision/tape, exact-recovery, analytic-transfer, and bit H1-H5 obligations
+remain inherited. Passing finite checks does not discharge these assumptions.
diff --git a/research/r480-owner-optimum/README.md b/research/r480-owner-optimum/README.md
new file mode 100644
index 0000000000..4fa54b2da8
--- /dev/null
+++ b/research/r480-owner-optimum/README.md
@@ -0,0 +1,101 @@
+# R480 owner optimum and an attaining construction
+
+The frozen seven-slot k8 word has a complete owner construction with
+`kappa = 0.001674097969905390`. An exact supporting inequality proves that
+no positive replica count can give a larger complex root for this word and
+its whole-helper capacity inventory. The construction attains the bound at
+37 replicas. Both endpoints of the certified root interval give the same
+maximum grid value under the fixed outer recipe.
+
+This is a conditional construction and a scoped optimum theorem. It does
+not prove the full integer-multiplication theorem or a practical speed gain.
+It does not change the selected result.
+
+Run from a checkout at the exact base, with this package added:
+
+```sh
+python3 -B research/r480-owner-optimum/check.py --work /tmp/r480-owner-check
+```
+
+Use a new output directory. No network access, solver, or third-party Python
+package is needed. The expected final line is:
+
+```text
+PASS_R480_ALL_REPLICA_OPTIMUM_AND_ATTAINING_CONSTRUCTION 0.00167409796990539
+```
+
+The check covers the 1,163-pattern dual, an independent fill recurrence,
+two rational moment engines, all 47 outer inequalities, 18 certificate CLI
+controls, exact flow-to-owner reconstruction, 159,840 literal owner roles,
+333 complete calls, actual source-event windows, orthogonal charts, the full
+finite invoice, and strict global admission. The global replay also runs
+15 controller, 7 independent owner, 69 admission, and 12 bit-supplier controls.
+The bit endpoint and its exceptional-residue surcharge are unchanged.
+
+The finite prefix bound is 775 bits. It needs the 1024-bit complex allowance.
+The physical row coefficient is 17,495, below 20,161. All seven finite
+bootstrap cutoffs use that larger complex allowance. The complete profile is
+
+```text
+{1:808818, 2:139194, 3:143856, 4:47286, 5:27306, 8:2664, 48:11302}.
+```
+
+The complex root lies in
+`[0.001676905273619680861300, 0.001676905273619680861301]`.
+The normalized residual optimum is `{1:5622/37, 48:11302/37}`.
+The complete deficit remains 320 per replica. The improvement changes the
+rank distribution, not that deficit.
+
+The exact experimental base is
+`abdc6a7002abdbcd9e21bfc5e1a795784deacfdf`. The fixed local source is PR1074
+at `052afc128954f7b6a2b3c409eb4d72248e4020f2`. `SOURCES.json` pins the proof
+inputs and rational engines. `SOURCE-FREEZE.json` pins this package's code
+and immutable data. The fresh global replay also checks the 21 inherited
+upstream pins before it reads the bank envelope.
+
+`inputs/local` contains the fixed native local artifacts. A concurrent sprint
+worker rebuilt the unchanged base, k8 cell, full local chain, seven-slot step,
+scalar replay, wrappers, and all 2,896 exact phase edges. The corresponding
+command receipts are in `evidence/local-source`. The owner check consumes this
+source-bound local admission; it does not rebuild every upstream local step.
+Use `--local PATH` to replay with a separately rebuilt local directory. The
+same semantic and artifact contracts must pass. In a sparse checkout,
+`--main PATH` may name a complete checkout with the pinned base dependencies.
+
+`PROOF.md` states the all-replica argument and the matching construction.
+`PATTERN-FLOW.json` and `OWNERS.json.gz` are exact certificates.
+`construct.py` rebuilds the owners with integer counts and bipartite matching.
+`independent_owner.py` derives windows and charts from actual source events.
+It imports no flow or constructor code. `CODE-DERIVATION.patch` and
+`INDEPENDENT-DERIVATION.patch` expose all changes to inherited admission code.
+No source patch is applied at runtime.
+
+`SEARCH.json` records the search domain and stopping rule. The full tight-face
+chronology LP reached its time limit. Restriction to the nine-pattern optimal
+basis then gave an exact integer flow. That timeout is not an impossibility
+claim. The delivered optimum follows from the exact bound and attaining map,
+not from solver optimality or a failed search.
+
+At refresh, main `ba82555c64e1879e4b7decce28186f208fcb8262` selected PR1042
+at `kappa = 0.001672188119205421`. PR1082 at
+`0c2e294ec204e83846d27344f829d15ed9ee7cc6` gave a T16 repack at
+`0.001672653061493085`. This theorem closes the fixed-word gap across all
+positive replica counts. PR1107 at
+`6123fc5d57db16aaa3e8a26b4a11a34b46c0c391` changes a rank-seven helper end
+and reports `0.001672765980186726`; its changed word is outside this theorem.
+PR1094 at `0fc329d0bec93ca7cd288eaea1295172e8789810` gives another same-word
+T16 repack at `0.001672660197076918`. PR1117 at
+`342b67f23dfa8f41a520a0d58978b2875e9eb0dd` reports
+`0.001672846995880185` with the changed rank-seven-end word. It is also
+outside this theorem. These comparisons are records of the stated heads,
+not admission of those PRs. PR1091 at
+`b4c13a228acb80f74c682b7097f0ce9bbf51bc4e` independently checked fifteen
+T16 maps. This package follows its explicit disjoint-pending-axis check and
+extends that finite check to the attaining T37 map.
+
+All-size/compiler, common-label/mutable-source, whole-call hosting,
+precision/tape, exact-recovery, analytic-transfer, and bit H1-H5 obligations
+remain inherited. A different local word, split helpers, new capacity stock,
+or another outer recipe can exceed this scoped ceiling.
+
+See `NOTICE.md` for predecessor credit, licenses, and substantial AI assistance.
diff --git a/research/r480-owner-optimum/SEARCH.json b/research/r480-owner-optimum/SEARCH.json
new file mode 100644
index 0000000000..677eb1e419
--- /dev/null
+++ b/research/r480-owner-optimum/SEARCH.json
@@ -0,0 +1,57 @@
+{
+  "route": "Fixed R480 seven-slot k8 all-replica owner optimum",
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "source_head": "052afc128954f7b6a2b3c409eb4d72248e4020f2",
+  "candidates": [
+    "Exact signed bin dual and supporting moment inequality",
+    "Mixed T16/T21/T37 owner lifts for the fixed word",
+    "Higher-replica owner construction on the tight dual face"
+  ],
+  "choice": "Combine the first and third approaches at the least possible equality replica count T=37.",
+  "domain": {
+    "widths": [4, 5, 7, 8, 9],
+    "capacities": [8, 16, 32, 48],
+    "bin_patterns_exhausted": 1163,
+    "dual_tight_patterns": 20,
+    "constructive_basis_patterns": 9,
+    "call_order": "The frozen PR942 T37 order",
+    "physical_groups": "Replica, capacity, and exact source-event window; paired child sides have 224 ports."
+  },
+  "attempts": [
+    {
+      "method": "Continuous bin LP, then exact rational dual and moment support checks",
+      "result": "Nine-pattern optimum and equality denominator 37. Exact checks replace floating-point decisions."
+    },
+    {
+      "method": "Chronology LP with all 20 tight patterns",
+      "time_limit_seconds": 60,
+      "result": "Time limit. No infeasibility result was obtained."
+    },
+    {
+      "method": "Chronology LP restricted to the nine-pattern optimal basis",
+      "variables": 126128,
+      "constraints": 59478,
+      "matrix_nonzeros": 431038,
+      "elapsed_seconds": 20.65,
+      "result": "Feasible. The solution still had fractional entries."
+    },
+    {
+      "method": "Integer feasibility model on the same basis, all variables integral",
+      "time_limit_seconds": 180,
+      "elapsed_seconds": 177.92,
+      "result": "Feasible integer flow. All rounded entries pass the full exact integer equations and inequalities."
+    },
+    {
+      "method": "Bipartite matching decomposition of the frozen integer flow",
+      "result": "159840 literal whole-helper roles in 333 calls. Exact replay needs no optimizer."
+    }
+  ],
+  "discovery_environment": {
+    "scipy": "1.18.1",
+    "sympy": "1.14.0",
+    "threads": 1,
+    "randomness": "No custom random search or seed. The solver used its default internal settings."
+  },
+  "stopping_rule": "Stop when one full physical T37 map attains the exact bin ceiling. Do not search for further T16 increments.",
+  "coverage_limit": "Only the bin-pattern enumeration and its separate recurrence are exhaustive. Solver timeouts do not prove infeasibility. The exact certificate and owner checks establish the delivered result."
+}
diff --git a/research/r480-owner-optimum/SOURCE-FREEZE.json b/research/r480-owner-optimum/SOURCE-FREEZE.json
new file mode 100644
index 0000000000..a0d04efd89
--- /dev/null
+++ b/research/r480-owner-optimum/SOURCE-FREEZE.json
@@ -0,0 +1,74 @@
+{
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "files": {
+    "CERTIFICATE.json": "9bc2e6116d8ada1f5accd2011e161310ba18067cb7a8450ff89efc265bcc04e5",
+    "CODE-DERIVATION.json": "cc6b7ab7e8c9dc33be30875fe5f0f21a47f92b73f02f2ef42897a49b0b94953f",
+    "CODE-DERIVATION.patch": "1e37b85b1335595a366a4a8810b898869d9c63cc8231b5576b0fdaffd2009eef",
+    "INDEPENDENT-DERIVATION.patch": "bde2ae12f44a1d2310bb607a5ed2078cf67e58bf736b05a1b278eba772921323",
+    "NOTICE.md": "b97fb4731e84aef736c58a9c126334eb5b8d3a057a8d9d45b4ffff24af65c38b",
+    "ORDER.json": "2093ca4050e1ce95621f4702bebe8b01b36773b1ecfa2c0d6275e132bd33d578",
+    "OWNERS.json.gz": "c35ac0c6f77c6b7cb32bee953770de3ef8a575aef36efc4764e0bb3325a04737",
+    "PATTERN-FLOW.json": "de533d6a4f978c2abd433a6521798ace3773ad952dce683ec5c2ecc489962643",
+    "PROOF.md": "ef9d835a15aee46d7c502644666d6221ca62a031c52352b00df5d3baa16efafb",
+    "README.md": "fbed39077a7220643feaf542f402bda7ba50a5fa3fe0b384c6cbaa26a830b8f8",
+    "SEARCH.json": "b0f24b26647971f7295ea1d6cf3f8a3752fe174b9d41e08b1dd5afceea3a40fa",
+    "SOURCES.json": "f232bbe4ebfe5482760f61d61ad1f46e6f7a7a0cef3f0e5fed0f81e772cecf24",
+    "check.py": "6ece11990002e022aa3cd4670b9baa3579521419408cf899116a9588030d689f",
+    "code/assemble.py": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a",
+    "code/assembly_controls.py": "29ba6742d899d2318a96745c8ec21de06ba3968d4641c3400a15bc714e0d7f9e",
+    "code/audit_allcold.py": "a8d3c48e26957c5174ea35043545d3863a4c19c82422074ac42132b446533b4a",
+    "code/bind_providers_portable.py": "1d39bcc7b63ac158e021454beaae897d123e174360573762aecade3cd43193f6",
+    "code/bit_supplier_controls.py": "e6d33fb61a570c3f50669412acc467a3fd06ef0b806da6a75bc296c6ba2142a5",
+    "code/emit_allcold.py": "3219e0706d497a2e6b595cec0a0d5bdbfbd1d991bf70136762eada44126a9ac1",
+    "code/freeze_spec.py": "e9132a9d195c66123f2747a17f7ef404b4d1e3ef6263ab4c28c983a052cf10bd",
+    "code/generated_identity.py": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+    "code/invoice_allcold.py": "e97c74d1ccfb0b0e26260e65bb780fa0103f4c716647e238f943a2e840a1f566",
+    "code/prepare_global.py": "8c0dae301a8f34b77a5a462f840952d08ed120576212adf5051bc09bcad874dc",
+    "code/restore_parent.py": "69b7b25ff85e9b8160e233c1d415cc6a0272019e5c486dcec14cb6c349e7024d",
+    "code/witness.py": "779c5172894b992131e85be1e592ed2a1aec8c287b872ff42007d36a7291e444",
+    "construct.py": "5d06e8f5f3ed4015171d6cbfaa995eb1d1a0a14e687595910391caffcf3ca474",
+    "controls.py": "fd3c0152e2670813bee2772a800beed104429f81aa82d89a387a4a30435c667e",
+    "data/PLAN.json": "9c2c12f6d0fbd22bc688909c18f18d9c93192aa8d80d7e936983a262e6ca1562",
+    "data/SPEC.json": "7dabffb3f25e95233025e55235b76db51d96fa070d6f5bfd0a28005f5efa2642",
+    "independent_owner.py": "bbd9c43b3db12d61a4ae1050949320cd6d7e610ef2aa9ccabd309d7b5e07ad82",
+    "inputs/PLAN.json": "68c110602df12bd7de3749514224021ef1ef0ebcf072d7c727f9b66099fbebb1",
+    "inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "inputs/RESULT.json": "ebf3577df9efccc213998a6cf43f25fb3cd1a26893847b68d60d276e3b76440c",
+    "inputs/SPEC.json": "7f5f710df21fe48079b4c79727953ff41cd8bec688592578554109ebf6b6d929",
+    "inputs/local/CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+    "inputs/local/CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+    "inputs/local/CLIFFORD-REVIEW.json": "dd57b86b730923b19f64e5d09d8885149366db636607dcd5e2acf9a56d11e72b",
+    "inputs/local/FULL-WORD.json.gz": "49596aa4ed4fd36cd4582fd0e8ddeb09fd80370a7d8aea1ede52a135b536d289",
+    "inputs/local/INDEPENDENT-LOCAL-REPLAY.json": "13dd18297162569532983db1a2ab67926b064330cd7edd3587e7b546b2dedf17",
+    "inputs/local/LOCAL-CHECKS.json": "2b8b1891a736598010232bfb26abc31973b265a53a2009a3fcfd9138b5ecadb4",
+    "inputs/local/LOCAL-PROGRAMS.json.gz": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+    "inputs/local/RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c",
+    "inputs/local/SCALAR-FRAME-AUDIT.json": "2861f75f7667b10ed7235ab4d932da4797f7e7e4a26d4bc467110114bab77eec",
+    "inputs/local/WRAPPER-CHECKS.json": "0ae753d6fa6e922d8b8180da602828f6cb3f444fcd124d019acee74e145c0836",
+    "lift.py": "211a73218c8923b9b71093fa6affa21a3b906c0dc12931836fbc652e477e478b",
+    "replay.py": "11b00cd0a29f15e1d3fdfb1dbf15fdd3374c8d1a07a889ca8b0f30883ca8a20c",
+    "vendor/pr1074/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "vendor/pr1074/NOTICE.md": "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf",
+    "vendor/pr1074/T8/PLAN.json": "1dec4ca3af6d45d82286005cae4c5e56e7253adefb117d797da55c55c891af08",
+    "vendor/pr1074/UPSTREAM-NOTICE.md": "a75967ebc34e3bf2ff2c25c08e6c7f1a61b0c0d171cfd1b62196ae2caaf2c610",
+    "vendor/pr1074/UPSTREAM-PINS.json": "ccc37ab7fbf78947fe02c7f57ea672d2e4eae8454cb1158ed964c75bf423869b",
+    "vendor/pr1074/code/assemble.py": "15f6986a476bac76bcdc0bfcf51da115389b46f1950d2766b6822f757888b13a",
+    "vendor/pr1074/code/assembly_controls.py": "da7e981ae1b9f099d4e1524cb4f3ba1116011936ebe378692889b5dbfa99029d",
+    "vendor/pr1074/code/audit_allcold.py": "1467a2acb654e62552c69fb9a7c4c85f70a02120881d222313865058ab71a6cc",
+    "vendor/pr1074/code/bind_providers_portable.py": "1d39bcc7b63ac158e021454beaae897d123e174360573762aecade3cd43193f6",
+    "vendor/pr1074/code/bit_supplier_controls.py": "e6d33fb61a570c3f50669412acc467a3fd06ef0b806da6a75bc296c6ba2142a5",
+    "vendor/pr1074/code/emit_allcold.py": "354367e1fd6185a67b04f4268bcae4d502e47b18cb2131e247f5bcab5b3a769e",
+    "vendor/pr1074/code/freeze_spec.py": "5971eecac6d6fbcb53244b80f1b9d7232012dc32876fab511214a5addebbe6c2",
+    "vendor/pr1074/code/generated_identity.py": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+    "vendor/pr1074/code/invoice_allcold.py": "71eb57514e28ced97251e0507105f654f59885ec4d40486a780bf166098858a8",
+    "vendor/pr1074/code/prepare_global.py": "8c0dae301a8f34b77a5a462f840952d08ed120576212adf5051bc09bcad874dc",
+    "vendor/pr1074/code/restore_parent.py": "69b7b25ff85e9b8160e233c1d415cc6a0272019e5c486dcec14cb6c349e7024d",
+    "vendor/pr1074/code/witness.py": "779c5172894b992131e85be1e592ed2a1aec8c287b872ff42007d36a7291e444",
+    "vendor/pr1074/construction/leaver/PIVOT-SWAP-k8.json": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb",
+    "vendor/pr1074/data/SPEC-T8.json": "8e95ae8087124189cbd366d0e9d1c5ebededff536ff3501927b4b2a2e8dac70e",
+    "vendor/pr1074/inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "vendor/pr1074/t16/NOTICE.md": "902370e6bfcd39dbea2ece474f15fccbcce3b8e966b2b94066bd03e5174591b5",
+    "vendor/pr1074/t16/build_parent.py": "82e274d0c7a94f9bf0468dd37f0505d0c42017559ebb4ba8c079a1f4e403d91e",
+    "verify.py": "1ecc9f9a78fc4b0c3a100ee48fef70bf0f3b2d711d9be646623ffe781c2e596c"
+  }
+}
diff --git a/research/r480-owner-optimum/SOURCES.json b/research/r480-owner-optimum/SOURCES.json
new file mode 100644
index 0000000000..43834e837f
--- /dev/null
+++ b/research/r480-owner-optimum/SOURCES.json
@@ -0,0 +1,22 @@
+{
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "source_head": "052afc128954f7b6a2b3c409eb4d72248e4020f2",
+  "source_package": "research/gauge44-slots-t16",
+  "engine_directory": "research/complex-k492-owner-repair/vendor/multicold/engines",
+  "outer_driver": "research/complex-t21-owners/vendor/pr870/independent/price_profile_t16.py",
+  "bit_expected": "research/complex-t21-owners/vendor/pr870/inputs/PR589-EXPECTED.json",
+  "files": {
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "research/complex-t21-owners/vendor/pr870/independent/price_profile_t16.py": "53f8e62dcf27bee032c1bee0245d126a9c8a12ebcf24f6aaff65ea3122fffe29",
+    "research/complex-t21-owners/vendor/pr870/inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "research/complex-t37-owners/ALL-T-PROOF.md": "4c0c71ccd0afb850538af1b467e5208b7eb3edd0260fded84e02a8c01dfc868b",
+    "research/complex-t21-owner-bound/PROOF.md": "2aa0aa6ec1d87402138564c38749b5ca0f058c16817efdf58a2685d2d90cb417",
+    "package:inputs/SPEC.json": "7f5f710df21fe48079b4c79727953ff41cd8bec688592578554109ebf6b6d929",
+    "package:inputs/PLAN.json": "68c110602df12bd7de3749514224021ef1ef0ebcf072d7c727f9b66099fbebb1",
+    "package:inputs/RESULT.json": "ebf3577df9efccc213998a6cf43f25fb3cd1a26893847b68d60d276e3b76440c",
+    "research/complex-t21-owners/independent_check.py": "9d8c86bf45cdaef37f223c88704055ced503ee295645611e13f3fb9059a00e55",
+    "research/complex-t37-owners/ORDER.json": "2093ca4050e1ce95621f4702bebe8b01b36773b1ecfa2c0d6275e132bd33d578"
+  }
+}
diff --git a/research/r480-owner-optimum/check.py b/research/r480-owner-optimum/check.py
new file mode 100644
index 0000000000..acd338b479
--- /dev/null
+++ b/research/r480-owner-optimum/check.py
@@ -0,0 +1,45 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Check the exact bound and the frozen finite construction."""
+import argparse
+import json
+import os
+from pathlib import Path
+import subprocess
+import sys
+
+HERE = Path(__file__).resolve().parent
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, default=HERE.parents[1])
+    parser.add_argument('--local', type=Path, default=HERE / 'inputs/local')
+    parser.add_argument('--work', type=Path, required=True)
+    args = parser.parse_args()
+    if args.work.exists():
+        raise ValueError('Choose a new check directory')
+    if sys.flags.optimize:
+        raise ValueError('Retained checks require assertions')
+    args.work.mkdir(parents=True)
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', OPENBLAS_NUM_THREADS='1',
+               OMP_NUM_THREADS='1')
+    commands = [
+        ['verify.py', '--out', args.work / 'BOUND.json'],
+        ['controls.py', '--out', args.work / 'BOUND-CONTROLS.json'],
+        ['construct.py', '--out', args.work / 'construction'],
+        ['replay.py', '--main', args.main, '--local', args.local,
+         '--work', args.work / 'replay'],
+    ]
+    for script, *arguments in commands:
+        subprocess.run([sys.executable, '-B', str(HERE / script), *map(str, arguments)],
+                       env=env, check=True)
+    receipt = json.loads((args.work / 'replay/RESULT.json').read_text())
+    if receipt['status'] != 'PASS_R480_T37_STRICT_FINITE_CONSTRUCTION':
+        raise ValueError('Strict construction replay did not pass')
+    print('PASS_R480_ALL_REPLICA_OPTIMUM_AND_ATTAINING_CONSTRUCTION',
+          receipt['kappa_decimal'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/r480-owner-optimum/code/assemble.py b/research/r480-owner-optimum/code/assemble.py
new file mode 100644
index 0000000000..f6cc563542
--- /dev/null
+++ b/research/r480-owner-optimum/code/assemble.py
@@ -0,0 +1,241 @@
+"""Gauge44 complete global admission with the retained 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 PR589 supplier (PR555's punctured
+R439 word, v = 111, decoder constant 63, two A-section transports), shipped
+as inputs/PR589-EXPECTED.json and pinned by git blob id. Its rank-mass
+deficit is derived from the word's parameters, T(2Kv - L*cst) at nine
+stages (PR545/PR555 rank-mass identity), not hard-coded. 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,SPOT,spot_widths
+# Cited bit supplier: PR589's tune/EXPECTED.json (merged on main as research/e8-bit-p111-tuned/tune/EXPECTED.json).
+BIT_PATH=Path(__file__).resolve().parents[1]/'inputs/PR589-EXPECTED.json'
+BIT_BLOB='e293ddc557742637f9f679f083a1a282d87b1b13'
+# Nine-stage bit template (PR463/PR510 chain, 32 replicas): L stages, T replicas, K=(L-1)//2 pairs, moment width M=1+7L.
+BIT_L,BIT_T=9,32;BIT_K=(BIT_L-1)//2;BIT_M=1+7*BIT_L
+def git_blob(data):return hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()
+def load_bit(data):
+ """The pinned supplier record: its full record (word parameters) and its nine-stage price."""
+ assert git_blob(data)==BIT_BLOB,'bit supplier blob pin'
+ return json.loads(data)
+def bit_deficit(word,live):
+ """Rank-mass deficit M*live - mass = T(2Kv - L*cst) of a v-port bit word with decoder constant cst (PR545/PR555).
+ cst is the sum of the retained totals' COPY ranks and live = 2KvT data wires; both are cross-checked here, and the
+ caller checks the result against the priced profile, so neither v nor cst is free."""
+ v,cst,ranks=word['v'],word['decoder_constant'],word['copy_ranks']
+ assert type(v)is int and type(cst)is int and all(type(r)is int and 0<r<=8 for r in ranks)
+ assert len(ranks)==word['retained_totals']==BIT_L and cst==sum(ranks)
+ assert live==2*BIT_K*v*BIT_T
+ d=BIT_T*(2*BIT_K*v-BIT_L*cst);assert d>0;return d
+
+
+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
+ # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+ R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==333*R==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']==333
+ assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+ assert invoice['centres']==8
+ assert invoice['physical_stock_identity']==dict(data_and_owner_families=33152,local_helpers=R,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']==R and p['centres']==8 and p['n']==2*112+R 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*R-p['entrance_rank']-p['terminal_codimension'] and len(p['widths'])==R   # HPE: widths |final|-|start|
+  pin(K+'width_digest',digest(p['widths']));assert tuple(p['widths'][h]for h in SPOT)==spot_widths()
+  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 in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):pin(K+'artifacts.'+name,p['artifacts'][name])
+  pin(K+'artifact_semantic_sha256',p['semantic_artifact_sha256'])
+  pin(K+'complete_contract',{k:v for k,v in p.items()if k!='artifacts'})
+  assert owner['provider_artifact_semantic_sha256'][pid]==p['semantic_artifact_sha256']
+  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']==2*112+R and z['dirty_helper_columns']==R
+   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']+p.get('cold_hyperplane_ended_helpers',0);pin(K+'wrappers',z['pre_wrappers'])   # COLD-HPE
+   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']+2*112+R+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)==333
+ 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(37)}
+ 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=55832,56346,74592
+ parent_banks,rem=divmod(parent_live-2*112*4*37,9);assert rem==0 and parent_physical==parent_live+504+8+2   # five bank groups with 8,8,8,8,5 active lanes and R0=504 helpers; shared private work is restored
+ assert owner['source_idle_children_charged']==parent_idle
+ bridges,shifts=2*112*333,4*112*37;moves=2*shifts
+ nonlocal_items=(4*112*37*9+2*112*37*9+2*333*R+parent_idle+9*parent_banks+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+(333*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']==1024
+ assert invoice['row_prefix_extra']==2048
+ assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+333+333+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+2048
+ 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_record=load_bit(BIT_PATH.read_bytes())
+ bit=bit_record['nine']
+ assert 'nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline']
+ c=Q(bit['bit_lower'])
+ bit_D=bit_deficit(bit_record['word'],bit['bit']['live'])
+ 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']==11840
+ 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()}
+ assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+ bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,11840,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+1024)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+1024)
+   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,11840,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,'package:inputs/PR589-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_GAUGE44_NATIVE_EXACT_GLOBAL_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_pr635_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=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),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 R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain.')
+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/r480-owner-optimum/code/assembly_controls.py b/research/r480-owner-optimum/code/assembly_controls.py
new file mode 100644
index 0000000000..cc4a8edb0e
--- /dev/null
+++ b/research/r480-owner-optimum/code/assembly_controls.py
@@ -0,0 +1,260 @@
+"""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 + 333 + 333 + 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) if len(PIDS)>1 else '__unregistered__'
+        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 is not c and (d['provider_id'] != P or len(PIDS)==1) 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),
+        ]
+        if len(PIDS)==1:
+            # Cross-provider substitutions require a second actual supplier.
+            # All single-provider program, phase, profile and dispatch bindings
+            # retain their direct mutations above and in the controller audit.
+            partner_only = {P+':stale_partner_program_consistent_call_hashes',
+                            P+':stale_partner_profile_consistent_child_total',
+                            P+':relocated_against_partner_same_counts',
+                            P+':compensating_false_profiles_with_'+Qp}
+            controls = [(name, fn) for name, fn in controls if name not in partner_only]
+        # 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 SPOT:
+            def cold_swap(o, i, P=P, h=h):
+                w = i['providers'][P]['widths']; j = w.index(9 if w[h] != 9 else 8); w[h], w[j] = w[j], w[h]   # never the identity
+            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/r480-owner-optimum/code/audit_allcold.py b/research/r480-owner-optimum/code/audit_allcold.py
new file mode 100644
index 0000000000..f4f71d0756
--- /dev/null
+++ b/research/r480-owner-optimum/code/audit_allcold.py
@@ -0,0 +1,254 @@
+"""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 *
+from generated_identity import artifact_identities
+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={};artifact_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=[len(c['frames'][c['final'][2*c['v']+h]])-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths();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']
+ artifact_semantic_hashes[pid]=artifact_identities(p)
+ pin('providers.%s.artifact_semantic_sha256'%pid,artifact_semantic_hashes[pid])
+ phase_semantic_hashes[pid]=artifact_semantic_hashes[pid]['CLIFFORD-REVIEW.json']
+ for h,w in enumerate(widths):
+  assert 0<w<=c['h']
+  f=c['start'][2*c['v']+h];u=c['final'][2*c['v']+h]
+  # COLD-HPE: a cold helper (f == 0) may end below FULL too; its wrapper is the '0:U' recipe (E = bottom instance of #593)
+  if u!=1:   # HPE: wrapper for T_U T_E^-1, keyed 'E:U', rank |U|-|E|
+   a=adapters['%d:%d'%(f,u)]
+   assert a['frame']==f and a['terminal']==u and a['vectors']==c['frames'][f] and a['terminal_vectors']==c['frames'][u]
+   assert a['rank']==w==len(c['frames'][u])-len(c['frames'][f]) and a['entrance_rank']==len(c['frames'][f]) and a['terminal_rank']==len(c['frames'][u])<c['h']
+  elif w<c['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'))
+# Independently compare ordered common frames; exact local carrier names remain
+# bound to each canonical word, program, phase receipt and residual adapters.
+for p in provider_ids:
+ c=providers[p]['canonical']
+ assert len(c['centers'])==len(c['center_frames'])==8
+ assert [c['frames'][f]for f in c['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+assert required_artifacts<=set(summary['source_artifacts'])
+prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=37;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=333;HOSTED=CALLS*R
+# The selected map is an input to check, not a claim from the emitter.
+
+assert len(DISPATCH)==333 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'])==333 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))==333
+ all_local=[];perrep={r:[]for r in range(37)};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<37 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']<333 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(37)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==11840 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=333)
+
+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))
+# Single-provider dispatch still has all source/program/width binding controls.
+if len(provider_ids)==1:
+ P=provider_ids[0]
+ at_p=lambda q:next(c for c in q['calls']if c['provider_id']==P)
+ narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+ reject(P+': wrong provider at its invocation',lambda q:at_p(q).__setitem__('provider_id','__unregistered__'))
+ reject(P+': stale per-call local program hash',lambda q:at_p(q).__setitem__('local_program_sha256','0'*64))
+ reject(P+': stale serialized provider program',lambda q:q['local_providers'][P]['local_programs']['forward'].pop())
+ reject(P+': unbound residual adapter hash',lambda q:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+ reject(P+': wrong provider width registry',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,providers[P]['widths'][narrow]-1))
+ reject(P+': wrong per-call residual width',lambda q:at_p(q)['owners'][2*V+narrow][1].__setitem__(3,at_p(q)['owners'][2*V+narrow][1][3]-1))
+ reject(P+': wrong sweep provider',lambda q:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep').__setitem__('provider_id','__unregistered__'))
+ reject(P+': entering helper width silently restored to nine',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,9))
+else:
+ # 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=11840,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,provider_artifact_semantic_sha256=artifact_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=11840,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,provider_artifact_semantic_sha256=artifact_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/r480-owner-optimum/code/bind_providers_portable.py b/research/r480-owner-optimum/code/bind_providers_portable.py
new file mode 100644
index 0000000000..97e28da17e
--- /dev/null
+++ b/research/r480-owner-optimum/code/bind_providers_portable.py
@@ -0,0 +1,67 @@
+"""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 *
+from generated_identity import artifact_identities
+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={};helpers=set()   # R: helper count per provider word; all providers must agree
+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'],len(word['centers']))==(112,9,8) and type(word['R']) is int and word['R']>0;helpers.add(word['R'])
+ assert word['ports']==desc['ports'] and word['centers']==desc['centers']
+ widths=[len(word['frames'][word['final'][r]])-len(word['frames'][word['start'][r]])for r in range(2*112,2*112+word['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths()
+ 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']
+ identities=artifact_identities(d)
+ pin('providers.%s.artifact_semantic_sha256'%pid,identities)
+ assert identities==desc['artifact_semantic_sha256']
+ for name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):
+  assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-reference artifact')
+ 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'])
+assert len(helpers)==1,'providers disagree on helper count R: %s'%sorted(helpers)
+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','runtime_source_plan_sha256'])
+(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(receipt['status'])
diff --git a/research/r480-owner-optimum/code/bit_supplier_controls.py b/research/r480-owner-optimum/code/bit_supplier_controls.py
new file mode 100644
index 0000000000..e86b8527b4
--- /dev/null
+++ b/research/r480-owner-optimum/code/bit_supplier_controls.py
@@ -0,0 +1,111 @@
+"""Negative controls for the cited PR589 bit supplier and its derived rank-mass deficit.
+
+Apache-2.0. Each control mutates one input of the changed bit-supplier sites in assemble.py (the pinned record, the
+deficit derivation from the word's parameters, the profile/live binding, the claimed endpoint) and runs the unchanged
+assemble() on the fresh owner/invoice receipts. Every control must be rejected; the unmutated run must pass.
+`revert_hardcoded_9984` restores the PR543 constant the parent package hard-coded: with PR589's word it must fail.
+"""
+import argparse
+import copy
+import hashlib
+import json
+import os
+import tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+
+assert __debug__, 'Assertions required'
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    import assemble as A
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    args = (owner, invoice, sha(owner_path), sha(invoice_path))
+    baseline = A.assemble(*args)
+    data = A.BIT_PATH.read_bytes()
+    record = A.load_bit(data)
+    word = record['word']
+    assert A.bit_deficit(word, record['nine']['bit']['live']) == 10272 == 32 * (8 * 111 - 9 * 63)
+
+    real_load, real_deficit = A.load_bit, A.bit_deficit
+
+    def with_record(mutate):
+        def load(d):
+            r = copy.deepcopy(real_load(d)); mutate(r); return r
+        return load
+
+    def shift_profile(r):  # one rank-1 child becomes rank 2: rank mass +1, totals unchanged
+        p = r['nine']['profile']; p['1'] -= 1; p['2'] += 1; r['nine']['bit']['rank_mass'] += 1
+
+    bumped = data.replace(record['nine']['bit_lower'].encode(),
+                          str(Q(record['nine']['bit_lower']) + Q(1, 10**24)).encode(), 1)
+    assert bumped != data
+    pr543 = (source_package / 'inputs/PR543-EXPECTED.json').read_bytes()
+    controls = [
+        # deficit site: the parent's hard-coded constant, restored
+        ('revert_hardcoded_9984', dict(bit_deficit=lambda w, live: 9984)),
+        # deficit site: each word parameter perturbed alone
+        ('ports_112', dict(load_bit=with_record(lambda r: r['word'].__setitem__('v', 112)))),
+        ('decoder_constant_64_copy_ranks_unchanged', dict(load_bit=with_record(lambda r: r['word'].__setitem__('decoder_constant', 64)))),
+        # v=111, cst=64 derives 32*(888-576)=9984: consistent word, wrong for the priced profile
+        ('decoder_constant_64_with_one_copy_rank_8', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('decoder_constant', 64), r['word']['copy_ranks'].__setitem__(0, 8))))),
+        ('eight_retained_totals', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('copy_ranks', [7] * 8), r['word'].__setitem__('decoder_constant', 56))))),
+        ('live_minus_one', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('live', r['nine']['bit']['live'] - 1)))),
+        # profile binding: same totals, rank mass +1
+        ('profile_rank_mass_plus_one', dict(load_bit=with_record(shift_profile))),
+        ('profile_rank_mass_receipt_mismatch', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('rank_mass', r['nine']['bit']['rank_mass'] + 1)))),
+        # endpoint: the next 1e-24 grid point
+        ('bit_lower_next_grid', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('bit_lower', str(Q(r['nine']['bit_lower']) + Q(1, 10**24)))))),
+        ('not_nine_stage_record', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('pipeline', r['nine']['pipeline'].replace('nine-stage', 'eleven-stage'))))),
+        # pinned-input site: tampered bytes and the parent's PR543 file under the PR589 pin
+        ('tampered_bytes_next_grid', dict(read=bumped)),
+        ('pr543_file_under_pr589_pin', dict(read=pr543)),
+    ]
+    rejected = []
+    scratch = Path(tempfile.mkdtemp(prefix='bitctl-'))
+    for name, patch in controls:
+        saved_path = A.BIT_PATH
+        try:
+            if 'read' in patch:
+                tmp = scratch / (name + '.json'); tmp.write_bytes(patch['read']); A.BIT_PATH = tmp
+            A.load_bit = patch.get('load_bit', real_load)
+            A.bit_deficit = patch.get('bit_deficit', real_deficit)
+            try:
+                A.assemble(*args)
+            except (AssertionError, KeyError):
+                rejected.append(name)
+            else:
+                raise AssertionError('Invalid bit supplier accepted: ' + name)
+        finally:
+            A.load_bit, A.bit_deficit, A.BIT_PATH = real_load, real_deficit, saved_path
+            if 'read' in patch:
+                tmp.unlink()
+    scratch.rmdir()
+    assert rejected == [n for n, _ in controls]
+    again = A.assemble(*args)
+    assert again['kappa'] == baseline['kappa'] and again['bit_lower'] == baseline['bit_lower']
+    return dict(
+        status='PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS',
+        kappa=baseline['kappa_decimal'], bit_lower=baseline['bit_lower'], bit_decimal=baseline['bit_decimal'],
+        binding=baseline['binding'], bit_supplier=baseline['bit_supplier'],
+        derived_deficit=baseline['bit_supplier']['derived_deficit'],
+        rejected_controls=rejected,
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+    )
+
+
+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', newline='\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/r480-owner-optimum/code/emit_allcold.py b/research/r480-owner-optimum/code/emit_allcold.py
new file mode 100644
index 0000000000..7f76f14819
--- /dev/null
+++ b/research/r480-owner-optimum/code/emit_allcold.py
@@ -0,0 +1,150 @@
+"""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))==333;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=37;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,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')
+ # Carrier names belong to the independently checked local program. The global
+ # controller's centre contract is the ordered eight exact common frame bases.
+ assert(pc['v'],pc['h'],pc['ports'])==(V,9,canon['ports'])
+ assert len(pc['centers'])==len(pc['center_frames'])==len(canon['centers'])==8
+ assert [pc['frames'][f]for f in pc['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+ R=pc['R'];assert type(R)is int and R>0 and all(x['R']==R for x in registry.values()),'providers disagree on helper count R'
+ 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=[len(pc['frames'][pc['final'][2*V+h]])-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)]   # HPE: residual width |final|-|start|
+ 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)
+assert len(roles)==333*R   # one whole-owner role per (call, provider helper)
+selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+assert len(selected)==333 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())==11840
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R0+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-R%d-asynchronous-whole-owner-v1'%R,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=11840,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/r480-owner-optimum/code/freeze_spec.py b/research/r480-owner-optimum/code/freeze_spec.py
new file mode 100644
index 0000000000..e4e72b5a07
--- /dev/null
+++ b/research/r480-owner-optimum/code/freeze_spec.py
@@ -0,0 +1,29 @@
+"""Freeze independently recomputed discovery values before strict replay."""
+import argparse
+import json
+from pathlib import Path
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--spec', type=Path, required=True)
+ap.add_argument('--discovery', type=Path, required=True)
+a = ap.parse_args()
+spec = json.loads(a.spec.read_text())
+for line in (a.discovery/'WITNESS-RECORD.jsonl').read_text().splitlines():
+    key, value = json.loads(line)
+    parts = key.split('.')
+    if len(parts)>3 and parts[0]=='providers' and parts[2]=='artifacts':
+        parts = parts[:3] + ['.'.join(parts[3:])]
+    target = spec
+    for part in parts[:-1]:
+        target = target.setdefault(part, {})
+    if parts[-1] in target:
+        assert target[parts[-1]]==value, 'Conflicting independent recomputations: '+key
+    target[parts[-1]] = value
+assembly = json.loads((a.discovery/'ASSEMBLY.json').read_text())
+for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+    spec['expected'][key] = assembly[key]
+spec['expected']['assembly_controls_rejected'] = 69
+spec['expected']['provider_counts'] = {'gauge44':333}
+spec['expected']['mutations_rejected'] = 15
+a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
diff --git a/research/r480-owner-optimum/code/generated_identity.py b/research/r480-owner-optimum/code/generated_identity.py
new file mode 100644
index 0000000000..74a9b60479
--- /dev/null
+++ b/research/r480-owner-optimum/code/generated_identity.py
@@ -0,0 +1,62 @@
+"""Proof-relevant identities for generated artifacts, independent of gzip streams.
+
+Immutable source archives retain their exact byte hashes. For freshly emitted
+artifacts, gzip identity is the exact decompressed payload and JSON identity
+retains every field. Only CLIFFORD-REVIEW's root timing field is excluded.
+Literal receipt references are checked against actual files before replacing
+the three gzip references (and the phase recipe reference) with content hashes.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import copy
+import gzip
+import hashlib
+import json
+import math
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+
+FILES=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+       'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+       'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json')
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+def json_identity(value):
+    return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode('utf-8')).hexdigest()
+
+def payload_identity(path):
+    return hashlib.sha256(gzip.decompress(Path(path).read_bytes())).hexdigest()
+
+def phase_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'CLIFFORD-REVIEW.json').read_bytes())if value is None else value)
+    assert value['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz'),'stale phase canonical word reference'
+    assert value['recipe_sha256']==sha(directory/'CLIFFORD-RECIPES.json'),'stale phase recipe reference'
+    seconds=value.pop('seconds')
+    assert type(seconds)in(int,float) and math.isfinite(seconds) and seconds>=0,'invalid phase timing metadata'
+    value['canonical_word_sha256']=payload_identity(directory/'CANONICAL-WORD.json.gz')
+    value['recipe_sha256']=json_identity(json.loads((directory/'CLIFFORD-RECIPES.json').read_bytes()))
+    return value
+
+def native_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'INDEPENDENT-LOCAL-REPLAY.json').read_bytes())if value is None else value)
+    for field,name in [('canonical_word_sha256','CANONICAL-WORD.json.gz'),('local_programs_sha256','LOCAL-PROGRAMS.json.gz')]:
+        assert value[field]==sha(directory/name),'stale native artifact reference: '+field
+        value[field]=payload_identity(directory/name)
+    return value
+
+def artifact_identities(directory):
+    directory=Path(directory)
+    result={}
+    for name in FILES:
+        path=directory/name
+        if name.endswith('.gz'):
+            result[name]=payload_identity(path)
+        else:
+            value=phase_value(directory)if name=='CLIFFORD-REVIEW.json'else native_value(directory)if name=='INDEPENDENT-LOCAL-REPLAY.json'else json.loads(path.read_bytes())
+            result[name]=json_identity(value)
+    return result
diff --git a/research/r480-owner-optimum/code/invoice_allcold.py b/research/r480-owner-optimum/code/invoice_allcold.py
new file mode 100644
index 0000000000..1ada7c24e8
--- /dev/null
+++ b/research/r480-owner-optimum/code/invoice_allcold.py
@@ -0,0 +1,329 @@
+"""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 generated_identity import artifact_identities
+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,h)==(112,9) and type(helpers) is int and helpers>0
+    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 = [len(w['frames'][w['final'][r]])-len(w['frames'][w['start'][r]]) for r in range(2*v, 2*v+helpers)]  # HPE: |final|-|start|
+    terminal_codim = sum(h-len(w['frames'][w['final'][r]]) for r in range(2*v, 2*v+helpers))  # HPE: 0 for FULL-ended helpers
+    ends = {r: f for r, f in enumerate(w['final']) if r >= 2*v and f != 1}
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    wrapped = {**entrances, **{r: 0 for r in ends if r not in entrances}}   # COLD-HPE: cold hyperplane-ended helpers carry wrappers too
+    cold_ends = len(wrapped) - 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, *end = event
+                assert kind in wrappers and wrapped.get(register) == frame
+                assert end == ([ends[register]] if register in ends else [])  # HPE: R_{E,U}^-1 and L_{E,U}^-1 name U
+                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(wrapped)
+        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')
+    return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n,
+                entering_helpers=entering,entrance_rank=sum(len(w['frames'][f]) for f in w['start'][2*v:]),
+                terminal_codimension=terminal_codim, hyperplane_ended_helpers=len(ends),  # HPE: always reported (0 for FULL-ended words)
+                **({'cold_hyperplane_ended_helpers': cold_ends} if cold_ends else {}),  # COLD-HPE: absent without cold ends
+                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=artifact_identities(local_dir))
+
+
+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]
+    # R is read from the provider words (all must agree); the parent dedicated-bank
+    # envelope keeps its own helper count R0 from the parent split-centres word.
+    assert len({p['helpers'] for p in providers.values()})==1,'providers disagree on helper count R'
+    v,h,m,centres=112,9,73,8
+    helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+    assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+    parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+    stages,replicas,blocks_per_stream=9,37,4
+    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+parent_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']==11840
+    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=1024
+    if retained_invoice is not None:
+        previous=read(retained_invoice)
+        assert previous['compiler']==compiler and previous['charged_prefix_bits']==512
+        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. The fixed provider uses 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 333 invocation and 333 bridge sweeps and take the maximum local scalar/Horner prefix over both orientations of the fixed provider. 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/r480-owner-optimum/code/prepare_global.py b/research/r480-owner-optimum/code/prepare_global.py
new file mode 100644
index 0000000000..655c9470f6
--- /dev/null
+++ b/research/r480-owner-optimum/code/prepare_global.py
@@ -0,0 +1,124 @@
+"""Bind a frozen explicit owner map to exact native local artifacts.
+
+This preparer nominates a witness. The separate serialized controller audit,
+finite invoice, two exact moment engines and strict pinned replay admit it.
+Apache-2.0; prepared with OpenAI assistance. See NOTICE.md.
+"""
+import argparse
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+from generated_identity import artifact_identities, FILES
+
+assert __debug__, 'Assertions required'
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--parent', type=Path, required=True)
+ap.add_argument('--owners', type=Path, required=True)
+ap.add_argument('--local', type=Path, required=True)
+ap.add_argument('--data', type=Path, required=True)
+args = ap.parse_args()
+args.data.mkdir(parents=True, exist_ok=True)
+parent_path = args.parent / 'data/PLAN.json'
+assert sha(parent_path) == '258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda'
+plan = read(parent_path)
+word = read(args.local / 'CANONICAL-WORD.json.gz')
+checks = read(args.local / 'LOCAL-CHECKS.json')
+assert (word['v'], word['h'], word['R']) == (112, 9, 492)
+widths = [len(word['frames'][word['final'][224+h]]) -
+          len(word['frames'][word['start'][224+h]]) for h in range(492)]
+profile = {int(k): v for k, v in word['local_profile'].items()}
+assert profile == {1: 2514, 2: 404, 3: 448, 4: 160, 5: 56, 8: 8}
+assert Counter(widths) == {4: 52, 5: 48, 7: 34, 8: 114, 9: 244}
+assert sum(widths) == 3794
+owners = read(args.owners)
+assert len(owners) == 72 * 492
+order = [tuple(x) for x in plan['order']]
+times = {x: i for i, x in enumerate(order)}
+used, call_helpers, call_families = defaultdict(set), defaultdict(set), defaultdict(set)
+for z in owners:
+    key = (z['stage'], z['replica'])
+    h, i, rep, port = z['helper'], z['child'], z['owner_replica'], z['port']
+    assert key in times and 0 <= h < 492 and 0 <= rep < 8 and 0 <= port < 112
+    assert z['time'] == times[key] and h not in call_helpers[key]
+    assert z['family'] not in call_families[key]
+    call_helpers[key].add(h)
+    call_families[key].add(z['family'])
+    cap, allowed = plan['windows'][f'{rep},{i}']
+    assert z['time'] in allowed and z['width'] == widths[h]
+    assert z['copy'] == rep * 112 + port
+    assert z['family'] == rep * 896 + (2*plan['pairs'][str(i)] + plan['sides'][str(i)])*112 + port
+    assert 0 <= z['offset'] and z['offset'] + z['width'] <= cap
+    cells = set(range(z['offset'], z['offset'] + z['width']))
+    group = (i, rep, port)
+    assert not used[group] & cells
+    used[group].update(cells)
+assert set(call_helpers) == set(order)
+assert all(hs == set(range(492)) for hs in call_helpers.values())
+idle = Counter()
+for key, (cap, _) in plan['windows'].items():
+    rep, i = map(int, key.split(','))
+    for port in range(112):
+        cells = used[i, rep, port]
+        assert cells == set(range(len(cells)))
+        left = cap - len(cells)
+        if left:
+            idle[left] += 1
+global_profile = Counter({r: 72*n for r, n in profile.items()}) + idle
+assert sum(r*n for r, n in global_profile.items()) == 520704
+assert 73*7168 - sum(r*n for r, n in global_profile.items()) == 2560
+pid = 'gauge44'
+for c in plan['provider_calls']:
+    c['provider'] = pid
+    c['local_program_sha256'] = checks[c['orientation']]['sha256']
+for c in plan['per_call_widths']:
+    c['widths'] = widths
+artifacts = {name: sha(args.local / name) for name in FILES}
+identities = artifact_identities(args.local)
+plan['provider_registry'] = {pid: dict(
+    directory='providers/' + pid, artifact_sha256=artifacts,
+    ports=word['ports'], centers=word['centers'], widths=widths,
+    actual_paid_profile=word['local_profile'],
+    orientation_program_sha256={k: v['sha256'] for k, v in checks.items()},
+    artifact_semantic_sha256=identities)}
+plan.update(status='FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION',
+            mode='gauge44-all72', profile=dict(sorted(global_profile.items())),
+            solver_status='deterministic-capacity-matching', gap=None,
+            source_plan_sha256=sha(parent_path),
+            source_owners_sha256=sha(args.parent / 'data/OWNERS.json.gz'),
+            assignment_sha256=sha(args.owners))
+target_owners = args.data / 'OWNERS.json.gz'
+if args.owners.resolve() != target_owners.resolve():
+    shutil.copyfile(args.owners, target_owners)
+dump(args.data / 'PLAN.json', plan)
+spec = dict(schema='witness-spec/1', name='gauge44-all72',
+            data=dict(plan_sha256=sha(args.data / 'PLAN.json'), owners_sha256=sha(target_owners)),
+            dispatch=[[s, r, pid] for s in range(9) for r in range(8)],
+            call_order=plan['order'], width_spot_helpers=[264, 276, 288, 300],
+            providers={pid: {}}, expected=dict(gain_baseline_kappa='0.001636241501576388'))
+dump(args.data / 'SPEC.json', spec)
+dump(args.data / 'PREPARATION.json', dict(
+    status='PASS_EXPLICIT_MAP_AND_FRESH_PROVIDER_NOMINATION',
+    parent_plan_sha256=sha(parent_path), source_owners_sha256=sha(args.owners),
+    global_profile=dict(sorted(global_profile.items())), idle_profile=dict(sorted(idle.items())),
+    roles=len(owners), rank_mass=520704, deficit=2560,
+    remaining='Independent emitted-controller audit, fresh finite invoice, exact moments and outer assembly.'))
+print('Prepared all72 gauge44 candidate:', dict(sorted(global_profile.items())))
diff --git a/research/r480-owner-optimum/code/restore_parent.py b/research/r480-owner-optimum/code/restore_parent.py
new file mode 100644
index 0000000000..21135f898a
--- /dev/null
+++ b/research/r480-owner-optimum/code/restore_parent.py
@@ -0,0 +1,67 @@
+"""Materialize the omitted generated PR558 parent, then require its reviewed hash.
+
+The integrated review contains the native inputs and INTEGRATION.json but
+omits GLOBAL-TEMPLATE.json.gz. This is only the deterministic template
+binding from the inherited prepare_supplier_base.py; no old circuit or
+phase calculation is rerun. The whole exact payload must match the review.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source',type=Path,required=True)
+ap.add_argument('--baseline',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+assert not a.out.exists()
+base=a.out/'complex-global/base'
+shutil.copytree(a.baseline/'complex-global/base',base)
+d=base/'split-centres'
+parent=a.source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz'
+old=read(parent);can=read(d/'CANONICAL-WORD.json.gz')
+checks=read(d/'LOCAL-CHECKS.json');programs=read(d/'LOCAL-PROGRAMS.json.gz')
+v,h,r=can['v'],can['h'],can['R'];c=len(can['centers']);m,t,l,k=73,8,9,4
+assert(v,h,r,c)==(112,9,504,8)
+widths=[h-len(can['frames'][f])for f in can['start'][2*v:]]
+data=2*k*t*v;live=data+l*r;physical=live+r+c+2
+word=copy.deepcopy(old)
+word.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=live,physical=physical,local_programs=programs)
+word['private_namespace']={'centers':[live,live+c],'reserved_tableau':[live+c,live+c+r],'coefficient':[physical-2,physical]}
+for call in word['calls']:
+ s,rep=call['stage'],call['replica'];owners=copy.deepcopy(call['owners'][:2*v])
+ for helper,w in enumerate(widths):
+  route=[2,rep]if w==9 else[2,rep*w,w,list(range(t*w,t*w+9-w))]
+  owners.append([data+s*r+helper,route])
+ call['owners']=owners;call['local_program_sha256']=checks[call['orientation']]['sha256']
+children=[]
+for s in range(l):
+ for helper,w in enumerate(widths):
+  axes=list(range(t*w,m))
+  children.append(dict(family=data+s*r+helper,rank=len(axes),axis_indices=axes,orthogonal_axes=[1<<j for j in axes]))
+word['bank_padding']={'families':list(range(data,live)),'children':children,
+ 'semantics':'Each listed complement frame is applied once after the eight disjoint residual blocks of that dedicated bank. The final hosted derivative has empty families and children.'}
+word['cover_final_correction'].update(families=[0,live],charged_calls_per_cover=live)
+for i,e in enumerate(word['execution_schedule']):
+ if e['kind']=='bank_padding_cover_sweep':word['execution_schedule'][i]={'kind':'bank_padding_cover_sweep','families':[data,live],'children_source':'bank_padding.children'}
+ elif e['kind']=='translate_every_live_family':e.update(word['cover_final_correction'])
+word['exact_data_phase_recipe_sha256']=sha(base/'work/complex-nine-native/DATA-PHASES.json')
+word['exact_local_clifford_recipe_sha256']=sha(d/'CLIFFORD-RECIPES.json')
+word['residual_adapter_sha256']=sha(d/'RESIDUAL-ADAPTERS.json')
+word['supplier_substitution']={'parent_template_sha256':sha(parent),
+ 'old_canonical_word_sha256':sha(a.baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz'),
+ 'new_canonical_word_sha256':sha(d/'CANONICAL-WORD.json.gz'),
+ 'exact_same_ports':True,'data_contract':'The same ordered 112 data ports and both complete-invocation identity-shear orientations feed the unchanged nine-stage controller. No old local program or helper profile is reused.'}
+word['route_semantics']['helper']='Dedicated family DATA+stage*R+helper; one helper per bank per complete invocation. Width-nine route[2,replica] uses axes9*replica..9*replica+8. Width-w entering route[2,w*replica,w,spectators] uses the disjoint residual block and paid normalization wrappers; spectator axes start at8*w, beyond all residual blocks.'
+raw=json.dumps(word,sort_keys=True,separators=(',',':')).encode()
+expected=read(d/'INTEGRATION.json')['global_template_sha256']
+assert hashlib.sha256(raw).hexdigest()==expected=='7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3'
+(d/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+print('PASS_EXACT_REVIEWED_PARENT_TEMPLATE_RESTORED',expected)
diff --git a/research/r480-owner-optimum/code/witness.py b/research/r480-owner-optimum/code/witness.py
new file mode 100644
index 0000000000..c5c7fbc114
--- /dev/null
+++ b/research/r480-owner-optimum/code/witness.py
@@ -0,0 +1,55 @@
+"""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']]
+# width-8 spot helpers: PR558's helpers 270, 282, 294, 306, or their images under a K-triangle word's 504 -> R helper map
+# (verify.py checks the spec value against the constructor's HELPER-MAP.json)
+SPOT=tuple(SPEC.get('width_spot_helpers',(270,282,294,306)))
+# A pivot swap moves a kernel family's pivot role p -> x; the old pivot p becomes an ordinary cold helper and its width
+# goes 8 -> 9 (construction/layers, PR641 PROOF-NOTE-PIVOT). Expected spot widths are derived from the package's pinned
+# pivot-swap recipe (path and sha256 in the spec), not from free data: 9 at a swapped-out pivot, 8 otherwise.
+_PKG=Path(os.environ['WITNESS_SPEC']).resolve().parents[1]
+def _old_pivots():
+ ps=SPEC.get('pivot_swap')
+ if not ps:return frozenset()
+ raw=(_PKG/ps['recipe']).read_bytes();import hashlib
+ assert hashlib.sha256(raw).hexdigest()==ps['sha256'],'pivot-swap recipe pin'
+ return frozenset(s['pivot']for s in json.loads(raw)['swaps'])
+OLD_PIVOTS=_old_pivots()
+def spot_widths(v=112):
+ """Expected residual widths at the spot helpers (helper indices) of the gauge44 provider."""
+ return tuple(9 if 2*v+h in OLD_PIVOTS else 8 for h in SPOT)
+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:
+  if os.environ.get('WITNESS_RECORD'):   # discovery bookkeeping only: append (key, value) for the spec writer
+   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))
+  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/r480-owner-optimum/construct.py b/research/r480-owner-optimum/construct.py
new file mode 100644
index 0000000000..04e2a22e24
--- /dev/null
+++ b/research/r480-owner-optimum/construct.py
@@ -0,0 +1,108 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Rebuild literal owners from the exact pattern-flow certificate."""
+import argparse,json,gzip,hashlib
+from collections import Counter,defaultdict
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--out',type=Path,required=True)
+args=parser.parse_args()
+if not __debug__:raise ValueError('Construction checks require assertions')
+if args.out.exists():raise ValueError('Choose a new construction directory')
+D=json.loads((HERE/'PATTERN-FLOW.json').read_text())
+assert D['T']==37 and D['order']==json.loads((HERE/'ORDER.json').read_text())
+S=json.loads((HERE/'inputs/SPEC.json').read_text())
+P=json.loads((HERE/'inputs/PLAN.json').read_text())
+widths=S['providers']['gauge44']['complete_contract']['widths'];ws=(4,5,7,8,9)
+xs={};ys=defaultdict(Counter)
+for entry,n in D['entries']:
+ assert type(n) is int and n>0
+ if entry[0]=='x':_,g,p=entry;xs[g,p]=n
+ else:_,g,p,t,w=entry;ys[g,p][t,w]+=n
+assign=defaultdict(list);global_count=Counter();idle=Counter();offsets=defaultdict(int)
+for gi,(r,cap,ts,children) in enumerate(D['groups']):
+ port_index=0
+ for pi,pat in enumerate(D['patterns'][str(cap)]):
+  N=xs.get((gi,pi),0)
+  if not N:continue
+  v=ys[gi,pi]
+  assert all(t in ts for t,w in v)
+  assert Counter({w:sum(n for (t,ww),n in v.items() if w==ww) for w,num in enumerate(pat) if num})==Counter({w:N*num for w,num in enumerate(pat) if num})
+  assert all(sum(n for (tt,w),n in v.items() if tt==t)<=N for t in ts)
+  slot_width=[w for w,n in enumerate(pat) for _ in range(n)]
+  graph=[Counter() for _ in slot_width]
+  # Split each width vertex into vertices of degree N.
+  for w in set(slot_width):
+   slots=[s for s,ww in enumerate(slot_width) if ww==w];j=0;used=0
+   for (t,ww),n in sorted(v.items()):
+    if ww!=w:continue
+    while n:
+     count=min(n,N-used);graph[slots[j]][t]+=count;used+=count;n-=count
+     if used==N:used=0;j+=1
+   assert j==len(slots) and used==0
+  assert all(sum(a.values())==N for a in graph)
+  for remaining in range(N,0,-1):
+   degree=Counter()
+   for adj in graph:degree.update(adj)
+   assert max(degree.values(),default=0)<=remaining
+   required=sorted(t for t,n in degree.items() if n==remaining)
+   st={};tt={}
+   def match_time(t,seen):
+    for s,adj in enumerate(graph):
+     if adj[t]==0 or s in seen:continue
+     seen.add(s)
+     if s not in st or match_time(st[s],seen):
+      st[s]=t;tt[t]=s;return True
+    return False
+   for t in required:assert match_time(t,set())
+   def match_slot(s,seen):
+    for t,n in sorted(graph[s].items()):
+     if not n or t in seen:continue
+     seen.add(t)
+     if t not in tt or match_slot(tt[t],seen):
+      tt[t]=s;st[s]=t;return True
+    return False
+   for s in range(len(graph)):
+    if s not in st:assert match_slot(s,set())
+   assert len(st)==len(tt)==len(graph) and all(t in tt for t in required)
+   child=children[port_index//112];port=port_index%112;port_index+=1
+   offset=0
+   for s,t in sorted(st.items(),key=lambda it:(it[1],it[0])):
+    w=ws[slot_width[s]];graph[s][t]-=1
+    assign[t,w].append((r,child,port,offset))
+    offset+=w;global_count[w]+=1
+   assert offset<=cap
+   idle[cap-offset]+=1
+  assert all(not any(adj.values()) for adj in graph)
+ assert port_index==112*len(children)
+roles=[]
+for t,(stage,replica) in enumerate(D['order']):
+ for h,w in enumerate(widths):
+  owner,child,port,offset=assign[t,w].pop()
+  family=896*owner+112*(2*P['pairs'][str(child)]+P['sides'][str(child)])+port
+  roles.append(dict(time=t,stage=stage,replica=replica,helper=h,width=w,owner_replica=owner,child=child,port=port,offset=offset,copy=112*owner+port,family=family))
+assert not any(assign.values());assert len(roles)==37*9*480
+print('literal roles',len(roles),'idle',dict(sorted(idle.items())))
+# Separate direct check from the aggregate model.
+used=defaultdict(set);seen=defaultdict(set);coverage=defaultdict(set)
+windows={(r,ch):(cap,set(ts)) for r,cap,ts,chs in D['groups'] for ch in chs}
+for z in roles:
+ t=z['time'];key=z['owner_replica'],z['child'];cap,ts=windows[key]
+ assert t in ts and z['family'] not in seen[t];seen[t].add(z['family'])
+ g=key+(z['port'],);cells=set(range(z['offset'],z['offset']+z['width']))
+ assert not cells&used[g] and all(0<=x<cap for x in cells);used[g]|=cells;coverage[t].add(z['helper'])
+for t,hh in coverage.items():assert hh==set(range(480))
+left=Counter()
+for key,(cap,ts) in windows.items():
+ for port in range(112):
+  cell=used[key+(port,)];assert cell==set(range(len(cell)));left[cap-len(cell)]+=1
+assert left==idle
+raw=json.dumps(roles,sort_keys=True,separators=(',',':')).encode()
+frozen=json.loads(gzip.decompress((HERE/'OWNERS.json.gz').read_bytes()))
+assert roles==frozen, 'Frozen owner map differs from exact decomposition'
+out=args.out;out.mkdir(parents=True)
+(out/'OWNERS.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+(out/'ORDER.json').write_text(json.dumps(D['order'])+'\n')
+(out/'GEOMETRY-CHECK.json').write_text(json.dumps({'roles':len(roles),'idle':dict(sorted(idle.items())),'owner_content_sha256':hashlib.sha256(raw).hexdigest(),'status':'PASS_LITERAL_WHOLE_HELPER_GEOMETRY'},indent=2)+'\n')
+print('PASS_LITERAL_WHOLE_HELPER_GEOMETRY',hashlib.sha256(raw).hexdigest())
diff --git a/research/r480-owner-optimum/controls.py b/research/r480-owner-optimum/controls.py
new file mode 100644
index 0000000000..06a64ff5d3
--- /dev/null
+++ b/research/r480-owner-optimum/controls.py
@@ -0,0 +1,71 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Run certificate controls through the public command-line checker."""
+import argparse
+import copy
+import json
+from pathlib import Path
+import subprocess
+import sys
+import tempfile
+
+HERE = Path(__file__).resolve().parent
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    if args.out.exists():
+        raise ValueError('Choose a new output file')
+    certificate = json.loads((HERE / 'CERTIFICATE.json').read_text())
+    cases = [
+        ('boolean_width_price', lambda d: d['width_prices'].__setitem__('4', True), 'integer width prices'),
+        ('float_width_price', lambda d: d['width_prices'].__setitem__('4', -1.0), 'integer width prices'),
+        ('boolean_capacity_bonus', lambda d: d['capacity_bonuses'].__setitem__('8', True), 'integer capacity bonuses'),
+        ('float_capacity_bonus', lambda d: d['capacity_bonuses'].__setitem__('8', 2.0), 'integer capacity bonuses'),
+        ('boolean_row_capacity', lambda d: d['packing'][0].__setitem__('capacity', True), 'integer packing capacity'),
+        ('float_row_capacity', lambda d: d['packing'][0].__setitem__('capacity', 8.0), 'integer packing capacity'),
+        ('boolean_bin_count', lambda d: d['packing'][0].__setitem__('bins', True), 'positive packing multiplicity'),
+        ('float_width_count', lambda d: d['packing'][0]['width_counts'].__setitem__(3, 1.0), 'integer packing vector'),
+        ('missing_bin', lambda d: d['packing'][0].__setitem__('bins', 24863), 'complete bin stock'),
+        ('missing_width_four', lambda d: d['packing'][3]['width_counts'].__setitem__(0, 1), 'complete helper inventory'),
+        ('nonintegral_replica_count', lambda d: d.__setitem__('replicas', 16), 'integral residual counts'),
+        ('negative_bin_count', lambda d: d['packing'][0].__setitem__('bins', -1), 'positive packing multiplicity'),
+        ('false_zero_price', lambda d: d['capacity_bonuses'].__setitem__('8', 3), 'zero and maximum residual'),
+        ('wrong_root_interval', lambda d: d.__setitem__('root_interval', ['0.001676905273619680861301', '0.001676905273619680861302']), 'two exact root signs: lower'),
+        ('next_outer_grid', lambda d: d.__setitem__('kappa_grid', '0.001674097969905391'), 'same outer grid cell'),
+        ('float_root', lambda d: d['root_interval'].__setitem__(0, 0.0016769052736196808), 'rational root strings'),
+    ]
+    outcomes = []
+    with tempfile.TemporaryDirectory(prefix='r480-owner-controls-') as tmp:
+        directory = Path(tmp)
+        for name, change, reason in cases:
+            mutated = copy.deepcopy(certificate)
+            change(mutated)
+            path, result = directory / (name+'.json'), directory / (name+'-output.json')
+            path.write_text(json.dumps(mutated)+'\n')
+            command = [sys.executable, '-B', str(HERE / 'verify.py'), '--certificate', str(path), '--out', str(result)]
+            process = subprocess.run(command, capture_output=True, text=True)
+            if process.returncode == 0 or ('ValueError: '+reason) not in process.stderr or result.exists():
+                raise ValueError('Wrong rejection for '+name+': '+process.stdout+process.stderr)
+            outcomes.append(dict(name=name, rejected_by=reason, output_created=False))
+        old = directory / 'retained.json'
+        old.write_text('retain exact bytes\n')
+        command = [sys.executable, '-B', str(HERE / 'verify.py'), '--out', str(old)]
+        process = subprocess.run(command, capture_output=True, text=True)
+        if process.returncode == 0 or old.read_text() != 'retain exact bytes\n':
+            raise ValueError('Output preservation control failed')
+        outcomes.append(dict(name='output_preservation', rejected_by='Choose a new output file', retained_bytes=True))
+        optimized = directory / 'optimized.json'
+        process = subprocess.run([sys.executable, '-O', '-B', str(HERE / 'verify.py'), '--out', str(optimized)], capture_output=True, text=True)
+        if process.returncode == 0 or 'Retained outer assertions require Python without -O' not in process.stderr or optimized.exists():
+            raise ValueError('Optimization guard failed')
+        outcomes.append(dict(name='optimization_guard', rejected_by='Retained outer assertions require Python without -O'))
+    result = dict(status='PASS_R480_OWNER_CERTIFICATE_CONTROLS', count=len(outcomes), cases=outcomes)
+    args.out.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], 'cases='+str(result['count']))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/r480-owner-optimum/data/PLAN.json b/research/r480-owner-optimum/data/PLAN.json
new file mode 100644
index 0000000000..7eea82fa03
--- /dev/null
+++ b/research/r480-owner-optimum/data/PLAN.json
@@ -0,0 +1,233067 @@
+{
+  "status": "FROZEN_EXPLICIT_R480_T37_OWNER_NOMINATION",
+  "mode": "seven-slot-k8-all-replica-optimum",
+  "K": 4,
+  "T": 37,
+  "M": 73,
+  "L": 9,
+  "live": 33152,
+  "deficit": 11840,
+  "profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664,
+    "48": 11302
+  },
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+  "source_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "assignment_content_sha256": "592dd6d5c3dc29a33472f75425f9652c73993a8e38bdc17c7372b321aaeefa03",
+  "replica_lift": {
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+    "replicas": 37,
+    "parent_template_content_sha256": "514e59314c8e2fa3c22d0a48083816f6686211090835e8f8775318c1c3e992d8",
+    "owners_file_sha256": "c35ac0c6f77c6b7cb32bee953770de3ef8a575aef36efc4764e0bb3325a04737",
+    "schedule_content_sha256": "9fcc4f3481709ec34509075a7587a6b0a043acfef6d6811f72b322bd3ecaaf2a",
+    "window_semantics": "Strict physical source-event intervals, including bridges"
+  }
+}
diff --git a/research/r480-owner-optimum/data/SPEC.json b/research/r480-owner-optimum/data/SPEC.json
new file mode 100644
index 0000000000..579a28450e
--- /dev/null
+++ b/research/r480-owner-optimum/data/SPEC.json
@@ -0,0 +1,3670 @@
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+    "kappa_decimal": "0.00167409796990539",
+    "complex_lower": "16769052736196808613/10000000000000000000000",
+    "conservative_complex_lower": "1676905270756896217493/1000000000000000000000000",
+    "kappa": "167409796990539/100000000000000000",
+    "assembly_controls_rejected": 69,
+    "provider_counts": {
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+    "mutations_rejected": 15
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+  "pivot_swap": {
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+    "sha256": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb"
+  }
+}
diff --git a/research/r480-owner-optimum/evidence/ADMISSION-CONTROLS.json b/research/r480-owner-optimum/evidence/ADMISSION-CONTROLS.json
new file mode 100644
index 0000000000..3e1de0e531
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "167409796990539/100000000000000000",
+  "input_sha256": {
+    "owner_audit": "ed4074eafe47ffd95a272436e3d4f654e4066dc57d12e77cf4be62e970f6c671",
+    "fresh_invoice": "a56e07538d1fff4af1d172ce81f0bf1d6b6ae3e4f1bd3401d3c2c530f641ba6b",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_258",
+    "gauge44:cold_helper_width_swap_270",
+    "gauge44:cold_helper_width_swap_282",
+    "gauge44:cold_helper_width_swap_294",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "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."
+}
diff --git a/research/r480-owner-optimum/evidence/ASSEMBLY.json b/research/r480-owner-optimum/evidence/ASSEMBLY.json
new file mode 100644
index 0000000000..0e696d96ee
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/ASSEMBLY.json
@@ -0,0 +1,344 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "167409796990539/100000000000000000",
+  "kappa_decimal": "0.00167409796990539",
+  "complex_lower": "16769052736196808613/10000000000000000000000",
+  "complex_decimal": "0.0016769052736196808613",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "gain_over_pr635_percent": "2.313623526388391711421361679688421607983496591569222376409213845570493",
+  "complex_profile": {
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+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664,
+    "48": 11302
+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  },
+  "conservative_complex_lower": "1676905270756896217493/1000000000000000000000000",
+  "conservative_complex_decimal": "0.001676905270756896217493",
+  "conservative_kappa": "1674097967052183/1000000000000000000",
+  "conservative_kappa_decimal": "0.001674097967052183",
+  "conservative_moments": [
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+      "side": "conservative_complex",
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+      "endpoint": "1676905270756896217493/1000000000000000000000000",
+      "accept": true,
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+      ],
+      "base_two": [
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+        "-13377806215429592073551/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
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+    "dimension_above_kappa": "4991615473631901598248625446311311543042727510567653600802459170731283801375246070312361422916597626101962903606428820814472987944842205608248249728987361774139646320837501600621652608232454229797671530422108947000466484440351476010009777842230582359724791989023495516996139285491440399103500970110709744232612064200043654873722449313080535795449308517777789580391502675112645022129352528474901576464487656981/5008384526368098404306194504685927084279795759975809942826787280201433473653747581200972450889357390246246159812484889822111934454985571645210498610180855266112585919464027025961857754640262519698882864591111299987109236946452061522854595726016508804945527097521287432513405122013076782533036034734398672399177007754230335146501861493610643149278763638046633218420853145261131155138206842032100000000000000000"
+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Conditional R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain."
+}
diff --git a/research/r480-owner-optimum/evidence/AXIS-CLI-CONTROL.json b/research/r480-owner-optimum/evidence/AXIS-CLI-CONTROL.json
new file mode 100644
index 0000000000..4d667945ea
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/AXIS-CLI-CONTROL.json
@@ -0,0 +1,25 @@
+{
+  "command": [
+    "/opt/homebrew/opt/python@3.14/bin/python3.14",
+    "-B",
+    "/tmp/k9-owner-package/independent_owner.py",
+    "--baseline-parent",
+    "/tmp/k9-owner-strict1/replay/global8/base/split-centres/GLOBAL-TEMPLATE.json.gz",
+    "--owners",
+    "/tmp/k9-owner-package/OWNERS.json.gz",
+    "--word",
+    "/tmp/k9-owner-package/inputs/local/CANONICAL-WORD.json.gz",
+    "--out",
+    "/tmp/k9-owner-bad-phase-result.json",
+    "--replicas",
+    "37",
+    "--expected-idle",
+    "{\"1\":5622,\"48\":11302}",
+    "--phases",
+    "/tmp/k9-owner-bad-phases.json"
+  ],
+  "exit_code": 1,
+  "reason": "overlapping pending children on one family",
+  "output_created": false,
+  "status": "PASS_ACTUAL_CLI_PENDING_AXIS_REJECTION"
+}
diff --git a/research/r480-owner-optimum/evidence/BIT-CONTROLS.json b/research/r480-owner-optimum/evidence/BIT-CONTROLS.json
new file mode 100644
index 0000000000..42f029308f
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/BIT-CONTROLS.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS",
+  "kappa": "0.00167409796990539",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "derived_deficit": 10272,
+  "rejected_controls": [
+    "revert_hardcoded_9984",
+    "ports_112",
+    "decoder_constant_64_copy_ranks_unchanged",
+    "decoder_constant_64_with_one_copy_rank_8",
+    "eight_retained_totals",
+    "live_minus_one",
+    "profile_rank_mass_plus_one",
+    "profile_rank_mass_receipt_mismatch",
+    "bit_lower_next_grid",
+    "not_nine_stage_record",
+    "tampered_bytes_next_grid",
+    "pr543_file_under_pr589_pin"
+  ],
+  "assembler_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a"
+}
diff --git a/research/r480-owner-optimum/evidence/BOUND-CONTROLS.json b/research/r480-owner-optimum/evidence/BOUND-CONTROLS.json
new file mode 100644
index 0000000000..d9d490bb71
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/BOUND-CONTROLS.json
@@ -0,0 +1,95 @@
+{
+  "status": "PASS_R480_OWNER_CERTIFICATE_CONTROLS",
+  "count": 18,
+  "cases": [
+    {
+      "name": "boolean_width_price",
+      "rejected_by": "integer width prices",
+      "output_created": false
+    },
+    {
+      "name": "float_width_price",
+      "rejected_by": "integer width prices",
+      "output_created": false
+    },
+    {
+      "name": "boolean_capacity_bonus",
+      "rejected_by": "integer capacity bonuses",
+      "output_created": false
+    },
+    {
+      "name": "float_capacity_bonus",
+      "rejected_by": "integer capacity bonuses",
+      "output_created": false
+    },
+    {
+      "name": "boolean_row_capacity",
+      "rejected_by": "integer packing capacity",
+      "output_created": false
+    },
+    {
+      "name": "float_row_capacity",
+      "rejected_by": "integer packing capacity",
+      "output_created": false
+    },
+    {
+      "name": "boolean_bin_count",
+      "rejected_by": "positive packing multiplicity",
+      "output_created": false
+    },
+    {
+      "name": "float_width_count",
+      "rejected_by": "integer packing vector",
+      "output_created": false
+    },
+    {
+      "name": "missing_bin",
+      "rejected_by": "complete bin stock",
+      "output_created": false
+    },
+    {
+      "name": "missing_width_four",
+      "rejected_by": "complete helper inventory",
+      "output_created": false
+    },
+    {
+      "name": "nonintegral_replica_count",
+      "rejected_by": "integral residual counts",
+      "output_created": false
+    },
+    {
+      "name": "negative_bin_count",
+      "rejected_by": "positive packing multiplicity",
+      "output_created": false
+    },
+    {
+      "name": "false_zero_price",
+      "rejected_by": "zero and maximum residual",
+      "output_created": false
+    },
+    {
+      "name": "wrong_root_interval",
+      "rejected_by": "two exact root signs: lower",
+      "output_created": false
+    },
+    {
+      "name": "next_outer_grid",
+      "rejected_by": "same outer grid cell",
+      "output_created": false
+    },
+    {
+      "name": "float_root",
+      "rejected_by": "rational root strings",
+      "output_created": false
+    },
+    {
+      "name": "output_preservation",
+      "rejected_by": "Choose a new output file",
+      "retained_bytes": true
+    },
+    {
+      "name": "optimization_guard",
+      "rejected_by": "Retained outer assertions require Python without -O"
+    }
+  ]
+}
diff --git a/research/r480-owner-optimum/evidence/BOUND.json b/research/r480-owner-optimum/evidence/BOUND.json
new file mode 100644
index 0000000000..5b7fb9d029
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/BOUND.json
@@ -0,0 +1,302 @@
+{
+  "status": "PASS_R480_ALL_REPLICA_BIN_OPTIMUM",
+  "scope": "Exact owner bin relaxation. Time windows, per-call family matching, charts, local admission and finite invoices are separate.",
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "source_head": "052afc128954f7b6a2b3c409eb4d72248e4020f2",
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+    "research/complex-t21-owners/independent_check.py": "9d8c86bf45cdaef37f223c88704055ced503ee295645611e13f3fb9059a00e55",
+    "research/complex-t37-owners/ORDER.json": "2093ca4050e1ce95621f4702bebe8b01b36773b1ecfa2c0d6275e132bd33d578"
+  }
+}
diff --git a/research/r480-owner-optimum/evidence/CONSTRUCTION.json b/research/r480-owner-optimum/evidence/CONSTRUCTION.json
new file mode 100644
index 0000000000..a4f3de140d
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/CONSTRUCTION.json
@@ -0,0 +1,10 @@
+{
+  "roles": 159840,
+  "idle": {
+    "0": 57668,
+    "1": 5622,
+    "48": 11302
+  },
+  "owner_content_sha256": "592dd6d5c3dc29a33472f75425f9652c73993a8e38bdc17c7372b321aaeefa03",
+  "status": "PASS_LITERAL_WHOLE_HELPER_GEOMETRY"
+}
diff --git a/research/r480-owner-optimum/evidence/CONTROLLER-AUDIT.json b/research/r480-owner-optimum/evidence/CONTROLLER-AUDIT.json
new file mode 100644
index 0000000000..6145d9aa5d
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/CONTROLLER-AUDIT.json
@@ -0,0 +1,74 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "aac9224bbdf8f198c7873c0b2042caee9043ffae594f0a1835896d5ed43920f4",
+  "complex_template_sha256": "aac9224bbdf8f198c7873c0b2042caee9043ffae594f0a1835896d5ed43920f4",
+  "complex_live": 33152,
+  "complex_profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664,
+    "48": 11302
+  },
+  "complex_hosted_residuals": 159840,
+  "physical": 33642,
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "entering_helper_roles": 79920,
+  "cross_replica_helper_roles": 151156,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 159840,
+  "complete_invocations": 333,
+  "actual_orthogonal_73column_maps": 11150,
+  "actual_sigma_stream_sha256": "1e243d977e2e67af21554555dbc0dee5a92e8745a5361c7df3e007f5a963af33",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 16924,
+  "mutations_rejected": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong provider width registry",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "mutation_controls_run": true,
+  "provider_phase_semantic_sha256": {
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+      "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3",
+      "LOCAL-CHECKS.json": "18f09b79835aa352f04d27041d86d1338c5ad0094b888588c1c05af2dc399ffd",
+      "INDEPENDENT-LOCAL-REPLAY.json": "2d4680965c62db1fde1236c4857b19bf7bc97af58805e6b4109afbc452f0fdd8",
+      "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+      "CLIFFORD-REVIEW.json": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+      "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+    }
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+      "5": 32,
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+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "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."
+}
diff --git a/research/r480-owner-optimum/evidence/INDEPENDENT-OWNER.json b/research/r480-owner-optimum/evidence/INDEPENDENT-OWNER.json
new file mode 100644
index 0000000000..19bb5f3f4b
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/INDEPENDENT-OWNER.json
@@ -0,0 +1,119 @@
+{
+  "status": "PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW",
+  "roles": 159840,
+  "calls": 333,
+  "source_events_per_replica": 30,
+  "expanded_replica_events": 1110,
+  "bridge_events": 333,
+  "literal_windows": 666,
+  "checked_whole_helper_widths": 159840,
+  "checked_busy_family_windows": 159840,
+  "orthogonal_port_bases": 112,
+  "actual_73_axis_charts": 11150,
+  "checked_slice_prefixes": 74592,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 432,
+    "4": 142,
+    "5": 82,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "idle": {
+    "1": 5622,
+    "48": 11302
+  },
+  "profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664,
+    "48": 11302
+  },
+  "live": 33152,
+  "physical": 33642,
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "namespace": {
+    "data": [
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+      33152
+    ],
+    "centres": [
+      33152,
+      33160
+    ],
+    "tableau": [
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+      33640
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+    "coefficient": [
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+      33642
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+  },
+  "local_prefix_bits": 68,
+  "local_prefix_from_native_receipt": true,
+  "local_profile_recounted": true,
+  "prefix_formula": {
+    "local_scalar": 68,
+    "input_l2": 37,
+    "invocations": 333,
+    "bridges": 333,
+    "margin": 4
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+  "prefix_bits": 775,
+  "charged_prefix_bits": 1024,
+  "physical_stock_bits": 2643,
+  "physical_row_coefficient": 17495,
+  "row_limit": 20161,
+  "scope": "Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.",
+  "disjoint_pending_child_axis_checks": 2016,
+  "controls_rejected": [
+    {
+      "name": "private_namespace_collision",
+      "reason": "private-namespace collision"
+    },
+    {
+      "name": "copy_replica_alias",
+      "reason": "role invocation time"
+    },
+    {
+      "name": "missing_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "split_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "truncated_helper_width",
+      "reason": "whole-helper residual width"
+    },
+    {
+      "name": "cross_idle_boundary",
+      "reason": "strict bridge-aware idle window"
+    },
+    {
+      "name": "cross_child_pending_axis_alias",
+      "reason": "overlapping pending children on one family"
+    }
+  ],
+  "input_sha256": {
+    "/private/tmp/k9-owner-parent-check/replay/global8/base/split-centres/GLOBAL-TEMPLATE.json.gz": "ab8448de2036a23d9b55a196a8846512dc24fdf09855c1e0f0caa5b7a6965f7b",
+    "/private/tmp/k9-owner-parent-check/replay/global8/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "/private/tmp/k9-owner-parent-check/replay/global8/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "/Users/aliromman/.codex/worktrees/kappa9-lane03/IntegerMultiplicationBounds/research/r480-owner-optimum/inputs/local/CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+    "/Users/aliromman/.codex/worktrees/kappa9-lane03/IntegerMultiplicationBounds/research/r480-owner-optimum/inputs/local/INDEPENDENT-LOCAL-REPLAY.json": "13dd18297162569532983db1a2ab67926b064330cd7edd3587e7b546b2dedf17",
+    "/Users/aliromman/.codex/worktrees/kappa9-lane03/IntegerMultiplicationBounds/research/r480-owner-optimum/OWNERS.json.gz": "c35ac0c6f77c6b7cb32bee953770de3ef8a575aef36efc4764e0bb3325a04737"
+  }
+}
diff --git a/research/r480-owner-optimum/evidence/OVERLAP.json b/research/r480-owner-optimum/evidence/OVERLAP.json
new file mode 100644
index 0000000000..50f5ad8cab
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/OVERLAP.json
@@ -0,0 +1,43 @@
+{
+  "at_utc": "2026-10-13T18:41:00Z",
+  "scope": "Exact heads read before local handoff. Reported PR values are comparisons, not an independent admission of those PRs.",
+  "selected_main": {
+    "commit": "ba82555c64e1879e4b7decce28186f208fcb8262",
+    "selected_pr": 1042,
+    "kappa": "0.001672188119205421"
+  },
+  "same_word": [
+    {
+      "pr": 1082,
+      "head": "0c2e294ec204e83846d27344f829d15ed9ee7cc6",
+      "kappa": "0.001672653061493085"
+    },
+    {
+      "pr": 1094,
+      "head": "0fc329d0bec93ca7cd288eaea1295172e8789810",
+      "kappa": "0.001672660197076918"
+    }
+  ],
+  "changed_word": [
+    {
+      "pr": 1107,
+      "head": "6123fc5d57db16aaa3e8a26b4a11a34b46c0c391",
+      "kappa": "0.001672765980186726"
+    },
+    {
+      "pr": 1117,
+      "head": "342b67f23dfa8f41a520a0d58978b2875e9eb0dd",
+      "kappa": "0.001672846995880185"
+    },
+    {
+      "pr": 1121,
+      "head": "61e816c29165a94f6cfc57d9e195063a5b027bc2",
+      "kappa": "0.001672965558289236"
+    }
+  ],
+  "independent_audit": {
+    "pr": 1091,
+    "head": "b4c13a228acb80f74c682b7097f0ce9bbf51bc4e"
+  },
+  "distinct_contribution": "All positive replica counts for the fixed R480 seven-slot k8 inventory; exact integral T37 attainment, actual windows/charts and full finite admission. Changed-word PRs are outside the theorem."
+}
diff --git a/research/r480-owner-optimum/evidence/PREFIX-AND-INVOICE.json b/research/r480-owner-optimum/evidence/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..1d68c15e2f
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/PREFIX-AND-INVOICE.json
@@ -0,0 +1,5649 @@
+{
+  "status": "PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "aac9224bbdf8f198c7873c0b2042caee9043ffae594f0a1835896d5ed43920f4",
+  "parent_template_sha256": "514e59314c8e2fa3c22d0a48083816f6686211090835e8f8775318c1c3e992d8",
+  "owner_audit_sha256": "ed4074eafe47ffd95a272436e3d4f654e4066dc57d12e77cf4be62e970f6c671",
+  "controller_audit_sha256": "50cb933ed29b9d894ada2f8343b16b8e3fc6ee676e1e4414a0c8f47a4f308f32",
+  "providers": {
+    "gauge44": {
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+          "macros": 19693,
+          "real_component_primitives": 198814,
+          "prefix_l1": "14824960514781440791821/64",
+          "prefix_bits": 68,
+          "coefficient_work_primitive_count": 98365,
+          "all_exact_columns": 704,
+          "dirty_helper_columns": 480,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 240,
+          "post_wrappers": 240,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        },
+        "forward": {
+          "events": 24767,
+          "macros": 19693,
+          "real_component_primitives": 198766,
+          "prefix_l1": "2765345294379392599/1024",
+          "prefix_bits": 52,
+          "coefficient_work_primitive_count": 98333,
+          "all_exact_columns": 704,
+          "dirty_helper_columns": 480,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 240,
+          "post_wrappers": 240,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        }
+      },
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+      "centres": 8,
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+      "h": 9,
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+      "entering_helpers": 192,
+      "entrance_rank": 384,
+      "terminal_codimension": 206,
+      "hyperplane_ended_helpers": 78,
+      "cold_hyperplane_ended_helpers": 48,
+      "width_inventory": {
+        "4": 56,
+        "5": 32,
+        "7": 30,
+        "8": 122,
+        "9": 240
+      },
+      "widths": [
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+  },
+  "finite": {
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+    "literal_bits": 35286,
+    "physical_row_coefficient": 17495,
+    "retained_row_coefficient": 20161,
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+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. The fixed provider uses 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."
+}
diff --git a/research/r480-owner-optimum/evidence/STRICT-REPLAY.json b/research/r480-owner-optimum/evidence/STRICT-REPLAY.json
new file mode 100644
index 0000000000..dcdf30a995
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/STRICT-REPLAY.json
@@ -0,0 +1,91 @@
+{
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+    },
+    {
+      "name": "lift",
+      "seconds": 4.799,
+      "exit_code": 0,
+      "log_sha256": "c8f864806d6a40d8899bcf4e4f94d8914bc1e7d67b77b30af71e38c9784c6e36"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.614,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 18.002,
+      "exit_code": 0,
+      "log_sha256": "62dd713211fe1fb69d0b36a8c350a41a12f23139dc53a09ec1ca6e95a96adcc4"
+    },
+    {
+      "name": "audit",
+      "seconds": 54.656,
+      "exit_code": 0,
+      "log_sha256": "50cb933ed29b9d894ada2f8343b16b8e3fc6ee676e1e4414a0c8f47a4f308f32"
+    },
+    {
+      "name": "invoice",
+      "seconds": 2.028,
+      "exit_code": 0,
+      "log_sha256": "7a24483ea6432bc7616837eba11ae00c0ecffa307a98aff58237db8b0c443188"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.519,
+      "exit_code": 0,
+      "log_sha256": "7032142fbd0dd614840f381755a7e2dcf39933c10a5ab68c836e432f39ce6ad7"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.775,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    },
+    {
+      "name": "bit-controls",
+      "seconds": 1.065,
+      "exit_code": 0,
+      "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+    },
+    {
+      "name": "independent-owner",
+      "seconds": 2.724,
+      "exit_code": 0,
+      "log_sha256": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e"
+    }
+  ],
+  "local_input_sha256": {
+    "CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+    "RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c",
+    "LOCAL-PROGRAMS.json.gz": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+    "LOCAL-CHECKS.json": "2b8b1891a736598010232bfb26abc31973b265a53a2009a3fcfd9138b5ecadb4",
+    "CLIFFORD-REVIEW.json": "dd57b86b730923b19f64e5d09d8885149366db636607dcd5e2acf9a56d11e72b",
+    "INDEPENDENT-LOCAL-REPLAY.json": "13dd18297162569532983db1a2ab67926b064330cd7edd3587e7b546b2dedf17",
+    "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+    "FULL-WORD.json.gz": "49596aa4ed4fd36cd4582fd0e8ddeb09fd80370a7d8aea1ede52a135b536d289",
+    "SCALAR-FRAME-AUDIT.json": "2861f75f7667b10ed7235ab4d932da4797f7e7e4a26d4bc467110114bab77eec",
+    "WRAPPER-CHECKS.json": "0ae753d6fa6e922d8b8180da602828f6cb3f444fcd124d019acee74e145c0836"
+  },
+  "scope": "Finite owner, controller, chart, invoice and assembly replay. Local scalar and phase replay and inherited all-size obligations are recorded separately."
+}
diff --git a/research/r480-owner-optimum/evidence/VALIDATION.json b/research/r480-owner-optimum/evidence/VALIDATION.json
new file mode 100644
index 0000000000..3cc9897aea
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/VALIDATION.json
@@ -0,0 +1,48 @@
+{
+  "status": "PASS_FOCUSED_FINITE_AND_EXACT_BOUND_CHECKS",
+  "base": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "python": "3.14.7 (main, Aug  5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]",
+  "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O",
+  "one_command": [
+    "python3",
+    "-B",
+    "research/r480-owner-optimum/check.py",
+    "--work",
+    "/tmp/r480-owner-check"
+  ],
+  "executed_check_work": "/tmp/k9-owner-strict1",
+  "exact_bound_patterns": 1163,
+  "certificate_cli_controls": 18,
+  "literal_roles": 159840,
+  "controller_mutations": 15,
+  "independent_owner_controls": 7,
+  "pending_child_port_basis_checks": 2016,
+  "admission_controls": 69,
+  "bit_supplier_controls": 12,
+  "outer_constraints": 47,
+  "charged_complex_prefix_bits": 1024,
+  "actual_prefix_bits": 775,
+  "physical_row_coefficient": 17495,
+  "kappa": "167409796990539/100000000000000000",
+  "post_strict_change": "The independent checker added a disjoint-pending-axis guard and its seventh control. Targeted and actual-CLI checks passed. The coordinator then reran the complete public check with the final code and inputs; every stage passed.",
+  "derived_code_reproduction": "All six source-to-derived edit lists reproduce their target byte for byte.",
+  "syntax_check": "Every packaged Python file parsed.",
+  "shared_baseline_make_verify": {
+    "status": "RUNNING_AT_HANDOFF",
+    "log": "work/nine-pr-sprint-20261013/baseline-verification/make-verify.log",
+    "scope": "Unchanged exact base; run once by the sprint coordinator."
+  },
+  "limits": [
+    "The local source chain was rebuilt by the concurrent sprint worker. The one-command owner replay consumes its source-bound artifacts.",
+    "The cited PR589 bit circuit is not rebuilt here; its full profile and exceptional-residue surcharge are repriced.",
+    "All inherited asymptotic obligations remain conditional.",
+    "No selected-result pointer was changed."
+  ],
+  "independent_full_replay": {
+    "status": "PASS_R480_ALL_REPLICA_OPTIMUM_AND_ATTAINING_CONSTRUCTION",
+    "work": "/tmp/k9-owner-parent-check",
+    "reviewer": "Separate coordinator agent",
+    "source_freeze_sha256": "2780bd3f6ffa6584ae92993a7fe7223f01002860ae4bb6c52c9fc5203f08b025",
+    "scope": "The coordinator read PROOF.md, README.md, all derived-code changes and the pending-axis guard. It separately ran the complete public check with the final code and inputs."
+  }
+}
diff --git a/research/r480-owner-optimum/evidence/local-source/BASE-STEPS.json b/research/r480-owner-optimum/evidence/local-source/BASE-STEPS.json
new file mode 100644
index 0000000000..8d74a9b9a9
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/local-source/BASE-STEPS.json
@@ -0,0 +1,37 @@
+[
+  {
+    "step": "shadow-early",
+    "exit_code": 0,
+    "seconds": 0.312
+  },
+  {
+    "step": "shadow-prefix",
+    "exit_code": 0,
+    "seconds": 0.472
+  },
+  {
+    "step": "gauge-forward",
+    "exit_code": 0,
+    "seconds": 0.45
+  },
+  {
+    "step": "port0",
+    "exit_code": 0,
+    "seconds": 0.346
+  },
+  {
+    "step": "port1",
+    "exit_code": 0,
+    "seconds": 0.356
+  },
+  {
+    "step": "port2",
+    "exit_code": 0,
+    "seconds": 0.354
+  },
+  {
+    "step": "port3",
+    "exit_code": 0,
+    "seconds": 0.442
+  }
+]
diff --git a/research/r480-owner-optimum/evidence/local-source/CELL-STEPS.json b/research/r480-owner-optimum/evidence/local-source/CELL-STEPS.json
new file mode 100644
index 0000000000..5fdf17814b
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/local-source/CELL-STEPS.json
@@ -0,0 +1,32 @@
+[
+  {
+    "step": "gauge-forward",
+    "exit_code": 0,
+    "seconds": 0.395
+  },
+  {
+    "step": "port0",
+    "exit_code": 0,
+    "seconds": 0.374
+  },
+  {
+    "step": "port1",
+    "exit_code": 0,
+    "seconds": 0.482
+  },
+  {
+    "step": "port2",
+    "exit_code": 0,
+    "seconds": 0.517
+  },
+  {
+    "step": "port3",
+    "exit_code": 0,
+    "seconds": 0.442
+  },
+  {
+    "step": "cold44",
+    "exit_code": 0,
+    "seconds": 2.81
+  }
+]
diff --git a/research/r480-owner-optimum/evidence/local-source/CHAIN-STEPS.json b/research/r480-owner-optimum/evidence/local-source/CHAIN-STEPS.json
new file mode 100644
index 0000000000..bf5c0e6f62
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/local-source/CHAIN-STEPS.json
@@ -0,0 +1,107 @@
+[
+  {
+    "step": "pivot-swap",
+    "exit_code": 0,
+    "seconds": 10.172
+  },
+  {
+    "step": "cold44-exact",
+    "exit_code": 0,
+    "seconds": 2.01
+  },
+  {
+    "step": "lec-p6n",
+    "exit_code": 0,
+    "seconds": 117.763
+  },
+  {
+    "step": "promotion",
+    "exit_code": 0,
+    "seconds": 0.264
+  },
+  {
+    "step": "promo-controls",
+    "exit_code": 0,
+    "seconds": 7.186
+  },
+  {
+    "step": "lec-promo",
+    "exit_code": 0,
+    "seconds": 81.834
+  },
+  {
+    "step": "jx",
+    "exit_code": 0,
+    "seconds": 0.174
+  },
+  {
+    "step": "jx-control-C0_identity",
+    "exit_code": 0,
+    "seconds": 0.127
+  },
+  {
+    "step": "jx-control-C1_741_only",
+    "exit_code": 0,
+    "seconds": 0.128
+  },
+  {
+    "step": "jx-control-N3_plain_join_moved_reads",
+    "exit_code": 0,
+    "seconds": 0.133
+  },
+  {
+    "step": "lec-jx",
+    "exit_code": 0,
+    "seconds": 105.512
+  },
+  {
+    "step": "hybrids",
+    "exit_code": 0,
+    "seconds": 0.105
+  },
+  {
+    "step": "hybrid-controls",
+    "exit_code": 0,
+    "seconds": 13.119
+  },
+  {
+    "step": "lec-hyb",
+    "exit_code": 0,
+    "seconds": 88.857
+  },
+  {
+    "step": "frames",
+    "exit_code": 0,
+    "seconds": 0.521
+  },
+  {
+    "step": "lec-frames",
+    "exit_code": 0,
+    "seconds": 90.473
+  },
+  {
+    "step": "native",
+    "exit_code": 0,
+    "seconds": 1.243
+  },
+  {
+    "step": "ledgers",
+    "exit_code": 0,
+    "seconds": 0.822
+  },
+  {
+    "step": "local-replay",
+    "exit_code": 0,
+    "seconds": 5.213
+  },
+  {
+    "step": "wrappers",
+    "exit_code": 0,
+    "seconds": 2.337
+  },
+  {
+    "step": "phases",
+    "exit_code": 0,
+    "seconds": 191.38
+  }
+]
diff --git a/research/r480-owner-optimum/evidence/local-source/NATIVE-REPLAY-NOTES.txt b/research/r480-owner-optimum/evidence/local-source/NATIVE-REPLAY-NOTES.txt
new file mode 100644
index 0000000000..1b0738f3b8
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/local-source/NATIVE-REPLAY-NOTES.txt
@@ -0,0 +1,7 @@
+Base main: abdc6a7002abdbcd9e21bfc5e1a795784deacfdf, shared lane01.
+Sources: PR1074 052afc128954f7b6a2b3c409eb4d72248e4020f2 (gauge44-leaver8 and gauge44-slots); PR635 a6895a69f8ad98ab45777b03e9e6f48888c39f6f (complex-571-cold14-st2).
+Base scalar driver: /tmp/k9-leaver-base/STEPS.json
+Cell scalar driver: /tmp/k9-leaver-cell/STEPS.json
+Full unchanged k8 chain driver: /tmp/k9-leaver-chain/STEPS.json. All 21 steps including phases passed.
+Slot scalar/native/ledger/endpoint/wrapper command receipt: /tmp/k9-leaver-slots/STEPS.json. All word, canonical and forward/backward pins matched SLOT-PINS-k8.json.
+Slot phase replay: phases.log (PASS exact local phases; 2896 edges; 339.109 seconds; recipe SHA256 d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731). Source-specific slot controls remain separate from these native checks.
diff --git a/research/r480-owner-optimum/evidence/local-source/SLOTS-STEPS.json b/research/r480-owner-optimum/evidence/local-source/SLOTS-STEPS.json
new file mode 100644
index 0000000000..582d5773e5
--- /dev/null
+++ b/research/r480-owner-optimum/evidence/local-source/SLOTS-STEPS.json
@@ -0,0 +1,84 @@
+[
+  {
+    "step": "slots",
+    "command": [
+      "python3",
+      "-B",
+      "/tmp/k9-leaver-sources/research/gauge44-leaver8/construction/barch/build_tri.py",
+      "/tmp/k9-leaver-chain/frames/FULL-WORD.json.gz",
+      "/tmp/k9-leaver-sources/research/gauge44-slots/construction/slots/RECIPE-SLOTS-k8.json",
+      "/tmp/k9-leaver-slots/FULL-WORD.json.gz"
+    ],
+    "exit_code": 0,
+    "seconds": 0.14077299972996116
+  },
+  {
+    "step": "native",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/tmp/k9-leaver-sources/research/complex-571-cold14-st2/code/hpe_audit_and_transport.py",
+      "--raw",
+      "/tmp/k9-leaver-slots/FULL-WORD.json.gz",
+      "--routing",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz",
+      "--out",
+      "/tmp/k9-leaver-slots/local"
+    ],
+    "exit_code": 0,
+    "seconds": 1.8713445831090212
+  },
+  {
+    "step": "ledgers",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/tmp/k9-leaver-sources/research/complex-571-cold14-st2/code/hpe_emit_local.py",
+      "/tmp/k9-leaver-slots/local"
+    ],
+    "exit_code": 0,
+    "seconds": 1.0618331669829786
+  },
+  {
+    "step": "local-replay",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/tmp/k9-leaver-sources/research/complex-571-cold14-st2/code/hpe_audit_local.py",
+      "/tmp/k9-leaver-slots/local"
+    ],
+    "exit_code": 0,
+    "seconds": 6.432917749974877
+  },
+  {
+    "step": "wrappers",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/tmp/k9-leaver-sources/research/complex-571-cold14-st2/code/hpe_adapters_local.py",
+      "/tmp/k9-leaver-slots/local/CANONICAL-WORD.json.gz",
+      "/tmp/k9-leaver-slots/local/RESIDUAL-ADAPTERS.json",
+      "/tmp/k9-leaver-slots/local/WRAPPER-CHECKS.json"
+    ],
+    "exit_code": 0,
+    "seconds": 2.5233489158563316
+  },
+  {
+    "step": "exact-phases",
+    "command": [
+      "python3",
+      "-B",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/code/phases_full.py",
+      "/tmp/k9-leaver-slots/local",
+      "/Users/aliromman/.codex/worktrees/kappa9-lane01/IntegerMultiplicationBounds/research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/vendor/clifford"
+    ],
+    "exit_code": 0,
+    "seconds": 339.10877466667444,
+    "clifford_recipes_sha256": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731"
+  }
+]
diff --git a/research/r480-owner-optimum/independent_owner.py b/research/r480-owner-optimum/independent_owner.py
new file mode 100644
index 0000000000..bf2de9be49
--- /dev/null
+++ b/research/r480-owner-optimum/independent_owner.py
@@ -0,0 +1,343 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Prepared for haoyan with substantial OpenAI Codex assistance.
+"""Independent source-event, owner, chart, and finite-reserve audit.
+
+This derivative fixes the R480 seven-slot k8 word and 37 replicas. It charges
+1024 complex prefix bits and checks disjoint pending children on each family.
+The source is Hao Yan's variable-replica checker at the pinned repository base.
+SOURCES.json and INDEPENDENT-DERIVATION.patch identify that source and all edits.
+
+Inputs are read-only. No owner constructor or controller auditor is imported.
+--word is the canonical local supplier JSON.gz, with a hash-bound native
+INDEPENDENT-LOCAL-REPLAY.json beside it (override with --local-replay).
+--baseline-parent is the original eight-replica GLOBAL-TEMPLATE.json.gz.
+Its sibling CANONICAL-WORD.json.gz supplies the ports and centre frames.
+DATA-PHASES.json defaults to ../work/complex-nine-native/DATA-PHASES.json
+(override with --phases). The checker recounts local widths and paid ranks.
+--out names a JSON receipt. Checks remain enabled under python -O.
+"""
+import argparse
+import copy
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+
+V, H, M, T, R = 112, 9, 73, 37, 480
+EXPECTED_IDLE = None
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+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 basis(vectors):
+    pivots = {}
+    for x in vectors:
+        require(type(x) is int and 0 <= x < 1 << H, 'invalid local frame vector')
+        while x:
+            bit = x.bit_length() - 1
+            if bit in pivots:
+                x ^= pivots[bit]
+            else:
+                pivots[bit] = x
+                break
+    for bit in sorted(pivots):
+        for upper in pivots:
+            if upper > bit and pivots[upper] >> bit & 1:
+                pivots[upper] ^= pivots[bit]
+    return tuple(pivots[bit] for bit in sorted(pivots, reverse=True))
+
+
+def local_inventory(word, replay):
+    require((word['v'], word['h'], word['R']) == (V, H, R), 'local supplier dimensions')
+    frames = [basis(frame) for frame in word['frames']]
+    n = 2 * V + R
+    require(len(word['start']) == len(word['final']) == n, 'local frame vector lengths')
+    current = [frames[f] for f in word['start']]
+    paid = Counter()
+
+    def climb(register, frame):
+        require(basis(current[register] + frame) == frame, 'nonmonotone local frame')
+        jump = len(frame) - len(current[register])
+        if jump:
+            paid[jump] += 1
+        current[register] = frame
+
+    require(not word['target_levels'], 'this audit requires the current zero-level centre interface')
+    for section in ('A', 'B', 'tail'):
+        if section == 'B':
+            require(all(current[t] == () for t in range(V, 2 * V)), 'target centre level')
+            for q, frame_id in zip(word['centers'], word['center_frames']):
+                require(current[q] == frames[frame_id], 'centre carrier frame')
+                paid[len(frames[frame_id])] += 1
+        for gate in word[section]:
+            registers = gate[1:3] if gate[0] == 'add' else gate[1:2]
+            require(gate[0] in ('add', 'scale'), 'unknown scalar gate')
+            for register in registers:
+                climb(register, frames[gate[-1]])
+    for register, frame_id in enumerate(word['final']):
+        climb(register, frames[frame_id])
+    require(dict(paid) == {int(r): count for r, count in word['local_profile'].items()}, 'local paid-profile recount')
+    for orientation in ('forward', 'backward'):
+        require(dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}, 'local replay profile binding')
+    widths = [len(frames[word['final'][q]]) - len(frames[word['start'][q]]) for q in range(2 * V, n)]
+    require(Counter(widths) == {4: 56, 5: 32, 7: 30, 8: 122, 9: 240}, 'current supplier width inventory')
+    return widths, paid
+
+
+def make_context(parent, phases, ports, word, replay, roles):
+    widths, paid = local_inventory(word, replay)
+    require(len(parent['calls']) == 72 and {(c['stage'], c['replica']) for c in parent['calls']} == {(s, r) for s in range(9) for r in range(8)}, 'original eight-replica baseline calls')
+    require(len(roles) == 9 * T * R, 'complete helper role count')
+    address = {}
+    for role in roles:
+        key = (role['stage'], role['replica'])
+        time = role['time']
+        require(time not in address or address[time] == key, 'inconsistent invocation time address')
+        address[time] = key
+    require(set(address) == set(range(9 * T)), 'contiguous invocation times')
+    order = [address[t] for t in range(9 * T)]
+    require(set(order) == {(s, r) for s in range(9) for r in range(T)}, 'stage/replica inventory')
+    # Arbitrary interleaving: the exact per-replica projection is checked below.
+    rank = {child['child']: child['rank'] for child in parent['idle_children']}
+    source = parent['execution_schedule']
+    blocks, stage = {}, None
+    for index, event in enumerate(source):
+        if event['kind'] in ('bank_padding_cover_sweep', 'translate_every_live_family'):
+            continue
+        if event['kind'] == 'local_cover_sweep':
+            stage = event['stage']
+            blocks[stage] = []
+        require(stage is not None, 'source event before first invocation')
+        blocks[stage].append((index, event))
+    require(set(blocks) == set(range(9)), 'source stage inventory')
+    events = [(index, event, replica, time) for time, (stage, replica) in enumerate(order) for index, event in blocks[stage]]
+    projections = defaultdict(list)
+    for index, event, replica, time in events:
+        projections[replica].append(index)
+    require(set(projections) == set(range(T)) and all(p == list(range(30)) for p in projections.values()), 'per-replica source-event projection')
+    stage_pair = {e['stage']: e['pair'] for e in parent['recipe'] if e['kind'] == 'local'}
+    last, windows, callpos, child_pair, side = {}, {}, {}, {}, {}
+    bridges = 0
+    for position, (_, event, replica, _) in enumerate(events):
+        kind = event['kind']
+        if kind == 'local_cover_sweep':
+            stage = event['stage']
+            callpos[stage, replica] = position
+            last[replica, stage_pair[stage]] = position
+        elif kind == 'bridge':
+            last[replica, event['src']] = last[replica, event['dst']] = position
+            bridges += 1
+        elif kind == 'idle_cover_sweep':
+            for sd, child in enumerate(event['child_indices']):
+                if child in rank:
+                    windows[replica, child] = (last.get((replica, event['pair']), -1), position)
+                    child_pair[child], side[child] = event['pair'], sd
+    require(len(windows) == T * len(rank), 'actual window inventory')
+    require(len(ports) == V, 'port count')
+    bases = []
+    for q in ports:
+        zero = next(i for i in range(H) if not (q >> i & 1))
+        correction = q ^ (1 << zero)
+        axes = list(range(H))
+        axes[0], axes[zero] = axes[zero], axes[0]
+        frame = [(1 << i) ^ (correction if correction >> i & 1 else 0) for i in axes] + [1 << i for i in range(H, M)]
+        require(all((x & y).bit_count() % 2 == int(i == j) for i, x in enumerate(frame) for j, y in enumerate(frame)), 'nonorthogonal owner basis')
+        bases.append(frame)
+    return dict(widths=widths, paid=paid, order=order, at={key:t for t,key in enumerate(order)}, rank=rank,
+                windows=windows, callpos=callpos, child_pair=child_pair, side=side, stage_pair=stage_pair,
+                bases=bases, phases=phases, bridges=bridges, event_count=len(events), replay=replay)
+
+
+def check_pending_axes(context):
+    checked = 0
+    for port, frame in enumerate(context['bases']):
+        used = defaultdict(set)
+        for child, rank in context['rank'].items():
+            axes = list(map(int, context['phases']['recipes'][port]['idle_children'][child]['orthogonal_axes']))
+            require(len(axes) == rank and len(set(axes)) == rank and set(axes) <= set(frame),
+                    'pending child orthogonal basis')
+            family = context['child_pair'][child], context['side'][child]
+            require(not used[family] & set(axes), 'overlapping pending children on one family')
+            used[family].update(axes)
+            checked += 1
+    return checked
+
+
+def check_roles(context, roles):
+    c = context
+    live, physical = T * 8 * V, T * 8 * V + 8 + R + 2
+    require(len(roles) == 9 * T * R, 'complete helper role count')
+    helpers, families, used = defaultdict(set), defaultdict(set), defaultdict(set)
+    charts, chart_cache = set(), {}
+    for z in roles:
+        s, r, helper = z['stage'], z['replica'], z['helper']
+        owner, child, port = z['owner_replica'], z['child'], z['port']
+        offset, width, family = z['offset'], z['width'], z['family']
+        call = (s, r)
+        require(call in c['at'] and 0 <= helper < R and 0 <= owner < T and 0 <= port < V, 'role coordinates')
+        require(z['time'] == c['at'][call], 'role invocation time')
+        require(width == c['widths'][helper], 'whole-helper residual width')
+        require(0 <= family < live, 'private-namespace collision')
+        require(child in c['rank'], 'unknown idle child')
+        require(z['copy'] == V * owner + port and family == owner * 896 + (2 * c['child_pair'][child] + c['side'][child]) * V + port, 'physical family identity')
+        lo, hi = c['windows'][owner, child]
+        require(lo < c['callpos'][call] < hi, 'strict bridge-aware idle window')
+        require(family // 224 != r * 4 + c['stage_pair'][s], 'helper aliases active data pair')
+        require(helper not in helpers[call] and family not in families[call], 'duplicate helper or family within whole invocation')
+        helpers[call].add(helper)
+        families[call].add(family)
+        cells = set(range(offset, offset + width))
+        bin_key = (owner, child, port)
+        require(offset >= 0 and offset + width <= c['rank'][child] and not used[bin_key] & cells, 'overlapping or out-of-capacity slice')
+        used[bin_key].update(cells)
+        chart_key = (port, child, offset, width)
+        if chart_key not in chart_cache:
+            frame = c['bases'][port]
+            pending = list(map(int, c['phases']['recipes'][port]['idle_children'][child]['orthogonal_axes']))
+            require(len(pending) == c['rank'][child], 'phase child rank')
+            occupied = [frame.index(x) for x in pending[offset:offset + width]]
+            spectators = [i for i in range(M) if i not in occupied][:H - width]
+            permutation = occupied + spectators + [i for i in range(M) if i not in occupied and i not in spectators]
+            require(len(occupied) == width and len(set(occupied + spectators)) == H and sorted(permutation) == list(range(M)), 'residual/spectator permutation')
+            require([frame[i] for i in permutation[:width]] == pending[offset:offset + width], 'pending-axis binding')
+            chart_cache[chart_key] = tuple(frame[i] for i in permutation)
+        charts.add(chart_cache[chart_key])
+    require(set(helpers) == set(c['order']) and all(h == set(range(R)) for h in helpers.values()), 'complete per-call helper inventory')
+    idle = Counter()
+    for owner, child in c['windows']:
+        for port in range(V):
+            cells = used[owner, child, port]
+            require(cells == set(range(len(cells))), 'gap in pending prefix')
+            left = c['rank'][child] - len(cells)
+            if left:
+                idle[left] += 1
+    require(dict(idle) == EXPECTED_IDLE, 'nominated idle profile')
+    profile = Counter({rank: 9 * T * count for rank, count in c['paid'].items()})
+    profile.update(idle)
+    mass = sum(rank * count for rank, count in profile.items())
+    require(M * live - mass == 320*T, 'replica-scaled rank deficit')
+    require(c['bridges'] == 9*T, 'actual bridge count')
+    localbits = max(x['prefix_bits_upper'] for x in c['replay']['local'].values())
+    prefix = localbits + (M + 1) // 2 + len(c['order']) + c['bridges'] + 4
+    group = 2 ** (36 * 36)
+    for i in range(1, 37):
+        group *= 2 ** (2 * i) - 1
+    stock = group * physical
+    row = 2 * stock.bit_length() + 9909 + 252 + 2 * 1024
+    require(prefix < 1024, 'prefix reserve')
+    require(row < 20161 and M * M > 2 * max(profile) ** 2, 'row or halving reserve')
+    return dict(status='PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW', roles=len(roles), calls=len(c['order']),
+                source_events_per_replica=30, expanded_replica_events=c['event_count'], bridge_events=c['bridges'],
+                literal_windows=len(c['windows']), checked_whole_helper_widths=len(roles), checked_busy_family_windows=len(roles),
+                orthogonal_port_bases=len(c['bases']), actual_73_axis_charts=len(charts), checked_slice_prefixes=len(c['windows']) * V,
+                local_profile=dict(sorted(c['paid'].items())), width_inventory=dict(sorted(Counter(c['widths']).items())),
+                idle=dict(sorted(idle.items())), profile=dict(sorted(profile.items())), live=live, physical=physical,
+                rank_mass=mass, deficit=320*T, namespace={'data':[0,live], 'centres':[live,live+8], 'tableau':[live+8,live+8+R], 'coefficient':[live+8+R,physical]},
+                local_prefix_bits=localbits, local_prefix_from_native_receipt=True, local_profile_recounted=True,
+                prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], margin=4),
+                prefix_bits=prefix, charged_prefix_bits=1024, physical_stock_bits=stock.bit_length(),
+                physical_row_coefficient=row, row_limit=20161,
+                scope='Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.')
+
+
+def controls(context, roles):
+    candidates = []
+    first = roles[0]
+    bad = dict(first, family=896*T)
+    candidates.append(('private_namespace_collision', [bad] + roles[1:], 'private-namespace collision'))
+    index = next(i for i, z in enumerate(roles) if z['replica'] >= 1)
+    bad = dict(roles[index], replica=roles[index]['replica'] - 1)
+    candidates.append(('copy_replica_alias', [bad] + roles[:index] + roles[index+1:], 'role invocation time'))
+    candidates.append(('missing_whole_helper', roles[1:], 'complete helper role count'))
+    split = dict(first, width=first['width'] - 1)
+    fragment = dict(first, offset=first['offset'] + first['width'] - 1, width=1)
+    candidates.append(('split_whole_helper', [split, fragment] + roles[1:], 'complete helper role count'))
+    candidates.append(('truncated_helper_width', [split] + roles[1:], 'whole-helper residual width'))
+    # Keep the family and chart valid, but move one complete role past its
+    # actual idle event. Freeze the original invocation order for controls.
+    crossing = None
+    for index, z in enumerate(roles):
+        lo, hi = context['windows'][z['owner_replica'], z['child']]
+        later = next((key for key in context['order'] if context['callpos'][key] >= hi), None)
+        if later is not None:
+            crossing = [dict(z, stage=later[0], replica=later[1], time=context['at'][later])] + roles[:index] + roles[index+1:]
+            break
+    require(crossing is not None, 'no idle-boundary control could be constructed')
+    candidates.append(('cross_idle_boundary', crossing, 'strict bridge-aware idle window'))
+    rejected = []
+    for name, bad, expected in candidates:
+        try:
+            check_roles(context, bad)
+        except ValueError as exc:
+            require(str(exc) == expected, 'control rejected at unexpected predicate: ' + name)
+            rejected.append(dict(name=name, reason=str(exc)))
+        else:
+            raise ValueError('accepted negative control: ' + name)
+    bad = dict(context, phases=copy.deepcopy(context['phases']))
+    pair = next((a, b) for a in context['rank'] for b in context['rank']
+                if a < b and (context['child_pair'][a], context['side'][a]) ==
+                (context['child_pair'][b], context['side'][b]))
+    children = bad['phases']['recipes'][0]['idle_children']
+    children[pair[1]]['orthogonal_axes'][0] = children[pair[0]]['orthogonal_axes'][0]
+    try:
+        check_pending_axes(bad)
+    except ValueError as exc:
+        require(str(exc) == 'overlapping pending children on one family',
+                'pending-axis control rejected at unexpected predicate')
+        rejected.append(dict(name='cross_child_pending_axis_alias', reason=str(exc)))
+    else:
+        raise ValueError('accepted negative control: cross_child_pending_axis_alias')
+    return rejected
+
+
+def main():
+    global T, EXPECTED_IDLE
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--baseline-parent', type=Path, required=True)
+    parser.add_argument('--owners', type=Path, required=True)
+    parser.add_argument('--word', type=Path, required=True)
+    parser.add_argument('--phases', type=Path)
+    parser.add_argument('--local-replay', type=Path)
+    parser.add_argument('--out', type=Path, required=True)
+    parser.add_argument("--replicas", type=int, required=True)
+    parser.add_argument("--expected-idle", required=True)
+    args = parser.parse_args()
+    T = args.replicas
+    require(T == 37, "replica range")
+    EXPECTED_IDLE = {int(k): v for k,v in json.loads(args.expected_idle).items()}
+    phases_path = args.phases or args.baseline_parent.parent.parent / 'work/complex-nine-native/DATA-PHASES.json'
+    canonical_path = args.baseline_parent.parent / 'CANONICAL-WORD.json.gz'
+    replay_path = args.local_replay or args.word.parent / 'INDEPENDENT-LOCAL-REPLAY.json'
+    parent, phases, canonical, word, replay, roles = map(read, (args.baseline_parent, phases_path, canonical_path, args.word, replay_path, args.owners))
+    require(replay['status'] == 'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY', 'local replay status')
+    require(replay['canonical_word_sha256'] == filehash(args.word), 'local word/replay hash binding')
+    require(set(replay['local']) == {'forward', 'backward'}, 'both native prefix orientations')
+    require(word['ports'] == canonical['ports'], 'local/controller port interface')
+    require(len(word['center_frames']) == len(canonical['center_frames']) == 8, 'eight centre interfaces')
+    require([basis(word['frames'][f]) for f in word['center_frames']] == [basis(canonical['frames'][f]) for f in canonical['center_frames']], 'ordered centre-frame interface')
+    context = make_context(parent, phases, canonical['ports'], word, replay, roles)
+    pending = check_pending_axes(context)
+    receipt = check_roles(context, roles)
+    receipt['disjoint_pending_child_axis_checks'] = pending
+    receipt['controls_rejected'] = controls(context, roles)
+    receipt['input_sha256'] = {str(path): filehash(path) for path in (args.baseline_parent, phases_path, canonical_path, args.word, replay_path, args.owners)}
+    args.out.write_text(json.dumps(receipt, indent=2) + '\n', encoding='utf-8')
+    print(receipt['status'], 'roles=' + str(receipt['roles']), 'controls=' + str(len(receipt['controls_rejected'])))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/r480-owner-optimum/inputs/PLAN.json b/research/r480-owner-optimum/inputs/PLAN.json
new file mode 100644
index 0000000000..d5bc63d31b
--- /dev/null
+++ b/research/r480-owner-optimum/inputs/PLAN.json
@@ -0,0 +1,85660 @@
+{
+  "status": "FROZEN_EXPLICIT_T16_TWO_BANK_DIRECT_SUM_OWNER_NOMINATION",
+  "mode": "gauge44-all144-t16-idle-concentration",
+  "K": 4,
+  "T": 16,
+  "M": 73,
+  "L": 9,
+  "live": 14336,
+  "deficit": 5120,
+  "profile": {
+    "1": 349602,
+    "2": 60193,
+    "3": 62592,
+    "4": 20448,
+    "5": 11808,
+    "7": 4,
+    "8": 1152,
+    "48": 4866
+  },
+  "order": [
+    [
+      0,
+      0
+    ],
+    [
+      0,
+      8
+    ],
+    [
+      0,
+      1
+    ],
+    [
+      0,
+      9
+    ],
+    [
+      1,
+      0
+    ],
+    [
+      1,
+      8
+    ],
+    [
+      0,
+      2
+    ],
+    [
+      0,
+      10
+    ],
+    [
+      1,
+      1
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+    [
+      1,
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+    ],
+    [
+      2,
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+    ],
+    [
+      2,
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+    ],
+    [
+      0,
+      3
+    ],
+    [
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+    ],
+    [
+      1,
+      2
+    ],
+    [
+      1,
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+    [
+      2,
+      1
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+    [
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+    [
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+    [
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+    [
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+    [
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+    [
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+    [
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+    [
+      2,
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+    [
+      2,
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+    [
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+    [
+      3,
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+    [
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+    [
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+    [
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+    ],
+    [
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+    [
+      6,
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+    [
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+    [
+      7,
+      5
+    ],
+    [
+      7,
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+    [
+      8,
+      4
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+    [
+      8,
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+    [
+      6,
+      7
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+    [
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+    [
+      7,
+      6
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+    [
+      7,
+      14
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+    [
+      8,
+      5
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diff --git a/research/r480-owner-optimum/inputs/PR589-EXPECTED.json b/research/r480-owner-optimum/inputs/PR589-EXPECTED.json
new file mode 100644
index 0000000000..e293ddc557
--- /dev/null
+++ b/research/r480-owner-optimum/inputs/PR589-EXPECTED.json
@@ -0,0 +1,222 @@
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+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_lower_decimal": "0.001733427039589844234749",
+  "profile": {
+   "1": 381024,
+   "2": 400416,
+   "3": 22752,
+   "4": 26880,
+   "5": 29376,
+   "6": 17376,
+   "7": 26784,
+   "42": 288
+  },
+  "bit": {
+   "live": 28416,
+   "physical": 28425,
+   "maxchild": 42,
+   "rank_mass": 1808352,
+   "hosted_residuals": 126432,
+   "bank_assignments": 0,
+   "prefix_bits": 177,
+   "charged_prefix_bits": 192,
+   "coefficient_bits": 177,
+   "two_level_coefficient_bits": 393,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "eleven": {
+  "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting), parameterised by PR #545's code/adapt.py",
+  "bit_lower": "855475950388791987811/500000000000000000000000",
+  "bit_lower_decimal": "0.001710951900777583975622",
+  "profile": {
+   "1": 116424,
+   "2": 121648,
+   "3": 6952,
+   "4": 7424,
+   "5": 8976,
+   "6": 4520,
+   "7": 8776,
+   "56": 2600
+  },
+  "bit": {
+   "live": 8880,
+   "physical": 8889,
+   "maxchild": 56,
+   "rank_mass": 689304,
+   "hosted_residuals": 38632,
+   "prefix_bits": 4304,
+   "charged_prefix_bits": 4352,
+   "coefficient_bits": 4304,
+   "three_level_coefficient_bits": 12966,
+   "charged_three_level_coefficient_bits": 12992,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "793b6f40c9aa4b8db57fec0ac0973e16884dae28707e482ee8f7a2349a5d5a4b",
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "base": {
+  "nine_bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "nine_bit_lower_decimal": "0.001733052823330162099157",
+  "eleven_bit_lower": "427652201524503168379/250000000000000000000000",
+  "eleven_bit_lower_decimal": "0.001710608806098012673516",
+  "note": "PR #555's EXPECTED.json (untuned word); the tune/ pipeline is the same, with the same frozen hosting selections"
+ }
+}
diff --git a/research/r480-owner-optimum/inputs/RESULT.json b/research/r480-owner-optimum/inputs/RESULT.json
new file mode 100644
index 0000000000..c34aef055f
--- /dev/null
+++ b/research/r480-owner-optimum/inputs/RESULT.json
@@ -0,0 +1,109 @@
+{
+  "status": "PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY",
+  "kappa": "66906048756761/40000000000000000",
+  "kappa_decimal": "0.001672651218919025",
+  "conservative_kappa_decimal": "0.001672651216067113",
+  "complex_lower": "67018146741598030641/40000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "complex_profile": {
+    "1": 349602,
+    "2": 60193,
+    "3": 62592,
+    "4": 20448,
+    "5": 11808,
+    "7": 4,
+    "8": 1152,
+    "48": 4866
+  },
+  "idle_remainder_profile": {
+    "1": 2274,
+    "2": 1,
+    "3": 384,
+    "7": 4,
+    "48": 4866
+  },
+  "complete_invocations": 144,
+  "roles": 69120,
+  "prefix_bits": 397,
+  "charged_prefix_bits": 512,
+  "physical_row_coefficient": 16469,
+  "retained_row_coefficient": 20161,
+  "actual_73_axis_charts": 10200,
+  "controls": {
+    "admission": 69,
+    "bit_supplier": 12,
+    "independent_t16": 6,
+    "controller_mutations": 15
+  },
+  "t8_kappa": "167166528321877/100000000000000000",
+  "spec_sha256": "7f5f710df21fe48079b4c79727953ff41cd8bec688592578554109ebf6b6d929",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 3.719,
+      "exit_code": 0,
+      "log_sha256": "3aea2a4b68e7aaeadd9ffef649be0d25e2dff1535d9a61bffeaf6d92e55ba6a8"
+    },
+    {
+      "name": "bind8",
+      "seconds": 0.922,
+      "exit_code": 0,
+      "log_sha256": "78a081673d6b4fde10a86e6f767d53648b868d1f0cac2441d12951434ad7341b"
+    },
+    {
+      "name": "lift16",
+      "seconds": 4.437,
+      "exit_code": 0,
+      "log_sha256": "f38fc6d2a39b8779e04f7c787c4d668c2f9e359a1de069b63a6c177a9ca9b2bc"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.734,
+      "exit_code": 0,
+      "log_sha256": "78a081673d6b4fde10a86e6f767d53648b868d1f0cac2441d12951434ad7341b"
+    },
+    {
+      "name": "emit",
+      "seconds": 10.468,
+      "exit_code": 0,
+      "log_sha256": "67bc257d4a163312137b43eef4270bffca031b565e7221e96c476216ee007565"
+    },
+    {
+      "name": "audit",
+      "seconds": 59.969,
+      "exit_code": 0,
+      "log_sha256": "089b0fa21e04d000d0601c61895aa5adfeacdc9fcd192ea1ef859ad48ef8f1cd"
+    },
+    {
+      "name": "invoice",
+      "seconds": 3.343,
+      "exit_code": 0,
+      "log_sha256": "caa1229b78eca961462d35e8ee458be536111111a985294a153e4dd74b9171a8"
+    },
+    {
+      "name": "assembly",
+      "seconds": 1.156,
+      "exit_code": 0,
+      "log_sha256": "eee609c93b4647fc340f4041ba763ced4d2df47cb94dd3d7ed83ceb3005b56ce"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 1.391,
+      "exit_code": 0,
+      "log_sha256": "34527ddfe1e53bec71dc5759eb9a26417be6d4e93e76cbf80575d9bafebd876b"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 1.703,
+      "exit_code": 0,
+      "log_sha256": "c648542cd6dddbb154af7d02a41aaed1025603d9a4ab54f7c249d2b683e22249"
+    },
+    {
+      "name": "independent-t16",
+      "seconds": 3.062,
+      "exit_code": 0,
+      "log_sha256": "d2c13b333d463a5c2de42078e9c47a89209075e1d1beac24cf3fc1f573f18c05"
+    }
+  ],
+  "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. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. 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."
+}
diff --git a/research/r480-owner-optimum/inputs/SPEC.json b/research/r480-owner-optimum/inputs/SPEC.json
new file mode 100644
index 0000000000..482797694f
--- /dev/null
+++ b/research/r480-owner-optimum/inputs/SPEC.json
@@ -0,0 +1,1973 @@
+{
+  "schema": "witness-spec/1",
+  "name": "gauge44-t16-two-bank",
+  "data": {
+    "plan_sha256": "68c110602df12bd7de3749514224021ef1ef0ebcf072d7c727f9b66099fbebb1",
+    "owners_sha256": "2e1252f4e459bb957160e36715b212f3670d50979666d8496b99f39a50142271"
+  },
+  "dispatch": [
+    [
+      0,
+      0,
+      "gauge44"
+    ],
+    [
+      0,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      1,
+      "gauge44"
+    ],
+    [
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+      9,
+      "gauge44"
+    ],
+    [
+      1,
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+      "gauge44"
+    ],
+    [
+      1,
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+      "gauge44"
+    ],
+    [
+      0,
+      2,
+      "gauge44"
+    ],
+    [
+      0,
+      10,
+      "gauge44"
+    ],
+    [
+      1,
+      1,
+      "gauge44"
+    ],
+    [
+      1,
+      9,
+      "gauge44"
+    ],
+    [
+      2,
+      0,
+      "gauge44"
+    ],
+    [
+      2,
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+      "gauge44"
+    ],
+    [
+      0,
+      3,
+      "gauge44"
+    ],
+    [
+      0,
+      11,
+      "gauge44"
+    ],
+    [
+      1,
+      2,
+      "gauge44"
+    ],
+    [
+      1,
+      10,
+      "gauge44"
+    ],
+    [
+      2,
+      1,
+      "gauge44"
+    ],
+    [
+      2,
+      9,
+      "gauge44"
+    ],
+    [
+      3,
+      0,
+      "gauge44"
+    ],
+    [
+      3,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      4,
+      "gauge44"
+    ],
+    [
+      0,
+      12,
+      "gauge44"
+    ],
+    [
+      1,
+      3,
+      "gauge44"
+    ],
+    [
+      1,
+      11,
+      "gauge44"
+    ],
+    [
+      2,
+      2,
+      "gauge44"
+    ],
+    [
+      2,
+      10,
+      "gauge44"
+    ],
+    [
+      3,
+      1,
+      "gauge44"
+    ],
+    [
+      3,
+      9,
+      "gauge44"
+    ],
+    [
+      4,
+      0,
+      "gauge44"
+    ],
+    [
+      4,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      5,
+      "gauge44"
+    ],
+    [
+      0,
+      13,
+      "gauge44"
+    ],
+    [
+      1,
+      4,
+      "gauge44"
+    ],
+    [
+      1,
+      12,
+      "gauge44"
+    ],
+    [
+      2,
+      3,
+      "gauge44"
+    ],
+    [
+      2,
+      11,
+      "gauge44"
+    ],
+    [
+      3,
+      2,
+      "gauge44"
+    ],
+    [
+      3,
+      10,
+      "gauge44"
+    ],
+    [
+      4,
+      1,
+      "gauge44"
+    ],
+    [
+      4,
+      9,
+      "gauge44"
+    ],
+    [
+      5,
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
+      0,
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+      "gauge44"
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+    [
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+      "gauge44"
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+    [
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+    [
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+    [
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+      "gauge44"
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+    [
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+    [
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+      "gauge44"
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+    [
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+      "gauge44"
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+    [
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+      "gauge44"
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+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
+      0,
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+      "gauge44"
+    ],
+    [
+      0,
+      15,
+      "gauge44"
+    ],
+    [
+      6,
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+      "gauge44"
+    ],
+    [
+      6,
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+      "gauge44"
+    ],
+    [
+      1,
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+      "gauge44"
+    ],
+    [
+      1,
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
+      3,
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+      "gauge44"
+    ],
+    [
+      4,
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+      "gauge44"
+    ],
+    [
+      4,
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+      "gauge44"
+    ],
+    [
+      5,
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+      "gauge44"
+    ],
+    [
+      5,
+      10,
+      "gauge44"
+    ],
+    [
+      6,
+      1,
+      "gauge44"
+    ],
+    [
+      6,
+      9,
+      "gauge44"
+    ],
+    [
+      1,
+      7,
+      "gauge44"
+    ],
+    [
+      1,
+      15,
+      "gauge44"
+    ],
+    [
+      7,
+      0,
+      "gauge44"
+    ],
+    [
+      7,
+      8,
+      "gauge44"
+    ],
+    [
+      2,
+      6,
+      "gauge44"
+    ],
+    [
+      2,
+      14,
+      "gauge44"
+    ],
+    [
+      3,
+      5,
+      "gauge44"
+    ],
+    [
+      3,
+      13,
+      "gauge44"
+    ],
+    [
+      4,
+      4,
+      "gauge44"
+    ],
+    [
+      4,
+      12,
+      "gauge44"
+    ],
+    [
+      5,
+      3,
+      "gauge44"
+    ],
+    [
+      5,
+      11,
+      "gauge44"
+    ],
+    [
+      6,
+      2,
+      "gauge44"
+    ],
+    [
+      6,
+      10,
+      "gauge44"
+    ],
+    [
+      7,
+      1,
+      "gauge44"
+    ],
+    [
+      7,
+      9,
+      "gauge44"
+    ],
+    [
+      2,
+      7,
+      "gauge44"
+    ],
+    [
+      2,
+      15,
+      "gauge44"
+    ],
+    [
+      8,
+      0,
+      "gauge44"
+    ],
+    [
+      8,
+      8,
+      "gauge44"
+    ],
+    [
+      3,
+      6,
+      "gauge44"
+    ],
+    [
+      3,
+      14,
+      "gauge44"
+    ],
+    [
+      4,
+      5,
+      "gauge44"
+    ],
+    [
+      4,
+      13,
+      "gauge44"
+    ],
+    [
+      5,
+      4,
+      "gauge44"
+    ],
+    [
+      5,
+      12,
+      "gauge44"
+    ],
+    [
+      6,
+      3,
+      "gauge44"
+    ],
+    [
+      6,
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
+      7,
+      10,
+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
+      4,
+      14,
+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
+      5,
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
+      6,
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
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+      "gauge44"
+    ],
+    [
+      5,
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+      "gauge44"
+    ],
+    [
+      5,
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+      "gauge44"
+    ],
+    [
+      6,
+      6,
+      "gauge44"
+    ],
+    [
+      6,
+      14,
+      "gauge44"
+    ],
+    [
+      7,
+      5,
+      "gauge44"
+    ],
+    [
+      7,
+      13,
+      "gauge44"
+    ],
+    [
+      8,
+      4,
+      "gauge44"
+    ],
+    [
+      8,
+      12,
+      "gauge44"
+    ],
+    [
+      6,
+      7,
+      "gauge44"
+    ],
+    [
+      6,
+      15,
+      "gauge44"
+    ],
+    [
+      7,
+      6,
+      "gauge44"
+    ],
+    [
+      7,
+      14,
+      "gauge44"
+    ],
+    [
+      8,
+      5,
+      "gauge44"
+    ],
+    [
+      8,
+      13,
+      "gauge44"
+    ],
+    [
+      7,
+      7,
+      "gauge44"
+    ],
+    [
+      7,
+      15,
+      "gauge44"
+    ],
+    [
+      8,
+      6,
+      "gauge44"
+    ],
+    [
+      8,
+      14,
+      "gauge44"
+    ],
+    [
+      8,
+      7,
+      "gauge44"
+    ],
+    [
+      8,
+      15,
+      "gauge44"
+    ]
+  ],
+  "call_order": [
+    [
+      0,
+      0
+    ],
+    [
+      0,
+      8
+    ],
+    [
+      0,
+      1
+    ],
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+          "macros": 19693,
+          "real_component_primitives": 198766,
+          "prefix_l1": "2765345294379392599/1024",
+          "coefficient_work_primitive_count": 98333
+        },
+        "backward": {
+          "events": 24767,
+          "macros": 19693,
+          "real_component_primitives": 198814,
+          "prefix_l1": "14824960514781440791821/64",
+          "coefficient_work_primitive_count": 98365
+        }
+      },
+      "wrappers": 240
+    }
+  },
+  "expected": {
+    "gain_baseline_kappa": "0.001636241501576388",
+    "hosted_residuals": 69120,
+    "rank_mass": 1041408,
+    "actual_73column_sigmas": 10200,
+    "cross_replica_helper_roles": 58061,
+    "idle_remainders": 7529,
+    "idle_remainder_profile": {
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+      "2": 1,
+      "3": 384,
+      "7": 4,
+      "48": 4866
+    },
+    "global_profile": {
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+      "2": 60193,
+      "3": 62592,
+      "4": 20448,
+      "5": 11808,
+      "7": 4,
+      "8": 1152,
+      "48": 4866
+    },
+    "live": 14336,
+    "physical": 14826,
+    "conservative_kappa_decimal": "0.001672651216067113",
+    "kappa_decimal": "0.001672651218919025",
+    "complex_lower": "67018146741598030641/40000000000000000000000",
+    "conservative_complex_lower": "335090733135694858631/200000000000000000000000",
+    "kappa": "66906048756761/40000000000000000",
+    "assembly_controls_rejected": 69,
+    "provider_counts": {
+      "gauge44": 144
+    },
+    "mutations_rejected": 15
+  },
+  "pivot_swap": {
+    "recipe": "construction/leaver/PIVOT-SWAP-k8.json",
+    "sha256": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb"
+  }
+}
diff --git a/research/r480-owner-optimum/inputs/local/CANONICAL-WORD.json.gz b/research/r480-owner-optimum/inputs/local/CANONICAL-WORD.json.gz
new file mode 100644
index 0000000000..5f9ef68098
Binary files /dev/null and b/research/r480-owner-optimum/inputs/local/CANONICAL-WORD.json.gz differ
diff --git a/research/r480-owner-optimum/inputs/local/CLIFFORD-RECIPES.json b/research/r480-owner-optimum/inputs/local/CLIFFORD-RECIPES.json
new file mode 100644
index 0000000000..552286d316
--- /dev/null
+++ b/research/r480-owner-optimum/inputs/local/CLIFFORD-RECIPES.json
@@ -0,0 +1 @@
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diff --git a/research/r480-owner-optimum/inputs/local/CLIFFORD-REVIEW.json b/research/r480-owner-optimum/inputs/local/CLIFFORD-REVIEW.json
new file mode 100644
index 0000000000..e93d41a899
--- /dev/null
+++ b/research/r480-owner-optimum/inputs/local/CLIFFORD-REVIEW.json
@@ -0,0 +1,19 @@
+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
+  "canonical_word_sha256": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+  "frames": 1004,
+  "directed_edges": 2896,
+  "ranks": {
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+    "3": 408,
+    "8": 16,
+    "4": 124,
+    "5": 40
+  },
+  "endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+  "seconds": 339.10877466667444,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations."
+}
diff --git a/research/r480-owner-optimum/inputs/local/FULL-WORD.json.gz b/research/r480-owner-optimum/inputs/local/FULL-WORD.json.gz
new file mode 100644
index 0000000000..723decbca8
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diff --git a/research/r480-owner-optimum/inputs/local/INDEPENDENT-LOCAL-REPLAY.json b/research/r480-owner-optimum/inputs/local/INDEPENDENT-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..51603cca3f
--- /dev/null
+++ b/research/r480-owner-optimum/inputs/local/INDEPENDENT-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+  "local_programs_sha256": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+  "v": 112,
+  "helpers": 480,
+  "local": {
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+      "prefix_l1_upper": "2765345294379392599/1024",
+      "prefix_bits_upper": 52,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    },
+    "backward": {
+      "all_exact_columns": 704,
+      "prefix_l1_upper": "14824960514781440791821/64",
+      "prefix_bits_upper": 68,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    }
+  },
+  "paid_profiles": {
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+      "4": 142,
+      "8": 8,
+      "3": 432,
+      "2": 418,
+      "5": 82
+    },
+    "backward": {
+      "1": 2412,
+      "4": 142,
+      "8": 8,
+      "3": 432,
+      "2": 418,
+      "5": 82
+    }
+  },
+  "entering_helpers": 192,
+  "cold_hyperplane_ended_helpers": 48,
+  "negative_controls_rejected": [
+    "wrong_scale",
+    "missing_center",
+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "hpe_pre_wrapper_resolved_to_full_recipe",
+    "hpe_post_wrapper_without_terminal_frame",
+    "hpe_post_wrapper_wrong_terminal_frame",
+    "hpe_tail_gate_at_full_frame",
+    "hpe_tail_climb_dropped",
+    "hpe_helper_exit_adapter_to_full",
+    "hpe_tail_gate_moved_into_full_cleanup",
+    "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+    "cold_hpe_pre_wrapper_dropped",
+    "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+    "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+    "cold_hpe_wrapper_with_nonzero_entrance",
+    "cold_hpe_post_wrapper_wrong_terminal_frame",
+    "cold_hpe_premix_gate_before_pre_wrapper"
+  ],
+  "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate."
+}
diff --git a/research/r480-owner-optimum/inputs/local/LOCAL-CHECKS.json b/research/r480-owner-optimum/inputs/local/LOCAL-CHECKS.json
new file mode 100644
index 0000000000..1b7664d822
--- /dev/null
+++ b/research/r480-owner-optimum/inputs/local/LOCAL-CHECKS.json
@@ -0,0 +1,36 @@
+{
+  "forward": {
+    "sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8",
+    "events": 24767,
+    "scalar_macros": 19693,
+    "real_component_primitive_bound": 198766,
+    "paid_profile": {
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+      "2": 418,
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+      "4": 142,
+      "5": 82,
+      "8": 8
+    },
+    "all_columns": 704,
+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  },
+  "backward": {
+    "sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23",
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+  "target_port_order_matches_baseline": true,
+  "seconds": 1.7840579589828849,
+  "scope": "Fresh exact forward and inverse-transpose scalar replay on every arbitrary input; all native frame chains and dyadic primitives. Phase lowering, wrappers, global owners and global assembly are separate.",
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+  ],
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+  ],
+  "refactored_cleanup_gates": 6796,
+  "refactored_cleanup": {
+    "cold_low_frame_ended_helpers": [
+      273,
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+    ],
+    "construction": "; G44Stack premix-only factored entering ends 554,555,566,567 (start frame [24]); G44Stack premix-only factored entering ends 586,588,531,543 (start frame [30]); CarrierBypass premix-only factored cold ends 513,574,575,573,581,582; CarrierBypass premix-only factored cold ends 572,583,580,512; CarrierBypass premix-only factored cold ends 500,501,311,498,510,327",
+    "entering_low_frame_ended_helpers": [
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+    ],
+    "exact_non_target_isolation_checked": true,
+    "forward_absorption_A_indices": [],
+    "forward_absorptions": 0,
+    "high_inverse": "dyadic_sparse_Gauss_Jordan",
+    "kind": "source_branch_gauge_and_retired_completion_cold44",
+    "lower_frame_gates": 81,
+    "new_cold_ends": 32,
+    "premix_gates": 1190,
+    "premix_target_writes": 0
+  }
+}
diff --git a/research/r480-owner-optimum/inputs/local/WRAPPER-CHECKS.json b/research/r480-owner-optimum/inputs/local/WRAPPER-CHECKS.json
new file mode 100644
index 0000000000..8b07253ef3
--- /dev/null
+++ b/research/r480-owner-optimum/inputs/local/WRAPPER-CHECKS.json
@@ -0,0 +1,396 @@
+{
+ "status": "PASS_RESIDUAL_WRAPPERS_ARE_EXACT",
+ "frames": 22,
+ "hyperplane_end_pairs": [
+  {
+   "frame": 0,
+   "terminal": 124,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
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+   "terminal": 153,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
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+   "entrance_rank": 0,
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+   "residual_width": 4
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+   "entrance_rank": 0,
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+   "residual_width": 4
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+  {
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+   "entrance_rank": 0,
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+  },
+  {
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+   "entrance_rank": 0,
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+   "residual_width": 4
+  },
+  {
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+   "terminal": 1000,
+   "entrance_rank": 0,
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+   "residual_width": 8
+  },
+  {
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+  {
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+   "entrance_rank": 0,
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+   "residual_width": 8
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+  {
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+   "residual_width": 7
+  }
+ ],
+ "cold_hyperplane_end_pairs": 12,
+ "wrappers_reject": [
+  "wrong global phase",
+  "wrong translation",
+  "wrong quadratic form",
+  "sides swapped",
+  "wrong width",
+  "hpe: U-wrapper decoded against a FULL ending",
+  "hpe: width misreported as 9 - dim E",
+  "hpe: wrong terminal hyperplane",
+  "hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}",
+  "hpe: wrong global phase",
+  "cold hpe: identity pre wrapper instead of R_{0,U}",
+  "cold hpe: identity post wrapper instead of L_{0,U}",
+  "cold hpe: no wrappers (cold FULL convention L = R = I)",
+  "cold hpe: U-wrapper decoded against a FULL ending",
+  "cold hpe: width misreported as 9",
+  "cold hpe: wrong terminal hyperplane",
+  "cold hpe: wrong global phase"
+ ],
+ "all_even_weight": false,
+ "all_totally_isotropic": false,
+ "detail": [
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+  }
+ ]
+}
diff --git a/research/r480-owner-optimum/lift.py b/research/r480-owner-optimum/lift.py
new file mode 100644
index 0000000000..7864acbe03
--- /dev/null
+++ b/research/r480-owner-optimum/lift.py
@@ -0,0 +1,178 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Build the fixed T37 bank envelope and its source-event windows."""
+import argparse
+import copy
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import importlib.util
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+
+
+def need(ok, reason):
+    if not ok:
+        raise ValueError(reason)
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+
+def canonical(value):
+    return json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+
+
+def identity(value):
+    return hashlib.sha256(canonical(value)).hexdigest()
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def write_gzip(path, value):
+    raw = bytearray(gzip.compress(canonical(value), mtime=0))
+    raw[9] = 255
+    path.write_bytes(raw)
+
+
+def lift(source):
+    need((source['live'], source['physical']) == (11704, 12218), 'T8 source stock')
+    data0, bank0, data, live = 7168, 4536, 33152, 55832
+    groups = (8, 8, 8, 8, 5)
+    target = copy.deepcopy(source)
+    target['calls'] = []
+    for call in source['calls']:
+        for group, lanes in enumerate(groups):
+            if call['replica'] >= lanes:
+                continue
+            new = copy.deepcopy(call)
+            new['replica'] += 8*group
+            new['owners'] = [[family+data0*group if family < data0 else
+                              data+group*bank0+family-data0, route]
+                             for family, route in new['owners']]
+            target['calls'].append(new)
+    for child in target['idle_children']:
+        need(child['replicas'] == 8, 'T8 idle multiplicity')
+        child['replicas'] = 37
+    for event in target['execution_schedule']:
+        if 'replicas' in event:
+            need(event['replicas'] == list(range(8)), 'T8 sweep multiplicity')
+            event['replicas'] = list(range(37))
+        if event['kind'] == 'bank_padding_cover_sweep':
+            event['families'] = [data, live]
+        elif event['kind'] == 'translate_every_live_family':
+            event.update(families=[0, live], charged_calls_per_cover=live)
+    target['bank_padding']['families'], target['bank_padding']['children'] = [], []
+    for group, lanes in enumerate(groups):
+        for child in source['bank_padding']['children']:
+            new = copy.deepcopy(child)
+            new['family'] = data+group*bank0+child['family']-data0
+            width, remainder = divmod(73-child['rank'], 8)
+            need(remainder == 0 and 1 <= width <= 9, 'dedicated bank width')
+            need(child['axis_indices'] == list(range(8*width, 73)), 'original complement indices')
+            need(list(map(int, child['orthogonal_axes'])) ==
+                 [1 << i for i in child['axis_indices']], 'original complement axes')
+            new.update(axis_indices=list(range(lanes*width, 73)), rank=73-lanes*width)
+            new['orthogonal_axes'] = [1 << i for i in new['axis_indices']]
+            target['bank_padding']['children'].append(new)
+            target['bank_padding']['families'].append(new['family'])
+    target['bank_padding']['semantics'] = (
+        'Each complement follows the complete calls in its bank group. '
+        'Final hosting removes all dedicated banks and their padding children.')
+    target['cover_final_correction'].update(families=[0, live], charged_calls_per_cover=live)
+    target['private_namespace'] = {key: [live+x-source['live'] for x in interval]
+                                  for key, interval in source['private_namespace'].items()}
+    target.update(live=live, physical=live+514, version='r480-t37-bank-envelope-v1')
+    target['route_semantics']['helper'] = (
+        'The bank group is replica//8. Each local lane is replica%8. '
+        'Residual and spectator routes retain their source coordinates.')
+    target['replica_lift'] = dict(groups=list(groups), replicas=37, data_stock=data,
+                                 bank_stock=22680, source_template_content_sha256=identity(source),
+                                 phase_recipe_unchanged=True)
+    return target
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--base', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    need(not args.out.exists(), 'Choose a new lift directory')
+    original = read(HERE / 'vendor/pr1074/T8/PLAN.json')
+    owner_path = HERE / 'OWNERS.json.gz'
+    owners, order = read(owner_path), read(HERE / 'ORDER.json')
+    source = read(args.base / 'split-centres/GLOBAL-TEMPLATE.json.gz')
+    need(source['exact_data_phase_recipe_sha256'] ==
+         sha(args.base / 'work/complex-nine-native/DATA-PHASES.json'), 'data phase binding')
+    module_path = HERE / 'vendor/pr1074/t16/build_parent.py'
+    spec = importlib.util.spec_from_file_location('source_windows', module_path)
+    windows_module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(windows_module)
+    need(windows_module.actual_windows(source, original['order'])[0] == original['windows'],
+         'T8 source window replay')
+    parent = lift(source)
+    windows, schedule = windows_module.actual_windows(parent, order)
+    used = defaultdict(set)
+    at = {tuple(key): time for time, key in enumerate(order)}
+    need(len(at) == 333 and len(owners) == 159840, 'complete call and helper inventory')
+    for role in owners:
+        need(role['time'] == at[role['stage'], role['replica']], 'role call time')
+        capacity, times = windows[f"{role['owner_replica']},{role['child']}"]
+        need(role['time'] in times, 'source-event window')
+        group = role['owner_replica'], role['child'], role['port']
+        cells = set(range(role['offset'], role['offset']+role['width']))
+        need(not (used[group] & cells) and max(cells) < capacity, 'whole-helper capacity')
+        used[group].update(cells)
+    idle = Counter()
+    for key, (capacity, _) in windows.items():
+        replica, child = map(int, key.split(','))
+        for port in range(112):
+            cells = used[replica, child, port]
+            need(cells == set(range(len(cells))), 'pending prefix')
+            if len(cells) < capacity:
+                idle[capacity-len(cells)] += 1
+    need(idle == {1: 5622, 48: 11302}, 'attaining idle profile')
+    local = {int(r): n for r, n in original['provider_registry']['gauge44']['actual_paid_profile'].items()}
+    profile = Counter({r: 333*n for r, n in local.items()})
+    profile.update(idle)
+    plan = copy.deepcopy(original)
+    plan.update(T=37, live=33152, deficit=11840, order=order, windows=windows,
+                profile={str(r): n for r, n in sorted(profile.items())},
+                status='FROZEN_EXPLICIT_R480_T37_OWNER_NOMINATION',
+                mode='seven-slot-k8-all-replica-optimum',
+                solver_status='Frozen exact pattern flow and bipartite matching decomposition', gap=None)
+    for field in ('provider_calls', 'per_call_widths'):
+        bycall = {(c['stage'], c['replica']): c for c in original[field]}
+        plan[field] = []
+        for time, (stage, replica) in enumerate(order):
+            call = copy.deepcopy(bycall[stage, replica % 8])
+            call['replica'] = replica
+            if 'time' in call:
+                call['time'] = time
+            plan[field].append(call)
+    plan['assignment_sha256'] = sha(owner_path)
+    plan['assignment_content_sha256'] = identity(owners)
+    plan['replica_lift'] = dict(groups=[8, 8, 8, 8, 5], source_replicas=8, replicas=37,
+                               parent_template_content_sha256=identity(parent),
+                               owners_file_sha256=sha(owner_path), schedule_content_sha256=identity(schedule),
+                               window_semantics='Strict physical source-event intervals, including bridges')
+    need(sum(r*n for r, n in profile.items()) == 73*33152-11840, 'T37 rank mass')
+    args.out.mkdir(parents=True)
+    write_gzip(args.out / 'GLOBAL-TEMPLATE.json.gz', parent)
+    (args.out / 'PLAN.json').write_text(json.dumps(plan, indent=2)+'\n')
+    receipt = dict(status='PASS_R480_T37_BANK_LIFT_AND_WINDOWS', calls=333, roles=159840,
+                   parent_live=55832, parent_physical=56346, bank_groups=[8,8,8,8,5],
+                   idle=dict(sorted(idle.items())), literal_windows=len(windows),
+                   parent_content_sha256=identity(parent), schedule_content_sha256=identity(schedule))
+    (args.out / 'PARENT-LIFT.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(receipt['status'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/r480-owner-optimum/replay.py b/research/r480-owner-optimum/replay.py
new file mode 100644
index 0000000000..35ece52ee0
--- /dev/null
+++ b/research/r480-owner-optimum/replay.py
@@ -0,0 +1,154 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Replay the fixed R480 T37 owner construction and its full finite invoice."""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import time
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def read(path):
+    return json.loads(path.read_text())
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def main():
+    need(not sys.flags.optimize, 'Retained checks require assertions')
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, default=ROOT)
+    parser.add_argument('--local', type=Path, default=HERE / 'inputs/local')
+    parser.add_argument('--work', type=Path, required=True)
+    parser.add_argument('--discover', action='store_true')
+    args = parser.parse_args()
+    main, local, work = args.main.resolve(), args.local.resolve(), args.work.resolve()
+    need(not work.exists(), 'Choose a new replay directory')
+    for relative, expected in read(HERE / 'SOURCE-FREEZE.json')['files'].items():
+        need(sha(HERE / relative) == expected, 'Package source changed: ' + relative)
+    upstream = main / 'research/complex-k492-owner-repair/vendor/multicold'
+    baseline = main / 'research/community-k492-audit/pr622/replay/baseline558'
+    source1074 = HERE / 'vendor/pr1074'
+    for relative, expected in read(source1074 / 'UPSTREAM-PINS.json').items():
+        need(sha(main / relative) == expected, 'Upstream dependency changed: ' + relative)
+    need(local.is_dir(), 'Native local directory is missing')
+    work.mkdir(parents=True)
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1',
+               PYTHONINTMAXSTRDIGITS='0', OPENBLAS_NUM_THREADS='1', OMP_NUM_THREADS='1',
+               MULTICOLD_SOURCE=str(upstream), GAIN_PR564_SOURCE=str(upstream))
+    for key in ('PYTHONOPTIMIZE', 'WITNESS_DISCOVER', 'WITNESS_RECORD', 'WITNESS_SPEC'):
+        env.pop(key, None)
+    stages = []
+
+    def run(name, script, *arguments, spec=None, discover=False):
+        started = time.monotonic()
+        command = [sys.executable, '-B', str(upstream / 'code/run_portable.py'),
+                   str(script), *map(str, arguments)]
+        childenv = dict(env)
+        if spec:
+            childenv['WITNESS_SPEC'] = str(spec)
+        if discover:
+            childenv.update(WITNESS_DISCOVER='1', WITNESS_RECORD=str(work / 'WITNESS-RECORD.jsonl'))
+        log = work / (name + '.log')
+        with log.open('w') as output:
+            result = subprocess.run(command, env=childenv, stdout=output, stderr=subprocess.STDOUT)
+        stages.append(dict(name=name, seconds=round(time.monotonic()-started, 3),
+                           exit_code=result.returncode, log_sha256=sha(log)))
+        (work / 'STAGES.json').write_text(json.dumps(stages, indent=2)+'\n')
+        need(result.returncode == 0, name + ' failed:\n' + log.read_text()[-6000:])
+        print('PASS', name, stages[-1]['seconds'], flush=True)
+
+    spec8 = source1074 / 'data/SPEC-T8.json'
+    run('restore-parent', source1074 / 'code/restore_parent.py', '--source', upstream,
+        '--baseline', baseline, '--out', work / 'parent558')
+    run('bind8', source1074 / 'code/bind_providers_portable.py', '--baseline', work / 'parent558',
+        '--provider', 'gauge44='+str(local), '--plan', source1074 / 'T8/PLAN.json',
+        '--out', work / 'global8', spec=spec8)
+    run('lift', HERE / 'lift.py', '--base', work / 'global8/base', '--out', work / 'lift')
+    plan = work / 'lift/PLAN.json'
+    if not args.discover:
+        need(read(plan) == read(HERE / 'data/PLAN.json'), 'Frozen T37 plan differs')
+    runtime = work / 'runtime'
+    (runtime / 'data').mkdir(parents=True)
+    shutil.copytree(source1074 / 'construction', runtime / 'construction')
+    specpath = runtime / 'data/SPEC.json'
+    if args.discover:
+        spec = read(spec8)
+        spec['name'] = 'r480-seven-slot-k8-t37-owner-optimum'
+        spec['call_order'] = read(HERE / 'ORDER.json')
+        spec['dispatch'] = [[s, r, 'gauge44'] for s, r in spec['call_order']]
+        spec['providers'] = {}
+        spec['expected'] = {'gain_baseline_kappa': spec['expected']['gain_baseline_kappa']}
+        spec['data'] = dict(plan_sha256=sha(plan), owners_sha256=sha(HERE / 'OWNERS.json.gz'))
+        specpath.write_text(json.dumps(spec, indent=2)+'\n')
+    else:
+        shutil.copyfile(HERE / 'data/SPEC.json', specpath)
+    parent = work / 'parent37'
+    shutil.copytree(work / 'parent558', parent)
+    shutil.copyfile(work / 'lift/GLOBAL-TEMPLATE.json.gz',
+                    parent / 'complex-global/base/split-centres/GLOBAL-TEMPLATE.json.gz')
+    code, global_ = HERE / 'code', work / 'global'
+    def stage(name, script, *arguments):
+        run(name, code / script, *arguments, spec=specpath, discover=args.discover)
+    stage('bind', 'bind_providers_portable.py', '--baseline', parent, '--provider',
+          'gauge44='+str(local), '--plan', plan, '--out', global_)
+    stage('emit', 'emit_allcold.py', '--base', global_ / 'base', '--owners', HERE / 'OWNERS.json.gz',
+          '--plan', global_ / 'PLAN.json', '--out', global_ / 'hosted')
+    stage('audit', 'audit_allcold.py', global_ / 'base', global_ / 'hosted',
+          global_ / 'audit/ASYNC-AUDIT.json', '--mutation-controls')
+    retained = upstream / 'vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json'
+    stage('invoice', 'invoice_allcold.py', '--base', global_ / 'base', '--hosted', global_ / 'hosted',
+          '--audit', global_ / 'audit', '--out', global_ / 'audit', '--retained-invoice', retained)
+    stage('assembly', 'assemble.py', upstream, global_, work / 'ASSEMBLY.json')
+    if args.discover:
+        run('freeze', code / 'freeze_spec.py', '--spec', specpath, '--discovery', work)
+    else:
+        for name, script, filename in [('admission-controls', 'assembly_controls.py', 'ADMISSION-CONTROLS.json'),
+                                        ('bit-controls', 'bit_supplier_controls.py', 'BIT-CONTROLS.json')]:
+            stage(name, script, '--source-package', upstream, '--owner', global_ / 'audit/OWNERS-AND-PROFILE.json',
+                  '--invoice', global_ / 'audit/PREFIX-AND-INVOICE.json', '--out', work / filename)
+    run('independent-owner', HERE / 'independent_owner.py', '--baseline-parent',
+        work / 'global8/base/split-centres/GLOBAL-TEMPLATE.json.gz', '--owners', HERE / 'OWNERS.json.gz',
+        '--word', local / 'CANONICAL-WORD.json.gz', '--out', work / 'INDEPENDENT-OWNER.json',
+        '--replicas', 37, '--expected-idle', '{"1":5622,"48":11302}')
+    assembly = read(work / 'ASSEMBLY.json')
+    owner = read(work / 'INDEPENDENT-OWNER.json')
+    invoice = read(global_ / 'audit/PREFIX-AND-INVOICE.json')
+    need(owner['profile'] == assembly['complex_profile'], 'Independent complete profile')
+    need(owner['prefix_bits'] == invoice['global_prefix_bits'] < 1024, 'Independent prefix bound')
+    need(owner['physical_row_coefficient'] == invoice['finite']['physical_row_coefficient'] < 20161,
+         'Independent physical row bound')
+    need(owner['roles'] == 159840 and owner['calls'] == 333 and owner['deficit'] == 11840,
+         'Complete fixed construction')
+    need(assembly['kappa_decimal'] == '0.00167409796990539', 'Attained bound')
+    if not args.discover:
+        admission, bit = read(work / 'ADMISSION-CONTROLS.json'), read(work / 'BIT-CONTROLS.json')
+        need(len(admission['rejected_controls']) == 69 and not admission['discovery_accepted_controls'],
+             'Complete strict admission controls')
+        need(len(bit['rejected_controls']) == 12, 'Complete bit controls')
+    receipt = dict(status='DISCOVERY_R480_T37' if args.discover else 'PASS_R480_T37_STRICT_FINITE_CONSTRUCTION',
+                   kappa=assembly['kappa'], kappa_decimal=assembly['kappa_decimal'],
+                   roles=159840, calls=333, prefix_bits=owner['prefix_bits'], charged_prefix_bits=1024,
+                   physical_row_coefficient=owner['physical_row_coefficient'],
+                   stages=stages, local_input_sha256={p.name: sha(p) for p in local.iterdir() if p.is_file()},
+                   scope='Finite owner, controller, chart, invoice and assembly replay. Local scalar and phase replay and inherited all-size obligations are recorded separately.')
+    (work / 'RESULT.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(receipt['status'], receipt['kappa_decimal'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/r480-owner-optimum/vendor/pr1074/LICENSE b/research/r480-owner-optimum/vendor/pr1074/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
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+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
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+
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+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
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+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
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+
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+
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+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
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+   limitations under the License.
diff --git a/research/r480-owner-optimum/vendor/pr1074/NOTICE.md b/research/r480-owner-optimum/vendor/pr1074/NOTICE.md
new file mode 100644
index 0000000000..30d0c8cd3c
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/NOTICE.md
@@ -0,0 +1,24 @@
+# Gauge44 attribution and scope
+
+New contributions by icekylinx, with OpenAI GPT-6 Astra assistance.
+Local review and packaging used OpenAI Codex. Apache-2.0 applies;
+the license is included. The full original PR635 notice is preserved as
+UPSTREAM-NOTICE.md and construction/UPSTREAM-NOTICE.md.
+
+The new contribution is the changed source-branch gauge and retired-row
+completion, source-carried coordinate totals, exact 44-cold-end realization,
+and explicit all72 whole-family assignment using concave capacity matching
+with integer majorization certificates. The center-carrier generalization
+retains the exact ordered common frames and complete native local contract.
+Independent local, price, interface and owner fixed-point checks are included.
+
+The construction retains the credited PR635 K-triangle and porting machinery,
+earlier joint-prefix/HPE/frame ancestry and icekylinx's prior factory work.
+#645 used the same cited PR543 bit supplier as PR635. This package (research/gauge44-leaver8) cites the merged PR589 bit supplier instead, with a derived rank-mass deficit (PROOF-NOTE-BIT.md); #645's retained PR543-based evidence is historical. It builds #645's word without K-triangles (PartialK) and stacks earlier community jp8 layers on it (G44Stack), adds the p6n ends (NoTriReopen), entrance promotions (BlockInvert) a read-set exchange (BRoute), chafreaky's #741 frames, JointXF's joint exchange, NewBArch's triangle-hybrid B rewrite and LeaverSAT's eight k8 leaver cells (with LeaverSAT2's frame re-optimisation); see README. All-size, realization,
+hosting, precision/tape, analytic-transfer and bit H1-H5 assumptions remain
+conditional. No upstream license, credit, source pin or AI disclosure is
+replaced by this notice.
+
+PR641 and PR642 were checked as concurrent reported frontier comparisons.
+Their endpoints and owner maps are not included here. See CONSTRUCTION.md,
+hosting/PROOF.md, independent/ and README.md for the exact contribution scope.
diff --git a/research/r480-owner-optimum/vendor/pr1074/T8/PLAN.json b/research/r480-owner-optimum/vendor/pr1074/T8/PLAN.json
new file mode 100644
index 0000000000..0465492a1f
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/T8/PLAN.json
@@ -0,0 +1,40249 @@
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+      },
+      "orientation_program_sha256": {
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+        "backward": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+      },
+      "artifact_semantic_sha256": {
+        "CANONICAL-WORD.json.gz": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+        "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3",
+        "LOCAL-CHECKS.json": "18f09b79835aa352f04d27041d86d1338c5ad0094b888588c1c05af2dc399ffd",
+        "INDEPENDENT-LOCAL-REPLAY.json": "2d4680965c62db1fde1236c4857b19bf7bc97af58805e6b4109afbc452f0fdd8",
+        "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+        "CLIFFORD-REVIEW.json": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+        "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+      }
+    }
+  },
+  "source_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "assignment_sha256": "32ca30cd1c652ef6ad43657273a08a157e1df3545e759ab36306a0d0b516fb4a",
+  "source_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add"
+}
diff --git a/research/r480-owner-optimum/vendor/pr1074/UPSTREAM-NOTICE.md b/research/r480-owner-optimum/vendor/pr1074/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/r480-owner-optimum/vendor/pr1074/UPSTREAM-PINS.json b/research/r480-owner-optimum/vendor/pr1074/UPSTREAM-PINS.json
new file mode 100644
index 0000000000..68486b84e3
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/UPSTREAM-PINS.json
@@ -0,0 +1,23 @@
+{
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-RECIPES.json": "534ace870cabe515987e00f50f71550030965006ea18978e0924590ac6944345",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-REVIEW.json": "ee9b86428278392d2c933f76d60e51f5af90d4ab67e4d3937ed2fa416e7755ab",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-LOCAL-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INTEGRATION.json": "5c14538134dfffbc58fa4b4d2f26b270ec5f56d17d4bf23752c82964f45171db",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-CHECKS.json": "79177449e404403964ce1b2f4a9a8bd49e1916daba3123d7fd7f5cfd1f1ac0ea",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-PROGRAMS.json.gz": "99a18eede965accf65943e490b8d2b2ffb9f1c9bc6babdb825413a80cbea2cde",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/RESIDUAL-ADAPTERS.json": "baafef737acc16dafbe1150896feb16744f3d669fa123bb2bff19ecc4e71b275",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/SCALAR-FRAME-AUDIT.json": "73b3601a6239502475a272ea0c46945fd42034486aaf43e66a212eb4f012ca44",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/WRAPPER-CHECKS.json": "9a09146e686c4f535b04fdef3753fe01dad8f5e8881a69408a91394acb5b48f5",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "research/complex-k492-owner-repair/vendor/multicold/inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py": "f5eae94aca965d0008bc07cff8245ccb7509042ccad457d3bcb7d51c1e9409f0"
+}
diff --git a/research/r480-owner-optimum/vendor/pr1074/code/assemble.py b/research/r480-owner-optimum/vendor/pr1074/code/assemble.py
new file mode 100644
index 0000000000..581dd9cb29
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/assemble.py
@@ -0,0 +1,241 @@
+"""Gauge44 complete global admission with the retained 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 PR589 supplier (PR555's punctured
+R439 word, v = 111, decoder constant 63, two A-section transports), shipped
+as inputs/PR589-EXPECTED.json and pinned by git blob id. Its rank-mass
+deficit is derived from the word's parameters, T(2Kv - L*cst) at nine
+stages (PR545/PR555 rank-mass identity), not hard-coded. 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,SPOT,spot_widths
+# Cited bit supplier: PR589's tune/EXPECTED.json (merged on main as research/e8-bit-p111-tuned/tune/EXPECTED.json).
+BIT_PATH=Path(__file__).resolve().parents[1]/'inputs/PR589-EXPECTED.json'
+BIT_BLOB='e293ddc557742637f9f679f083a1a282d87b1b13'
+# Nine-stage bit template (PR463/PR510 chain, 32 replicas): L stages, T replicas, K=(L-1)//2 pairs, moment width M=1+7L.
+BIT_L,BIT_T=9,32;BIT_K=(BIT_L-1)//2;BIT_M=1+7*BIT_L
+def git_blob(data):return hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()
+def load_bit(data):
+ """The pinned supplier record: its full record (word parameters) and its nine-stage price."""
+ assert git_blob(data)==BIT_BLOB,'bit supplier blob pin'
+ return json.loads(data)
+def bit_deficit(word,live):
+ """Rank-mass deficit M*live - mass = T(2Kv - L*cst) of a v-port bit word with decoder constant cst (PR545/PR555).
+ cst is the sum of the retained totals' COPY ranks and live = 2KvT data wires; both are cross-checked here, and the
+ caller checks the result against the priced profile, so neither v nor cst is free."""
+ v,cst,ranks=word['v'],word['decoder_constant'],word['copy_ranks']
+ assert type(v)is int and type(cst)is int and all(type(r)is int and 0<r<=8 for r in ranks)
+ assert len(ranks)==word['retained_totals']==BIT_L and cst==sum(ranks)
+ assert live==2*BIT_K*v*BIT_T
+ d=BIT_T*(2*BIT_K*v-BIT_L*cst);assert d>0;return d
+
+
+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
+ # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+ R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==144*R==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']==144
+ assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+ assert invoice['centres']==8
+ assert invoice['physical_stock_identity']==dict(data_and_owner_families=14336,local_helpers=R,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']==R and p['centres']==8 and p['n']==2*112+R 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*R-p['entrance_rank']-p['terminal_codimension'] and len(p['widths'])==R   # HPE: widths |final|-|start|
+  pin(K+'width_digest',digest(p['widths']));assert tuple(p['widths'][h]for h in SPOT)==spot_widths()
+  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 in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):pin(K+'artifacts.'+name,p['artifacts'][name])
+  pin(K+'artifact_semantic_sha256',p['semantic_artifact_sha256'])
+  pin(K+'complete_contract',{k:v for k,v in p.items()if k!='artifacts'})
+  assert owner['provider_artifact_semantic_sha256'][pid]==p['semantic_artifact_sha256']
+  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']==2*112+R and z['dirty_helper_columns']==R
+   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']+p.get('cold_hyperplane_ended_helpers',0);pin(K+'wrappers',z['pre_wrappers'])   # COLD-HPE
+   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']+2*112+R+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)==144
+ 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(16)}
+ 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=23408,23922,32256
+ parent_banks,rem=divmod(parent_live-2*112*4*16,9);assert rem==0 and parent_physical==parent_live+504+8+2   # two independent bank groups, each with R0=504 helpers; restored private workspace is shared
+ assert owner['source_idle_children_charged']==parent_idle
+ bridges,shifts=2*112*144,4*112*16;moves=2*shifts
+ nonlocal_items=(4*112*16*9+2*112*16*9+2*144*R+parent_idle+9*parent_banks+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+(144*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+144+144+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_record=load_bit(BIT_PATH.read_bytes())
+ bit=bit_record['nine']
+ assert 'nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline']
+ c=Q(bit['bit_lower'])
+ bit_D=bit_deficit(bit_record['word'],bit['bit']['live'])
+ 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']==5120
+ 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()}
+ assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+ bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,5120,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,5120,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,'package:inputs/PR589-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_GAUGE44_NATIVE_EXACT_GLOBAL_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_pr635_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=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),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. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. 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/r480-owner-optimum/vendor/pr1074/code/assembly_controls.py b/research/r480-owner-optimum/vendor/pr1074/code/assembly_controls.py
new file mode 100644
index 0000000000..096ba9cdfe
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/assembly_controls.py
@@ -0,0 +1,260 @@
+"""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 + 144 + 144 + 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) if len(PIDS)>1 else '__unregistered__'
+        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 is not c and (d['provider_id'] != P or len(PIDS)==1) 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),
+        ]
+        if len(PIDS)==1:
+            # Cross-provider substitutions require a second actual supplier.
+            # All single-provider program, phase, profile and dispatch bindings
+            # retain their direct mutations above and in the controller audit.
+            partner_only = {P+':stale_partner_program_consistent_call_hashes',
+                            P+':stale_partner_profile_consistent_child_total',
+                            P+':relocated_against_partner_same_counts',
+                            P+':compensating_false_profiles_with_'+Qp}
+            controls = [(name, fn) for name, fn in controls if name not in partner_only]
+        # 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 SPOT:
+            def cold_swap(o, i, P=P, h=h):
+                w = i['providers'][P]['widths']; j = w.index(9 if w[h] != 9 else 8); w[h], w[j] = w[j], w[h]   # never the identity
+            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/r480-owner-optimum/vendor/pr1074/code/audit_allcold.py b/research/r480-owner-optimum/vendor/pr1074/code/audit_allcold.py
new file mode 100644
index 0000000000..923bf7b675
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/audit_allcold.py
@@ -0,0 +1,254 @@
+"""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 *
+from generated_identity import artifact_identities
+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={};artifact_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=[len(c['frames'][c['final'][2*c['v']+h]])-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths();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']
+ artifact_semantic_hashes[pid]=artifact_identities(p)
+ pin('providers.%s.artifact_semantic_sha256'%pid,artifact_semantic_hashes[pid])
+ phase_semantic_hashes[pid]=artifact_semantic_hashes[pid]['CLIFFORD-REVIEW.json']
+ for h,w in enumerate(widths):
+  assert 0<w<=c['h']
+  f=c['start'][2*c['v']+h];u=c['final'][2*c['v']+h]
+  # COLD-HPE: a cold helper (f == 0) may end below FULL too; its wrapper is the '0:U' recipe (E = bottom instance of #593)
+  if u!=1:   # HPE: wrapper for T_U T_E^-1, keyed 'E:U', rank |U|-|E|
+   a=adapters['%d:%d'%(f,u)]
+   assert a['frame']==f and a['terminal']==u and a['vectors']==c['frames'][f] and a['terminal_vectors']==c['frames'][u]
+   assert a['rank']==w==len(c['frames'][u])-len(c['frames'][f]) and a['entrance_rank']==len(c['frames'][f]) and a['terminal_rank']==len(c['frames'][u])<c['h']
+  elif w<c['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'))
+# Independently compare ordered common frames; exact local carrier names remain
+# bound to each canonical word, program, phase receipt and residual adapters.
+for p in provider_ids:
+ c=providers[p]['canonical']
+ assert len(c['centers'])==len(c['center_frames'])==8
+ assert [c['frames'][f]for f in c['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+assert required_artifacts<=set(summary['source_artifacts'])
+prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=16;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=144;HOSTED=CALLS*R
+# The selected map is an input to check, not a claim from the emitter.
+
+assert len(DISPATCH)==144 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'])==144 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))==144
+ all_local=[];perrep={r:[]for r in range(16)};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<16 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']<144 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(16)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==5120 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=144)
+
+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))
+# Single-provider dispatch still has all source/program/width binding controls.
+if len(provider_ids)==1:
+ P=provider_ids[0]
+ at_p=lambda q:next(c for c in q['calls']if c['provider_id']==P)
+ narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+ reject(P+': wrong provider at its invocation',lambda q:at_p(q).__setitem__('provider_id','__unregistered__'))
+ reject(P+': stale per-call local program hash',lambda q:at_p(q).__setitem__('local_program_sha256','0'*64))
+ reject(P+': stale serialized provider program',lambda q:q['local_providers'][P]['local_programs']['forward'].pop())
+ reject(P+': unbound residual adapter hash',lambda q:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+ reject(P+': wrong provider width registry',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,providers[P]['widths'][narrow]-1))
+ reject(P+': wrong per-call residual width',lambda q:at_p(q)['owners'][2*V+narrow][1].__setitem__(3,at_p(q)['owners'][2*V+narrow][1][3]-1))
+ reject(P+': wrong sweep provider',lambda q:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep').__setitem__('provider_id','__unregistered__'))
+ reject(P+': entering helper width silently restored to nine',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,9))
+else:
+ # 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=5120,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,provider_artifact_semantic_sha256=artifact_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=5120,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,provider_artifact_semantic_sha256=artifact_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/r480-owner-optimum/vendor/pr1074/code/bind_providers_portable.py b/research/r480-owner-optimum/vendor/pr1074/code/bind_providers_portable.py
new file mode 100644
index 0000000000..97e28da17e
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/bind_providers_portable.py
@@ -0,0 +1,67 @@
+"""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 *
+from generated_identity import artifact_identities
+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={};helpers=set()   # R: helper count per provider word; all providers must agree
+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'],len(word['centers']))==(112,9,8) and type(word['R']) is int and word['R']>0;helpers.add(word['R'])
+ assert word['ports']==desc['ports'] and word['centers']==desc['centers']
+ widths=[len(word['frames'][word['final'][r]])-len(word['frames'][word['start'][r]])for r in range(2*112,2*112+word['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths()
+ 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']
+ identities=artifact_identities(d)
+ pin('providers.%s.artifact_semantic_sha256'%pid,identities)
+ assert identities==desc['artifact_semantic_sha256']
+ for name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):
+  assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-reference artifact')
+ 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'])
+assert len(helpers)==1,'providers disagree on helper count R: %s'%sorted(helpers)
+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','runtime_source_plan_sha256'])
+(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(receipt['status'])
diff --git a/research/r480-owner-optimum/vendor/pr1074/code/bit_supplier_controls.py b/research/r480-owner-optimum/vendor/pr1074/code/bit_supplier_controls.py
new file mode 100644
index 0000000000..e86b8527b4
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/bit_supplier_controls.py
@@ -0,0 +1,111 @@
+"""Negative controls for the cited PR589 bit supplier and its derived rank-mass deficit.
+
+Apache-2.0. Each control mutates one input of the changed bit-supplier sites in assemble.py (the pinned record, the
+deficit derivation from the word's parameters, the profile/live binding, the claimed endpoint) and runs the unchanged
+assemble() on the fresh owner/invoice receipts. Every control must be rejected; the unmutated run must pass.
+`revert_hardcoded_9984` restores the PR543 constant the parent package hard-coded: with PR589's word it must fail.
+"""
+import argparse
+import copy
+import hashlib
+import json
+import os
+import tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+
+assert __debug__, 'Assertions required'
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    import assemble as A
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    args = (owner, invoice, sha(owner_path), sha(invoice_path))
+    baseline = A.assemble(*args)
+    data = A.BIT_PATH.read_bytes()
+    record = A.load_bit(data)
+    word = record['word']
+    assert A.bit_deficit(word, record['nine']['bit']['live']) == 10272 == 32 * (8 * 111 - 9 * 63)
+
+    real_load, real_deficit = A.load_bit, A.bit_deficit
+
+    def with_record(mutate):
+        def load(d):
+            r = copy.deepcopy(real_load(d)); mutate(r); return r
+        return load
+
+    def shift_profile(r):  # one rank-1 child becomes rank 2: rank mass +1, totals unchanged
+        p = r['nine']['profile']; p['1'] -= 1; p['2'] += 1; r['nine']['bit']['rank_mass'] += 1
+
+    bumped = data.replace(record['nine']['bit_lower'].encode(),
+                          str(Q(record['nine']['bit_lower']) + Q(1, 10**24)).encode(), 1)
+    assert bumped != data
+    pr543 = (source_package / 'inputs/PR543-EXPECTED.json').read_bytes()
+    controls = [
+        # deficit site: the parent's hard-coded constant, restored
+        ('revert_hardcoded_9984', dict(bit_deficit=lambda w, live: 9984)),
+        # deficit site: each word parameter perturbed alone
+        ('ports_112', dict(load_bit=with_record(lambda r: r['word'].__setitem__('v', 112)))),
+        ('decoder_constant_64_copy_ranks_unchanged', dict(load_bit=with_record(lambda r: r['word'].__setitem__('decoder_constant', 64)))),
+        # v=111, cst=64 derives 32*(888-576)=9984: consistent word, wrong for the priced profile
+        ('decoder_constant_64_with_one_copy_rank_8', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('decoder_constant', 64), r['word']['copy_ranks'].__setitem__(0, 8))))),
+        ('eight_retained_totals', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('copy_ranks', [7] * 8), r['word'].__setitem__('decoder_constant', 56))))),
+        ('live_minus_one', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('live', r['nine']['bit']['live'] - 1)))),
+        # profile binding: same totals, rank mass +1
+        ('profile_rank_mass_plus_one', dict(load_bit=with_record(shift_profile))),
+        ('profile_rank_mass_receipt_mismatch', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('rank_mass', r['nine']['bit']['rank_mass'] + 1)))),
+        # endpoint: the next 1e-24 grid point
+        ('bit_lower_next_grid', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('bit_lower', str(Q(r['nine']['bit_lower']) + Q(1, 10**24)))))),
+        ('not_nine_stage_record', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('pipeline', r['nine']['pipeline'].replace('nine-stage', 'eleven-stage'))))),
+        # pinned-input site: tampered bytes and the parent's PR543 file under the PR589 pin
+        ('tampered_bytes_next_grid', dict(read=bumped)),
+        ('pr543_file_under_pr589_pin', dict(read=pr543)),
+    ]
+    rejected = []
+    scratch = Path(tempfile.mkdtemp(prefix='bitctl-'))
+    for name, patch in controls:
+        saved_path = A.BIT_PATH
+        try:
+            if 'read' in patch:
+                tmp = scratch / (name + '.json'); tmp.write_bytes(patch['read']); A.BIT_PATH = tmp
+            A.load_bit = patch.get('load_bit', real_load)
+            A.bit_deficit = patch.get('bit_deficit', real_deficit)
+            try:
+                A.assemble(*args)
+            except (AssertionError, KeyError):
+                rejected.append(name)
+            else:
+                raise AssertionError('Invalid bit supplier accepted: ' + name)
+        finally:
+            A.load_bit, A.bit_deficit, A.BIT_PATH = real_load, real_deficit, saved_path
+            if 'read' in patch:
+                tmp.unlink()
+    scratch.rmdir()
+    assert rejected == [n for n, _ in controls]
+    again = A.assemble(*args)
+    assert again['kappa'] == baseline['kappa'] and again['bit_lower'] == baseline['bit_lower']
+    return dict(
+        status='PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS',
+        kappa=baseline['kappa_decimal'], bit_lower=baseline['bit_lower'], bit_decimal=baseline['bit_decimal'],
+        binding=baseline['binding'], bit_supplier=baseline['bit_supplier'],
+        derived_deficit=baseline['bit_supplier']['derived_deficit'],
+        rejected_controls=rejected,
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+    )
+
+
+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', newline='\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/r480-owner-optimum/vendor/pr1074/code/emit_allcold.py b/research/r480-owner-optimum/vendor/pr1074/code/emit_allcold.py
new file mode 100644
index 0000000000..28a08a79da
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/emit_allcold.py
@@ -0,0 +1,150 @@
+"""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))==144;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=16;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,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')
+ # Carrier names belong to the independently checked local program. The global
+ # controller's centre contract is the ordered eight exact common frame bases.
+ assert(pc['v'],pc['h'],pc['ports'])==(V,9,canon['ports'])
+ assert len(pc['centers'])==len(pc['center_frames'])==len(canon['centers'])==8
+ assert [pc['frames'][f]for f in pc['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+ R=pc['R'];assert type(R)is int and R>0 and all(x['R']==R for x in registry.values()),'providers disagree on helper count R'
+ 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=[len(pc['frames'][pc['final'][2*V+h]])-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)]   # HPE: residual width |final|-|start|
+ 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)
+assert len(roles)==144*R   # one whole-owner role per (call, provider helper)
+selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+assert len(selected)==144 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())==5120
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R0+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-R%d-asynchronous-whole-owner-v1'%R,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=5120,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/r480-owner-optimum/vendor/pr1074/code/freeze_spec.py b/research/r480-owner-optimum/vendor/pr1074/code/freeze_spec.py
new file mode 100644
index 0000000000..4fe3b88915
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/freeze_spec.py
@@ -0,0 +1,29 @@
+"""Freeze independently recomputed discovery values before strict replay."""
+import argparse
+import json
+from pathlib import Path
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--spec', type=Path, required=True)
+ap.add_argument('--discovery', type=Path, required=True)
+a = ap.parse_args()
+spec = json.loads(a.spec.read_text())
+for line in (a.discovery/'WITNESS-RECORD.jsonl').read_text().splitlines():
+    key, value = json.loads(line)
+    parts = key.split('.')
+    if len(parts)>3 and parts[0]=='providers' and parts[2]=='artifacts':
+        parts = parts[:3] + ['.'.join(parts[3:])]
+    target = spec
+    for part in parts[:-1]:
+        target = target.setdefault(part, {})
+    if parts[-1] in target:
+        assert target[parts[-1]]==value, 'Conflicting independent recomputations: '+key
+    target[parts[-1]] = value
+assembly = json.loads((a.discovery/'ASSEMBLY.json').read_text())
+for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+    spec['expected'][key] = assembly[key]
+spec['expected']['assembly_controls_rejected'] = 69
+spec['expected']['provider_counts'] = {'gauge44':144}
+spec['expected']['mutations_rejected'] = 15
+a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
diff --git a/research/r480-owner-optimum/vendor/pr1074/code/generated_identity.py b/research/r480-owner-optimum/vendor/pr1074/code/generated_identity.py
new file mode 100644
index 0000000000..74a9b60479
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/generated_identity.py
@@ -0,0 +1,62 @@
+"""Proof-relevant identities for generated artifacts, independent of gzip streams.
+
+Immutable source archives retain their exact byte hashes. For freshly emitted
+artifacts, gzip identity is the exact decompressed payload and JSON identity
+retains every field. Only CLIFFORD-REVIEW's root timing field is excluded.
+Literal receipt references are checked against actual files before replacing
+the three gzip references (and the phase recipe reference) with content hashes.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import copy
+import gzip
+import hashlib
+import json
+import math
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+
+FILES=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+       'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+       'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json')
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+def json_identity(value):
+    return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode('utf-8')).hexdigest()
+
+def payload_identity(path):
+    return hashlib.sha256(gzip.decompress(Path(path).read_bytes())).hexdigest()
+
+def phase_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'CLIFFORD-REVIEW.json').read_bytes())if value is None else value)
+    assert value['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz'),'stale phase canonical word reference'
+    assert value['recipe_sha256']==sha(directory/'CLIFFORD-RECIPES.json'),'stale phase recipe reference'
+    seconds=value.pop('seconds')
+    assert type(seconds)in(int,float) and math.isfinite(seconds) and seconds>=0,'invalid phase timing metadata'
+    value['canonical_word_sha256']=payload_identity(directory/'CANONICAL-WORD.json.gz')
+    value['recipe_sha256']=json_identity(json.loads((directory/'CLIFFORD-RECIPES.json').read_bytes()))
+    return value
+
+def native_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'INDEPENDENT-LOCAL-REPLAY.json').read_bytes())if value is None else value)
+    for field,name in [('canonical_word_sha256','CANONICAL-WORD.json.gz'),('local_programs_sha256','LOCAL-PROGRAMS.json.gz')]:
+        assert value[field]==sha(directory/name),'stale native artifact reference: '+field
+        value[field]=payload_identity(directory/name)
+    return value
+
+def artifact_identities(directory):
+    directory=Path(directory)
+    result={}
+    for name in FILES:
+        path=directory/name
+        if name.endswith('.gz'):
+            result[name]=payload_identity(path)
+        else:
+            value=phase_value(directory)if name=='CLIFFORD-REVIEW.json'else native_value(directory)if name=='INDEPENDENT-LOCAL-REPLAY.json'else json.loads(path.read_bytes())
+            result[name]=json_identity(value)
+    return result
diff --git a/research/r480-owner-optimum/vendor/pr1074/code/invoice_allcold.py b/research/r480-owner-optimum/vendor/pr1074/code/invoice_allcold.py
new file mode 100644
index 0000000000..d1dd221291
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/invoice_allcold.py
@@ -0,0 +1,329 @@
+"""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 generated_identity import artifact_identities
+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,h)==(112,9) and type(helpers) is int and helpers>0
+    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 = [len(w['frames'][w['final'][r]])-len(w['frames'][w['start'][r]]) for r in range(2*v, 2*v+helpers)]  # HPE: |final|-|start|
+    terminal_codim = sum(h-len(w['frames'][w['final'][r]]) for r in range(2*v, 2*v+helpers))  # HPE: 0 for FULL-ended helpers
+    ends = {r: f for r, f in enumerate(w['final']) if r >= 2*v and f != 1}
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    wrapped = {**entrances, **{r: 0 for r in ends if r not in entrances}}   # COLD-HPE: cold hyperplane-ended helpers carry wrappers too
+    cold_ends = len(wrapped) - 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, *end = event
+                assert kind in wrappers and wrapped.get(register) == frame
+                assert end == ([ends[register]] if register in ends else [])  # HPE: R_{E,U}^-1 and L_{E,U}^-1 name U
+                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(wrapped)
+        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')
+    return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n,
+                entering_helpers=entering,entrance_rank=sum(len(w['frames'][f]) for f in w['start'][2*v:]),
+                terminal_codimension=terminal_codim, hyperplane_ended_helpers=len(ends),  # HPE: always reported (0 for FULL-ended words)
+                **({'cold_hyperplane_ended_helpers': cold_ends} if cold_ends else {}),  # COLD-HPE: absent without cold ends
+                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=artifact_identities(local_dir))
+
+
+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]
+    # R is read from the provider words (all must agree); the parent dedicated-bank
+    # envelope keeps its own helper count R0 from the parent split-centres word.
+    assert len({p['helpers'] for p in providers.values()})==1,'providers disagree on helper count R'
+    v,h,m,centres=112,9,73,8
+    helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+    assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+    parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+    stages,replicas,blocks_per_stream=9,16,4
+    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+parent_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']==5120
+    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 144 invocation and 144 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/r480-owner-optimum/vendor/pr1074/code/prepare_global.py b/research/r480-owner-optimum/vendor/pr1074/code/prepare_global.py
new file mode 100644
index 0000000000..655c9470f6
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/prepare_global.py
@@ -0,0 +1,124 @@
+"""Bind a frozen explicit owner map to exact native local artifacts.
+
+This preparer nominates a witness. The separate serialized controller audit,
+finite invoice, two exact moment engines and strict pinned replay admit it.
+Apache-2.0; prepared with OpenAI assistance. See NOTICE.md.
+"""
+import argparse
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+from generated_identity import artifact_identities, FILES
+
+assert __debug__, 'Assertions required'
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--parent', type=Path, required=True)
+ap.add_argument('--owners', type=Path, required=True)
+ap.add_argument('--local', type=Path, required=True)
+ap.add_argument('--data', type=Path, required=True)
+args = ap.parse_args()
+args.data.mkdir(parents=True, exist_ok=True)
+parent_path = args.parent / 'data/PLAN.json'
+assert sha(parent_path) == '258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda'
+plan = read(parent_path)
+word = read(args.local / 'CANONICAL-WORD.json.gz')
+checks = read(args.local / 'LOCAL-CHECKS.json')
+assert (word['v'], word['h'], word['R']) == (112, 9, 492)
+widths = [len(word['frames'][word['final'][224+h]]) -
+          len(word['frames'][word['start'][224+h]]) for h in range(492)]
+profile = {int(k): v for k, v in word['local_profile'].items()}
+assert profile == {1: 2514, 2: 404, 3: 448, 4: 160, 5: 56, 8: 8}
+assert Counter(widths) == {4: 52, 5: 48, 7: 34, 8: 114, 9: 244}
+assert sum(widths) == 3794
+owners = read(args.owners)
+assert len(owners) == 72 * 492
+order = [tuple(x) for x in plan['order']]
+times = {x: i for i, x in enumerate(order)}
+used, call_helpers, call_families = defaultdict(set), defaultdict(set), defaultdict(set)
+for z in owners:
+    key = (z['stage'], z['replica'])
+    h, i, rep, port = z['helper'], z['child'], z['owner_replica'], z['port']
+    assert key in times and 0 <= h < 492 and 0 <= rep < 8 and 0 <= port < 112
+    assert z['time'] == times[key] and h not in call_helpers[key]
+    assert z['family'] not in call_families[key]
+    call_helpers[key].add(h)
+    call_families[key].add(z['family'])
+    cap, allowed = plan['windows'][f'{rep},{i}']
+    assert z['time'] in allowed and z['width'] == widths[h]
+    assert z['copy'] == rep * 112 + port
+    assert z['family'] == rep * 896 + (2*plan['pairs'][str(i)] + plan['sides'][str(i)])*112 + port
+    assert 0 <= z['offset'] and z['offset'] + z['width'] <= cap
+    cells = set(range(z['offset'], z['offset'] + z['width']))
+    group = (i, rep, port)
+    assert not used[group] & cells
+    used[group].update(cells)
+assert set(call_helpers) == set(order)
+assert all(hs == set(range(492)) for hs in call_helpers.values())
+idle = Counter()
+for key, (cap, _) in plan['windows'].items():
+    rep, i = map(int, key.split(','))
+    for port in range(112):
+        cells = used[i, rep, port]
+        assert cells == set(range(len(cells)))
+        left = cap - len(cells)
+        if left:
+            idle[left] += 1
+global_profile = Counter({r: 72*n for r, n in profile.items()}) + idle
+assert sum(r*n for r, n in global_profile.items()) == 520704
+assert 73*7168 - sum(r*n for r, n in global_profile.items()) == 2560
+pid = 'gauge44'
+for c in plan['provider_calls']:
+    c['provider'] = pid
+    c['local_program_sha256'] = checks[c['orientation']]['sha256']
+for c in plan['per_call_widths']:
+    c['widths'] = widths
+artifacts = {name: sha(args.local / name) for name in FILES}
+identities = artifact_identities(args.local)
+plan['provider_registry'] = {pid: dict(
+    directory='providers/' + pid, artifact_sha256=artifacts,
+    ports=word['ports'], centers=word['centers'], widths=widths,
+    actual_paid_profile=word['local_profile'],
+    orientation_program_sha256={k: v['sha256'] for k, v in checks.items()},
+    artifact_semantic_sha256=identities)}
+plan.update(status='FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION',
+            mode='gauge44-all72', profile=dict(sorted(global_profile.items())),
+            solver_status='deterministic-capacity-matching', gap=None,
+            source_plan_sha256=sha(parent_path),
+            source_owners_sha256=sha(args.parent / 'data/OWNERS.json.gz'),
+            assignment_sha256=sha(args.owners))
+target_owners = args.data / 'OWNERS.json.gz'
+if args.owners.resolve() != target_owners.resolve():
+    shutil.copyfile(args.owners, target_owners)
+dump(args.data / 'PLAN.json', plan)
+spec = dict(schema='witness-spec/1', name='gauge44-all72',
+            data=dict(plan_sha256=sha(args.data / 'PLAN.json'), owners_sha256=sha(target_owners)),
+            dispatch=[[s, r, pid] for s in range(9) for r in range(8)],
+            call_order=plan['order'], width_spot_helpers=[264, 276, 288, 300],
+            providers={pid: {}}, expected=dict(gain_baseline_kappa='0.001636241501576388'))
+dump(args.data / 'SPEC.json', spec)
+dump(args.data / 'PREPARATION.json', dict(
+    status='PASS_EXPLICIT_MAP_AND_FRESH_PROVIDER_NOMINATION',
+    parent_plan_sha256=sha(parent_path), source_owners_sha256=sha(args.owners),
+    global_profile=dict(sorted(global_profile.items())), idle_profile=dict(sorted(idle.items())),
+    roles=len(owners), rank_mass=520704, deficit=2560,
+    remaining='Independent emitted-controller audit, fresh finite invoice, exact moments and outer assembly.'))
+print('Prepared all72 gauge44 candidate:', dict(sorted(global_profile.items())))
diff --git a/research/r480-owner-optimum/vendor/pr1074/code/restore_parent.py b/research/r480-owner-optimum/vendor/pr1074/code/restore_parent.py
new file mode 100644
index 0000000000..21135f898a
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/restore_parent.py
@@ -0,0 +1,67 @@
+"""Materialize the omitted generated PR558 parent, then require its reviewed hash.
+
+The integrated review contains the native inputs and INTEGRATION.json but
+omits GLOBAL-TEMPLATE.json.gz. This is only the deterministic template
+binding from the inherited prepare_supplier_base.py; no old circuit or
+phase calculation is rerun. The whole exact payload must match the review.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source',type=Path,required=True)
+ap.add_argument('--baseline',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+assert not a.out.exists()
+base=a.out/'complex-global/base'
+shutil.copytree(a.baseline/'complex-global/base',base)
+d=base/'split-centres'
+parent=a.source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz'
+old=read(parent);can=read(d/'CANONICAL-WORD.json.gz')
+checks=read(d/'LOCAL-CHECKS.json');programs=read(d/'LOCAL-PROGRAMS.json.gz')
+v,h,r=can['v'],can['h'],can['R'];c=len(can['centers']);m,t,l,k=73,8,9,4
+assert(v,h,r,c)==(112,9,504,8)
+widths=[h-len(can['frames'][f])for f in can['start'][2*v:]]
+data=2*k*t*v;live=data+l*r;physical=live+r+c+2
+word=copy.deepcopy(old)
+word.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=live,physical=physical,local_programs=programs)
+word['private_namespace']={'centers':[live,live+c],'reserved_tableau':[live+c,live+c+r],'coefficient':[physical-2,physical]}
+for call in word['calls']:
+ s,rep=call['stage'],call['replica'];owners=copy.deepcopy(call['owners'][:2*v])
+ for helper,w in enumerate(widths):
+  route=[2,rep]if w==9 else[2,rep*w,w,list(range(t*w,t*w+9-w))]
+  owners.append([data+s*r+helper,route])
+ call['owners']=owners;call['local_program_sha256']=checks[call['orientation']]['sha256']
+children=[]
+for s in range(l):
+ for helper,w in enumerate(widths):
+  axes=list(range(t*w,m))
+  children.append(dict(family=data+s*r+helper,rank=len(axes),axis_indices=axes,orthogonal_axes=[1<<j for j in axes]))
+word['bank_padding']={'families':list(range(data,live)),'children':children,
+ 'semantics':'Each listed complement frame is applied once after the eight disjoint residual blocks of that dedicated bank. The final hosted derivative has empty families and children.'}
+word['cover_final_correction'].update(families=[0,live],charged_calls_per_cover=live)
+for i,e in enumerate(word['execution_schedule']):
+ if e['kind']=='bank_padding_cover_sweep':word['execution_schedule'][i]={'kind':'bank_padding_cover_sweep','families':[data,live],'children_source':'bank_padding.children'}
+ elif e['kind']=='translate_every_live_family':e.update(word['cover_final_correction'])
+word['exact_data_phase_recipe_sha256']=sha(base/'work/complex-nine-native/DATA-PHASES.json')
+word['exact_local_clifford_recipe_sha256']=sha(d/'CLIFFORD-RECIPES.json')
+word['residual_adapter_sha256']=sha(d/'RESIDUAL-ADAPTERS.json')
+word['supplier_substitution']={'parent_template_sha256':sha(parent),
+ 'old_canonical_word_sha256':sha(a.baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz'),
+ 'new_canonical_word_sha256':sha(d/'CANONICAL-WORD.json.gz'),
+ 'exact_same_ports':True,'data_contract':'The same ordered 112 data ports and both complete-invocation identity-shear orientations feed the unchanged nine-stage controller. No old local program or helper profile is reused.'}
+word['route_semantics']['helper']='Dedicated family DATA+stage*R+helper; one helper per bank per complete invocation. Width-nine route[2,replica] uses axes9*replica..9*replica+8. Width-w entering route[2,w*replica,w,spectators] uses the disjoint residual block and paid normalization wrappers; spectator axes start at8*w, beyond all residual blocks.'
+raw=json.dumps(word,sort_keys=True,separators=(',',':')).encode()
+expected=read(d/'INTEGRATION.json')['global_template_sha256']
+assert hashlib.sha256(raw).hexdigest()==expected=='7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3'
+(d/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+print('PASS_EXACT_REVIEWED_PARENT_TEMPLATE_RESTORED',expected)
diff --git a/research/r480-owner-optimum/vendor/pr1074/code/witness.py b/research/r480-owner-optimum/vendor/pr1074/code/witness.py
new file mode 100644
index 0000000000..c5c7fbc114
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/code/witness.py
@@ -0,0 +1,55 @@
+"""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']]
+# width-8 spot helpers: PR558's helpers 270, 282, 294, 306, or their images under a K-triangle word's 504 -> R helper map
+# (verify.py checks the spec value against the constructor's HELPER-MAP.json)
+SPOT=tuple(SPEC.get('width_spot_helpers',(270,282,294,306)))
+# A pivot swap moves a kernel family's pivot role p -> x; the old pivot p becomes an ordinary cold helper and its width
+# goes 8 -> 9 (construction/layers, PR641 PROOF-NOTE-PIVOT). Expected spot widths are derived from the package's pinned
+# pivot-swap recipe (path and sha256 in the spec), not from free data: 9 at a swapped-out pivot, 8 otherwise.
+_PKG=Path(os.environ['WITNESS_SPEC']).resolve().parents[1]
+def _old_pivots():
+ ps=SPEC.get('pivot_swap')
+ if not ps:return frozenset()
+ raw=(_PKG/ps['recipe']).read_bytes();import hashlib
+ assert hashlib.sha256(raw).hexdigest()==ps['sha256'],'pivot-swap recipe pin'
+ return frozenset(s['pivot']for s in json.loads(raw)['swaps'])
+OLD_PIVOTS=_old_pivots()
+def spot_widths(v=112):
+ """Expected residual widths at the spot helpers (helper indices) of the gauge44 provider."""
+ return tuple(9 if 2*v+h in OLD_PIVOTS else 8 for h in SPOT)
+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:
+  if os.environ.get('WITNESS_RECORD'):   # discovery bookkeeping only: append (key, value) for the spec writer
+   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))
+  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/r480-owner-optimum/vendor/pr1074/construction/leaver/PIVOT-SWAP-k8.json b/research/r480-owner-optimum/vendor/pr1074/construction/leaver/PIVOT-SWAP-k8.json
new file mode 100644
index 0000000000..7a8edeb1e4
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/construction/leaver/PIVOT-SWAP-k8.json
@@ -0,0 +1 @@
+{"input_content_sha256": "00aeefe0c778ff64125628d7c869ae1aa27db60911f0289a2d4283af5cff85d2", "output_content_sha256": "377ab10c2bf6173498c8af15f8654060331ec9ee232e58cc75956dc015b23685", "swaps": [{"pivot": 482, "new_pivot": 554, "entrance": [24], "gates": [{"part": "B", "index": 331, "before": ["add", 554, 482, -1, 1, [24]], "after": ["add", 482, 554, -1, 1, [24]]}, {"part": "B", "index": 332, "before": ["add", 616, 482, 2, 1, [24]], "after": ["add", 616, 554, -2, 1, [24]]}, {"part": "B", "index": 333, "before": ["add", 618, 482, -2, 1, [24]], "after": ["add", 618, 554, 2, 1, [24]]}, {"part": "B", "index": 334, "before": ["add", 664, 482, 1, 1, [24]], "after": ["add", 664, 554, -1, 1, [24]]}, {"part": "B", "index": 335, "before": ["add", 666, 482, -1, 1, [24]], "after": ["add", 666, 554, 1, 1, [24]]}]}, {"pivot": 483, "new_pivot": 555, "entrance": [24], "gates": [{"part": "B", "index": 468, "before": ["add", 123, 483, 1, 1, [24]], "after": ["add", 123, 555, -1, 1, [24]]}, {"part": "B", "index": 504, "before": ["add", 187, 483, -1, 1, [24]], "after": ["add", 187, 555, 1, 1, [24]]}, {"part": "B", "index": 734, "before": ["add", 555, 483, -1, 1, [24]], "after": ["add", 483, 555, -1, 1, [24]]}]}, {"pivot": 494, "new_pivot": 566, "entrance": [24], "gates": [{"part": "B", "index": 128, "before": ["add", 628, 494, 2, 1, [24]], "after": ["add", 628, 566, -2, 1, [24]]}, {"part": "B", "index": 130, "before": ["add", 628, 494, -2, 1, [24]], "after": ["add", 628, 566, 2, 1, [24]]}, {"part": "B", "index": 230, "before": ["add", 676, 494, -2, 1, [24]], "after": ["add", 676, 566, 2, 1, [24]]}, {"part": "B", "index": 232, "before": ["add", 676, 494, 2, 1, [24]], "after": ["add", 676, 566, -2, 1, [24]]}, {"part": "B", "index": 750, "before": ["add", 566, 494, -1, 1, [24]], "after": ["add", 494, 566, -1, 1, [24]]}]}, {"pivot": 495, "new_pivot": 567, "entrance": [24], "gates": [{"part": "B", "index": 49, "before": ["add", 211, 495, -1, 1, [24]], "after": ["add", 211, 567, 1, 1, [24]]}, {"part": "B", "index": 477, "before": ["add", 147, 495, 1, 1, [24]], "after": ["add", 147, 567, -1, 1, [24]]}, {"part": "B", "index": 752, "before": ["add", 567, 495, -1, 1, [24]], "after": ["add", 495, 567, -1, 1, [24]]}]}, {"pivot": 507, "new_pivot": 531, "entrance": [30], "gates": [{"part": "B", "index": 459, "before": ["add", 115, 507, -1, 1, [30]], "after": ["add", 115, 531, 1, 1, [30]]}, {"part": "B", "index": 495, "before": ["add", 179, 507, 1, 1, [30]], "after": ["add", 179, 531, -1, 1, [30]]}, {"part": "B", "index": 770, "before": ["add", 531, 507, -1, 1, [30]], "after": ["add", 507, 531, -1, 1, [30]]}]}, {"pivot": 519, "new_pivot": 543, "entrance": [30], "gates": [{"part": "B", "index": 486, "before": ["add", 155, 519, -1, 1, [30]], "after": ["add", 155, 543, 1, 1, [30]]}, {"part": "B", "index": 521, "before": ["add", 219, 519, 1, 1, [30]], "after": ["add", 219, 543, -1, 1, [30]]}, {"part": "B", "index": 788, "before": ["add", 543, 519, -1, 1, [30]], "after": ["add", 519, 543, -1, 1, [30]]}]}]}
\ No newline at end of file
diff --git a/research/r480-owner-optimum/vendor/pr1074/data/SPEC-T8.json b/research/r480-owner-optimum/vendor/pr1074/data/SPEC-T8.json
new file mode 100644
index 0000000000..6ac06e4b75
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/data/SPEC-T8.json
@@ -0,0 +1,1327 @@
+{
+  "schema": "witness-spec/1",
+  "name": "gauge44-all72",
+  "data": {
+    "plan_sha256": "1dec4ca3af6d45d82286005cae4c5e56e7253adefb117d797da55c55c891af08",
+    "owners_sha256": "32ca30cd1c652ef6ad43657273a08a157e1df3545e759ab36306a0d0b516fb4a"
+  },
+  "dispatch": [
+    [
+      0,
+      0,
+      "gauge44"
+    ],
+    [
+      0,
+      1,
+      "gauge44"
+    ],
+    [
+      0,
+      2,
+      "gauge44"
+    ],
+    [
+      0,
+      3,
+      "gauge44"
+    ],
+    [
+      0,
+      4,
+      "gauge44"
+    ],
+    [
+      0,
+      5,
+      "gauge44"
+    ],
+    [
+      0,
+      6,
+      "gauge44"
+    ],
+    [
+      0,
+      7,
+      "gauge44"
+    ],
+    [
+      1,
+      0,
+      "gauge44"
+    ],
+    [
+      1,
+      1,
+      "gauge44"
+    ],
+    [
+      1,
+      2,
+      "gauge44"
+    ],
+    [
+      1,
+      3,
+      "gauge44"
+    ],
+    [
+      1,
+      4,
+      "gauge44"
+    ],
+    [
+      1,
+      5,
+      "gauge44"
+    ],
+    [
+      1,
+      6,
+      "gauge44"
+    ],
+    [
+      1,
+      7,
+      "gauge44"
+    ],
+    [
+      2,
+      0,
+      "gauge44"
+    ],
+    [
+      2,
+      1,
+      "gauge44"
+    ],
+    [
+      2,
+      2,
+      "gauge44"
+    ],
+    [
+      2,
+      3,
+      "gauge44"
+    ],
+    [
+      2,
+      4,
+      "gauge44"
+    ],
+    [
+      2,
+      5,
+      "gauge44"
+    ],
+    [
+      2,
+      6,
+      "gauge44"
+    ],
+    [
+      2,
+      7,
+      "gauge44"
+    ],
+    [
+      3,
+      0,
+      "gauge44"
+    ],
+    [
+      3,
+      1,
+      "gauge44"
+    ],
+    [
+      3,
+      2,
+      "gauge44"
+    ],
+    [
+      3,
+      3,
+      "gauge44"
+    ],
+    [
+      3,
+      4,
+      "gauge44"
+    ],
+    [
+      3,
+      5,
+      "gauge44"
+    ],
+    [
+      3,
+      6,
+      "gauge44"
+    ],
+    [
+      3,
+      7,
+      "gauge44"
+    ],
+    [
+      4,
+      0,
+      "gauge44"
+    ],
+    [
+      4,
+      1,
+      "gauge44"
+    ],
+    [
+      4,
+      2,
+      "gauge44"
+    ],
+    [
+      4,
+      3,
+      "gauge44"
+    ],
+    [
+      4,
+      4,
+      "gauge44"
+    ],
+    [
+      4,
+      5,
+      "gauge44"
+    ],
+    [
+      4,
+      6,
+      "gauge44"
+    ],
+    [
+      4,
+      7,
+      "gauge44"
+    ],
+    [
+      5,
+      0,
+      "gauge44"
+    ],
+    [
+      5,
+      1,
+      "gauge44"
+    ],
+    [
+      5,
+      2,
+      "gauge44"
+    ],
+    [
+      5,
+      3,
+      "gauge44"
+    ],
+    [
+      5,
+      4,
+      "gauge44"
+    ],
+    [
+      5,
+      5,
+      "gauge44"
+    ],
+    [
+      5,
+      6,
+      "gauge44"
+    ],
+    [
+      5,
+      7,
+      "gauge44"
+    ],
+    [
+      6,
+      0,
+      "gauge44"
+    ],
+    [
+      6,
+      1,
+      "gauge44"
+    ],
+    [
+      6,
+      2,
+      "gauge44"
+    ],
+    [
+      6,
+      3,
+      "gauge44"
+    ],
+    [
+      6,
+      4,
+      "gauge44"
+    ],
+    [
+      6,
+      5,
+      "gauge44"
+    ],
+    [
+      6,
+      6,
+      "gauge44"
+    ],
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diff --git a/research/r480-owner-optimum/vendor/pr1074/inputs/PR589-EXPECTED.json b/research/r480-owner-optimum/vendor/pr1074/inputs/PR589-EXPECTED.json
new file mode 100644
index 0000000000..e293ddc557
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/inputs/PR589-EXPECTED.json
@@ -0,0 +1,222 @@
+{
+ "word": {
+  "file": "tune/bitE8mut-p111-tuned.json.gz",
+  "file_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f",
+  "content_sha256": "5642fd0e35a1acc11acff8d0c08350c1617e95f310d4d35ad63a651f9eeeba0b",
+  "v": 111,
+  "R": 439,
+  "punctured": [
+   10,
+   15,
+   51,
+   53,
+   56,
+   66,
+   72,
+   89,
+   111
+  ],
+  "retained_totals": 9,
+  "copy_ranks": [
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7
+  ],
+  "decoder_constant": 63,
+  "gates": {
+   "D": 111,
+   "A": 2075,
+   "B": 712,
+   "C": 2574
+  },
+  "local_histogram": {
+   "1": 1323,
+   "2": 1342,
+   "3": 79,
+   "4": 44,
+   "5": 102,
+   "6": 11,
+   "7": 19
+  },
+  "legality": {
+   "records": 27234,
+   "common_frame_ADDs": 24305,
+   "rank_mass": 5129
+  },
+  "five_stage_columns": 883,
+  "five_stage_payload_bits": 93,
+  "nine_stage_columns": 1327,
+  "nine_stage_payload_bits": 93,
+  "eleven_stage_columns": 1549,
+  "eleven_stage_payload_bits": 93,
+  "base_content_sha256": "d0df3c89ae84989f4045ba1681a5e2e9fcdfa38ed0301c8abf5185537155cbe3"
+ },
+ "interface": {
+  "hypotheses": {
+   "H1_no_target_feeds_z": true,
+   "H2_D_frame0_targets_from_helpers": true,
+   "H3_A_z_only_scatter_targets_B_split": true,
+   "H4_C_literal_reverse_at_full": true,
+   "H5_V_identity": true
+  },
+  "conclusion": {
+   "U_block_form": true,
+   "J_identity": true,
+   "K_equals_D": true,
+   "C_is_U_inverse": true
+  },
+  "interleaving": {
+   "z_gates_A": 2075,
+   "source_writes_A": 0,
+   "z_gates_B": 499,
+   "source_writes_B": 483,
+   "helper_writes_B": 16,
+   "sources_rewritten_B": 108,
+   "B_z_write_frame_dims": {
+    "4": 388,
+    "6": 111
+   },
+   "B_z_operand_kinds": {
+    "helper<-helper": 3,
+    "helper<-source": 13,
+    "source<-helper": 108,
+    "source<-source": 375
+   },
+   "B_z_operand_kinds_by_dim": {
+    "dim4:helper<-source": 13,
+    "dim4:source<-source": 375,
+    "dim6:helper<-helper": 3,
+    "dim6:source<-helper": 108
+   },
+   "B_z_writes_after_a_target_read_of_the_same_register": 454,
+   "B_target_reads_of_registers_rewritten_earlier_in_B": 111,
+   "target_reads_of_targets": 0,
+   "cleanup_gates": 2574
+  }
+ },
+ "nine": {
+  "pipeline": "PR #510 (PR #463 nine-stage template, 32 replicas, PR #442 hosting, PR #493 outer assembly), parameterised for v <= 120 by code/adapt9p.py",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_lower_decimal": "0.001733427039589844234749",
+  "profile": {
+   "1": 381024,
+   "2": 400416,
+   "3": 22752,
+   "4": 26880,
+   "5": 29376,
+   "6": 17376,
+   "7": 26784,
+   "42": 288
+  },
+  "bit": {
+   "live": 28416,
+   "physical": 28425,
+   "maxchild": 42,
+   "rank_mass": 1808352,
+   "hosted_residuals": 126432,
+   "bank_assignments": 0,
+   "prefix_bits": 177,
+   "charged_prefix_bits": 192,
+   "coefficient_bits": 177,
+   "two_level_coefficient_bits": 393,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "eleven": {
+  "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting), parameterised by PR #545's code/adapt.py",
+  "bit_lower": "855475950388791987811/500000000000000000000000",
+  "bit_lower_decimal": "0.001710951900777583975622",
+  "profile": {
+   "1": 116424,
+   "2": 121648,
+   "3": 6952,
+   "4": 7424,
+   "5": 8976,
+   "6": 4520,
+   "7": 8776,
+   "56": 2600
+  },
+  "bit": {
+   "live": 8880,
+   "physical": 8889,
+   "maxchild": 56,
+   "rank_mass": 689304,
+   "hosted_residuals": 38632,
+   "prefix_bits": 4304,
+   "charged_prefix_bits": 4352,
+   "coefficient_bits": 4304,
+   "three_level_coefficient_bits": 12966,
+   "charged_three_level_coefficient_bits": 12992,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "793b6f40c9aa4b8db57fec0ac0973e16884dae28707e482ee8f7a2349a5d5a4b",
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "base": {
+  "nine_bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "nine_bit_lower_decimal": "0.001733052823330162099157",
+  "eleven_bit_lower": "427652201524503168379/250000000000000000000000",
+  "eleven_bit_lower_decimal": "0.001710608806098012673516",
+  "note": "PR #555's EXPECTED.json (untuned word); the tune/ pipeline is the same, with the same frozen hosting selections"
+ }
+}
diff --git a/research/r480-owner-optimum/vendor/pr1074/t16/NOTICE.md b/research/r480-owner-optimum/vendor/pr1074/t16/NOTICE.md
new file mode 100644
index 0000000000..403f4afffb
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/t16/NOTICE.md
@@ -0,0 +1,39 @@
+# Attribution and license
+
+Apache-2.0. New construction and integration: Hao Yan (@FanPUYen), 2026.
+Prepared with substantial OpenAI Codex assistance, including separately tasked
+AI agents for owner construction, independent mathematical/code checking and
+native verification. These are not claims of independent human peer review.
+
+The exact local supplier is Jeremy Kothe's accepted PR799 X4 word, layered on
+Chafik Boukhalfa's PR741 frame changes and PR685 owner construction. Chafik's
+PR795 fixed-inventory optimality result motivated changing the replica count.
+The original owner bytes, scalar program, local frame and width inventory,
+native phase and wrapper implementations retain their existing authorship.
+
+Credit icekylinx for the source gauge and supplier/admission pipeline;
+DreamingOfClouds for the PR589 bit transport and inherited cold-end work;
+eumemic for the PR555 bit supplier and earlier supplier work; Rohan Arun for
+the native exact-complex recurrence correction; Jeremy Diviney, jaymosley07,
+and the other retained owner/allocation contributors; and the complete
+PR514/PR484/PR507/PR558 controller, physical hosting and verification lineage.
+This list is cumulative credit, not approval of every claim in those PRs.
+
+All original notices and licenses remain in the referenced source packages:
+
+- `research/gauge44-frames-x/{NOTICE,UPSTREAM-NOTICE}.md`
+- `research/complex-sw4-frame8/PROVENANCE.md`
+- `research/e8-bit-p111-tuned/tune/README.md`
+- the repository `CONTRIBUTORS.md` and source-package licenses.
+
+The verifier copies pinned global source files into an external replay
+directory and applies an explicit checked edit list. Original attribution
+comments are preserved in those generated derivatives. No original source
+file or historical certificate is rewritten.
+
+The optional ancestry-reuse coverage guard addresses the omission issue
+identified by Lucas (@ljste) in PR838 and the related PR847 integration by
+Chinmay (@chinmayarvind23). Its fixed inventories were read from the accepted
+PR741 source; no pending implementation is imported. Charles Bethin's
+concurrent PR850 strengthens the fixed-inventory owner-profile theorem and
+was checked for overlap before publication; that inventory is changed here.
diff --git a/research/r480-owner-optimum/vendor/pr1074/t16/build_parent.py b/research/r480-owner-optimum/vendor/pr1074/t16/build_parent.py
new file mode 100644
index 0000000000..bd9e28bd2d
--- /dev/null
+++ b/research/r480-owner-optimum/vendor/pr1074/t16/build_parent.py
@@ -0,0 +1,281 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Copyright (c) 2026 Hao Yan (@FanPUYen)
+"""Lift the PR741 controller and PR799 provider plan to sixteen replicas.
+
+Authored with OpenAI Codex assistance. Precursor credit: the PR514/PR484/PR507
+controller lineage, PR558/PR589 admission, Chafik Boukhalfa's PR741 frames
+and owner map, and Jeremy Kothe's PR799 paired-read-exchange provider.
+This script changes only the global replica namespace and the nominated owner
+map; it reuses the exact local programs and exact data-phase recipes.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from collections import Counter
+from pathlib import Path
+
+SOURCE_PLAN_SHA256 = '5f40e7ccfca61f298539b4f41286d2a9d62caf947057f9cec82aa53f73f707fd'
+SOURCE_OWNERS_SHA256 = '99d1c4caf85855c353d30f122d9efbd9e51562914facded13027f347b18a6082'
+
+
+def require(condition, reason):
+    if not condition:
+        raise ValueError(reason)
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def canonical(value):
+    return json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+
+
+def portable_gzip(raw):
+    compressed = bytearray(gzip.compress(raw, mtime=0))
+    compressed[9] = 255  # RFC1952 OS=unknown, independent of zlib/Python platform.
+    return bytes(compressed)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def content_sha(value):
+    return hashlib.sha256(canonical(value)).hexdigest()
+
+
+def lift_parent(source, copies=2):
+    """A direct sum of bank/data stocks; erased private streams are shared.
+
+    copies=1 is deliberately the identity, byte-for-byte after canonicalization.
+    The helper routes retain replica lanes 0..7 in each *separate* bank group.
+    No axis index is inferred from the new global replica label 8..15.
+    """
+    require(type(copies) is int and copies in (1, 2), 'only identity or T16 lift')
+    t = copy.deepcopy(source)
+    if copies == 1:
+        return t
+    require(source['m'] == 73, 'source dimension')
+    require(len(source['calls']) == 72, 'source calls')
+    data = 8*8*112
+    bank_stock = source['live'] - data
+    private_stock = source['physical'] - source['live']
+    require((bank_stock, private_stock) == (9*504, 504+8+2), 'source namespace')
+    require({(c['stage'], c['replica']) for c in source['calls']} ==
+            {(s, r) for s in range(9) for r in range(8)}, 'source coverage')
+    new_data = copies*data
+    new_live = copies*source['live']
+    new_physical = new_live + private_stock
+    t['calls'] = []
+    for c in source['calls']:
+        for group in range(copies):
+            new = copy.deepcopy(c)
+            new['replica'] = c['replica'] + 8*group
+            owners = []
+            for family, route in c['owners']:
+                require(0 <= family < source['live'], 'owner outside live stock')
+                mapped = (family + data*group if family < data else
+                          new_data + group*bank_stock + family - data)
+                owners.append([mapped, copy.deepcopy(route)])
+            new['owners'] = owners
+            t['calls'].append(new)
+    # Every data/idle recipe is a portwise direct sum, hence only multiplicity
+    # changes. Its local axis labels and exact phase words stay unchanged.
+    for child in t['idle_children']:
+        require(child['replicas'] == 8, 'source idle multiplicity')
+        child['replicas'] *= copies
+    for event in t['execution_schedule']:
+        if 'replicas' in event:
+            require(event['replicas'] == list(range(8)), 'source sweep replicas')
+            event['replicas'] = list(range(8*copies))
+        if event['kind'] == 'bank_padding_cover_sweep':
+            event['families'] = [new_data, new_live]
+        elif event['kind'] == 'translate_every_live_family':
+            event['families'] = [0, new_live]
+            event['charged_calls_per_cover'] = new_live
+    t['bank_padding']['families'] = []
+    t['bank_padding']['children'] = []
+    for group in range(copies):
+        for family in source['bank_padding']['families']:
+            t['bank_padding']['families'].append(new_data + group*bank_stock + family - data)
+        for child in source['bank_padding']['children']:
+            new = copy.deepcopy(child)
+            new['family'] = new_data + group*bank_stock + child['family'] - data
+            t['bank_padding']['children'].append(new)
+    t['cover_final_correction'].update(families=[0, new_live], charged_calls_per_cover=new_live)
+    t['private_namespace'] = {
+        key: [new_live + x - source['live'] for x in interval]
+        for key, interval in source['private_namespace'].items()
+    }
+    t.update(live=new_live, physical=new_physical,
+             version='t16-direct-sum-two-bank-groups-parent-v1')
+    t['route_semantics']['helper'] = (
+        'Two independent groups of nine dedicated banks. Group floor(replica/8) '
+        'selects the bank namespace; the stored original helper route retains '
+        'lane replica%8. All original residual/spectator axes are unchanged.')
+    t['loop_order'] = (
+        'For each recipe phase: the explicit calls order, then every cover class d; '
+        'each local invocation completes before the next. Each original replica '
+        'has a disjoint data and bank namespace in its group; private erased '
+        'streams are reused between completed calls.')
+    t['replica_lift'] = dict(
+        source_template_content_sha256=content_sha(source), groups=copies,
+        source_replicas=8, replicas=8*copies, data_stock=new_data,
+        bank_stock=copies*bank_stock, banks_per_stage=copies*504,
+        private_helpers=504, local_programs_content_sha256=content_sha(source['local_programs']),
+        construction='direct sum of data and dedicated banks; share only restored private streams',
+        phase_recipe_unchanged=True)
+    # Source data and helper owner routes are preserved literally in each copy.
+    for c in t['calls']:
+        group, replica = divmod(c['replica'], 8)
+        old = next(z for z in source['calls'] if (z['stage'], z['replica']) == (c['stage'], replica))
+        require([r for f, r in c['owners']] == [r for f, r in old['owners']], 'route changed')
+        require(c['window'] == old['window'], 'local window changed')
+        require(len({f for f, r in c['owners']}) == len(c['owners']), 'per-call owner alias')
+    require(t['local_programs'] == source['local_programs'], 'program changed')
+    require(t['recipe'] == source['recipe'], 'data recipe changed')
+    require(len(t['bank_padding']['children']) == copies*bank_stock, 'bank padding count')
+    require(t['physical'] == t['live']+514, 'private namespace size')
+    return t
+
+
+def expanded_schedule(parent, order):
+    blocks = {}
+    globals_ = []
+    stage = None
+    for index, event in enumerate(parent['execution_schedule']):
+        if event['kind'] in ('bank_padding_cover_sweep', 'translate_every_live_family'):
+            globals_.append((index, event))
+            continue
+        if event['kind'] == 'local_cover_sweep':
+            stage = event['stage']
+            blocks[stage] = []
+        require(stage is not None, 'event precedes first stage')
+        blocks[stage].append((index, event))
+    schedule = []
+    for time, (stage, replica) in enumerate(order):
+        for index, event in blocks[stage]:
+            new = copy.deepcopy(event)
+            new.update(source_event=index, replica=replica, replicas=[replica], time=time)
+            schedule.append(new)
+    for index, event in globals_:
+        schedule.append(dict(event, source_event=index))
+    return schedule
+
+
+def actual_windows(parent, order):
+    ranks = {c['child']: c['rank'] for c in parent['idle_children']}
+    stage_pair = {e['stage']: e['pair'] for e in parent['recipe'] if e['kind'] == 'local'}
+    last, intervals, callpos, perrep = {}, {}, {}, {}
+    schedule = expanded_schedule(parent, order)
+    for pos, event in enumerate(schedule):
+        if 'replica' not in event:
+            continue
+        replica = event['replica']
+        perrep.setdefault(replica, []).append(event['source_event'])
+        if event['kind'] == 'local_cover_sweep':
+            last[replica, stage_pair[event['stage']]] = pos
+            callpos[event['time']] = pos
+        elif event['kind'] == 'bridge':
+            last[replica, event['src']] = last[replica, event['dst']] = pos
+        elif event['kind'] == 'idle_cover_sweep':
+            for child in event['child_indices']:
+                if child in ranks:
+                    intervals[replica, child] = (last.get((replica, event['pair']), -1), pos)
+    require(all(events == list(range(30)) for events in perrep.values()), 'per-replica projection')
+    require([e['source_event'] for e in schedule if 'replica' not in e] == [30, 31], 'global tail')
+    require(set(callpos) == set(range(len(order))), 'complete schedule')
+    windows = {f'{replica},{child}': [ranks[child], [time for time, pos in sorted(callpos.items()) if start < pos < stop]]
+               for (replica, child), (start, stop) in intervals.items()}
+    return windows, schedule
+
+
+def lift_plan(source, parent, owners, source_plan_sha, source_owners_sha, owners_sha):
+    p = copy.deepcopy(source)
+    require(source['T'] == 8 and len(source['order']) == 72, 'source plan dimensions')
+    order = [[stage, replica + 8*group] for stage, replica in source['order'] for group in range(2)]
+    windows, schedule = actual_windows(parent, order)
+    # These windows are recomputed from actual source-event touches, not copied
+    # from the old nomination. Their T8 restriction must recover the old plan.
+    rank = Counter({int(k): 2*v for k, v in source['profile'].items()})
+    rank.update({48: 1, 44: -1, 3: -2, 2: 1})
+    rank = +rank
+    p.update(status='FROZEN_EXPLICIT_T16_TWO_BANK_DIRECT_SUM_OWNER_NOMINATION',
+             mode='gauge44-all144-t16-idle-concentration', T=16, live=14336,
+             deficit=5120, profile=dict(sorted(rank.items())), order=order, windows=windows,
+             solver_status='explicit two-role augmenting path and two-bin recombination', gap=None,
+             source_plan_sha256=source_plan_sha, source_owners_sha256=source_owners_sha,
+             assignment_sha256=owners_sha, assignment_content_sha256=content_sha(owners))
+    for field in ('provider_calls', 'per_call_widths'):
+        p[field] = []
+        for old in source[field]:
+            for group in range(2):
+                new = copy.deepcopy(old)
+                new['replica'] += 8*group
+                if 'time' in new:
+                    new['time'] = 2*old['time']+group
+                p[field].append(new)
+    at = {tuple(x): i for i, x in enumerate(order)}
+    for field in ('provider_calls', 'per_call_widths'):
+        p[field].sort(key=lambda c: at[c['stage'], c['replica']])
+    p['replica_lift'] = dict(groups=2, source_replicas=8, replicas=16,
+                             parent_template_content_sha256=content_sha(parent), owners_file_sha256=owners_sha,
+                             window_semantics='strict physical source-event touch intervals, including bridges',
+                             schedule_content_sha256=content_sha(schedule))
+    require(len(owners) == 144*504, 'owner role count')
+    for role in owners:
+        require(role['time'] == at[role['stage'], role['replica']], 'role call time')
+        require(role['time'] in windows[f"{role['owner_replica']},{role['child']}"][1],
+                'owner outside actual source-event window')
+    require(sum(int(k)*v for k,v in p['profile'].items()) == 73*p['live']-p['deficit'], 'rank mass')
+    return p, schedule
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--base', type=Path, required=True)
+    parser.add_argument('--source-plan', type=Path, required=True)
+    parser.add_argument('--source-owners', type=Path, required=True)
+    parser.add_argument('--owners', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    require(not args.out.exists(), 'output directory already exists')
+    require(sha(args.source_plan) == SOURCE_PLAN_SHA256, 'source plan byte pin')
+    require(sha(args.source_owners) == SOURCE_OWNERS_SHA256, 'source owners byte pin')
+    source_path = args.base/'split-centres/GLOBAL-TEMPLATE.json.gz'
+    source = read(source_path)
+    original_plan = read(args.source_plan)
+    require(lift_parent(source, 1) == source, 'T8 identity control')
+    require(actual_windows(source, original_plan['order'])[0] == original_plan['windows'], 'T8 source-window replay')
+    require(source['exact_data_phase_recipe_sha256'] == sha(args.base/'work/complex-nine-native/DATA-PHASES.json'), 'source exact data-phase binding')
+    parent = lift_parent(source)
+    owners = read(args.owners)
+    plan, schedule = lift_plan(original_plan, parent, owners, sha(args.source_plan), sha(args.source_owners), sha(args.owners))
+    args.out.mkdir(parents=True)
+    (args.out/'GLOBAL-TEMPLATE.json.gz').write_bytes(portable_gzip(canonical(parent)))
+    (args.out/'PLAN.json').write_bytes((json.dumps(plan, indent=2)+'\n').encode('utf-8'))
+    receipt = dict(status='PASS_T16_DIRECT_SUM_PARENT_AND_LITERAL_SOURCE_WINDOWS',
+                   source_template_file_sha256=sha(source_path), source_template_content_sha256=content_sha(source),
+                   source_plan_sha256=sha(args.source_plan), source_owners_sha256=sha(args.source_owners),
+                   owners_sha256=sha(args.owners),
+                   parent_template_file_sha256=sha(args.out/'GLOBAL-TEMPLATE.json.gz'),
+                   parent_template_content_sha256=content_sha(parent), plan_sha256=sha(args.out/'PLAN.json'),
+                   T8_identity_control=True, T8_source_window_identity=True,
+                   local_programs_identical=True, exact_data_phases_identical=True,
+                   parent_live=parent['live'], parent_physical=parent['physical'],
+                   bank_stock=9072, banks_per_stage=1008, private_helpers=504,
+                   source_idle_children_charged=sum(c['replicas'] for c in parent['idle_children']),
+                   events=len(schedule), replica_source_events=30, global_source_events=[30,31],
+                   calls=len(plan['order']), roles=len(owners), actual_window_membership_checked=len(owners),
+                   scope='Legal direct-sum parent namespace and actual source-event windows; full global emitter, geometry, finite invoice, and recurrence admission remain separate checks.')
+    (args.out/'PARENT-LIFT-RECEIPT.json').write_bytes((json.dumps(receipt, indent=2)+'\n').encode('utf-8'))
+    print(json.dumps(receipt, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/r480-owner-optimum/verify.py b/research/r480-owner-optimum/verify.py
new file mode 100644
index 0000000000..877a0c73e0
--- /dev/null
+++ b/research/r480-owner-optimum/verify.py
@@ -0,0 +1,228 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Check the fixed R480 owner bound with exact rational arithmetic."""
+import argparse
+from collections import Counter
+from fractions import Fraction as Q
+import hashlib
+import importlib.util
+import itertools
+import json
+from pathlib import Path
+import sys
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+
+
+def need(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def read(path):
+    return json.loads(path.read_text())
+
+
+def digest(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def source_contract():
+    pins = read(HERE / 'SOURCES.json')
+    for relative, expected in pins['files'].items():
+        path = HERE / relative[8:] if relative.startswith('package:') else ROOT / relative
+        need(digest(path) == expected, 'source drift: ' + relative)
+    spec, plan = read(HERE / 'inputs/SPEC.json'), read(HERE / 'inputs/PLAN.json')
+    provider = spec['providers']['gauge44']
+    local = {int(r): n for r, n in provider['expected_profile'].items()}
+    widths = {int(w): n for w, n in provider['inventory'].items()}
+    registry = plan['provider_registry']['gauge44']
+    need(Counter(registry['widths']) == widths, 'source width contract')
+    need({int(r): n for r, n in registry['actual_paid_profile'].items()} == local,
+         'source paid profile contract')
+    T = plan['T']
+    need(len(plan['order']) == 9*T and set(map(tuple, plan['order'])) ==
+         set(itertools.product(range(9), range(T))), 'source call coverage')
+    byrep = {r: Counter() for r in range(T)}
+    for key, (capacity, times) in plan['windows'].items():
+        replica, child = map(int, key.split(','))
+        byrep[replica][capacity] += 112
+    need(all(stock == byrep[0] for stock in byrep.values()), 'replica capacity contract')
+    need(plan['M'] == 73 and plan['live'] == 896*T, 'source stock contract')
+    engine = ROOT / pins['engine_directory']
+    modules = [load(engine / (name + '.py'), 'r480_' + name)
+               for name in ('moment', 'base_two_moment', 'outer')]
+    driver = load(ROOT / pins['outer_driver'], 'r480_outer_driver')
+    return local, widths, byrep[0], modules, driver, pins
+
+
+def enumerate_bins(widths, prices, bonuses):
+    upper, patterns = {}, []
+    for capacity, bonus in sorted(bonuses.items()):
+        for counts in itertools.product(*(range(capacity//w+1) for w in widths)):
+            used = sum(w*n for w, n in zip(widths, counts))
+            if used > capacity:
+                continue
+            residual = capacity - used
+            value = bonus + sum(p*n for p, n in zip(prices, counts))
+            upper[residual] = max(upper.get(residual, -10**9), value)
+            patterns.append((capacity, counts, residual, value))
+    # This recurrence uses ordered fills, without a count-vector product.
+    second = {}
+    for capacity, bonus in sorted(bonuses.items()):
+        best = {0: 0}
+        for used in range(capacity+1):
+            if used not in best:
+                continue
+            for width, price in zip(widths, prices):
+                if used+width <= capacity:
+                    best[used+width] = max(best.get(used+width, -10**9), best[used]+price)
+        for used, value in best.items():
+            r = capacity-used
+            second[r] = max(second.get(r, -10**9), bonus+value)
+    need(upper == second, 'independent bin recurrence')
+    return upper, patterns
+
+
+def phi(engine, kind, rank, endpoint):
+    if kind == 'mercator':
+        a, b = engine.logarithm(Q(73, rank))
+        lo, hi = engine.exponential(endpoint*a, endpoint*b)
+    else:
+        a, b = engine.log_bounds(Q(73, rank))
+        lo, hi = engine.exp_bounds(endpoint*a)[0], engine.exp_bounds(endpoint*b)[1]
+    return rank*lo, rank*hi
+
+
+def supporting_certificate(engine, kind, upper, lower, higher):
+    # Enclose all exponents in the root interval, not only one grid point.
+    values = {r: (phi(engine, kind, r, lower)[0], phi(engine, kind, r, higher)[1])
+              for r in upper if r}
+    cost = {r: (48*lo-r*values[48][1], 48*hi-r*values[48][0])
+            for r, (lo, hi) in values.items() if r < 48}
+    credit = {r: 48*upper[r]-r*upper[48] for r in cost}
+    need(credit[1] > 0 and cost[1][0] > 0, 'positive rank-one multiplier')
+    margins = {}
+    for rank, (lo, hi) in cost.items():
+        if rank == 1:
+            continue
+        coefficient = credit[rank]
+        rhs = coefficient*cost[1][1 if coefficient >= 0 else 0]/credit[1]
+        margins[rank] = lo-rhs
+        need(margins[rank] > 0, 'strict rank support: ' + str(rank))
+    return {'multiplier_interval': [str(x/credit[1]) for x in cost[1]],
+            'strict_margins': {r: str(x) for r, x in sorted(margins.items())},
+            'minimum_strict_margin': str(min(margins.values()))}
+
+
+def check(certificate):
+    need(not sys.flags.optimize, 'Retained outer assertions require Python without -O')
+    local, inventory, stock, (M, B, A), outer, pins = source_contract()
+    widths = tuple(sorted(inventory))
+    need(set(certificate['width_prices']) == set(map(str, widths)), 'width price keys')
+    need(all(type(n) is int for n in certificate['width_prices'].values()), 'integer width prices')
+    need(all(type(n) is int for n in certificate['capacity_bonuses'].values()), 'integer capacity bonuses')
+    need(set(certificate['capacity_bonuses']) == set(map(str, stock)), 'capacity price keys')
+    prices = tuple(certificate['width_prices'][str(w)] for w in widths)
+    bonuses = {int(c): x for c, x in certificate['capacity_bonuses'].items()}
+    need(set(bonuses) == set(stock), 'capacity price coverage')
+    upper, patterns = enumerate_bins(widths, prices, bonuses)
+    need(upper[0] == 0 and max(upper) == 48, 'zero and maximum residual')
+    mass = sum(c*n for c, n in stock.items())-9*sum(w*n for w, n in inventory.items())
+    signed = sum(stock[c]*bonuses[c] for c in stock)+9*sum(inventory[w]*p for w, p in zip(widths, prices))
+    credit = 48*signed-upper[48]*mass
+    unit = 48*upper[1]-upper[48]
+    need(credit > 0 and unit > 0, 'positive credit demand')
+    formal = {1: Q(credit, unit)}
+    formal[48] = (mass-formal[1])/48
+    T = certificate['replicas']
+    need(type(T) is int and T > 0, 'positive integral replicas')
+    need(all((n*T).denominator == 1 for n in formal.values()), 'integral residual counts')
+    idle = Counter({r: int(n*T) for r, n in formal.items()})
+    counts, bins, actual_idle = Counter(), Counter(), Counter()
+    for row in certificate['packing']:
+        capacity, vector, multiplicity = row['capacity'], row['width_counts'], row['bins']
+        need(type(capacity) is int, 'integer packing capacity')
+        need(type(multiplicity) is int and multiplicity > 0, 'positive packing multiplicity')
+        need(len(vector) == len(widths) and all(type(n) is int and n >= 0 for n in vector),
+             'integer packing vector')
+        used = sum(w*n for w, n in zip(widths, vector))
+        need(capacity in stock and used <= capacity, 'whole-helper capacity')
+        bins[capacity] += multiplicity
+        counts.update({w: multiplicity*n for w, n in zip(widths, vector)})
+        if capacity > used:
+            actual_idle[capacity-used] += multiplicity
+    need(bins == Counter({c: n*T for c, n in stock.items()}), 'complete bin stock')
+    need(counts == Counter({w: 9*T*n for w, n in inventory.items()}), 'complete helper inventory')
+    need(actual_idle == idle, 'attaining residual profile')
+    profile = Counter({r: 9*T*n for r, n in local.items()})
+    profile.update(idle)
+    live = 896*T
+    need(73*live-sum(r*n for r, n in profile.items()) == 320*T, 'complete rank deficit')
+    need(73**2 > 2*max(profile)**2, 'proper-child halving guard')
+    need(len(certificate['root_interval']) == 2 and all(type(x) is str for x in certificate['root_interval']), 'rational root strings')
+    need(type(certificate['kappa_grid']) is str, 'rational kappa string')
+    lower, higher = map(Q, certificate['root_interval'])
+    need(higher-lower == Q(1, 10**24), 'root interval width')
+    signs = {}
+    for name, endpoint in [('lower', lower), ('upper', higher)]:
+        first, second = M.moment(profile, 73, live, endpoint), B.moment(73, live, list(profile.items()), endpoint)
+        need((first[1] < 1 and second[1] < 1) if name == 'lower' else
+             (first[0] > 1 and second[0] > 1), 'two exact root signs: ' + name)
+        signs[name] = {'mercator': [str(x-1) for x in first],
+                       'atanh': [str(x-1) for x in second]}
+    supports = {kind: supporting_certificate(engine, kind, upper, lower, higher)
+                for kind, engine in [('mercator', M), ('atanh', B)]}
+    result1074 = read(HERE / 'inputs/RESULT.json')
+    bit_record = read(ROOT / pins['bit_expected'])
+    bit = bit_record['nine']
+    c = Q(bit['bit_lower'])
+    need(c == Q(result1074['bit_lower']), 'unchanged bit endpoint')
+    bit_histogram = {int(r): n for r, n in bit['profile'].items()}
+    bit_deficit = outer.pr589_deficit(bit_record['word'], bit['bit']['live'])
+    bit_checks = outer.moment_checks(M, B, bit_histogram, 64, bit['bit']['live'], c, bit_deficit, True)
+    prices = {key: outer.outer47(c, b, A) for key, b in [('lower', lower), ('upper', higher)]}
+    need(all(Q(p['kappa']) == Q(certificate['kappa_grid']) for p in prices.values()), 'same outer grid cell')
+    minT = 1
+    import math
+    for n in formal.values():
+        minT = math.lcm(minT, n.denominator)
+    return {'status': 'PASS_R480_ALL_REPLICA_BIN_OPTIMUM',
+            'scope': 'Exact owner bin relaxation. Time windows, per-call family matching, charts, local admission and finite invoices are separate.',
+            'base': pins['base'], 'source_head': pins['source_head'],
+            'inventory': inventory, 'local_profile': local, 'capacity_stock': stock,
+            'bin_patterns': len(patterns), 'upper_price_by_residual': upper,
+            'idle_mass_per_replica': mass, 'signed_price_per_replica': signed,
+            'credit_per_replica': credit, 'rank_one_credit': unit,
+            'normalized_idle': {r: str(n) for r, n in formal.items()},
+            'minimum_equality_replicas': minT, 'packing_replicas': T,
+            'packing_idle': dict(sorted(idle.items())), 'profile': dict(sorted(profile.items())),
+            'live': live, 'deficit': 320*T, 'root_interval': [str(lower), str(higher)],
+            'two_engine_signs': signs, 'support_over_root_interval': supports,
+            'bit_moments_with_surcharge': bit_checks, 'outer': prices, 'kappa_grid_ceiling': certificate['kappa_grid'],
+            'headroom_over_pr1074': str(Q(certificate['kappa_grid'])-Q(result1074['kappa'])),
+            'source_sha256': pins['files']}
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--certificate', type=Path, default=HERE / 'CERTIFICATE.json')
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    need(not args.out.exists(), 'Choose a new output file')
+    result = check(read(args.certificate))
+    args.out.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], 'patterns='+str(result['bin_patterns']),
+          'kappa_grid_ceiling='+str(Q(result['kappa_grid_ceiling'])))
+
+
+if __name__ == '__main__':
+    main()