diff --git a/research/adaptive-kernel-demotion/LICENSE b/research/adaptive-kernel-demotion/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/adaptive-kernel-demotion/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/adaptive-kernel-demotion/MANIFEST.json b/research/adaptive-kernel-demotion/MANIFEST.json
new file mode 100644
index 0000000000..902eca9295
--- /dev/null
+++ b/research/adaptive-kernel-demotion/MANIFEST.json
@@ -0,0 +1,74 @@
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diff --git a/research/adaptive-kernel-demotion/NOTICE.md b/research/adaptive-kernel-demotion/NOTICE.md
new file mode 100644
index 0000000000..30d0c8cd3c
--- /dev/null
+++ b/research/adaptive-kernel-demotion/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/adaptive-kernel-demotion/README.md b/research/adaptive-kernel-demotion/README.md
new file mode 100644
index 0000000000..d6180f4004
--- /dev/null
+++ b/research/adaptive-kernel-demotion/README.md
@@ -0,0 +1,95 @@
+# Adaptive kernel demotion on the rank-seven T16 supplier
+
+**Conditional kappa: 0.001673260706543984.** Conservative endpoint:
+**0.001673260703699378**. Frozen comparison: PR1117 at
+`342b67f23dfa8f41a520a0d58978b2875e9eb0dd`, kappa
+0.001672846995880185. Absolute improvement: 0.000000413710663799.
+Public proposals were read through PR1120; this comparison is to that snapshot.
+
+From the repository root, with Python 3.10+ and a fresh output directory:
+
+```sh
+python -I -B research/adaptive-kernel-demotion/verify.py --out ../adaptive-result
+```
+
+The replay is sequential and standard-library-only. It launches bounded native
+Python children at BelowNormal priority on Windows. It does not run C++, WSL,
+GPU software, Lean, optimizers, network requests or persistent background jobs.
+Five providers are independently reconstructed and checked; allow roughly two
+minutes for the complete run on a typical desktop. Generated programs, charts,
+receipts and logs go outside the immutable package.
+
+## Construction and exact result
+
+Five jointly checked entrance-demotion prefixes use groups 635, 603, 611, 619,
+627. The provider selected at each literal call depends on the actual pending
+axis capacity. Final dispatch uses prefixes zero through five 41, 24, 8, 15, 6,
+50 times. This realizes 359 group demotions over 103 calls, plus one legal
+three-owner cycle. All 69,120 roles are retained exactly once. The complete paid
+profile is:
+
+```text
+{1:344363, 2:65097, 3:62855, 4:19012, 5:11808,
+ 7:8, 8:1152, 11:2, 48:4873}
+```
+
+Rank mass 1,041,408; live stock 14,336; deficit 5,120; paid idle remainders 6,034;
+actual 73-column chart types 9,898. The complete literal owner difference has
+4,594 changed rows. It reconstructs the final table from the retained old table.
+Both exact rational moment engines price the complete profile, followed by all
+47 strict outer constraints; numerical gains from other PRs are never added.
+
+The new invoice charges the entire fresh per-vertex bill 3,588,959,010,714,576 on
+top of the pinned old allowance 2,877,946,989,724,568, giving
+6,466,906,000,439,144. All nine finite inequalities and four corruption controls
+are checked. The mixed owner audit includes all actual pending axes and 11
+corruption controls. Each local provider is checked on all 704 arbitrary input
+columns in both orientations, with 25 emitted-program controls and additional
+exact changed-phase controls.
+
+## Two distinct OpenAI-source mechanisms per worker
+
+These are mathematical adaptations, not new kernel certificates or eight
+independently additive exponent gains. Sources were inspected in the registered
+[OpenAI math collection](https://github.com/openai/math). Exact source hashes,
+declarations and their contribution are recorded in the following notes:
+
+| Worker | Two structures adapted | Notes and exact source ledger |
+|---|---|---|
+| Local supplier | Rank-increment accounting; terminal-product restriction/transfer | [Mechanisms](notes/cells/OPENAI-MECHANISMS.md), [sources](notes/cells/OPENAI-SOURCE-LEDGER.json) |
+| Owners | Alternating matching switches; disjoint first-hit projector partitions | [Mechanisms and sources](notes/owners/OPENAI-MECHANISMS.md) |
+| Whole controller | Species-allocation bijections; integer contingency-table exchanges | [Proof and sources](notes/recurrence/GAP-AWARE-DEMOTION.md), [source ledger](notes/recurrence/OPENAI-SOURCES.json) |
+| Assembly | Positive normalized Jensen-gap weights; discrete convex secants | [Mechanisms](notes/lead/OPENAI-MECHANISMS.md), [sources](notes/lead/OPENAI-SOURCES.json) |
+
+The sufficient demotion theorem proves a strict complete moment saving for all
+0 < b < 1 for the three realized gap patterns. See
+[the proof](notes/owners/SUFFICIENT-DEMOTION-THEOREMS.md) and
+[the combined route](notes/owners/MULTIGROUP-SUFFICIENT-PROOF.md).
+[The fresh invoice proof](notes/recurrence/FRESH-INVOICE-PROOF.md) records literal
+work and restoration accounting. Other notes retain bounded searches, fallback
+constructions and discarded routes without awarding them numerical gains.
+
+## Scope, inheritance and reproducibility
+
+This is a finite certificate of an improved **conditional** construction. Fresh
+checks cover every changed local word, changed phase edges and wrappers, literal
+owner geometry, complete histogram, invoice inequalities and exact assembly.
+Unchanged old scalar admission and phase edges, compiler/all-size contracts,
+common-label and mutable-source realization, whole-call hosting, precision/tape,
+exact recovery, analytic transfer and the inherited bit circuit remain explicit
+interfaces. The pinned bit profile's arithmetic bracket is rechecked; its entire
+circuit is not replayed. No unconditional multiplication theorem, new Lean
+formalization, upstream CI pass or packing optimum is claimed.
+
+`MANIFEST.json` binds every other file by SHA-256; an exact inventory is checked
+before any replay. `vendor/pr1117/data/UPSTREAM-PINS.json` binds retained ancestor
+inputs. Generated gzip bytes may depend on the Python version; mathematical
+objects and fresh byte bindings are checked together. Upload sources without
+line-ending conversion; hashes intentionally reject changed source bytes.
+
+Direct inputs are PR1117, PR1111 and the PR1030 demotion context. Retained ancestry
+includes PR1018/987, PR1005/1004, PR1022/858, PR869, PR799, PR741, PR685, PR645,
+PR635 and the PR589 bit supplier. PR1063/1094 and PR1072 informed the owner and
+promotion comparisons. See `NOTICE.md`, `UPSTREAM-NOTICE.md`, the local notices
+and Apache-2.0 `LICENSE` for preserved attribution and AI disclosures. New work
+was prepared with OpenAI Codex assistance; no submitting-user name/email is added.
diff --git a/research/adaptive-kernel-demotion/UPSTREAM-NOTICE.md b/research/adaptive-kernel-demotion/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/adaptive-kernel-demotion/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/adaptive-kernel-demotion/audit_mixed.py b/research/adaptive-kernel-demotion/audit_mixed.py
new file mode 100644
index 0000000000..c0430f1a2a
--- /dev/null
+++ b/research/adaptive-kernel-demotion/audit_mixed.py
@@ -0,0 +1,115 @@
+"""Independent exact mixed-call owner, actual windows and 73-axis chart check.
+Standard-library only; frozen local semantic admission remains explicit.
+"""
+import argparse,collections,hashlib,importlib.util,json,time
+from pathlib import Path
+spec=importlib.util.spec_from_file_location('owner_core',Path(__file__).with_name('audit_owner_table.py'))
+O=importlib.util.module_from_spec(spec);spec.loader.exec_module(O)
+
+def basis(vs):
+ d={}
+ for x in vs:
+  O.need(type(x) is int and 0<=x<512,'invalid local frame')
+  while x:
+   p=x.bit_length()-1
+   if p in d:x^=d[p]
+   else:d[p]=x;break
+ return tuple(d[k] for k in sorted(d,reverse=True))
+
+def local_contract(native,inherited=None):
+ w=O.read(native/'CANONICAL-WORD.json.gz')
+ if inherited is None:
+  r=O.read(native/'INDEPENDENT-LOCAL-REPLAY.json')
+  O.need(O.sha(native/'CANONICAL-WORD.json.gz')==r['canonical_word_sha256'],'local canonical binding')
+  O.need(O.sha(native/'LOCAL-PROGRAMS.json.gz')==r['local_programs_sha256'],'local program binding')
+ else:
+  r=dict(paid_profiles={o:inherited['paid_profile'] for o in ('forward','backward')},local={o:dict(prefix_bits_upper=inherited['local'][o]['prefix_bits']) for o in ('forward','backward')},scope='old scalar semantic admission inherited; frame profile and width freshly recounted')
+ F=[basis(x) for x in w['frames']];now=[F[i] for i in w['start']];paid=collections.Counter()
+ def climb(q,to):
+  O.need(len(basis(now[q]+to))==len(to),'local nonmonotone frame')
+  jump=len(to)-len(now[q]);O.need(jump>=0,'negative local jump')
+  if jump:paid[jump]+=1
+  now[q]=to
+ O.need(not w['target_levels'],'zero target centre interface')
+ for sec in ('A','B','tail'):
+  if sec=='B':
+   O.need(all(not now[q] for q in range(w['v'],2*w['v'])),'target level interface')
+   for q,fi in zip(w['centers'],w['center_frames']):O.need(now[q]==F[fi],'centre frame');paid[len(F[fi])]+=1
+  for gate in w[sec]:
+   O.need(gate[0] in ('add','scale'),'local scalar gate')
+   for q in (gate[1:3] if gate[0]=='add' else gate[1:2]):climb(q,F[gate[-1]])
+ for q,fi in enumerate(w['final']):climb(q,F[fi])
+ O.need(dict(paid)=={int(k):v for k,v in w['local_profile'].items()},'complete local profile recount')
+ for orientation in ('forward','backward'):O.need(dict(paid)=={int(k):v for k,v in r['paid_profiles'][orientation].items()},'native local profile binding')
+ widths=[len(F[w['final'][q]])-len(F[w['start'][q]]) for q in range(2*w['v'],len(w['start']))]
+ O.need(len(widths)==480 and all(0<v<=9 for v in widths),'actual local widths')
+ return widths,dict(paid),r
+
+def run(package,owners,dispatch,old_native,new_native,canonical,phases,parent,variants=None):
+ P=O.read(package/'data/PLAN.json');S=O.read(package/'data/SPEC.json');rows=O.read(owners);D=O.read(dispatch)
+ ow,op,oldr=local_contract(old_native,S['providers']['gauge44']['complete_contract'])
+ O.need(ow==S['providers']['gauge44']['complete_contract']['widths'],'actual old widths contract')
+ O.need(op=={int(k):v for k,v in S['providers']['gauge44']['expected_profile'].items()},'actual old local profile')
+ group_order=[[411,413,414,415],[379,381,382,383],[387,389,390,391],[395,397,398,399],[403,405,406,407]]
+ contracts={};dirs=dict(variants or {});dirs.setdefault(1,new_native)
+ selected={d.get('variant',1) for d in D}
+ O.need(selected<=set(dirs),'missing actual native variant')
+ for k in sorted(selected):
+  O.need(type(k) is int and 1<=k<=5,'invalid variant')
+  nw,np,nr=local_contract(dirs[k]);expected=sum(group_order[:k],[])
+  O.need(sorted(i for i,(a,b) in enumerate(zip(ow,nw)) if a!=b)==sorted(expected),'exact changed helpers')
+  O.need(all(nw[i]==ow[i]+1 for i in expected),'exact widened helpers')
+  delta=collections.Counter(np);delta.subtract(op)
+  O.need({j:v for j,v in delta.items() if v}=={1:-8*k,2:8*k,3:4*k,4:-4*k},'exact joint demotion local delta')
+  O.need(sum(op.values())==sum(np.values()),'same local child count')
+  contracts[k]=(nw,np,nr)
+ wc={};pc={};seen=set();variant_counts=collections.Counter()
+ for d in D:
+  c=tuple(d['call']);O.need(c not in seen and P['order'][d['time']]==list(c),'literal dispatch time');seen.add(c);k=d.get('variant',1)
+  O.need(d['helpers']==sum(group_order[:k],[]),'literal changed helpers')
+  wc[c],pc[c],_=contracts[k];variant_counts[k]+=1
+ result=O.verify(rows,P,S,O.read(canonical),O.read(phases),widths_by_call=wc,profiles_by_call=pc,parent=O.read(parent))
+ result['mixed_calls']=len(D);result['default_calls']=144-len(D)
+ result['source_event_windows']='fresh reconstruction from source_schedule and actual phase-axis ranks'
+ result['local_contracts']='fresh complete frame profiles and widths on both canonical words; changed-word scalar receipt freshly bound; unchanged old scalar admission inherited'
+ result['variant_counts']=dict(sorted(variant_counts.items()))
+ result['local_prefix_bits']={o:max([oldr['local'][o]['prefix_bits_upper']]+[z[2]['local'][o]['prefix_bits_upper'] for z in contracts.values()]) for o in ('forward','backward')}
+ result['local_contract_count']=1+len(contracts)
+ return result,(rows,P,S,O.read(canonical),O.read(phases),wc,pc,O.read(parent))
+
+def negative_controls(context):
+ import copy
+ rows,plan,spec,canon,ph,wc,pc,parent=context
+ tests=[]
+ def reject(name,r=None,p=None,h=None,override=None,widths=None):
+  try:O.verify(rows if r is None else r,plan if p is None else p,spec,canon,ph if h is None else h,override=override,widths_by_call=wc if widths is None else widths,profiles_by_call=pc,parent=parent)
+  except RuntimeError as e:tests.append(dict(name=name,rejected=str(e)));return
+  raise RuntimeError('accepted mutation '+name)
+ r=rows.copy();r[1]=dict(r[0]);reject('duplicate_role',r)
+ r=rows.copy();r[0]=dict(r[0],width=r[0]['width']+1);reject('wrong_actual_width',r)
+ r=rows.copy();r[0]=dict(r[0],time=r[0]['time']+1);reject('wrong_call_time',r)
+ r=rows.copy();r[0]=dict(r[0],offset=-1);reject('negative_axis_offset',r)
+ r=rows.copy();r[1]=dict(r[1]);
+ for key in ['owner_replica','child','port','copy','family','offset']:r[1][key]=r[0][key]
+ reject('per_call_family_alias',r)
+ r=rows.copy();r[0]=dict(r[0],owner_replica=0,child=5,port=rows[0]['port'],copy=rows[0]['port'],family=(2*plan['pairs']['5']+plan['sides']['5'])*112+rows[0]['port'],offset=0);reject('out_of_window',r)
+ reject('wrong_73_axis_chart',override={0:O.idle_basis(canon['ports'][rows[0]['port']])[::-1]})
+ p=copy.deepcopy(plan);p['windows'][next(iter(p['windows']))][1].append(143);reject('tampered_source_event_window',p=p)
+ r=rows.copy();r[0]=dict(r[0],family=14336);reject('private_namespace_or_family_identity',r)
+ reject('forgot_widened_dispatch',widths={})
+ h=copy.deepcopy(ph);h['recipes'][0]['idle_children'][0]['orthogonal_axes'].pop();reject('incorrect_phase_rank',h=h)
+ return tests
+
+def main():
+ a=argparse.ArgumentParser()
+ for k in ('package','owners','dispatch','old-native','new-native','canonical','phases','parent','out'):a.add_argument('--'+k,type=Path,required=True)
+ a.add_argument('--controls',action='store_true');a.add_argument('--variant',action='append',default=[],help='K=actual-native-directory')
+ z=a.parse_args();O.need(not z.out.exists(),'fresh output required');t=time.monotonic();variants={int(x.split('=',1)[0]):Path(x.split('=',1)[1]) for x in z.variant}
+ result,context=run(z.package,z.owners,z.dispatch,z.old_native,z.new_native,z.canonical,z.phases,z.parent,variants=variants)
+ if z.controls:result['negative_controls']=negative_controls(context)
+ charts=result.pop('sigmas');remainders=result.pop('remainders')
+ import gzip
+ for suffix,data in [('SIGMAS',charts),('REMAINDERS',remainders)]:z.out.with_name(z.out.stem+'-'+suffix+'.json.gz').write_bytes(gzip.compress(json.dumps(data,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+ result.update(status='PASS_ACTUAL_MIXED_OWNER_WINDOWS_CHARTS_PROFILE',seconds=time.monotonic()-t,inputs={str(p):O.sha(p) for p in [z.package/'data/PLAN.json',z.package/'data/SPEC.json',z.owners,z.dispatch,z.canonical,z.phases,z.parent,z.old_native/'CANONICAL-WORD.json.gz',z.new_native/'CANONICAL-WORD.json.gz']})
+ z.out.write_text(json.dumps(result,indent=2)+'\n',encoding='utf-8',newline='\n');print(json.dumps({k:v for k,v in result.items() if k!='inputs'},indent=2))
+if __name__=='__main__':main()
diff --git a/research/adaptive-kernel-demotion/audit_owner_table.py b/research/adaptive-kernel-demotion/audit_owner_table.py
new file mode 100644
index 0000000000..199e9b181d
--- /dev/null
+++ b/research/adaptive-kernel-demotion/audit_owner_table.py
@@ -0,0 +1,104 @@
+"""Independent bounded check of an owner-table replacement; no source-package execution.
+Checks changed literal map using published, hash-pinned windows and phase axes.
+Inherited windows/local semantics are explicit assumptions; this is not whole-proof verification.
+"""
+import argparse,json,gzip,hashlib,collections,copy,time
+from pathlib import Path
+
+def read(p):
+ b=Path(p).read_bytes();return json.loads(gzip.decompress(b) if str(p).endswith('.gz') else b)
+def sha(p):return hashlib.sha256(Path(p).read_bytes()).hexdigest()
+def need(x,msg):
+ if not x:raise RuntimeError(msg)
+def idle_basis(q):
+ z=next(j for j in range(9) if not(q>>j)&1);u=q^(1<<z);order=list(range(9));order[0],order[z]=order[z],order[0]
+ return [(1<<j)^(u if (u>>j)&1 else 0) for j in order]+[1<<j for j in range(9,73)]
+
+def verify(rows,P,S,canon,ph,override=None,widths_by_call=None,profiles_by_call=None,parent=None):
+ T=P["T"]; nc=9*T; live=896*T; deficit=320*T
+ widths_by_call=widths_by_call or {}; profiles_by_call=profiles_by_call or {}
+ order=[tuple(x) for x in P['order']];at={k:i for i,k in enumerate(order)};need(len(order)==nc and len(at)==nc,'call order');need(order==[tuple(x) for x in S['call_order']],'published order');widths=S['providers']['gauge44']['complete_contract']['widths'];need(len(widths)==480,'provider width count')
+ need(len(rows)==nc*480,'role count');seen=set();families=collections.defaultdict(set);groups=collections.defaultdict(list);sigmas={};chart_cache={};chart_hashes={};stream=hashlib.sha256();cross=0
+ if parent is not None:
+  context=rebuild_windows(parent,order,T,ph);need(context['windows']==P['windows'],'actual source-event windows');need(context['pairs']==P['pairs'] and context['sides']==P['sides'],'actual child family identity')
+  for z in rows:
+   need(z['owner_replica']!=z['replica'] or int(P['pairs'][str(z['child'])])!=context['stage_pair'][z['stage']],'caller active family collision')
+ bases=[idle_basis(q) for q in canon['ports']];need(len(bases)==112 and ph['ports']==112 and [r['q'] for r in ph['recipes']]==canon['ports'],'phase port geometry')
+ for B in bases:
+  need(len(set(B))==73 and all(((x&y).bit_count()%2)==int(i==j) for i,x in enumerate(B) for j,y in enumerate(B)),'orthogonal basis')
+ for p,B in enumerate(bases):
+  reserved=collections.defaultdict(set)
+  for child,recipe in enumerate(ph['recipes'][p]['idle_children']):
+   axes=set(recipe['orthogonal_axes']);need(len(axes)==recipe['rank'] and axes<=set(B),'complete pending physical basis')
+   if not recipe['rank']:continue
+   need(str(child) in P['pairs'] and P['windows'][f'0,{child}'][0]==recipe['rank'],'complete pending cap')
+   key=(P['pairs'][str(child)],P['sides'][str(child)])
+   need(not(reserved[key]&axes),'distinct-child pending axes overlap');reserved[key].update(axes)
+ for idx,z in enumerate(rows):
+  need(all(type(z.get(k)) is int for k in ('stage','replica','helper','time','owner_replica','child','port','copy','family','offset','width')),'integer role schema')
+  st,r,h=z['stage'],z['replica'],z['helper'];time_=z['time'];o,c,p=z['owner_replica'],z['child'],z['port'];w,off=z['width'],z['offset'];role=(st,r,h)
+  need((st,r) in at and time_==at[st,r],'call time');need(0<=h<480 and w==widths_by_call.get((st,r),widths)[h],'helper width');need(role not in seen,'duplicate role');seen.add(role)
+  need(0<=o<T and 0<=p<112,'owner port');key=f'{o},{c}';need(key in P['windows'],'pending child');cap,allowed=P['windows'][key];need(time_ in allowed,'out of window');need(0<=off and off+w<=cap,'coordinate bound');need(z['copy']==112*o+p,'copy identity');need(z['family']==896*o+(2*P['pairs'][str(c)]+P['sides'][str(c)])*112+p,'family identity');need(z['family'] not in families[time_],'per-call family alias');families[time_].add(z['family']);groups[o,c,p].append(z);cross+=o!=r
+  ck=(p,c,off,w)
+  if ck not in chart_cache:
+   B=bases[p];pending=list(map(int,ph['recipes'][p]['idle_children'][c]['orthogonal_axes']));need(len(pending)==cap and len(set(pending))==cap,'pending axis rank');need(all(x in B for x in pending),'pending basis containment');occ=[B.index(x) for x in pending[off:off+w]];sp=[j for j in range(73) if j not in occ][:9-w];perm=occ+sp+[j for j in range(73) if j not in occ+sp];need(sorted(perm)==list(range(73)),'full chart permutation');sigma=[B[j] for j in perm];need(sigma[:w]==pending[off:off+w] and len(set(occ+sp))==9,'actual residual chart');chart_cache[ck]=sigma
+  sigma=chart_cache[ck]
+  if override and idx in override:need(override[idx]==sigma,'wrong chart')
+  if ck not in chart_hashes:chart_hashes[ck]=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest()
+  sh=chart_hashes[ck];sigmas[sh]=sigma;stream.update(json.dumps([st,r,h,z['family'],sh],separators=(',',':')).encode()+b'\n')
+ need(seen=={(s,r,h) for s in range(9) for r in range(T) for h in range(480)},'complete roles')
+ used={}
+ for k,zs in groups.items():
+  pointer=0
+  for z in sorted(zs,key=lambda z:(z['time'],z['helper'])):
+   need(z['offset']==pointer,'overlapping or non-chronological axes');pointer+=z['width']
+  used[k]=pointer
+ idle=collections.Counter();remainders=[]
+ for key,(cap,allowed) in P['windows'].items():
+  o,c=map(int,key.split(','))
+  for p in range(112):
+   used_=used.get((o,c,p),0);rem=cap-used_;need(rem>=0,'negative remainder')
+   if rem:
+    idle[rem]+=1;remainders.append({'owner_replica':o,'child':c,'port':p,'family':896*o+(2*P['pairs'][str(c)]+P['sides'][str(c)])*112+p,'pending_offset':used_,'rank':rem})
+ paid=collections.Counter()
+ for call in order:
+  paid.update({int(k):v for k,v in profiles_by_call.get(call,S['providers']['gauge44']['expected_profile']).items()})
+ paid.update(idle);mass=sum(k*v for k,v in paid.items());need(mass==S['expected']['rank_mass']==73*live-deficit,'rank mass');need(73*live-mass==deficit,'rank deficit')
+ return {'roles':len(rows),'calls':nc,'helper_per_call':480,'profile':dict(sorted(paid.items())),'idle_profile':dict(sorted(idle.items())),'idle_remainders':sum(idle.values()),'rank_mass':mass,'deficit':deficit,'cross_replica':cross,'actual_73column_sigmas':len(sigmas),'sigma_stream_sha256':stream.hexdigest(),'sigmas':sigmas,'remainders':remainders}
+
+
+def rebuild_windows(parent,order,T,ph=None):
+ """Reconstruct last-touch to idle boundaries from literal original32-event source."""
+ need(len(parent['calls'])==72,'original source call count')
+ source=parent.get('async_schedule',{}).get('source_schedule',parent['execution_schedule']);need(len(source)==32,'source event count')
+ blocks={};global_events=[];stage=None
+ for index,event in enumerate(source):
+  kind=event['kind']
+  if kind in ('bank_padding_cover_sweep','translate_every_live_family'):
+   global_events.append(index);continue
+  if kind=='local_cover_sweep':stage=event['stage'];blocks[stage]=[]
+  need(stage is not None,'event before invocation');blocks[stage].append((index,event))
+ need(global_events==[30,31],'source global tail')
+ events=[(idx,event,r,t) for t,(s,r) in enumerate(order) for idx,event in blocks[s]]
+ projections=collections.defaultdict(list)
+ for idx,event,r,t in events:projections[r].append(idx)
+ need(set(projections)==set(range(T)) and all(z==list(range(30)) for z in projections.values()),'per-replica event order')
+ ranks={c['child']:c['rank'] for c in parent['idle_children']}
+ if ph is not None:
+  ranks={j:z['rank'] for j,z in enumerate(ph['recipes'][0]['idle_children']) if z['rank']>0}
+  for recipe in ph['recipes']:
+   need({j:z['rank'] for j,z in enumerate(recipe['idle_children']) if z['rank']>0}==ranks,'phase rank geometry')
+   need(all(len(z['orthogonal_axes'])==z['rank'] for z in recipe['idle_children']),'actual phase axis rank')
+ stage_pair={x['stage']:x['pair'] for x in parent['recipe'] if x['kind']=='local'}
+ last={};bounds={};callpos={};pairs={};sides={}
+ for pos,(idx,event,r,t) in enumerate(events):
+  kind=event['kind']
+  if kind=='local_cover_sweep':last[r,stage_pair[event['stage']]]=pos;callpos[t]=pos
+  elif kind=='bridge':last[r,event['src']]=last[r,event['dst']]=pos
+  elif kind=='idle_cover_sweep':
+   for side,child in enumerate(event['child_indices']):
+    if child in ranks:
+     bounds[r,child]=(last.get((r,event['pair']),-1),pos);pairs[str(child)]=event['pair'];sides[str(child)]=side
+ need(set(callpos)==set(range(9*T)),'complete source invocation positions')
+ windows={f'{r},{c}':[ranks[c],[t for t,p in sorted(callpos.items()) if lo<p<hi]] for (r,c),(lo,hi) in bounds.items()}
+ return dict(windows=windows,pairs=pairs,sides=sides,stage_pair=stage_pair,events=len(events))
diff --git a/research/adaptive-kernel-demotion/data/CONSTRUCTION.json b/research/adaptive-kernel-demotion/data/CONSTRUCTION.json
new file mode 100644
index 0000000000..e7e7ffbb91
--- /dev/null
+++ b/research/adaptive-kernel-demotion/data/CONSTRUCTION.json
@@ -0,0 +1,7933 @@
+{
+  "status": "NOMINATION_REQUIRES_ACTUAL_VARIANT_PROFILE_AND_MIXED_CHART_CHECK",
+  "seconds": 3.6630081000002974,
+  "groups_applied": 359,
+  "calls_changed": 103,
+  "provider_calls": {
+    "0": 41,
+    "1": 24,
+    "2": 8,
+    "3": 15,
+    "4": 6,
+    "5": 50
+  },
+  "patterns": {
+    "(1, 1, 1, 1)": 356,
+    "(1, 1, 1, 3)": 2,
+    "(1, 1, 1, 2)": 1
+  },
+  "profile": {
+    "1": 344363,
+    "2": 65097,
+    "3": 62855,
+    "4": 19012,
+    "5": 11808,
+    "7": 8,
+    "8": 1152,
+    "11": 2,
+    "48": 4873
+  },
+  "rank_mass": 1041408,
+  "deficit": 5120,
+  "changed_rows": 4594,
+  "moves": [
+    {
+      "time": 1,
+      "new_variant": 1,
+      "target_rows": [
+        891,
+        893,
+        894,
+        895
+      ],
+      "donor_rows": [
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+      ],
+      "gap_pattern": [
+        1,
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+        1
+      ]
+    },
+    {
+      "time": 63,
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+      ],
+      "donor_rows": [
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+      ],
+      "gap_pattern": [
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+        1
+      ]
+    },
+    {
+      "time": 74,
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+      "target_rows": [
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+        35934,
+        35935
+      ],
+      "donor_rows": [
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+        35919
+      ],
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+        1,
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+        1
+      ]
+    },
+    {
+      "time": 96,
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+      "target_rows": [
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+      ],
+      "donor_rows": [
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+        1
+      ]
+    },
+    {
+      "time": 98,
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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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+      ],
+      "gap_pattern": [
+        1,
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+      ]
+    },
+    {
+      "time": 104,
+      "new_variant": 1,
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+        50335
+      ],
+      "donor_rows": [
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+        49994
+      ],
+      "gap_pattern": [
+        1,
+        1,
+        1,
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+      ]
+    },
+    {
+      "time": 136,
+      "new_variant": 1,
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+      ],
+      "donor_rows": [
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+      ],
+      "gap_pattern": [
+        1,
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+      ]
+    },
+    {
+      "time": 55,
+      "new_variant": 1,
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+      ],
+      "donor_rows": [
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+      ],
+      "gap_pattern": [
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+      ]
+    },
+    {
+      "time": 75,
+      "new_variant": 1,
+      "target_rows": [
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+      ],
+      "donor_rows": [
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+      ],
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+      ]
+    },
+    {
+      "time": 75,
+      "new_variant": 2,
+      "target_rows": [
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+      ],
+      "donor_rows": [
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+      ],
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+      ]
+    },
+    {
+      "time": 85,
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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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+      ]
+    },
+    {
+      "time": 20,
+      "new_variant": 1,
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+      ],
+      "donor_rows": [
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+      ],
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+      ]
+    },
+    {
+      "time": 20,
+      "new_variant": 2,
+      "target_rows": [
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+      ],
+      "donor_rows": [
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+      ],
+      "gap_pattern": [
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+      ]
+    },
+    {
+      "time": 62,
+      "new_variant": 1,
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+      ],
+      "donor_rows": [
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+      ],
+      "gap_pattern": [
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+    },
+    {
+      "time": 62,
+      "new_variant": 2,
+      "target_rows": [
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+      ],
+      "donor_rows": [
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+      ],
+      "gap_pattern": [
+        1,
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+      ]
+    },
+    {
+      "time": 83,
+      "new_variant": 1,
+      "target_rows": [
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+      ],
+      "donor_rows": [
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+      "gap_pattern": [
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+    },
+    {
+      "time": 83,
+      "new_variant": 2,
+      "target_rows": [
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+      ],
+      "donor_rows": [
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+      "gap_pattern": [
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+      ]
+    },
+    {
+      "time": 53,
+      "new_variant": 1,
+      "target_rows": [
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+      "donor_rows": [
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+      "donor_rows": [
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+      "donor_rows": [
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new file mode 100644
index 0000000000..e69f6327ec
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+        "cutoff_log2": 215554336613620250756139445512
+      },
+      {
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+        "gap": "21660265538804355842978587041832023374597709377414864790730688357784056476741751570387087772591613017326259539334356390405296245344396072741899573845934154621497086590318823134656045931257316250342651113883561393282204473065283880640382830126248142224378563672687008683321/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+        "cutoff_log2": 76731722564465580968238044656941067
+      },
+      {
+        "a": "1676065197731580997474980080720128993192878540998490814151198462871609015535615261129912688224661886807827565963029030682708910564264206986095101823023522110096333473520015436037179293419973528026852580053001584065197985235630898926278925968107304339213769112729596572566759493078527296222331369516041700393539983659278484126814900059/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+        "gap": "36304017243214673275226087680001509185848801537128390984464384738870087311775338113192172434036970969317291089435735793013904898176976477889903666526479984563962820706580026471973147419946998415934802014764369101073721074031892695660786230887270403427433240506921472703777668630483958299606460016340721515873185099941/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+        "cutoff_log2": 27314492207428343431093216780692006634313
+      },
+      {
+        "a": "1676065197731581033718149424095602939677512237937084454945239835685163464518346739136679087569333598319942573447373341183084387196451753559677986798810558863333617123628383275911490689341878251282572981579747271096665014802129025939210556518917085696600084701414988188629004495287666328838426454919116499627151973330795697585325824749272482436819913906580951768329566657256211907039/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+        "gap": "60847899839199328741453983062915545054760164314836535481653260863320912430666401680057426552626658816915612803548246440322013201189441136666382876371616724088509310658121748717427018420252728903334985197870974060789443481082914303399915298585011811370995504712333671161573545080883500372848026669204302414674175250727517563180086093419048231670433342743788092961/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+        "cutoff_log2": 9723246912942022594759025889724287053459986800
+      }
+    ]
+  },
+  "gain": "413710663799/1000000000000000000",
+  "profile": {
+    "1": 344363,
+    "2": 65097,
+    "3": 62855,
+    "4": 19012,
+    "5": 11808,
+    "7": 8,
+    "8": 1152,
+    "11": 2,
+    "48": 4873
+  }
+}
diff --git a/research/adaptive-kernel-demotion/expected/OWNER-AUDIT.json b/research/adaptive-kernel-demotion/expected/OWNER-AUDIT.json
new file mode 100644
index 0000000000..0a5bb027b4
--- /dev/null
+++ b/research/adaptive-kernel-demotion/expected/OWNER-AUDIT.json
@@ -0,0 +1,94 @@
+{
+  "roles": 69120,
+  "calls": 144,
+  "helper_per_call": 480,
+  "profile": {
+    "1": 344363,
+    "2": 65097,
+    "3": 62855,
+    "4": 19012,
+    "5": 11808,
+    "7": 8,
+    "8": 1152,
+    "11": 2,
+    "48": 4873
+  },
+  "idle_profile": {
+    "1": 771,
+    "2": 17,
+    "3": 363,
+    "7": 8,
+    "11": 2,
+    "48": 4873
+  },
+  "idle_remainders": 6034,
+  "rank_mass": 1041408,
+  "deficit": 5120,
+  "cross_replica": 58701,
+  "actual_73column_sigmas": 9898,
+  "sigma_stream_sha256": "58c93676cda7edb168bcf272131dc259571c4a5b6e86ebc547d028dc538b87b1",
+  "mixed_calls": 103,
+  "default_calls": 41,
+  "source_event_windows": "fresh reconstruction from source_schedule and actual phase-axis ranks",
+  "local_contracts": "fresh complete frame profiles and widths on both canonical words; changed-word scalar receipt freshly bound; unchanged old scalar admission inherited",
+  "variant_counts": {
+    "1": 24,
+    "2": 8,
+    "3": 15,
+    "4": 6,
+    "5": 50
+  },
+  "local_prefix_bits": {
+    "forward": 52,
+    "backward": 68
+  },
+  "local_contract_count": 6,
+  "negative_controls": [
+    {
+      "name": "duplicate_role",
+      "rejected": "duplicate role"
+    },
+    {
+      "name": "wrong_actual_width",
+      "rejected": "helper width"
+    },
+    {
+      "name": "wrong_call_time",
+      "rejected": "call time"
+    },
+    {
+      "name": "negative_axis_offset",
+      "rejected": "coordinate bound"
+    },
+    {
+      "name": "per_call_family_alias",
+      "rejected": "per-call family alias"
+    },
+    {
+      "name": "out_of_window",
+      "rejected": "out of window"
+    },
+    {
+      "name": "wrong_73_axis_chart",
+      "rejected": "wrong chart"
+    },
+    {
+      "name": "tampered_source_event_window",
+      "rejected": "actual source-event windows"
+    },
+    {
+      "name": "private_namespace_or_family_identity",
+      "rejected": "family identity"
+    },
+    {
+      "name": "forgot_widened_dispatch",
+      "rejected": "helper width"
+    },
+    {
+      "name": "incorrect_phase_rank",
+      "rejected": "actual phase axis rank"
+    }
+  ],
+  "status": "PASS_FINAL_MIXED_ALL_PENDING_AXES_CHARTS_CONTROLS",
+  "seconds": 3.3379742999986775
+}
diff --git a/research/adaptive-kernel-demotion/finite_invoice.py b/research/adaptive-kernel-demotion/finite_invoice.py
new file mode 100644
index 0000000000..9e43cb04f8
--- /dev/null
+++ b/research/adaptive-kernel-demotion/finite_invoice.py
@@ -0,0 +1,86 @@
+"""Fresh complete finite invoice for literal mixed admitted variants.
+All historical reserve formulas are retained; only the old charged allowance is read.
+Standard library; no subprocesses, WSL, networking, GPU or native binaries.
+"""
+import argparse,collections,gzip,hashlib,json
+from pathlib import Path
+
+def read(p):
+ b=p.read_bytes();return json.loads(gzip.decompress(b) if p.suffix=='.gz' else b)
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def need(x,m):
+ if not x:raise RuntimeError(m)
+def rank(vs):
+ d={}
+ for x in vs:
+  need(type(x) is int and 0<=x<512,'actual local binary frame')
+  while x:
+   i=x.bit_length()-1
+   if i in d:x^=d[i]
+   else:d[i]=x;break
+ return len(d)
+
+def guards(group,used,compiler,physical,mass,primitive,maxchild,prefix):
+ stock=group*physical;streamed=group*mass;logical=group*used+64
+ router=compiler*(logical+1)*(stock+1)**2
+ literal=2*(2**30000)*stock**2+8*streamed+4*stock+4+32*73
+ total=streamed+2**100000;row=2*stock.bit_length()+9909+252+2*512
+ checks=dict(local_primitive_bound=primitive<2**48,logical=logical<2**6050,router=router<2**30000,literal=literal<2**100000,mass=total<2**100001,precision=32*73*total*total<2**210000,tape=2*total+18<2**210000,row=row<20161,halving=73**2>2*maxchild**2)
+ return checks,dict(physical_stock_bits=stock.bit_length(),logical_bits=logical.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),total_mass_bits=total.bit_length(),precision_bits=(32*73*total*total).bit_length(),tape_bits=(2*total+18).bit_length(),physical_row_coefficient=row,global_prefix_bits=prefix)
+
+def calculate(spec,audit,dispatch,native,prior):
+ M,V,T,R=73,112,16,480;compiler=64*74**3;C=spec['providers']['gauge44']['complete_contract']
+ # k0 scalar admission stays inherited. All changed providers are read from fresh native output.
+ providers={0:dict(children=sum(C['paid_profile'].values()),local=C['local'],wrappers=C['entering_helpers']+C['cold_hyperplane_ended_helpers'],profile={int(k):v for k,v in C['paid_profile'].items()})}
+ native_bindings={}
+ for k,d in native.items():
+  w=read(d/'CANONICAL-WORD.json.gz');checks=read(d/'LOCAL-CHECKS.json');receipt=read(d/'INDEPENDENT-LOCAL-REPLAY.json');programs=read(d/'LOCAL-PROGRAMS.json.gz')
+  need(sha(d/'CANONICAL-WORD.json.gz')==receipt['canonical_word_sha256'] and sha(d/'LOCAL-PROGRAMS.json.gz')==receipt['local_programs_sha256'],'native source binding')
+  dims=[rank(x) for x in w['frames']];indices=range(224,704)
+  entering=sum(dims[w['start'][q]]>0 for q in indices);cold=sum(dims[w['start'][q]]==0 and dims[w['final'][q]]<9 for q in indices)
+  need(entering==receipt['entering_helpers']==192 and cold==receipt['cold_hyperplane_ended_helpers']==48,'actual wrapper-selected helper sets')
+  lp={int(r):n for r,n in w['local_profile'].items()};local={}
+  for o in ('forward','backward'):
+   z=checks[o];need(len(programs[o])==z['events'],'literal event count')
+   macros=sum(p[0]=='scalar' for p in programs[o]);need(macros==z['scalar_macros'],'literal macro count')
+   need(lp=={int(r):n for r,n in z['paid_profile'].items()}=={int(r):n for r,n in receipt['paid_profiles'][o].items()},'fresh local profile binding')
+   local[o]=dict(macros=macros,real_component_primitives=z['real_component_primitive_bound'],prefix_bits=receipt['local'][o]['prefix_bits_upper'])
+  providers[k]=dict(children=sum(lp.values()),local=local,wrappers=entering+cold,profile=lp)
+  native_bindings[str(k)]={x:sha(d/x) for x in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json')}
+ dt={tuple(d['call']):d.get('variant',1) for d in dispatch};need(len(dt)==len(dispatch),'dispatch uniqueness')
+ selected=[];paid=collections.Counter();counts=collections.Counter()
+ for s in range(9):
+  for r in range(16):
+   k=dt.get((s,r),0);need(k in providers,'missing actual provider');p=providers[k];o='backward' if s%2 else 'forward';z=p['local'][o]
+   selected.append(dict(stage=s,replica=r,variant=k,orientation=o,macros=z['macros'],real_component_primitives=z['real_component_primitives'],wrappers=2*p['wrappers']));paid.update(p['profile']);counts[k]+=1
+ idle={int(r):n for r,n in audit['idle_profile'].items()};local_paid=dict(paid);paid.update(idle)
+ need(dict(paid)=={int(r):n for r,n in audit['profile'].items()},'complete invoice profile');mass=sum(r*n for r,n in paid.items());need(mass==1041408 and 73*14336-mass==5120,'complete rank mass')
+ adapters={k:16*(max(z['macros'] for z in p['local'].values())+p['children']+224+480+8)+64*73 for k,p in providers.items()}
+ primitive={k:max(z['real_component_primitives'] for z in p['local'].values())+adapters[k]*compiler for k,p in providers.items()}
+ scalar=sum(x['real_component_primitives'] for x in selected);macros=sum(x['macros'] for x in selected);wrapper_factors=sum(x['wrappers'] for x in selected)*144
+ parent_live,parent_physical,parent_idle=23408,23922,32256;parent_banks=(parent_live-2*112*4*16)//9
+ bridges,shifts,moves=2*112*144,4*112*16,8*112*16
+ need(sum(idle.values())<=parent_idle,'complete remainder reserve')
+ nonlocal_items=(4*112*16*9+2*112*16*9+2*144*480+parent_idle+9*parent_banks+bridges+shifts+moves+parent_live+parent_physical+wrapper_factors)
+ outside=8*nonlocal_items+64*73
+ pervertex=scalar+bridges+shifts+moves+parent_live+(144*max(adapters.values())+outside)*compiler+64*parent_physical
+ live,physical=14336,14826;rebased=pervertex+65*(physical-parent_physical)+(live-parent_live)
+ need(prior['compiler']==compiler and prior['charged_prefix_bits']==512,'retained allowance interface')
+ used=max(pervertex,rebased,prior['conservative_pervertex_used']+pervertex)
+ prefix=max(z['prefix_bits'] for p in providers.values() for z in p['local'].values())+37+144+144+4;need(prefix<512,'whole controller prefix reserve')
+ group=2**(36*36)
+ for j in range(1,37):group*=2**(2*j)-1
+ checks,bits=guards(group,used,compiler,physical,mass,max(primitive.values()),max(paid),prefix);need(all(checks.values()),'strict finite guards')
+ controls=[]
+ for name,change in [('local_cap',dict(primitive=2**48)),('logical_cap',dict(used=2**6050)),('row_cap',dict(physical=2**2100)),('halving_cap',dict(maxchild=52))]:
+  args=dict(group=group,used=used,compiler=compiler,physical=physical,mass=mass,primitive=max(primitive.values()),maxchild=max(paid),prefix=prefix);args.update(change);failed=guards(**args)[0];need(not all(failed.values()),'accepted finite control');controls.append(dict(name=name,failed=[k for k,v in failed.items() if not v]))
+ return dict(status='PASS_FRESH_MIXED_COMPLETE_FINITE_INVOICE',provider_counts=dict(sorted(counts.items())),selected_calls=selected,selected_local_paid_profile=dict(sorted(local_paid.items())),global_profile=dict(sorted(paid.items())),idle_remainder_profile=idle,idle_remainders=sum(idle.values()),rank_mass=mass,deficit=5120,selected_real_component_primitives=scalar,selected_scalar_macros=macros,wrapper_elementary_factors_charged=wrapper_factors,local_adapters=max(adapters.values()),local_primitive_bound=max(primitive.values()),compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebased,retained_prior_allowance=prior['conservative_pervertex_used'],added_complete_new_pervertex=pervertex,conservative_pervertex_used=used,physical=physical,live=live,actual_73column_sigmas=audit['actual_73column_sigmas'],finite=bits,strict_checks=checks,negative_controls=controls,native_bindings=native_bindings,scope='Fresh literal changed-provider counts, wrappers, mixed call totals, complete histogram, actual charts and all nine finite guard inequalities. k0 scalar semantic admission, universal routing/compiler and historical reserve formulas are retained inherited contracts. Prior file contributes only its charged allowance, not a changed-map admission receipt.')
+
+def main():
+ a=argparse.ArgumentParser()
+ for k in ('spec','owner-audit','dispatch','prior','pins','out'):a.add_argument('--'+k,type=Path,required=True)
+ a.add_argument('--native',action='append',default=[],required=True);z=a.parse_args();need(not z.out.exists(),'fresh output required')
+ pins=read(z.pins);expected=next(v for k,v in pins.items() if k.endswith('vendor531/evidence/audit/PREFIX-AND-INVOICE.json'));need(sha(z.prior)==expected,'retained allowance exact source pin')
+ result=calculate(read(z.spec),read(z.owner_audit),read(z.dispatch),{int(x.split('=',1)[0]):Path(x.split('=',1)[1]) for x in z.native},read(z.prior));result['retained_source_sha256']=sha(z.prior)
+ z.out.write_text(json.dumps(result,indent=2)+'\n',encoding='utf-8',newline='\n');print(json.dumps({k:v for k,v in result.items() if k not in ('selected_calls','native_bindings')},indent=2))
+if __name__=='__main__':main()
diff --git a/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json b/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json
new file mode 100644
index 0000000000..d9a4f84211
--- /dev/null
+++ b/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json
@@ -0,0 +1 @@
+{"cover_correction":{"complete_small_cover_checks":[{"n":1,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":1},{"n":2,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":2},{"n":3,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":6},{"n":4,"nonzero_full_kernel_corrections":24,"orthogonal_matrices":48},{"n":5,"nonzero_full_kernel_corrections":600,"orthogonal_matrices":720}],"formula":"delta(g)_i = (weight(row_i(g))-1)/2 mod 2; apply X_delta(g) to EVERY final live stream in cover class g.","mandatory":true,"reason":"P_g C_all P_g^-1 = C_all X_delta(g) exactly. Orthogonality cancels all quadratic cross terms; both sides fix the uniform vector."},"global_phase_argument":"Every C_q and every linear address permutation fixes the uniform vector. Equality of the exact Z4 Fourier multiplier therefore fixes the scalar phase as 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complete recipe is unchanged except its port index; the retained parent polynomial checks establish every selected equality.","scope":"All compressed data boundary operators, idle children, terminal X_q and all-live cover correction. 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diff --git a/research/adaptive-kernel-demotion/inputs/PR589-EXPECTED.json b/research/adaptive-kernel-demotion/inputs/PR589-EXPECTED.json
new file mode 100644
index 0000000000..e293ddc557
--- /dev/null
+++ b/research/adaptive-kernel-demotion/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/adaptive-kernel-demotion/inputs/PRIOR-ALLOWANCE.json b/research/adaptive-kernel-demotion/inputs/PRIOR-ALLOWANCE.json
new file mode 100644
index 0000000000..a16bf40bcc
--- /dev/null
+++ b/research/adaptive-kernel-demotion/inputs/PRIOR-ALLOWANCE.json
@@ -0,0 +1,105 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "ed47b5454779f7ad6b32ae492a13f8b5172b11c94c3877cbc5cc5d7a4c357738",
+  "parent_template_sha256": "9bebafae2c7e21a8a134cc9f2d4709c075b1641abafc33825d116b2508253ceb",
+  "owner_audit_sha256": "e5f11e7b920f9985f085546c641dbac5b8d98231d562e1e030ab2566ccea4bd6",
+  "controller_audit_sha256": "01ea0015d4e08170ac65f1cdd051be64e07f622eba62eadbf39524317388cba7",
+  "independent_local_replay_sha256": "4149f3d2ec3041965c5d72869748090d9aeed422f36d753550c543bb7808b30b",
+  "canonical_word_sha256": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667",
+  "local_programs_sha256": "755a5c4ebe958fd9f7b5d4a6e7a506d2c802e31c4d9da46b63db1994c4d8ffa6",
+  "local_checks_sha256": "c6807681d40cb46c21a50edc1058044ddc758f2dd3e6b0bab16d7cb28d41732f",
+  "global_prefix_bits": 225,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "local": {
+    "backward": {
+      "events": 22937,
+      "macros": 17872,
+      "real_component_primitives": 177740,
+      "prefix_l1": "1014379823310",
+      "prefix_bits": 40,
+      "coefficient_work_primitive_count": 88098,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 152,
+      "post_wrappers": 152,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    },
+    "forward": {
+      "events": 22937,
+      "macros": 17872,
+      "real_component_primitives": 177692,
+      "prefix_l1": "86491024246",
+      "prefix_bits": 37,
+      "coefficient_work_primitive_count": 88066,
+      "all_exact_columns": 728,
+      "dirty_helper_columns": 504,
+      "all_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true,
+      "pre_wrappers": 152,
+      "post_wrappers": 152,
+      "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+    }
+  },
+  "helpers": 504,
+  "centres": 8,
+  "live": 7168,
+  "physical": 7682,
+  "physical_stock_identity": {
+    "data_and_owner_families": 7168,
+    "local_helpers": 504,
+    "private_centres": 8,
+    "coefficient_work": 2
+  },
+  "entering_helpers": 152,
+  "entrance_rank": 152,
+  "width_inventory": {
+    "8": 152,
+    "9": 352
+  },
+  "local_adapters": 357568,
+  "local_primitive_bound": 9273288832588,
+  "wrapper_elementary_factors_charged": 3151872,
+  "factors_per_wrapper": 144,
+  "compiler": 25934336,
+  "unhosted_pervertex": 1361655146111768,
+  "hosted_rebased_pervertex": 1361655145812392,
+  "conservative_pervertex_used": 2877946989724568,
+  "retained_prior_overcharge": {
+    "sha256": "bb43ef04791037a37d2596c395e81191991fde6581326118995cf4318ee472a3",
+    "previous_pervertex_allowance": 1516291843612800,
+    "added_complete_new_pervertex": 1361655146111768,
+    "policy": "Retain old allowance and add the entire fresh recount."
+  },
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7985,
+    "literal_bits": 35282,
+    "physical_row_coefficient": 16467,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged."
+}
diff --git a/research/adaptive-kernel-demotion/inputs/ROUND20-PARENT-TEMPLATE.json.gz b/research/adaptive-kernel-demotion/inputs/ROUND20-PARENT-TEMPLATE.json.gz
new file mode 100644
index 0000000000..3e28a9b59f
Binary files /dev/null and b/research/adaptive-kernel-demotion/inputs/ROUND20-PARENT-TEMPLATE.json.gz differ
diff --git a/research/adaptive-kernel-demotion/local/LICENSE b/research/adaptive-kernel-demotion/local/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
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diff --git a/research/adaptive-kernel-demotion/local/README.md b/research/adaptive-kernel-demotion/local/README.md
new file mode 100644
index 0000000000..87b7360a95
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/README.md
@@ -0,0 +1,29 @@
+# Five concrete local providers for adaptive entrance demotion
+
+This folder reconstructs PR1117's actual local word with one through five disjoint four-helper entrance demotions. The first group is PR1111's635 group; the additional603/611/619/627 groups extend the same legal mechanism into a concrete five-provider portfolio. A global call selects only the prefix whose additional coordinates fit its independently verified pending owner gaps.
+
+Prefix order, in raw register numbers:
+
+1.635,637,638,639
+2.603,605,606,607
+3.611,613,614,615
+4.619,621,622,623
+5.627,629,630,631
+
+The literal patch fields are pairwise disjoint. `data/PATCHES.json` gives every original frame and replacement. `data/PROVIDERS.json` gives each actual raw semantic hash and fully recounted profile/inventory. Every provider has480 helpers. The whole frame chains, all704 arbitrary-input columns in both orientations, every low-end cone and both emitted local programs were freshly checked; the ledger is not inferred by adding advertised gains.
+
+Run standard-library Python3.11+ offline, choosing a selector and a fresh output directory:
+
+    python -I -B check_local.py --selector 5 --out /path/to/fresh/local-output
+
+Windows example:
+
+    python -I -B check_local.py --selector 5 --out C:/temp/prefix-five-local
+
+Selectors1 through5 are supported. The parent selector0 is the unchanged inherited PR1117 provider and is checked by the global baseline binder separately. Development timings are about14-18 seconds per selected provider; each child has a20-second cap and below-normal Windows priority. No WSL, GPU, C++, network request or background service is launched.
+
+The verifier independently recounts every jump, checks zero entrance-dirt response and both full scalar maps, checks native transport, emits and replays both actual local programs, and rejects25 corruption controls. It freshly lowers and independently decodes every introduced frame edge and residual wrapper, including global phases: selector k has9k new directed edges and k new wrapper types, with10k phase mutations rejected. All unchanged phase edges and endpoint adapters are inherited from PR1117.
+
+Global owner assignments, disjoint coordinate reservations, charged remainder reductions, complete precision/tape reserve bounds and exact outer pricing are separate checks in the parent package. The all-size/compiler, realization and analytic contracts remain explicit inherited premises. No unconditional multiplication theorem, new Lean certification or independent human review is claimed.
+
+Credit: PR1111 entrance demotion; PR1117/PR1030 rank-seven ends; PR1018/PR987 slots; PR1005 word; PR635 native transport/wrappers; PR558/552 exact Clifford compiler; PR741/799/869 and all predecessor attribution preserved in UPSTREAM-NOTICE.md. Additional joint-provider construction and checks were produced with substantial OpenAI Codex assistance under Apache-2.0. The extension uses the existing demotion mechanism and does not claim priority for it.
diff --git a/research/adaptive-kernel-demotion/local/SOURCE-PINS.json b/research/adaptive-kernel-demotion/local/SOURCE-PINS.json
new file mode 100644
index 0000000000..f9cf35d296
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/SOURCE-PINS.json
@@ -0,0 +1,29 @@
+{
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "UPSTREAM-NOTICE.md": "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf",
+  "data/EXPECTED-1-CANONICAL-WORD.json.gz": "945da4bcfebdc0a165584fc93f3620a200318d0d3c9baf709429bda5f415c26d",
+  "data/EXPECTED-1-CHANGED-PHASES.json": "70876898aa3567e80c8e009b7c79a0d7d915a6fc51263d52330f64509f6e373b",
+  "data/EXPECTED-1-LOCAL-REPLAY.json": "4ae2eea29c666e4188f882ac34c238f57837e0a288ceac2557568260a56fdf21",
+  "data/EXPECTED-2-CANONICAL-WORD.json.gz": "fd3dcd5c213ce8a9c7313144392b0a98bbfe3dfb70473da225448dae254fa01b",
+  "data/EXPECTED-2-CHANGED-PHASES.json": "a5715153b2222a29bdac2e2ad3bfd0d57a321746cdb2ed8d376791c8e7d5107b",
+  "data/EXPECTED-2-LOCAL-REPLAY.json": "4f7c0e3b3ecbf9f372695c1184863b03e6391b6e476985d5d09220ef38c5aa06",
+  "data/EXPECTED-3-CANONICAL-WORD.json.gz": "c7cf7c4502a66c263c6ad308c66d697c121492e3575871c3fb1b5526c6cbb30a",
+  "data/EXPECTED-3-CHANGED-PHASES.json": "da0efa495a0e1e6e1019e21ababac216f3c6952153af072291a732984ff7c503",
+  "data/EXPECTED-3-LOCAL-REPLAY.json": "8d1b23973a12bfd4b2d97655bcd1208ab3daca992c10cbf78a7c39b088f15a54",
+  "data/EXPECTED-4-CANONICAL-WORD.json.gz": "5738f8430ae4a4d87bcbf0f8519a5830381c506f9a83e933339e1c5d34173c61",
+  "data/EXPECTED-4-CHANGED-PHASES.json": "fb62de4ebfe6446792de048e6a1178ab7d659f780a1735b397efcb69eb4a7328",
+  "data/EXPECTED-4-LOCAL-REPLAY.json": "775985d72bb6fb640783b75bf2b2b1ee780d56c6faeacf790b7f72881a238080",
+  "data/EXPECTED-5-CANONICAL-WORD.json.gz": "68832cd565314b92c036f240fa70bf1b3186936479b8df96eed9da1716090a4d",
+  "data/EXPECTED-5-CHANGED-PHASES.json": "4537595c58a3e750460e5574cc903ce6c317d4527a2f3fdf4216de40aef26265",
+  "data/EXPECTED-5-LOCAL-REPLAY.json": "4686ea9eb5748a4c3d9814fa4c46492d27e18f1867ab622a6d7eeadef861fe2e",
+  "data/OLD-CANONICAL-WORD.json.gz": "b93750aa257ed81ed074baac5ef6a4295a40b89a375b7c127aacfcf1751eddbd",
+  "data/PARENT-ROUTING.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "data/PATCHES.json": "71b3e4145b3ff6dcc218b770f08d8b3a0b924524f9c5cf39fd382b421823e0ac",
+  "data/PR1117-WORD.json.gz": "1812d7f96a985f613dffbbc9a66e42a30d1b01c347b737e283b0216123ddcd8b",
+  "data/PROVIDERS.json": "4ff5572bfe97a1274b6577ae268a7c1a36d35be762636f75a2009ba4c1397466",
+  "vendor/audit_local.py": "03afcfc9da428b3f6edac81c1fee7f277ab81b64998efae78380b63498dec6cd",
+  "vendor/hpe_audit_and_transport.py": "c9a05ff291016b870b4fc925b317abd9c3a604c73ffc8920dfdbbeb475e20aa3",
+  "vendor/hpe_audit_local.py": "6bd9a1e279c9c9e4f3767d9f82e537b559292906feb2ddab02f380fb6523a810",
+  "vendor/hpe_emit_local.py": "7e4a6fbc38c8228157b6311457d1496bf460291393043932d2c365f004f77805",
+  "vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+}
\ No newline at end of file
diff --git a/research/adaptive-kernel-demotion/local/UPSTREAM-NOTICE.md b/research/adaptive-kernel-demotion/local/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..30d0c8cd3c
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/UPSTREAM-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/adaptive-kernel-demotion/local/check_changed_phases.py b/research/adaptive-kernel-demotion/local/check_changed_phases.py
new file mode 100644
index 0000000000..14886e31e5
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/check_changed_phases.py
@@ -0,0 +1,36 @@
+"""Changed-edge exact lowering only; unchanged public PR1117 phases inherited.
+Uses upstream PR552 exact Clifford algebra, Apache-2.0 predecessor attribution.
+No discovery executable, WSL, GPU or background service.
+"""
+import sys,json,gzip,hashlib,time,copy
+from pathlib import Path
+P=Path(__file__).parent
+G=P/'vendor/clifford'
+sys.path.insert(0,str(G))
+from clifford_exact import canonical_frame,lower_child,diag,perm,xgate,Op,identity,fourier,rank,inverse,nullspace
+
+def read(p):return json.loads(gzip.decompress(p.read_bytes()))
+def edges(c):return {(tuple(c['frames'][a]),tuple(c['frames'][b])) for a,b in c['edges']}
+def wrappers(c):return {(tuple(c['frames'][c['start'][r]]),tuple(c['frames'][c['final'][r]])) for r in range(2*c['v'],len(c['start'])) if c['start'][r]!=0 or c['final'][r]!=1}
+def monomial(r):return diag(9,tuple(r['quadratic_rows']),tuple(r['linear_Z4'])).then(perm(9,tuple(r['matrix_rows']))).then(xgate(9,r['offset'])).then(Op(9,identity(9),[('phase',r['phase'])]))
+def equality(op,r):
+ o=monomial(r['left']) if r['rank']==0 else monomial(r['right']).then(fourier(9,range(r['rank']))).then(monomial(r['left']))
+ return o.tab==op.tab and o.zero_state()==op.zero_state()
+def main():
+ if not __debug__:raise RuntimeError("Assertion-based Clifford engine requires normal Python, not -O")
+ import argparse
+ ap=argparse.ArgumentParser();ap.add_argument('--old',type=Path,required=True);ap.add_argument('--new',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();assert not a.out.exists(),'fresh output required'
+ t=time.monotonic();old,new=[read(x) for x in (a.old,a.new)];changed=sorted(edges(new)-edges(old));wr=sorted(wrappers(new)-wrappers(old));newframes=set(map(tuple,new['frames']))-set(map(tuple,old['frames']));operations={}
+ for U in set(x for pair in changed+wr for x in pair):
+  op=canonical_frame(9,U);pre=[x|(z<<9) for x,z,p in inverse(op.tab)[9:]];L=[u|(u<<9) for u in U]+[v<<9 for v in nullspace(U,9)];assert rank(L)==9 and rank(L+pre)==9;assert rank([x for x,z,p in op.tab[9:]])==len(U);operations[U]=op
+ records=[];controls=[]
+ for kind,pairs in [('edge',changed),('wrapper',wr)]:
+  for U,V in pairs:
+   op=operations[U].adjoint().then(operations[V]);rec,comp=lower_child(op);assert rec['rank']==abs(len(V)-len(U));assert equality(op,rec)
+   mut=copy.deepcopy(rec);mut['left']['phase']=(mut['left']['phase']+1)%4;assert not equality(op,mut);controls.append(kind+':phase')
+   if kind=='wrapper':
+    wrapped=monomial(rec['right']).adjoint().then(op).then(monomial(rec['left']).adjoint());target=fourier(9,range(rec['rank']));assert wrapped.tab==target.tab and wrapped.zero_state()==target.zero_state()
+   records.append(dict(kind=kind,before=U,after=V,recipe=rec))
+ out=dict(status='PASS_CHANGED_EDGES_AND_WRAPPER_PHASE_EXACT',seconds=time.monotonic()-t,parent_canonical_sha256=hashlib.sha256(a.old.read_bytes()).hexdigest(),changed_canonical_sha256=hashlib.sha256(a.new.read_bytes()).hexdigest(),engine_sha256=hashlib.sha256((G/'clifford_exact.py').read_bytes()).hexdigest(),new_frames=sorted(newframes),changed_edges=len(changed),changed_wrappers=len(wr),controls=controls,records=records,scope='Fresh exact lowering and serialized independent monomial decode of every newly introduced edge and wrapper, including global phases. Identical unchanged public PR1117 edges/wrappers and endpoint adapters inherited, no full ancestor replay.')
+ a.out.write_text(json.dumps(out,indent=2));print('PASS',len(changed),'changededges',len(wr),'wrappers',len(controls),'controls',out['seconds'],'seconds')
+if __name__=='__main__':main()
diff --git a/research/adaptive-kernel-demotion/local/check_local.py b/research/adaptive-kernel-demotion/local/check_local.py
new file mode 100644
index 0000000000..627f20bb96
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/check_local.py
@@ -0,0 +1,41 @@
+"""Portable fresh changed-local replay, Windows-native/stdlib, bounded child jobs.
+No WSL, GPU, C++ executable, background service or network. Apache-2.0.
+Inherited unchanged PR1117 phase edges and adapters remain explicit assumptions.
+"""
+import argparse,gzip,json,hashlib,subprocess,sys,time
+from pathlib import Path
+from collections import Counter
+P=Path(__file__).resolve().parent
+
+def read(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+def enc(x):return json.dumps(x,sort_keys=True,separators=(',',':')).encode()
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def need(b,s):
+ if not b:raise RuntimeError(s)
+def construct(out,k):
+ w=read(P/'data/PR1117-WORD.json.gz');patch=read(P/'data/PATCHES.json');need(hashlib.sha256(enc(w)).hexdigest()==patch['parent_sha256']=='f64e0942edc5eb2d45b0a3b068ba942436f35ba9a077ff53d7e4424d1617b2cd','actual PR1117 word');seen=set()
+ for group in patch['groups'][:k]:
+  for q in group['helpers']:
+   key=('start_extra',q);need(key not in seen,'overlapping entrance patches');seen.add(key);need(w['start_extra'][str(q)]==group['before'],'old entrance');w['start_extra'][str(q)]=group['after']
+  for sec,i,old,new in group['frames']:
+   key=(sec,i);need(key not in seen,'overlapping gate patches');seen.add(key);need(w[sec][i][-1]==old,'old frame');w[sec][i][-1]=new
+ provider=read(P/'data/PROVIDERS.json')[k-1];need(provider['selector']==k,'provider selector');w['report'].update(local_profile=provider['local_profile'],local_rank_mass=provider['local_rank_mass'],width_inventory=provider['width_inventory'])
+ raw=enc(w);need(hashlib.sha256(raw).hexdigest()==provider['content_sha256'],'constructed new word');out.write_bytes(gzip.compress(raw,mtime=0));return out
+
+def main():
+ need(__debug__,'assertion-based vendor engines require normal Python, not -O')
+ ap=argparse.ArgumentParser();ap.add_argument('--out',type=Path,required=True);ap.add_argument('--selector',type=int,choices=range(1,6),required=True);a=ap.parse_args();need(not a.out.exists(),'fresh output directory required')
+ for name,digest in read(P/'SOURCE-PINS.json').items():need(sha(P/name)==digest,'input source pin '+name)
+ a.out.mkdir(parents=True);t=time.monotonic();raw=construct(a.out/'CHANGED-WORD.json.gz',a.selector);steps=[]
+ def run(label,script,args):
+  start=time.monotonic();flags=0x4000 if sys.platform=='win32' else 0
+  r=subprocess.run([sys.executable,'-I','-B',str(script),*map(str,args)],capture_output=True,text=True,timeout=20,creationflags=flags)
+  (a.out/(label+'.log')).write_text(r.stdout+r.stderr,encoding='utf-8');need(r.returncode==0,label+' failed '+r.stderr[-1200:]);steps.append(dict(step=label,seconds=time.monotonic()-start));print('PASS',label,flush=True)
+ native=a.out/'native';run('raw-independent',P/'vendor/audit_local.py',['--word',raw,'--output',a.out/'RAW-CHECK.json']);run('native',P/'vendor/hpe_audit_and_transport.py',['--raw',raw,'--routing',P/'data/PARENT-ROUTING.json.gz','--out',native]);run('emit',P/'vendor/hpe_emit_local.py',[native]);run('emitted-independent',P/'vendor/hpe_audit_local.py',[native]);need(read(native/'CANONICAL-WORD.json.gz')==read(P/'data'/f'EXPECTED-{a.selector}-CANONICAL-WORD.json.gz'),'fresh canonical exact equality')
+ replay=read(native/'INDEPENDENT-LOCAL-REPLAY.json');expected=read(P/'data'/f'EXPECTED-{a.selector}-LOCAL-REPLAY.json');need(replay['canonical_word_sha256']==sha(native/'CANONICAL-WORD.json.gz') and replay['local_programs_sha256']==sha(native/'LOCAL-PROGRAMS.json.gz'),'fresh emitted byte bindings'); need({k:v for k,v in replay.items() if k not in ('canonical_word_sha256','local_programs_sha256')}=={k:v for k,v in expected.items() if k not in ('canonical_word_sha256','local_programs_sha256')},'fresh emitted receipt mathematical equality')
+ run('changed-phases',P/'check_changed_phases.py',['--old',P/'data/OLD-CANONICAL-WORD.json.gz','--new',native/'CANONICAL-WORD.json.gz','--out',a.out/'CHANGED-PHASES.json']);ph=read(a.out/'CHANGED-PHASES.json');oldph=read(P/'data'/f'EXPECTED-{a.selector}-CHANGED-PHASES.json')
+ for k in ('new_frames','changed_edges','changed_wrappers','controls','records','engine_sha256'):need(ph[k]==oldph[k],'fresh phase result '+k)
+ result=dict(status='PASS_FRESH_COMBINED_LOCAL_SUPPLIER',actual_columns=704,orientations=2,selector=a.selector,changed_edges=ph['changed_edges'],changed_wrappers=ph['changed_wrappers'],emitted_controls=25,phase_controls=len(ph['controls']),local_profile=read(native/'CANONICAL-WORD.json.gz')['local_profile'],total_seconds=time.monotonic()-t,steps=steps,scope='Every changed local scalar endpoint/frame/low-end cone, emitted event program and changed phase/adapter. Unchanged PR1117 phase edges, endpoint adapters and global/compiler/analytic contracts inherited; global owner/precision/outer assembly checked separately.')
+ (a.out/'RESULT.json').write_text(json.dumps(result,indent=2),encoding='utf-8');print('PASS_FRESH_COMBINED_LOCAL_SUPPLIER',result['total_seconds'],'seconds')
+if __name__=='__main__':main()
+
diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-1-CANONICAL-WORD.json.gz b/research/adaptive-kernel-demotion/local/data/EXPECTED-1-CANONICAL-WORD.json.gz
new file mode 100644
index 0000000000..1d444a080f
Binary files /dev/null and b/research/adaptive-kernel-demotion/local/data/EXPECTED-1-CANONICAL-WORD.json.gz differ
diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-1-CHANGED-PHASES.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-1-CHANGED-PHASES.json
new file mode 100644
index 0000000000..3714a57351
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/data/EXPECTED-1-CHANGED-PHASES.json
@@ -0,0 +1,970 @@
+{
+  "status": "PASS_CHANGED_EDGES_AND_WRAPPER_PHASE_EXACT",
+  "seconds": 0.9671457000004011,
+  "parent_canonical_sha256": "b93750aa257ed81ed074baac5ef6a4295a40b89a375b7c127aacfcf1751eddbd",
+  "changed_canonical_sha256": "945da4bcfebdc0a165584fc93f3620a200318d0d3c9baf709429bda5f415c26d",
+  "engine_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+  "new_frames": [
+    [
+      257,
+      129,
+      102,
+      30
+    ]
+  ],
+  "changed_edges": 9,
+  "changed_wrappers": 1,
+  "controls": [
+    "edge:phase",
+    "edge:phase",
+    "edge:phase",
+    "edge:phase",
+    "edge:phase",
+    "edge:phase",
+    "edge:phase",
+    "edge:phase",
+    "edge:phase",
+    "wrapper:phase"
+  ],
+  "records": [
+    {
+      "kind": "edge",
+      "before": [
+        30
+      ],
+      "after": [
+        257,
+        129,
+        102,
+        30
+      ],
+      "recipe": {
+        "rank": 3,
+        "left": {
+          "matrix_rows": [
+            12,
+            18,
+            34,
+            64,
+            128,
+            258,
+            2,
+            5,
+            1
+          ],
+          "offset": 0,
+          "quadratic_rows": [
+            5,
+            2,
+            5,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          "linear_Z4": [
+            3,
+            3,
+            3,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          "phase": 0
+        },
+        "right": {
+          "matrix_rows": [
+            384,
+            38,
+            257,
+            385,
+            66,
+            68,
+            8,
+            16,
+            96
+          ],
+          "offset": 0,
+          "quadratic_rows": [
+            129,
+            102,
+            102,
+            0,
+            0,
+            102,
+            38,
+            129,
+            0
+          ],
+          "linear_Z4": [
+            1,
+            1,
+            1,
+            0,
+            0,
+            1,
+            2,
+            3,
+            0
+          ],
+          "phase": 0
+        }
+      }
+    },
+    {
+      "kind": "edge",
+      "before": [
+        257,
+        129,
+        102,
+        30
+      ],
+      "after": [
+        257,
+        129,
+        66,
+        36,
+        16,
+        14
+      ],
+      "recipe": {
+        "rank": 2,
+        "left": {
+          "matrix_rows": [
+            4,
+            9,
+            17,
+            35,
+            3,
+            66,
+            2,
+            128,
+            256
+          ],
+          "offset": 0,
+          "quadratic_rows": [
+            1,
+            2,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          "linear_Z4": [
+            3,
+            3,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          "phase": 0
+        },
+        "right": {
+          "matrix_rows": [
+            46,
+            40,
+            1,
+            90,
+            124,
+            16,
+            64,
+            128,
+            256
+          ],
+          "offset": 59,
+          "quadratic_rows": [
+            0,
+            118,
+            86,
+            56,
+            46,
+            26,
+            6,
+            0,
+            0
+          ],
+          "linear_Z4": [
+            0,
+            1,
+            1,
+            3,
+            0,
+            2,
+            0,
+            0,
+            0
+          ],
+          "phase": 1
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+}
\ No newline at end of file
diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-1-LOCAL-REPLAY.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-1-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..2b5130c24a
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/data/EXPECTED-1-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "945da4bcfebdc0a165584fc93f3620a200318d0d3c9baf709429bda5f415c26d",
+  "local_programs_sha256": "ad615ece6867754fbc108b475ee7c970603fcd4238d755f99e65a74954917355",
+  "v": 112,
+  "helpers": 480,
+  "local": {
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+      "charged_payload_bits": 192,
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+  "negative_controls_rejected": [
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+    "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/adaptive-kernel-demotion/local/data/EXPECTED-2-CANONICAL-WORD.json.gz b/research/adaptive-kernel-demotion/local/data/EXPECTED-2-CANONICAL-WORD.json.gz
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index 0000000000..1e7668e9bd
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diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-2-CHANGED-PHASES.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-2-CHANGED-PHASES.json
new file mode 100644
index 0000000000..a1652ef60c
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/data/EXPECTED-2-CHANGED-PHASES.json
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+}
\ No newline at end of file
diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-2-LOCAL-REPLAY.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-2-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..4a76e94f6b
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/data/EXPECTED-2-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
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+    "wrapper_on_a_target_register",
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+    "hpe_pre_wrapper_resolved_to_full_recipe",
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+    "hpe_post_wrapper_wrong_terminal_frame",
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+    "cold_hpe_pre_wrapper_dropped",
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+    "cold_hpe_post_wrapper_wrong_terminal_frame",
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+}
diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-3-CANONICAL-WORD.json.gz b/research/adaptive-kernel-demotion/local/data/EXPECTED-3-CANONICAL-WORD.json.gz
new file mode 100644
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diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-3-CHANGED-PHASES.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-3-CHANGED-PHASES.json
new file mode 100644
index 0000000000..1dadecb47a
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/data/EXPECTED-3-CHANGED-PHASES.json
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+}
\ No newline at end of file
diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-3-LOCAL-REPLAY.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-3-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..25861e8f74
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/data/EXPECTED-3-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "c7cf7c4502a66c263c6ad308c66d697c121492e3575871c3fb1b5526c6cbb30a",
+  "local_programs_sha256": "d9d96816946b1ebd406b649d973186199c3c0173498499144ba2e9d9a32327d2",
+  "v": 112,
+  "helpers": 480,
+  "local": {
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+      "prefix_l1_upper": "2765345294379392599/1024",
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+      "charged_payload_bits": 192,
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+    },
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+      "prefix_l1_upper": "14824960514781440791821/64",
+      "prefix_bits_upper": 68,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
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+  "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/adaptive-kernel-demotion/local/data/EXPECTED-4-CANONICAL-WORD.json.gz b/research/adaptive-kernel-demotion/local/data/EXPECTED-4-CANONICAL-WORD.json.gz
new file mode 100644
index 0000000000..f6e52d2baa
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diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-4-CHANGED-PHASES.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-4-CHANGED-PHASES.json
new file mode 100644
index 0000000000..577cb18c18
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/data/EXPECTED-4-CHANGED-PHASES.json
@@ -0,0 +1,3832 @@
+{
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+}
\ No newline at end of file
diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-4-LOCAL-REPLAY.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-4-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..952db3c87c
--- /dev/null
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+  "canonical_word_sha256": "5738f8430ae4a4d87bcbf0f8519a5830381c506f9a83e933339e1c5d34173c61",
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+  "v": 112,
+  "helpers": 480,
+  "local": {
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+  "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/adaptive-kernel-demotion/local/data/EXPECTED-5-CANONICAL-WORD.json.gz b/research/adaptive-kernel-demotion/local/data/EXPECTED-5-CANONICAL-WORD.json.gz
new file mode 100644
index 0000000000..36fe120642
Binary files /dev/null and b/research/adaptive-kernel-demotion/local/data/EXPECTED-5-CANONICAL-WORD.json.gz differ
diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-5-CHANGED-PHASES.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-5-CHANGED-PHASES.json
new file mode 100644
index 0000000000..d2a1a4890a
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/data/EXPECTED-5-CHANGED-PHASES.json
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+}
\ No newline at end of file
diff --git a/research/adaptive-kernel-demotion/local/data/EXPECTED-5-LOCAL-REPLAY.json b/research/adaptive-kernel-demotion/local/data/EXPECTED-5-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..1e906c33de
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/data/EXPECTED-5-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
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+    "width_inventory": {
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+      "7": 32,
+      "8": 120,
+      "9": 240
+    }
+  },
+  {
+    "selector": 2,
+    "content_sha256": "e062361fa749691d325600e843a721814bbb642f438e011086225fa41d3b8627",
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+    "width_inventory": {
+      "4": 48,
+      "5": 40,
+      "7": 32,
+      "8": 120,
+      "9": 240
+    }
+  },
+  {
+    "selector": 3,
+    "content_sha256": "607e7e1cfbc2cef9e299720f44c362df6e7fbeeb01201d9bce879520fbe20176",
+    "local_profile": {
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+      "2": 456,
+      "3": 436,
+      "4": 130,
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+    "width_inventory": {
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+      "5": 44,
+      "7": 32,
+      "8": 120,
+      "9": 240
+    }
+  },
+  {
+    "selector": 4,
+    "content_sha256": "303a11fe50cbc799fd421a196b2594e796541a8a9c6b0be3c36e132e46efc33b",
+    "local_profile": {
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+    "width_inventory": {
+      "4": 40,
+      "5": 48,
+      "7": 32,
+      "8": 120,
+      "9": 240
+    }
+  },
+  {
+    "selector": 5,
+    "content_sha256": "24c15962d303c319e3dbc39d97b124471a9964f7efe169324eb99dffa387b713",
+    "local_profile": {
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+    "width_inventory": {
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+      "8": 120,
+      "9": 240
+    }
+  }
+]
\ No newline at end of file
diff --git a/research/adaptive-kernel-demotion/local/vendor/audit_local.py b/research/adaptive-kernel-demotion/local/vendor/audit_local.py
new file mode 100644
index 0000000000..4744d8783c
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/vendor/audit_local.py
@@ -0,0 +1,171 @@
+"""Independent exact scalar/frame audit of the changed forward supplier.
+
+This does not import a generator, builder, stored compensation, or price.
+All claimed endpoint matrices are derived from the input word's gates.
+Optional --main checks the transported boundary against the pinned parent.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse,gzip,json,hashlib,time
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+
+def require(x,label):
+    if not x:raise RuntimeError(label)
+
+def basis(vs):
+    piv={}
+    for a in vs:
+        while a:
+            bit=a.bit_length()-1
+            if bit in piv:a^=piv[bit]
+            else:
+                piv[bit]=a;break
+    for k in sorted(piv):
+        for j in piv:
+            if j>k and piv[j]>>k&1:piv[j]^=piv[k]
+    return tuple(piv[k] for k in sorted(piv,reverse=True))
+
+def contained(a,b):return basis(a+b)==b
+
+def registers(e):return e[1:3] if e[0]=='add' else e[1:2]
+
+def apply(e,rows,dual=False):
+    if e[0]=='add':
+        t,s=e[1:3];q=F(e[3],e[4]);require(t!=s,'self add')
+        if dual:t,s,q=s,t,-q
+        dst=rows[t]
+        for k,x in list(rows[s].items()):
+            a=dst.get(k,F(0))+q*x
+            if a:dst[k]=a
+            else:dst.pop(k,None)
+    elif e[0]=='scale':
+        t=e[1];q=F(e[2],e[3]);require(q!=0,'zero scale')
+        if dual:q=1/q
+        rows[t]={k:q*x for k,x in rows[t].items()}
+    else:raise RuntimeError('unknown scalar primitive')
+
+def invert(e):
+    r=list(e)
+    if r[0]=='add':r[3]=-r[3]
+    else:r[2],r[3]=r[3],r[2]
+    return r
+
+def check_parent_interface(word,main):
+    # Read only the retained boundary data. No builder or local checker is imported.
+    relative="research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz"
+    path=main/relative;raw=path.read_bytes()
+    require(hashlib.sha256(raw).hexdigest()=="66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",'parent canonical input pin')
+    parent=json.loads(gzip.decompress(raw))
+    tau=lambda x:x^(43 if (x&43).bit_count()%2 else 0)
+    ports=parent['ports'];v=word['report']['v']
+    require(len(ports)==len(set(ports))==v,'parent port count')
+    require(set(map(tau,word['ports']))==set(ports),'transported source/target ports')
+    moved={i:ports.index(tau(p)) for i,p in enumerate(word['ports'])}
+    centers=[moved.get(r,r) for r in word['centers']]
+    actual=[list(basis([tau(x) for x in frame])) for frame in word['center_frames']]
+    expected=[parent['frames'][f] for f in parent['center_frames']]
+    require(len(centers)==len(set(centers))==len(actual)==8,'eight distinct centre carriers')
+    require(actual==expected and all(len(f)==8 for f in actual),'ordered centre frame interface')
+    return dict(parent_path=relative,parent_file_sha256=hashlib.sha256(raw).hexdigest(),
+                transport_tau=43,ordered_frame_bases_match=True,all_ports_match=True,
+                transported_centers=centers,source_centers=[r for r in centers if r<v],
+                ordered_frame_bases=actual)
+
+
+def run(path,out,main=None):
+    begin=time.monotonic();data=gzip.decompress(path.read_bytes());w=json.loads(data)
+    v,h,R=w['report']['v'],w['report']['h'],w['report']['R'];n=2*v+R
+    require((v,h)==(112,9),'wrong source geometry')
+    center_interface=check_parent_interface(w,main) if main is not None else None
+    ident=lambda:[{k:F(1)} for k in range(n)]
+    main=w['A']+w['cut']+w['B']
+    for e in main+w['precondition']+w['cleanup']:
+        require(all(0<=k<n for k in registers(e)),'register out of range')
+        q=F(e[3],e[4]) if e[0]=='add' else F(e[2],e[3])
+        require(q.denominator&(q.denominator-1)==0,'non-dyadic scalar')
+        if e[0]=='scale':require(abs(q.numerator)&(abs(q.numerator)-1)==0,'non-unit scale')
+    require(all(not(v<=e[2]<2*v) for e in w['A']+w['B'] if e[0]=='add' and not(v<=e[1]<2*v)), 'non-target reads target')
+    raw=ident()
+    for e in main:apply(e,raw)
+    dirt=[{} for _ in range(n)]
+    for y in range(v,2*v):dirt[y]={k:a for k,a in raw[y].items() if k>=2*v}
+    for e in w['precondition']:apply(e,dirt)
+    compensation=[['add',y,k,-a.numerator,a.denominator,[]] for y in range(v,2*v) for k,a in sorted(dirt[y].items())]
+    entering=set(map(int,w.get('start_extra',{})));lowends=set(map(int,w.get('helper_final',{})))
+    coldends=lowends-entering
+    require(not any(e[2] in entering for e in compensation),'nonzero entrance response')
+    require(not any(r in entering|coldends for e in w['precondition']+compensation for r in registers(e)), 'pre-wrapper touch of residual helper')
+    require(all(e[-1]==[] for e in w['precondition']+compensation),'nonzero frame precondition')
+    early=w.get('early_cleanup',[]);earlyids={i for i,U in early}
+    require(len(earlyids)==len(early),'duplicate early cleanup gate')
+    tail=[w['cleanup'][i][:-1]+[U] for i,U in early]
+    cleanup=[e for i,e in enumerate(w['cleanup']) if i not in earlyids]
+    prefix=w['precondition']+compensation+main
+    program=prefix+tail+cleanup
+    for dual in (False,True):
+        actual=ident()
+        for e in program:apply(e,actual,dual)
+        expected=ident()
+        for t in range(v):expected[t if dual else v+t][v+t if dual else t]=F(-1 if dual else 1)
+        bad=[i for i in range(n) if actual[i]!=expected[i]]
+        require(not bad,'all-column endpoint failure '+str((dual,bad[:8])))
+        print('endpoint', 'dual' if dual else 'forward','PASS',flush=True)
+    full=basis([1<<i for i in range(h)])
+    end=[full]*v+[basis([x for x in range(1,1<<h) if (x&p).bit_count()%2==0]) for p in w['ports']]+[full]*R
+    for q,U in w.get('helper_final',{}).items():end[int(q)]=basis(U)
+    start=[(p,) for p in w['ports']]+[()]*(v+R)
+    for q,U in w.get('start_extra',{}).items():
+        require(2*v<=int(q)<n,'non-helper entrance');start[int(q)]=basis(U)
+    cur=start.copy();paid=Counter()
+    def climb(q,U):
+        U=basis(U);require(contained(cur[q],U),'frame not monotone '+str((q,cur[q],U)))
+        d=len(U)-len(cur[q])
+        if d:paid[d]+=1
+        cur[q]=U
+    for section in ('A','B'):
+        if section=='B':
+            lev={int(t):basis(U) for t,U in w.get('target_levels',{}).items()}
+            require(all(cur[v+t]==lev.get(t,()) for t in range(v)),'target centre levels')
+            for q,U in zip(w['centers'],w['center_frames']):
+                U=basis(U);require(cur[q]==U,'center frame')
+                served={lev.get(e[1]-v,()) for e in w['cut'] if e[2]==q}
+                for T in sorted(served,key=lambda x:-len(x)):
+                    require(contained(T,U),'center path not nested')
+                    if T!=U:paid[len(U)-len(T)]+=1
+                    U=T
+        for e in w[section]:
+            for q in registers(e):climb(q,e[-1])
+    endB=cur.copy()
+    for e in tail:
+        for q in registers(e):climb(q,e[-1])
+    for q,U in enumerate(end):climb(q,U)
+    require(all(all(end[q]==full for q in registers(e)) for e in cleanup),'full cleanup reads a low end')
+    require(dict(paid)=={int(k):a for k,a in w['report']['local_profile'].items()},'paid profile mismatch')
+    inventory=Counter(len(end[q])-len(start[q]) for q in range(2*v,n))
+    require(dict(inventory)=={int(k):a for k,a in w['report']['width_inventory'].items()},'width inventory mismatch')
+    p=ident();pinv=ident()
+    for e in prefix:apply(e,p)
+    for e in reversed(prefix):apply(invert(e),pinv)
+    for q in lowends:
+        U=end[q]
+        require(all(contained(endB[k],U) for k in pinv[q]),'inverse-row cone '+str(q))
+        require(all(k==q or not p[k].get(q) or contained(endB[k],U) for k in range(n)),'dirt-column cone '+str(q))
+    report=dict(status='PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES',
+                input_file=path.name,content_sha256=hashlib.sha256(data).hexdigest(),
+                compressed_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),
+                parent_center_interface=center_interface,v=v,h=h,R=R,
+                entering=len(entering),lowends=len(lowends),coldends=len(coldends),
+                compensation_gates=len(compensation),local_profile=dict(sorted(paid.items())),
+                width_inventory=dict(sorted(inventory.items())),checked_columns=n,
+                elapsed_seconds=time.monotonic()-begin,
+                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.')
+    out.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2),flush=True)
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--word',type=Path,required=True,help='FULL-WORD.json.gz to check')
+    parser.add_argument('--output',type=Path,required=True,help='JSON receipt output path')
+    parser.add_argument('--main',type=Path,help='Optional pinned main checkout: also verify the transported centre/port interface')
+    args=parser.parse_args()
+    run(args.word,args.output,args.main)
diff --git a/research/adaptive-kernel-demotion/local/vendor/clifford/clifford_exact.py b/research/adaptive-kernel-demotion/local/vendor/clifford/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/vendor/clifford/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/adaptive-kernel-demotion/local/vendor/hpe_audit_and_transport.py b/research/adaptive-kernel-demotion/local/vendor/hpe_audit_and_transport.py
new file mode 100644
index 0000000000..d5d3509d90
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/vendor/hpe_audit_and_transport.py
@@ -0,0 +1,304 @@
+"""Rebuild arbitrary-dirt compensation and transport a changed local word.
+
+Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0.
+Adapted from PR425/433 (icekylinx), PR484's audit_gk.py
+(DreamingOfClouds), and Round19's 112-port transport. This auditor does not
+import a constructor, a nominated compensation table, or a global price.
+Only the changed scalar word and its actual frame chains are checked here.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def content_hash(path):
+    data = path.read_bytes()
+    return hashlib.sha256(gzip.decompress(data) if path.suffix == '.gz' else data).hexdigest()
+
+
+def basis(vs):
+    pivots = {}
+    for x in vs:
+        for k in sorted(pivots, reverse=True):
+            if x >> k & 1:
+                x ^= pivots[k]
+        if x:
+            k = x.bit_length() - 1
+            for j in pivots:
+                if pivots[j] >> k & 1:
+                    pivots[j] ^= x
+            pivots[k] = x
+    return tuple(pivots[k] for k in sorted(pivots, reverse=True))
+
+
+def apply(e, rows):
+    if e[0] == 'scale':
+        _, target, a, b, *_ = e
+        q = Q(a, b)
+        assert q
+        rows[target] = {j: q*x for j, x in rows[target].items()}
+    else:
+        _, target, source, a, b, *_ = e
+        assert target != source
+        q = Q(a, b)
+        for j, x in list(rows[source].items()):
+            value = rows[target].get(j, Q(0)) + q*x
+            if value:
+                rows[target][j] = value
+            else:
+                rows[target].pop(j, None)
+
+
+def inverse(e):
+    e = copy.deepcopy(e)
+    if e[0] == 'add':
+        e[3] *= -1
+    else:
+        e[2], e[3] = e[3], e[2]
+    return e
+
+
+def dual(e):
+    e = inverse(e)
+    if e[0] == 'add':
+        e[1], e[2] = e[2], e[1]
+    return e
+
+
+def state_maps(prefix, n):
+    """P = exact state map of the prefix (precondition + compensation + A + cut + B), and P^-1 (rows as sparse dicts)."""
+    P = [{r: Q(1)} for r in range(n)]
+    for e in prefix:
+        apply(e, P)
+    Pinv = [{r: Q(1)} for r in range(n)]
+    for e in reversed(prefix):
+        apply(inverse(e), Pinv)
+    return P, Pinv
+
+
+def cone_violations(P, Pinv, hpe, mapping, endB, final, frames):
+    """COLD-HPE / CONE PRE-CHECK.  Necessary conditions for helper h (raw index) to end at U = final[h] under ANY
+    monotone common-frame cleanup of the end-of-B state P (frames only climb, every gate at a common frame):
+      row    (J26-H dependency bound): every g in supp(row h of P^-1) has end-of-B frame <= U -- h is rebuilt from them;
+      column (dirt-column lemma):       every g != h with P[g][h] != 0 has end-of-B frame <= U -- the column of P at h,
+             restricted to rows whose frame is not <= U, changes only by invertible row operations unless h is read at a
+             frame not <= U, so it can reach e_h only if it is already zero there.
+    Both are implied by the exact endpoint replay plus the frame checks below; here they fail FAST, with the reason."""
+    inside = lambda a, b: basis(frames[a] + frames[b]) == frames[b]
+    viol = []
+    for h in hpe:
+        U = final[mapping[h]]
+        viol += [('row', h, g) for g, x in sorted(Pinv[h].items()) if x and not inside(endB[mapping[g]], U)]
+        viol += [('column', h, g) for g in range(len(P)) if g != h and P[g].get(h) and not inside(endB[mapping[g]], U)]
+    return viol
+
+
+def run(raw_path, routing_path, out):
+    start_time = time.monotonic()
+    word, routing = read(raw_path), read(routing_path)
+    v, h, helpers = word['report']['v'], word['report']['h'], word['report']['R']
+    assert h == 9 and v == 112 and routing['v'] == v
+    n = 2*v + helpers
+    ident = lambda: [{r: Q(1)} for r in range(n)]
+    main = word['A'] + word['cut'] + word['B']
+    assert all(not v <= e[2] < 2*v for e in word['A'] + word['B']
+               if e[0] == 'add' and not v <= e[1] < 2*v)
+    matrix = ident()
+    for e in main:
+        apply(e, matrix)
+    dirty = [{} for _ in range(n)]
+    for r in range(v, 2*v):
+        dirty[r] = {j: x for j, x in matrix[r].items() if j >= 2*v}
+    for e in word['precondition']:
+        apply(e, dirty)
+    compensation = [['add', r, j, -q.numerator, q.denominator, []]
+                    for r in range(v, 2*v) for j, q in sorted(dirty[r].items())]
+    entering = set(map(int, word.get('start_extra', {})))
+    assert all(e[2] not in entering for e in compensation), 'zero-frame compensation reads an entering helper'
+    cleanup = [inverse(e) for e in reversed(word['A'] + word['B'])
+               if not v <= e[1] < 2*v]
+    if 'refactored_cleanup' in word:
+        # REFACTORED CLEANUP (cold low-frame ends): the cleanup is not the literal reversed inverse of A+B but another exact
+        # factorisation of the same inverse.  Nothing about it is trusted: it may only touch non-target registers (T rows
+        # stay the compensated data accumulators), every gate is dyadic (checked below), and the arbitrary-dirt endpoint
+        # replay below must be exact in BOTH orientations for the full reordered program.  Inherited words keep the literal
+        # assertion (the else branch), so their outputs are unchanged.
+        assert all(not v <= r < 2*v for e in word['cleanup'] for r in ([e[1]] + ([e[2]] if e[0] == 'add' else []))), 'refactored cleanup touches a target'
+        assert all(e[0] in ('add', 'scale') for e in word['cleanup'])
+        cleanup = word['cleanup']
+    else:
+        assert [e[:-1] for e in cleanup] == [e[:-1] for e in word['cleanup']], 'cleanup is not the literal reversed inverse of A+B'
+    # HPE: hyperplane-ended helpers.  'early_cleanup' = [[cleanup index, frame vectors], ...] are cleanup gates executed
+    # right after B (before the final climbs) at the given frame; 'helper_final' = {helper: frame vectors} replaces FULL as
+    # that helper's terminal frame.  The scalar program is the reordered one and is replayed exactly below, so a move that
+    # does not commute with the skipped cleanup prefix is rejected by the arbitrary-dirt endpoint assertion.
+    early = [(int(i), f) for i, f in word.get('early_cleanup', [])]
+    helper_final = {int(r): f for r, f in word.get('helper_final', {}).items()}
+    early_idx = [i for i, _ in early]
+    assert len(set(early_idx)) == len(early_idx) and all(0 <= i < len(cleanup) for i in early_idx)
+    assert all(2*v <= r < n for r in helper_final)
+    # COLD-HPE: a COLD helper (not in start_extra, entrance frame 0 = bottom) may also end at a proper subspace U.
+    # It is the E = bottom instance of #593's theorems: its wrappers are the (0, U) recipes R_{0,U}, L_{0,U} (checked
+    # exactly by hpe_adapters_local), emitted as residual_adapter events like an entering helper's.
+    cold_hpe = sorted(r for r in helper_final if r not in entering)
+    # COLD-HPE wrapper order: R_{0,U}^-1 is emitted with the entry adapters, after the zero-frame precondition and
+    # compensation, so (exactly as for an entering helper, asserted above) nothing before it may touch a cold-ended helper.
+    assert all(r not in set(cold_hpe) for e in word['precondition'] + compensation for r in ([e[1]] + ([e[2]] if e[0] == 'add' else []))), 'zero-frame precondition/compensation touches a cold hyperplane-ended helper before its wrapper'
+    # ENTERING helpers (start frame E != 0): their wrapper R_E^-1 precedes every gate on them, so the zero-frame precondition
+    # and compensation may not touch them either (mirrors hpe_emit_local's start-frame-0 rule here, at the scalar audit).
+    assert all(r not in entering for e in word['precondition'] + compensation for r in ([e[1]] + ([e[2]] if e[0] == 'add' else []))), 'zero-frame precondition/compensation touches an entering helper'
+    tail =[word['cleanup'][i][:-1] + [f] for i, f in early]
+    rest = [e for i, e in enumerate(word['cleanup']) if i not in set(early_idx)]
+    program = word['precondition'] + compensation + main + tail + rest
+    for backward in (False, True):
+        actual = ident()
+        for e in program:
+            apply(dual(e) if backward else e, actual)
+        expected = ident()
+        for t in range(v):
+            expected[t if backward else v+t][v+t if backward else t] = Q(-1 if backward else 1)
+        assert actual == expected, ('arbitrary-dirt endpoint', backward)
+    # The native scalar compiler allows dyadic additions and signed binary scales.
+    for e in program:
+        q = Q(e[3], e[4]) if e[0] == 'add' else Q(e[2], e[3])
+        assert q.denominator & (q.denominator-1) == 0
+        if e[0] == 'scale':
+            a = abs(q.numerator)
+            assert a and a & (a-1) == 0
+
+    tau = lambda x: x ^ (43 if (x & 43).bit_count() % 2 else 0)
+    ports = routing['ports']
+    assert len(set(ports)) == v and set(map(tau, word['ports'])) == set(ports)
+    mapping = {i: ports.index(tau(p)) for i, p in enumerate(word['ports'])}
+    mapping.update({v+i: v+mapping[i] for i in range(v)})
+    mapping.update({r: r for r in range(2*v, n)})
+    full = tuple(1 << i for i in range(h-1, -1, -1))
+    frames, frame_ids = [(), full], {(): 0, full: 1}
+
+    def fid(vectors):
+        frame = basis(vectors)
+        if frame not in frame_ids:
+            frame_ids[frame] = len(frames)
+            frames.append(frame)
+        return frame_ids[frame]
+
+    def transform(e):
+        e = copy.deepcopy(e)
+        e[1] = mapping[e[1]]
+        if e[0] == 'add':
+            e[2] = mapping[e[2]]
+        if e[-1] is not None:
+            e[-1] = fid([tau(x) for x in e[-1]])
+        return e
+
+    canonical = {key: [transform(e) for e in word[key]]
+                 for key in ('A', 'B', 'cut', 'cleanup', 'precondition')}
+    canonical['compensation'] = [transform(e) for e in compensation]
+    if tail:
+        canonical['tail'] = [transform(e) for e in tail]                  # HPE (absent for inherited words: identical output)
+    canonical['cleanup'] = [transform(e) for e in rest]                   # HPE (full cleanup minus the early gates)
+    canonical['start'] = [fid([p]) for p in ports] + [0]*(v+helpers)
+    for r, frame in word.get('start_extra', {}).items():
+        assert 2*v <= int(r) < n
+        canonical['start'][int(r)] = fid([tau(x) for x in frame])
+    canonical['final'] = ([1]*v +
+        [fid(x for x in range(1, 1 << h) if (x & p).bit_count() % 2 == 0) for p in ports] +
+        [1]*helpers)
+    for r, frame in helper_final.items():                                 # HPE
+        canonical['final'][r] = fid([tau(x) for x in frame])
+    canonical.update(h=h, v=v, R=helpers, ports=ports, frames=frames,
+                     centers=[mapping[r] for r in word['centers']],
+                     center_frames=[fid(tau(x) for x in frame) for frame in word['center_frames']])
+    levels = {mapping[v+int(t)]-v: fid(tau(x) for x in frame)
+              for t, frame in word.get('target_levels', {}).items()}
+    canonical['target_levels'] = {str(t): f for t, f in levels.items()}
+    current, paid, edges = canonical['start'].copy(), Counter(), set()
+
+    def climb(r, f):
+        old = current[r]
+        assert basis(frames[old] + frames[f]) == frames[f], ('nonmonotone', r, old, f)
+        if old != f:
+            degree = len(frames[f]) - len(frames[old])
+            assert degree > 0
+            paid[degree] += 1
+            edges.add((old, f))
+            current[r] = f
+
+    for part in ('A', 'B'):
+        if part == 'B':
+            assert all(current[r] == f for r, f in zip(canonical['centers'], canonical['center_frames']))
+            assert all(current[v+t] == levels.get(t, 0) for t in range(v))
+            for r, frame in zip(canonical['centers'], canonical['center_frames']):
+                served = {levels.get(e[1]-v, 0) for e in canonical['cut'] if e[2] == r}
+                old = frame
+                for f in sorted(served, key=lambda f: -len(frames[f])):
+                    assert basis(frames[old] + frames[f]) == frames[old]
+                    if old != f:
+                        paid[len(frames[old])-len(frames[f])] += 1
+                        edges.add((old, f))
+                        edges.add((f, old))
+                        old = f
+        for e in canonical[part]:
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []):
+                climb(r, e[-1])
+    if helper_final:                                                      # COLD-HPE / CONE PRE-CHECK at the end-of-B frames
+        P, Pinv = state_maps(word['precondition'] + compensation + main, n)
+        cone = cone_violations(P, Pinv, sorted(helper_final), mapping, current.copy(), canonical['final'], frames)
+        assert not cone, ('hpe cone pre-check (row / column)', cone[:8])
+    for e in canonical.get('tail', []):                                   # HPE: early cleanup gates at their common frame
+        for r in [e[1]] + ([e[2]] if e[0] == 'add' else []):
+            climb(r, e[-1])
+    for r, f in enumerate(canonical['final']):
+        climb(r, f)
+    # HPE: the remaining cleanup runs at FULL, so it may touch only registers whose terminal frame is FULL; a
+    # hyperplane-ended helper is touched by nothing after its tail gates.
+    for e in canonical['cleanup']:
+        assert all(canonical['final'][r] == 1 for r in [e[1]] + ([e[2]] if e[0] == 'add' else [])), ('cleanup on non-FULL end', e)
+    assert all(len(frames[canonical['final'][r]]) < h for r in helper_final)
+    assert dict(paid) == {int(r): count for r, count in word['report']['local_profile'].items()}, 'paid local profile differs from the reported local_profile'
+    canonical['local_profile'] = dict(sorted(paid.items()))
+    canonical['edges'] = sorted(edges)
+    out.mkdir(parents=True, exist_ok=False)
+    payload = json.dumps(canonical, sort_keys=True, separators=(',', ':')).encode()
+    (out/'CANONICAL-WORD.json.gz').write_bytes(gzip.compress(payload, mtime=0))
+    (out/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word, sort_keys=True, separators=(',', ':')).encode(), mtime=0))
+    receipt = dict(status='PASS_CHANGED_WORD_ALL_COLUMNS_AND_NATIVE_FRAMES',
+                   input_content_sha256=content_hash(raw_path), routing_content_sha256=content_hash(routing_path),
+                   canonical_content_sha256=hashlib.sha256(payload).hexdigest(),
+                   live_columns_each_orientation=n, helpers=helpers,
+                   compensation_additions=len(compensation), scalar_operations=len(program),
+                   center_rank_sum=sum(map(len, word['center_frames'])),
+                   local_profile=dict(sorted(paid.items())), local_rank_mass=sum(r*z for r, z in paid.items()),
+                   widths=[len(frames[canonical['final'][r]])-len(frames[canonical['start'][r]]) for r in range(2*v, n)],
+                   frames=len(frames), directed_edges=len(edges),
+                   tau=43, target_port_order_matches_baseline=True,
+                   seconds=time.monotonic()-start_time,
+                   scope='Fresh exact forward and inverse-transpose scalar replay on every arbitrary input; all native frame chains and dyadic primitives. Phase lowering, wrappers, global owners and global assembly are separate.')
+    if tail or helper_final:
+        receipt.update(hyperplane_ended_helpers=sorted(helper_final), early_cleanup_gates=len(tail))
+    if cold_hpe:                                                          # COLD-HPE (absent for words without cold ends)
+        receipt.update(cold_hyperplane_ended_helpers=cold_hpe)
+    if 'refactored_cleanup' in word:                                      # REFACTORED CLEANUP (absent for inherited words)
+        receipt.update(refactored_cleanup_gates=len(word['cleanup']), refactored_cleanup=word['refactored_cleanup'])
+    (out/'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(json.dumps({k: value for k, value in receipt.items() if k != 'widths'}, indent=2), flush=True)
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--raw', type=Path, required=True)
+    parser.add_argument('--routing', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    run(args.raw, args.routing, args.out)
diff --git a/research/adaptive-kernel-demotion/local/vendor/hpe_audit_local.py b/research/adaptive-kernel-demotion/local/vendor/hpe_audit_local.py
new file mode 100644
index 0000000000..17bccb64fd
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/vendor/hpe_audit_local.py
@@ -0,0 +1,171 @@
+# Local-only extraction of the attributed PR514 / PR433 independent replay.
+# Prepared for icekylinx with OpenAI Codex assistance. Apache-2.0.
+# The complete local checker and its negative controls are retained verbatim.
+# Global hosting is verified separately for the changed 112-port geometry.
+import copy,gzip,hashlib,json,sys
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+OUT=Path(sys.argv[1])
+c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'))
+ir={'local_programs':json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'))}
+v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames']
+levels={int(t):f for t,f in c.get('target_levels',{}).items()}
+entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+plain={r for r in range(n) if r not in set(entering)}
+
+def contains(a,b):
+    for x in a:
+        for y in b:
+            if x>>(y.bit_length()-1)&1:x^=y
+        if x:return False
+    return True
+hpe={r for r in range(2*v,n) if c['final'][r]!=1}   # HPE: helpers whose terminal frame is a proper subspace U of FULL
+assert all(len(frames[c['final'][r]])<h for r in hpe)
+# COLD-HPE: cold helpers (start frame 0) ending at U carry the (0, U) wrappers too; without cold ends wrapped == entering
+cold=sorted(hpe-set(entering));wrapped=sorted(set(entering)|hpe);plain={r for r in range(n) if r not in set(wrapped)}
+def local(events,back):
+    rows={('L',r):{r:Q(1)} for r in range(n)}
+    norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={}
+    hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256();chain={};wrappers=[]
+    wset=set(wrapped);pre_seen=set();post_seen=set()   # WRAPPER ORDER (Lemma A): R^-1 precedes, L^-1 follows, every scalar touching a wrapped helper
+    allowed=['zero_frame_precondition','entry_adapters','A','centers','B']+(['cleanup_tail'] if c.get('tail') else [])+['final','exit_adapters','full_frame_cleanup','done']   # HPE
+    for event in events:
+        tag=event[0]
+        if tag=='phase':
+            phases.append(event[1]);assert phases==allowed[:len(phases)]
+            if event[1]=='A':assert entry==[(r,f) for r,f in enumerate(c['start']) if r in plain] and sorted(r for k_,r,f_ in wrappers if k_=='pre')==wrapped   # GK
+            if event[1]=='centers':assert all(cur[r]==levels.get(r-v,0) for r in range(v,2*v))   # GK
+            if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==[(r,f) for r,f in enumerate(c['final']) if r not in hpe]   # HPE: no old-convention exit for U-ended helpers
+            assert not private
+        elif tag=='residual_adapter':   # GK: paid wrappers of entering helpers: R_E^-1 before the invocation, L_E^-1 after the full-frame cleanup
+            _,kind,r,f,*end=event;assert r in wrapped and f==c['start'][r] and kind in ('pre','post')
+            # HPE: the post wrapper of a U-ended helper names U (= its terminal frame) and is L_{E,U}^-1; every other wrapper has no 5th field
+            # HPE: both wrappers of a U-ended helper name U, so the recipe is the (E,U) one, R_{E,U} and L_{E,U}
+            assert end==([c['final'][r]] if r in hpe else [])
+            if end and kind=='post':assert cur[r]==end[0]
+            assert (kind=='pre' and phases[-1]=='entry_adapters') or (kind=='post' and phases[-1]=='full_frame_cleanup')
+            assert (kind,r) not in {(k,x) for k,x,_ in wrappers};wrappers.append((kind,r,f))
+            (pre_seen if kind=='pre' else post_seen).add(r)
+        elif tag=='adapter':
+            assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]]
+            (entry if event[1]=='old_to_new' else exit).append((event[2],event[3]))
+        elif tag=='climb':
+            _,part,r,a,b,rank=event
+            assert not private and phases[-1]==part and cur[r]==a
+            assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0
+            hist[rank]+=1;cur[r]=b
+        elif tag=='center':
+            _,k,a,b,rank=event
+            assert phases[-1]=='centers' and private=={('C',k):a}
+            cf=c['center_frames'][k];cr=len(frames[cf])
+            # GK: stepwise descent cf -> served levels -> lowest (forward), reversed ascent (backward); each step is a nested child
+            assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a])
+            assert rank==abs(len(frames[a])-len(frames[b]))>0
+            chain.setdefault(k,[]).append((a,b))
+            private['C',k]=b;hist[rank]+=1;centers.append(k)
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None
+            if target[0]=='C' and op=='clear':
+                assert private.get(target,f)==f
+                private.pop(target,None)
+            else:
+                for r in (target,source):
+                    if r is None:continue
+                    if r[0]=='L':assert cur[r[1]]==f and (r[1] not in wset or (r[1] in pre_seen and r[1] not in post_seen)),('common frame / wrapper order',r,cur[r[1]],f)
+                    else:
+                        if r==target and r not in private:private[r]=f
+                        assert private[r]==f
+            if op=='clear':rows[target]={};norm[target]=Q(0)
+            elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source]
+            elif op=='scale':
+                q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator
+                assert a&(a-1)==0 and b&(b-1)==0
+                rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q)
+            else:
+                q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator
+                assert source!=target and b&(b-1)==0
+                # Independent symbolic replay of the cleared coefficient work.
+                w=0
+                for bit in bin(a)[2:]:w=2*w+int(bit)
+                assert Q(w,b)*(1 if q>0 else -1)==q
+                prefix=max(prefix,Q(a)*norm[source])
+                norm[target]=norm.get(target,Q(0))+abs(q)*norm[source]
+                row=rows.setdefault(target,{})
+                for j,x in list(rows[source].items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+            prefix=max(prefix,norm[target])
+        else:raise AssertionError(tag)
+    assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private
+    assert sorted(r for k,r,_ in wrappers if k=='pre')==wrapped and sorted(r for k,r,_ in wrappers if k=='post')==wrapped   # GK
+    for k,st in chain.items():   # GK: the steps of each centre chain link up and end at the centre frame
+        cf=c['center_frames'][k]
+        if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+        else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+    assert all(not row for reg,row in rows.items() if reg[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert rows['L',r]==expected
+    # A 192-bit local payload allowance vastly dominates even coefficient work.
+    assert prefix<2**192
+    return hist,{'all_exact_columns':n,'prefix_l1_upper':str(prefix),
+                 'prefix_bits_upper':prefix.numerator.bit_length()-prefix.denominator.bit_length()+1,
+                 'charged_payload_bits':192,'private_work_erased':True}
+
+profiles={};checks={}
+for name in ('forward','backward'):
+    profiles[name],checks[name]=local(ir['local_programs'][name],name=='backward')
+    assert dict(profiles[name])=={int(r):z for r,z in c['local_profile'].items()}
+    print('independent emitted replay PASS',name,flush=True)
+controls=[]
+for name,mut in [
+    ('wrong_scale',lambda es:next(e for e in es if e[0]=='scalar' and e[1][0]=='scale')[1].__setitem__(2,3)),
+    ('missing_center',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center'))),
+    ('wrong_common_frame',lambda es:next(e for e in es if e[0]=='scalar' and e[2]!=0).__setitem__(2,0)),
+    ('wrong_child_rank',lambda es:next(e for e in es if e[0]=='climb').__setitem__(5,99)),
+]+([
+    ('missing_pre_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre'))),
+    ('missing_post_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post'))),
+    ('wrapper_with_wrong_frame',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[2] in entering).__setitem__(3,0)),   # COLD-HPE: an ENTERING helper's wrapper (a cold one's frame is 0 already)
+    ('wrapper_in_wrong_phase',lambda es:es.insert(es.index(['phase','A']),es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post')))),
+    ('wrapper_on_a_data_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,3)),
+    ('wrapper_on_a_target_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,v+3)),
+    ('wrapper_on_a_centre_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,['C',0])),
+] if entering else [])+([
+    ('centre_step_not_nested',lambda es:next(e for e in es if e[0]=='center').__setitem__(3,next(f for f in range(len(frames)) if not contains(frames[f],frames[next(e for e in es if e[0]=='center')[2]]) and not contains(frames[next(e for e in es if e[0]=='center')[2]],frames[f])))),
+    ('centre_descent_step_skipped',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center' and e[3]!=0))),
+] if levels else [])+([
+    ('hpe_pre_wrapper_resolved_to_full_recipe',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[1]=='pre' and len(e)==5).pop()),
+    ('hpe_post_wrapper_without_terminal_frame',lambda es:next(e for e in es if e[0]=='residual_adapter' and len(e)==5).pop()),
+    ('hpe_post_wrapper_wrong_terminal_frame',lambda es:next(e for e in es if e[0]=='residual_adapter' and len(e)==5).__setitem__(4,1)),
+    ('hpe_tail_gate_at_full_frame',lambda es:next(e for e in es[es.index(['phase','cleanup_tail']):] if e[0]=='scalar').__setitem__(2,1)),
+    ('hpe_tail_climb_dropped',lambda es:es.pop(next(i for i in range(es.index(['phase','cleanup_tail']),len(es)) if es[i][0]=='climb'))),
+    ('hpe_helper_exit_adapter_to_full',lambda es:es.insert(es.index(['phase','full_frame_cleanup']),['adapter','new_to_old',min(hpe),1])),
+    ('hpe_tail_gate_moved_into_full_cleanup',lambda es:(lambda x:(x.__setitem__(2,1),es.insert(es.index(['phase','full_frame_cleanup'])+1,x)))(es.pop(next(i for i in range(es.index(['phase','cleanup_tail']),len(es)) if es[i][0]=='scalar')))),
+] if hpe else [])+([   # COLD-HPE controls on the first cold hyperplane-ended helper
+    ('cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter',lambda es:(lambda i:es.__setitem__(i,['adapter','old_to_new',cold[0],0]))(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]))),
+    ('cold_hpe_pre_wrapper_dropped',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]))),
+    ('cold_hpe_post_wrapper_replaced_by_exit_adapter',lambda es:(lambda i:es.__setitem__(i,['adapter','new_to_old',cold[0],c['final'][cold[0]]]))(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post' and e[2]==cold[0]))),
+    ('cold_hpe_pre_wrapper_resolved_to_cold_full_convention',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]).pop()),
+    ('cold_hpe_wrapper_with_nonzero_entrance',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]).__setitem__(3,1)),
+    ('cold_hpe_post_wrapper_wrong_terminal_frame',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[1]=='post' and e[2]==cold[0]).__setitem__(4,1)),
+    ('cold_hpe_premix_gate_before_pre_wrapper',lambda es:(lambda ev:es.insert(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]),ev))(es.pop(next(i for i,e in enumerate(es) if e[0]=='scalar' and (('L',cold[0]) in [tuple(e[1][1])]+([tuple(e[1][2])] if e[1][0] in ('add','copy') else []))))) ),
+] if cold else []):
+    es=copy.deepcopy(ir['local_programs']['forward']);mut(es)
+    try:local(es,False)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('mutation accepted: '+name)
+
+
+result={'status':'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY',
+'canonical_word_sha256':hashlib.sha256((OUT/'CANONICAL-WORD.json.gz').read_bytes()).hexdigest(),
+'local_programs_sha256':hashlib.sha256((OUT/'LOCAL-PROGRAMS.json.gz').read_bytes()).hexdigest(),
+'v':v,'helpers':R,'local':checks,'paid_profiles':{name:dict(H) for name,H in profiles.items()},
+'entering_helpers':len(entering),**({'cold_hyperplane_ended_helpers':len(cold)} if cold else {}),'negative_controls_rejected':controls,
+'scope':'Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate.'}
+(OUT/'INDEPENDENT-LOCAL-REPLAY.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],len(controls),'controls rejected',flush=True)
diff --git a/research/adaptive-kernel-demotion/local/vendor/hpe_emit_local.py b/research/adaptive-kernel-demotion/local/vendor/hpe_emit_local.py
new file mode 100644
index 0000000000..534fdc71f7
--- /dev/null
+++ b/research/adaptive-kernel-demotion/local/vendor/hpe_emit_local.py
@@ -0,0 +1,163 @@
+# GK: modified copy of PR #433's complex_emit.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted from PR425 by icekylinx with Codex assistance.
+"""Emit both local programs, integrate the fixed nine-stage geometry, and bill.
+
+The expanded scalar interface is justified in PROOF.txt. This script does not
+claim a Lean proof or discharge the inherited all-size/analytic interfaces.
+"""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path(_sys.argv[1]);cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp))
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def basis(vs):
+    b={}
+    for x in vs:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def dual(e):
+    e=list(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def scalar(e,back):
+    e=dual(e) if back else list(e)
+    if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]]
+    return ['scale',['L',e[1]],e[2],e[3]]
+def primitive_bound(e):
+    if e[0] in ('clear','copy'):return 1
+    q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])
+    a,b=abs(q.numerator),q.denominator
+    assert b&(b-1)==0
+    if e[0]=='scale':
+        assert a&(a-1)==0
+        return abs(a.bit_length()-b.bit_length())+int(q<0)
+    # Exact binary Horner multiplication on a cleared private stream, repeated
+    # halving, signed accumulation into the target, then clear the private stream.
+    return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1)
+
+def emit(back):
+    out=[];cur=c['start'].copy()
+    def event(e):out.append(e)
+    def scal(e,f):event(['scalar',e,f])
+    event(['phase','zero_frame_precondition'])
+    for e in c['precondition']+c['compensation']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['start'][r]==0 for r in regs)
+        scal(scalar(e,back),0)
+    event(['phase','entry_adapters'])
+    # GK: a helper that starts at a nonzero entrance frame has NO entry adapter; its paid wrapper R_E^-1 (Lemma A) precedes every gate
+    # that touches it and L_E^-1 follows the full-frame cleanup.  Words without entrances emit PR #433's events.
+    entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+    hpe={r for r in range(2*v,n) if c['final'][r]!=1}   # HPE: hyperplane-ended helpers (terminal frame != FULL)
+    # COLD-HPE: a cold helper (start frame 0) ending at U also carries the paid wrappers R_{0,U}^-1 / L_{0,U}^-1 (the
+    # E = bottom instance of #593); without cold ends wrapped == entering and the event stream is the inherited one.
+    wrapped=sorted(set(entering)|hpe)
+    for r,f in enumerate(c['start']):
+        if r in wrapped:event(['residual_adapter','pre',r,f]+([c['final'][r]] if c['final'][r]!=1 else []))   # HPE: R_{E,U}^-1 names U
+        else:event(['adapter','old_to_new',r,f])
+    def climb(r,f,part):
+        old=cur[r]
+        if old==f:return
+        assert basis(frames[old]+frames[f])==tuple(frames[f])
+        rank=len(frames[f])-len(frames[old]);assert rank>0
+        event(['climb',part,r,old,f,rank]);cur[r]=f
+    # HPE: 'cleanup_tail' = early cleanup gates at their own frames; emitted only when the word has them, so a word
+    # without hyperplane-ended helpers yields exactly the inherited event stream.
+    for part in ('A','centers','B')+(('cleanup_tail',) if c.get('tail') else ())+('final',):
+        event(['phase',part])
+        if part in ('A','B','cleanup_tail'):
+            for e in (c['tail'] if part=='cleanup_tail' else c[part]):
+                regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+                for r in regs:climb(r,e[-1],part)
+                scal(scalar(e,back),e[-1])
+        elif part=='centers':
+            # GK: targets sit at their nonzero-frame-compensation level (0 at the defaults); a centre copy descends
+            # cf -> served levels (descending chain) -> lowest served level and scatters into each target at its level
+            lv=lambda r:c.get('target_levels',{}).get(str(r-v),0)
+            assert all(cur[r]==lv(r) for r in range(v,2*v))
+            for k,r in enumerate(c['centers']):
+                cf=c['center_frames'][k];assert cur[r]==cf
+                terms=[e for e in c['cut'] if e[2]==r]
+                path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x]))
+                C=['C',k]
+                if not back:
+                    scal(['clear',C],cf);scal(['copy',C,['L',r]],cf)
+                    for a in range(len(path)):
+                        if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])])
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a])
+                    scal(['clear',C],path[-1])
+                else:
+                    scal(['clear',C],path[-1])
+                    for a in range(len(path)-1,-1,-1):
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a])
+                        if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])])
+                    scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf)
+        else:
+            for r,f in enumerate(c['final']):climb(r,f,part)
+    event(['phase','exit_adapters'])
+    for r,f in enumerate(c['final']):
+        if r not in hpe:event(['adapter','new_to_old',r,f])   # HPE: no old-convention exit for a helper that ends at U; its post wrapper is L_{E,U}^-1
+    event(['phase','full_frame_cleanup'])
+    for e in c['cleanup']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['final'][r]==1 for r in regs)
+        scal(scalar(e,back),1)
+    for r in wrapped:event(['residual_adapter','post',r,c['start'][r]]+([c['final'][r]] if r in hpe else []))   # HPE: 5th field = terminal frame U   # GK: L_E^-1 after the full-frame cleanup
+    event(['phase','done'])
+    return out
+
+def check_local(events,back):
+    # Literal scalar replay of the emitted stream, including center lifetimes.
+    state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0
+    for e in events:
+        if e[0]=='climb':assert not live;paid[e[5]]+=1
+        elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1
+        elif e[0]=='scalar':
+            op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op)
+            if tag=='clear':
+                state[t]={}
+                if t[0]=='C' and t[1] in live:live.remove(t[1])
+            elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1])
+            elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()}
+            else:
+                s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{})
+                if t[0]=='C' and t[1] not in live:live.append(t[1])
+                for j,x in list(state.get(s,{}).items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+    assert not live and all(not row for r,row in state.items() if r[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert state['L',r]==expected,('emitted column mismatch',back,r)
+    assert dict(paid)=={int(r):z for r,z in c['local_profile'].items()}
+    return {'sha256':digest(events),'events':len(events),'scalar_macros':macros,
+            'real_component_primitive_bound':prims,'paid_profile':dict(sorted(paid.items())),
+            'all_columns':n,'private_centers_cleared':True,'private_coefficient_stream_cleared_after_each_macro':True}
+
+programs={};checks={}
+for name,back in [('forward',False),('backward',True)]:
+    programs[name]=emit(back);checks[name]=check_local(programs[name],back)
+    print('PASS emitted',name,checks[name]['events'],'events',flush=True)
+
+
+(OUT/'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(json.dumps(programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'LOCAL-CHECKS.json').write_text(json.dumps(checks,indent=2)+'\n')
diff --git a/research/adaptive-kernel-demotion/notes/cells/OPENAI-MECHANISMS.md b/research/adaptive-kernel-demotion/notes/cells/OPENAI-MECHANISMS.md
new file mode 100644
index 0000000000..dada7f7709
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/cells/OPENAI-MECHANISMS.md
@@ -0,0 +1,57 @@
+# Two OpenAI proof mechanisms incorporated into the combined supplier
+
+These are source-informed mathematical uses, not fresh Lean kernel certification. Neither theorem alone establishes a multiplication exponent. Both are used in a sufficient construction whose exact changed local maps and frames have been checked.
+
+## 1. Rank-increment matching for exact frame invoices
+
+Source: F:/proof/leanlibs-20261009/openai-math-fd4aeeb2/src/lean/OAI/LinearAlgebra/RankMatching/Basic.lean.
+
+- `OAI.HahnWilson.RankMatching.finrank_sup_singleton`, line 79: for a finite-dimensional subspace S, dim(S + span(v)) = dim(S) + (0 if v belongs to S, otherwise1).
+- `blockRank_step`, line 137: blockRank(A,l,j) = blockRank(A,l,j-1) + increment(A,l,j).
+- `rank_matching`, line 329: for an upper-triangular matrix, the mixed block-rank differences are0/1, give at most one match in each row/column, and block rank equals the number of matches.
+
+Constructive frame lemma. Given a finite nested chain E0 <= E1 <= ... <= Ek, extend a basis successively across its stages. Every added vector receives its first stage index. The number of vectors born at stage i is exactly dim(Ei)-dim(Ei-1): each elementary vector contributes precisely the singleton increment above. This supplies the actual paid jump sizes, not merely total rank. Grouping these births in the original jump events gives the full histogram; no event is deleted because two traces have equal total rank.
+
+Application here. Recompute the complete chains after lowering the four entrances635/637/638/639 and their12 common B frames. The literal rank-seven endpoint patches574/575 have disjoint fields. The full recomputed histogram, including all fixed center descents, is
+
+    2398 H1 +440 H2 +428 H3 +138 H4 +82 H5 +8 H8.
+
+Relative to PR1117 this is exactly -8H1 +8H2 +4H3 -4H4, with local rank mass5588 instead of5584. The arbitrary-dirt endpoint and all low-end cones remain valid. Both the raw independent checker and the emitted event checker reproduce these jump counts. The role widths increase4->5 only at helperindices411/413/414/415. This exact invoice is essential: demotion is NOT free and the four additional units must come from paid pending remainders.
+
+## 2. Tensor-product restriction composition for independent residual factors
+
+Source: F:/proof/leanlibs-20261009/openai-math-fd4aeeb2/src/lean/OAI/LinearAlgebra/MatrixMultiplication/Tensor/TerminalProducts.lean.
+
+- `OAI.MatrixMultiplication.TerminalProducts.restrict_familyProduct`, line 16: restricting a product of coefficient tensors by tensor products of three local restriction matrices equals the product of the independently restricted factors.
+- `matrix_restriction_of_history_restrictions`, line 27: actual local matrix-tensor restrictions combine by explicit product and composed restriction matrices into one global matrix-tensor restriction.
+
+Constructive residual lemma. Suppose a pending physical transform is expressed in an explicitly verified coordinate chart as a tensor product over disjoint reserved axes and a remainder. Suppose each substituted local wrapped unit equals the required transform on its reserved axes and the identity on all other axes, for arbitrary dirty inputs. Execute each wrapped unit, and the paid remainder transform. By the product identity, the whole pending transform is recovered. Distinct local phases must be included; a tableau alone does not establish equality. No two units may reserve overlapping axes, and no unit may use the same physical family twice in one call.
+
+Application here. Each unchanged PR1117 wrapped factor retains its source-pinned identity. The combined local provider changes exactly one entrance/terminal wrapper type. It is freshly lowered and independently decoded as R^-1 S L^-1 = Fourier5 x Identity4, including the exact global phase. The9 newly introduced frame edges are separately checked. A mixed call can therefore replace four width4 roles by their concrete width5 counterparts, provided the owner checker explicitly supplies disjoint5-coordinate charts and debits the extra unit from each pending remainder. The global owner constructor is a separate worker; this lemma explains why its chart and remainder checks are sufficient once supplied. It does not assume an unknown local unit or unconstructed oracle.
+
+## Concrete verification scope
+
+- Actual PR1117 raw word semantic SHA256 f64e0942edc5eb2d45b0a3b068ba942436f35ba9a077ff53d7e4424d1617b2cd.
+- Combined raw word semantic SHA256 ca719f9b3b16a52dfd3774353bcb386d622a947a17023d7e9b261bb3132ab79a.
+- Both directions on all704 input columns, entrance-zero response, every frame chain, every low-end inverse-row and dirty-column cone: PASS.
+- Transported native word and emitted forward/backward programs: PASS.
+- Full emitted local replay with25 corruption controls: PASS in8.59 seconds.
+- All9 changed frame edges and the1 changed wrapper, tableau plus exact zero-state/global phase;10 phase mutations rejected: PASS in0.97 seconds.
+- Unchanged PR1117 phases, endpoint adapters, all-size/compiler, physical schedule, tape/precision and analytic contracts are inherited, not re-proved here.
+
+The stronger connection to rank-matching is the representation of a complete frame itinerary by vector-birth incidences. The stronger connection to terminal tensor products is the constructive recovery of the whole pending transform from independently dirty-restoring units plus an explicitly paid remainder. Neither justifies adding two advertised kappa gains.
+
+
+## Completed joint-provider extension
+
+The complete literal rank-five entrance islands are headed635,603,611,619,627, in that order. The sixth tested natural deletion, headed651, is not used. Each used island has four distinct entering helpers and12 shared B records. The five entrance-key sets and five B-record-index sets are pairwise disjoint; their union is explicitly checked in multigroup/data/PATCHES.json. Each variant applies a concrete prefix of these sets to the same actual PR1117 word.
+
+Disjoint annotations imply only that the literal edits commute. They do not by themselves imply paid-profile additivity or geometric admission. We reconstructed and freshly checked all five whole variants: every704 dirty input column in both orientations, all frame chains and low-end cones, both actual emitted programs with25 corruption controls, and every changed phase and wrapper. These actual checks establish the same complete profile formula for each k:
+
+    (2406-8k) H1 +(432+8k) H2 +(424+4k) H3 +(142-4k) H4 +82 H5 +8 H8.
+
+The actual width inventory is (56-4k) helpers of width4, (32+4k) of width5,32 of width7,120 of width8 and240 of width9. Local rank mass is5584+4k. These formulas summarize independently checked concrete data; they are not assumed from isolated patch totals.
+
+The rank-birth mechanism applies to each reconstructed chain and charges every real jump. The tensor-factor composition mechanism applies to the actual distinct pending coordinate factors and the separately paid remainder under the explicit global owner map. Thus each of the five variants is a concrete sufficient local provider for a call whose checked coordinate chart reserves its actual widths. No unbuilt gadget, presumed savings or unknown oracle is introduced.
+
+Portable reproduction is in multigroup/portable/check_local.py --selector k --out fresh-path, with exact source/data pins and no external dependencies beyond standard-library Python. All selectors were checked through their actual stage chain; selector5 additionally passed the complete standalone portable wrapper in17.46 seconds. Nothing was published and no persistent computational process remains.
diff --git a/research/adaptive-kernel-demotion/notes/cells/OPENAI-SOURCE-LEDGER.json b/research/adaptive-kernel-demotion/notes/cells/OPENAI-SOURCE-LEDGER.json
new file mode 100644
index 0000000000..f10c98b58c
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/cells/OPENAI-SOURCE-LEDGER.json
@@ -0,0 +1,36 @@
+[
+  {
+    "source": "F:\\proof\\leanlibs-20261009\\openai-math-fd4aeeb2\\src\\lean\\OAI\\LinearAlgebra\\RankMatching\\Basic.lean",
+    "sha256": "dd853803132873dcaef100d6d79ff4aaeecdc72ecb5e5fc25a33226445aaa5cd",
+    "declarations": [
+      {
+        "name": "finrank_sup_singleton",
+        "line": 79
+      },
+      {
+        "name": "blockRank_step",
+        "line": 137
+      },
+      {
+        "name": "rank_matching",
+        "line": 329
+      }
+    ],
+    "evidence": "SOURCE_INSPECTED_NOT_FRESHLY_KERNEL_REPLAYED"
+  },
+  {
+    "source": "F:\\proof\\leanlibs-20261009\\openai-math-fd4aeeb2\\src\\lean\\OAI\\LinearAlgebra\\MatrixMultiplication\\Tensor\\TerminalProducts.lean",
+    "sha256": "26dcc9d3c45e724dd21d72a6ba0deb7c9c78097e1319de43f1528369aef40533",
+    "declarations": [
+      {
+        "name": "restrict_familyProduct",
+        "line": 16
+      },
+      {
+        "name": "matrix_restriction_of_history_restrictions",
+        "line": 27
+      }
+    ],
+    "evidence": "SOURCE_INSPECTED_NOT_FRESHLY_KERNEL_REPLAYED"
+  }
+]
\ No newline at end of file
diff --git a/research/adaptive-kernel-demotion/notes/cells/PR-SYNOPSIS.md b/research/adaptive-kernel-demotion/notes/cells/PR-SYNOPSIS.md
new file mode 100644
index 0000000000..c9f345b959
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/cells/PR-SYNOPSIS.md
@@ -0,0 +1,43 @@
+# Public PR sweep, cells lane
+
+Frozen public snapshot: NEW-PRS-COMPLETE.json. Read full bodies PR1013 through PR1045. These are claims from public submissions, not fresh independent re-verifications.
+
+| PR | Mechanism and relevance |
+|---|---|
+|1013|Historical prime-subset ceiling provenance and harmonic checker; no new construction.|
+|1014|Parity-edge all-dimensional nesting obstructions and local repairs; no supplier.|
+|1015|Multi-write shear synthesis reduces ten R439 bit blocks; profile unchanged, no kappa.|
+|1016|PR952 frame-assignment scoped minimum; fixed gates/copies, no new result here.|
+|1017|R439 single-add fault atlas, including target-invisible helper faults.|
+|1018|Seven triangle-hybrid slots on K8 (five new beyond PR987); kappa .00167166528321877.|
+|1019|T37 finer rational grid; numerical refinement only.|
+|1020|First rank-six root-pair at 26 punctures; completed decoder costs69, no supplier gain.|
+|1021|Two-bank heterogeneous rank rigidity; excludes only stated partial-call interface.|
+|1022|T16 controller applied1018 plus owner repacking; kappa .001672081255752945.|
+|1023|Bit width8 hosting bound and hypothetical width7 gains; width7 construction missing.|
+|1024|R714 archive provenance and compensation check.|
+|1025|Averaged cyclotomic height lowers precision estimate to O(r^2 log^2 r); no full runtime supplier.|
+|1026|Core/Std Lean cyclic Schur elimination all lengths; execution/rounding/physical costs separate.|
+|1027|Historical bitR480 quad12 eleven-add circuit; full precision admission, unchanged profile.|
+|1028|T16 owner repacking only; .001672166670891177.|
+|1029|Sparse exact Clifford evaluator; identical phase recipes, no kappa.|
+|1030|Actual U8 helpers588/589 shrink to rank7 with changed B/cleanup frames; old baseline .00166202617947539. Distinct local lever potentially portable.|
+|1031|T16 packing refinement; .001672167430672016.|
+|1032|Persistent coefficient-work cache has orientation minima46/46/48/48; maximum48 unchanged.|
+|1033|Complex factory bounded local synthesis minima; five six-macro windows remain candidates, no kappa.|
+|1034|Mixed-provider shared-owner dual over frozen71-record catalogue; later favorable providers outside scope.|
+|1035|P112 free sink exclusions exact minors; no paid sink result.|
+|1036|Two-register coefficient synthesis and paid +/-2/3 substitutions; unchanged profile.|
+|1037|Turyn per-profile block rank9d; package context adaptation incomplete, no supplier.|
+|1038|Dirty quadratic-phase conjugation extends stride solver; all phases paid, no new bound.|
+|1039|Historical R715 cancellation and full frame itinerary replay; profile unchanged.|
+|1040|Retune target after helper mixing saves3 bit adds; unchanged profile.|
+|1041|Parallel exact phase generation byte-identical; timing tooling only.|
+|1042|T16 owner repacking; .001672188119205421.|
+|1043|Source-boundary persistence deletes one bit helperR439->438; bitendpoint rises, complex remains binding.|
+|1044|Exact reverse-DAG union propagation speeds historical audit, no kappa.|
+|1045|Four-helper semantic bit fusion below pair floor; unchanged paid profile, needs supplier adoption.|
+
+Direct local-cell lever for current frontier is low-end / entrance-frame geometry, not scalar ADD count alone. Every changed frame must retain actual global cone nesting, arbitrary-dirt restoration, adapter chart compatibility and complete invoice. The newest PR1117 combines rank7 ends with K8 slots and T16; old U8 rank7 savings must not be added again.
+
+Links: https://github.com/CrocSwap/integer-mult-bounds/pull/<number> for each row.
diff --git a/research/adaptive-kernel-demotion/notes/cells/RESULTS.md b/research/adaptive-kernel-demotion/notes/cells/RESULTS.md
new file mode 100644
index 0000000000..3e3f9cb321
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/cells/RESULTS.md
@@ -0,0 +1,33 @@
+# Cells lane final results
+
+Concrete combined local provider: PR1117's actual rank-seven ends574/575 plus PR1111's demotion of entrances635/637/638/639. The new semantic raw SHA256 is ca719f9b3b16a52dfd3774353bcb386d622a947a17023d7e9b261bb3132ab79a. It has480 helpers, local profile {1:2398,2:440,3:428,4:138,5:82,8:8}, rank mass5588, widths {4:52,5:36,7:32,8:120,9:240}. Helperindices411/413/414/415 increase4->5.
+
+Fresh checks passed:
+
+1. Reconstruct actual PR1117 source and both literal patch layers, matching each input field/content hash.
+2. All704 dirty input columns in both orientations, exact frame chains, entrance-zero response, wrapper exclusion and low-end inverse-row/dirt-column cones.
+3. Transport and emit24,767 forward and backward events. Full emitted semantic/frame/wrapper replay plus25 controls passes8.59 seconds.
+4. Compare actual old/new canonical geometries:1005 frames and2897 edges unchanged in count, one new frame,9 new edges and1 new residual-wrapper type. All changed lowerings and serialized monomial decodes agree including global phase;10 phase mutants reject in0.97 seconds.
+5. Standalone offline portable pipeline passes in13.81 seconds using Windows-native Python only. Source tree portable/ contains19 files/457484 bytes, no private absolute paths. Its root check_local.py reconstructs and freshly checks the changed local provider; global owner/pricing remain root/other workers' tasks.
+
+Two exact OpenAI proof mechanisms incorporated: vector-birth/rank-increment matching for complete frame invoices, and independent tensor-factor restriction composition for sufficient whole residual recovery. See OPENAI-MECHANISMS.md and OPENAI-SOURCE-LEDGER.json for exact statements, source paths, hashes and line numbers. Source inspection is not fresh Lean certification.
+
+Historical bounded fusion test:14 exact two-gate fusions legal on actual PR1005K8, all paid histograms unchanged. It does not bound arbitrary scalar circuits.
+
+New small future route: six natural rank-five kernel group demotions were screened in0.40 seconds. Groups headed603,611,619,627,635 all pass full monotone chain recount with the same delta -8H1+8H2+4H3-4H4; group651's chosen deleted direction fails nesting. Only635 has the fresh complete local/cone/phase proof this round. Applying other groups requires fresh cone and phase checks and owner gaps. Multiple groups potentially admit a new per-call portfolio; no gain is claimed until constructed and completely priced. This was saved for future work and is not a missing assumption in the shipped concrete provider.
+
+Read full public PR bodies1013..1045; synopsis is PR-SYNOPSIS.md. Frozen-source claims are distinguished from fresh local verification. Nothing published. No WSL, GPU, C++/binary searches, Claude-private processing or background jobs were launched. A partial8-second emitted-audit attempt was stopped at its cap and then completed under the root's20-second authorization; the complete check passed. All jobs now finished.
+
+## Completed joint-provider extension
+
+The complete literal rank-five entrance islands are headed635,603,611,619,627, in that order. The sixth tested natural deletion, headed651, is not used. Each used island has four distinct entering helpers and12 shared B records. The five entrance-key sets and five B-record-index sets are pairwise disjoint; their union is explicitly checked in multigroup/data/PATCHES.json. Each variant applies a concrete prefix of these sets to the same actual PR1117 word.
+
+Disjoint annotations imply only that the literal edits commute. They do not by themselves imply paid-profile additivity or geometric admission. We reconstructed and freshly checked all five whole variants: every704 dirty input column in both orientations, all frame chains and low-end cones, both actual emitted programs with25 corruption controls, and every changed phase and wrapper. These actual checks establish the same complete profile formula for each k:
+
+    (2406-8k) H1 +(432+8k) H2 +(424+4k) H3 +(142-4k) H4 +82 H5 +8 H8.
+
+The actual width inventory is (56-4k) helpers of width4, (32+4k) of width5,32 of width7,120 of width8 and240 of width9. Local rank mass is5584+4k. These formulas summarize independently checked concrete data; they are not assumed from isolated patch totals.
+
+The rank-birth mechanism applies to each reconstructed chain and charges every real jump. The tensor-factor composition mechanism applies to the actual distinct pending coordinate factors and the separately paid remainder under the explicit global owner map. Thus each of the five variants is a concrete sufficient local provider for a call whose checked coordinate chart reserves its actual widths. No unbuilt gadget, presumed savings or unknown oracle is introduced.
+
+Portable reproduction is in multigroup/portable/check_local.py --selector k --out fresh-path, with exact source/data pins and no external dependencies beyond standard-library Python. All selectors were checked through their actual stage chain; selector5 additionally passed the complete standalone portable wrapper in17.46 seconds. Nothing was published and no persistent computational process remains.
diff --git a/research/adaptive-kernel-demotion/notes/lead/OPENAI-MECHANISMS.md b/research/adaptive-kernel-demotion/notes/lead/OPENAI-MECHANISMS.md
new file mode 100644
index 0000000000..970ecf2407
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/lead/OPENAI-MECHANISMS.md
@@ -0,0 +1,9 @@
+# Two OpenAI-source mechanisms used in the final assembly
+
+These are source-informed mathematical adaptations. No new Lean kernel certification or priority claim is made.
+
+1. `OAI.LeanBlast.CourtadeKumar.JensenGaps_normalized_ratio_weights_data`, `lean/OAI/InformationTheory/SoftChannel/JensenGaps.lean`, lines 65-78. Its finite algebra normalizes nonnegative weights by their positive total mass and preserves the mean of ratios. For the actual complete histogram, take w_r=H_r, t_r=r, W=sum H_r*r and p_r=H_r*r/W. Thus sum p_r=1 and the full moment is M_b=(W/(m*N))*sum p_r*(m/r)^b. We verify every H_r>=0, W=1041408 and m*N-W=5120 before pricing. The signed edits are never themselves treated as probabilities. This prevents rank deficits or dropped children from being hidden in independent per-branch scores.
+
+2. `OAI.BackwardIntertwiners.DiscreteConvex.of_step` and `DiscreteConvex.secant_le`, `lean/OAI/Analysis/BackwardIntertwiners/ConvexEnvelope.lean`, lines 19-45. Discrete monotonicity of first differences supplies the finite convex calculus. For 0<b<1, G_b(n)=-n^(1-b), G_b(0)=0, is strictly discretely convex: its derivative on (0,infinity) is -(1-b)*n^(-b), strictly increasing. Summing five increasing differences proves G_b(11)-G_b(6)>G_b(6)-G_b(1), hence 11^(1-b)+1<2*6^(1-b). The legal three-owner cycle changes residuals (6,1,6) to (11,1,1), so this proves a strict complete moment improvement for every 0<b<1. All physical feasibility is independently checked; convexity alone does not authorize a cycle.
+
+Composition: first build the entire literal changed controller, including mixed native words, actual source windows, all coordinate charts and unused remainder transforms. Recount its one complete histogram and retained finite invoice. Both rational engines check the resulting moment, then the unchanged bit endpoint and all 47 strict outer inequalities select one exponent. No displayed PR gains or per-worker gains are added. The root contract is a constructive finite conditional improvement over pinned PR1117 at kappa 0.001672846995880185; it is not an unconditional all-size multiplication theorem.
diff --git a/research/adaptive-kernel-demotion/notes/lead/OPENAI-SOURCES.json b/research/adaptive-kernel-demotion/notes/lead/OPENAI-SOURCES.json
new file mode 100644
index 0000000000..b38b903bf9
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/lead/OPENAI-SOURCES.json
@@ -0,0 +1,12 @@
+[
+  {
+    "repository_path": "lean/OAI/InformationTheory/SoftChannel/JensenGaps.lean",
+    "sha256": "de6aead3ab4ffcd7e549248949a42498895064eab4c6d1e24b25ce902a2aa31b",
+    "evidence": "Registered source inspected; no fresh Lean replay"
+  },
+  {
+    "repository_path": "lean/OAI/Analysis/BackwardIntertwiners/ConvexEnvelope.lean",
+    "sha256": "deaaa06adfeff61a95702b23075758b6188acf02ddf5786d511c4cc1c213901f",
+    "evidence": "Registered source inspected; no fresh Lean replay"
+  }
+]
diff --git a/research/adaptive-kernel-demotion/notes/owners/MULTIGROUP-SUFFICIENT-PROOF.md b/research/adaptive-kernel-demotion/notes/owners/MULTIGROUP-SUFFICIENT-PROOF.md
new file mode 100644
index 0000000000..81a5c67496
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/owners/MULTIGROUP-SUFFICIENT-PROOF.md
@@ -0,0 +1,19 @@
+# Adaptive prefix demotion with exact donor ownership
+
+The concrete local providers are the ordered prefixes of groups 635,603,611,619,627, whose helper indices are respectively 411/413/414/415,379/381/382/383,387/389/390/391,395/397/398/399,403/405/406/407. Prefix k changes exactly 4k widths from 4 to 5. Each individual group has the previously checked local profile difference L=-8H1+8H2+4H3-4H4; the cells worker must verify each actual joint prefix, since disjoint annotations alone are not semantic evidence.
+
+The owner construction starts from the independently checked three-cycle map and increments one call's prefix at a time. It selects four distinct current width-four role occurrences with actual positive pending remainders. Selected helper occurrences eligible to donate to themselves are kept in place; the remaining selected occurrences are bijectively swapped with external donors in the same call. This is the concrete first-hit disjoint-partition mechanism documented in OPENAI-MECHANISMS.md. Only then do their widths become five. The construction decrements those four actual owner remainders and never reuses an exhausted gap. Subsequent calls see the updated global remainder dictionary, so overlapping pending windows are not treated independently.
+
+After every insertion, all unchanged roles remain, all changed roles are in the same call and retain a distinct physical family, each width increase fits one actual unused coordinate, and per-owner total load stays within capacity. Final offsets are rebuilt from actual chronological call/helper order. The sufficient dirty-restoration induction and complete paid-profile reconstruction are the same as in the one-group theorem; each local provider occurrence is now labelled by its actual prefix k.
+
+For each inserted group, the four pending remainders have pattern [1,1,1,r], r=1,2 or 3. SUFFICIENT-DEMOTION-THEOREMS.md proves its complete profile difference strictly lowers the moment for every 0 < b < 1. Therefore any finite sequence of these literal legal insertions also strictly lowers the moment; no numerical gains from different PRs are added. The complete final table and actual variant dispatch determine the profile.
+
+## Frozen finite witness
+
+359 group insertions across 103 of 144 calls:356 four-unit patterns,one [1,1,1,2],two [1,1,1,3]. Providers0..5 occur 41,24,8,15,6,50 times respectively. The full profile is
+
+{1:344363,2:65097,3:62855,4:19012,5:11808,7:8,8:1152,11:2,48:4873}.
+
+Rank mass 1041408 and deficit 5120 are unchanged. 4594 complete literal rows differ from the frozen PR1117 table. The prefix dispatcher and every source/destination family are explicit in multigroup/DISPATCH.json and multigroup/EDITS-FROM-PR1117.json. Construction took 3.66 seconds of single-process native Windows Python; no background process was left running.
+
+Actual joint local replay, mixed owner/chart checks, finite invoice and exact final kappa pricing are separate mandatory checks before a deliverable claim. The inherited all-size/compiler, precision/recovery and analytic assumptions are retained. This is not a Lean theorem, a global optimum, a human-review claim or an unconditional multiplication result.
diff --git a/research/adaptive-kernel-demotion/notes/owners/OPENAI-MECHANISMS.md b/research/adaptive-kernel-demotion/notes/owners/OPENAI-MECHANISMS.md
new file mode 100644
index 0000000000..843cea9f4c
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/owners/OPENAI-MECHANISMS.md
@@ -0,0 +1,31 @@
+# Two sourced OpenAI mechanisms for owner-cycle replacement
+
+## 1. Alternating overlays and reversible switches
+
+Source: `D:/proof/external/openai-math/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/build/main.tex`, lines 366-370 and 488-525 (Four-hole inequality, label `lem:four-holes`). The source overlays two matchings, retains parallel common edges, and switches an alternating path; the switch has an exact inverse and preserves the product weight. We use only that elementary combinatorial mechanism, not its FPRAS or counting conclusion.
+
+Adaptation: overlay the old and proposed role-to-owner maps. Their symmetric difference decomposes into alternating directed cycles whenever each affected owner loses and gains one role. Cycle switching preserves the exact role count and every local helper occurrence. Unlike a two-owner swap or a three-role cycle with an equal-width neutral third role, three arbitrary widths can change three residuals simultaneously and bypass a busy owner family at an intermediate call.
+
+Sufficient cycle replacement theorem: Let i_0,...,i_{k-1} be distinct literal roles with widths w_j and original distinct physical owner families A_j. Transfer i_j to A_{j+1}, indices modulo k. It is sufficient that (a) A_{j+1}'s inactivity window contains i_j's call time, (b) its family is unused in that call after all selected roles are removed, and (c) its new load u'_{j+1}=u_{j+1}-w_{j+1}+w_j is at most its rank capacity. Retain all other role assignments and order each owner's assigned axes chronologically, recomputing compact offsets. Then every role still occurs once, every per-call family remains unique, and each owner's coordinate blocks are disjoint. The old dirty/restoring local contract composes on the new disjoint axes. The exact remainder is r'_{j+1}=r_{j+1}+w_{j+1}-w_j, so the complete paid-profile difference is sum_j(H_{r'_j}-H_{r_j}), omitting H_0. Sum_j r'_j=sum_j r_j; local word, rank mass and deficit are unchanged. If sum_j (r'_j)^(1-b)<sum_j r_j^(1-b), this supplies a strictly lower recursive moment at that same admitted exponent. Independent chart and invoice checks remain mandatory.
+
+Proof: removal followed by insertion is a finite bijective relabelling. Conditions (a)-(c) are exactly window, occupancy and coordinate-capacity checks. Compact chronological blocks have cumulative length u'_j, so are pairwise disjoint and fit. Apply the inherited arbitrary-dirty-input restoration contract at each chronological call; the pending child's saved state is recovered. The new unclaimed axes form its one paid remainder. Telescoping the width differences proves mass preservation. Multiplication by positive 73^b transfers the last inequality to the actual moment.
+
+## Historical alternate source (not counted for this worker's two final mechanisms): species allocation
+
+Source: `D:/proof/external/openai-math/lean/OAI/Computability/BinPacking/Inventory/SpeciesAllocation.lean`, lines13-29; theorem `OAI.BinPackingGap.SpeciesAllocation.exists_allocation` and `allocation_species`. For finite Slot and request:Slot->Species, exact stock counts yield a bijection e:Slot ~= Sigma_s Fin(stock s), with `(e b).1=request b` for every slot.
+
+Adaptation: give every local helper role the species `(provider, orientation, helper index, width)`. Enumerate its exact call-labelled instances by the theorem's fibre bijection. Candidate owner changes operate only on these fixed literal instances; they never identify two equal-width helper occurrences or create a fake fractional helper. Cycles therefore keep the supplier inventory exactly, even when different calls host equal-width helpers. Within an eligibility class, a canonical representative can nominate a move; lifting still requires explicit family/window/capacity checks for every literal destination. The theorem licenses inventory correspondence, NOT arbitrary physical exchange. A width-only histogram is insufficient.
+
+The checker should independently recompute each instance's local width, call order and family identity, rather than trusting a requested species tag. This second mechanism supplies exact reconstruction and lossless accounting; it is not counted as an independent numerical gain or claimed as a new OpenAI theorem. No Lean compilation, import, new axiom or kernel-certification claim is made in this round.
+
+## Search and scope
+
+`cycle3.py` implements one bounded native-Windows Python nomination, at most eight seconds, with arbitrary three widths. Floating objective values nominate only. The independent owner/chart checker and root's exact moment engines determine whether any gain is admitted. No C++, GPU, WSL, background job, private Claude corpus or publication is used.
+
+## 2. Disjoint first-hit projector partition (final second mechanism)
+
+Exact source: `D:/proof/external/openai-math/preprints/Random-coordinate-frames-and-partial-permutation-laws-September-26-2026/build/sections/07a-disjoint-transfer-proof.tex`, paragraph “The common small-type cover,” equation `shear:eq:disjoint-projector-cover`. The source forms commuting orthogonal projections P_i and Q_i=P_i product_{j<i}(I-P_j), obtaining sum_i Q_i=I and Q_i Q_j=0. Its representation-theoretic conclusions are not imported here; the finite coordinate-indicator special case is the mechanism used.
+
+For each exact live donor candidate, let P1 indicate “already one of the four selected helper roles and its pending remainder is one”; let P2 indicate “pending remainder is one”; and let P3 indicate “remainder is two or three.” On the vector space with literal donor occurrences as basis, these are diagonal orthogonal projectors and commute. Restrict to their covered eligible set. Q1=P1, Q2=P2(I-P1), Q3=P3(I-P1)(I-P2) partition each eligible occurrence once. The construction takes selected self-donors first, then external unit-gap donors, then at most one rank-two/rank-three donor. Self-donors remain in place; the remaining selected roles are bijectively swapped with the remaining external donor roles. Consequently no donor occurrence or physical family is charged twice, and already legal selected slack is not accidentally excluded.
+
+Concrete effect: the first external-only construction realized 98 calls. The disjoint self/external partition construction plus the proved three-unit extension realizes 103 calls: 100 four-unit patterns, one [1,1,1,2] pattern and two [1,1,1,3] patterns. We do not attribute all five extra calls solely to the projector idea, because both changes were applied together. Its exact occurrence partition and reconstruction are present in `demote_gaps2.py`. Four different greedy orderings reproduce the same final paid profile. This is a sourced adaptation, not a new OpenAI proof or Lean import.
diff --git a/research/adaptive-kernel-demotion/notes/owners/PR1046-1080-SYNOPSIS.md b/research/adaptive-kernel-demotion/notes/owners/PR1046-1080-SYNOPSIS.md
new file mode 100644
index 0000000000..1c29f2391b
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/owners/PR1046-1080-SYNOPSIS.md
@@ -0,0 +1,284 @@
+# Frozen PR1046-1080 reading synopsis
+
+All 35 full bodies read from the frozen metadata. Published-source claims are not independently rerun here. No Claude-private working material is consumed.
+
+## PR1046 - Research: exact affine five-cube copy floor and four rank-eight totals (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1046
+
+Head: `7cadcb0a2fc71fdedc0066704dec3fec58c2ca2c`; full-body SHA256: `5f9c86ad16398b028661eed4e176b54f88ce0dfb574ebc0bf5ae62ebf92d4495`.
+
+Scoped structural theorem or obstruction, not a sufficient improved supplier. Retain distinctions of fields, affine masks and exact realization classes; do not package necessary conditions as the research result.
+
+## PR1047 - Local bit construction: save 14 ADDs with one restored post-PR967 helper shear
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1047
+
+Head: `a01bd602969e4086e55f0d1f392855b91cfe0507`; full-body SHA256: `ebb6933978e871c4f93275bc77c38ac1ca0b7a64832815582a31e1164f92a7f7`.
+
+Finite instruction/precision improvement on pinned older circuit. Homogeneous profile is unchanged or new hosting not supplied; no direct kappa claim. Important execution-cost support but not added as exponent savings.
+
+## PR1048 - Research: the bit paid profile is the whole bit supplier — exact pricer, and the reframing class is exhausted at #589 (no κ claim)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1048
+
+Head: `07730cd8302c378607259a9ad0efb73e0b57a2f2`; full-body SHA256: `86be75edd73b591edf11ad945138c404560d861a745efd7e0f69dedde0a1a52c`.
+
+Independent replay, arithmetic/source audit or scoped census. Read its mathematical findings without rerunning others' verification. No new kappa in its declared scope.
+
+## PR1049 - Research audit: independent check of PR1005/1018 mutable-leaver cells (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1049
+
+Head: `6d0a145e8b4774b1b0d4e3da56890af5adc9b04f`; full-body SHA256: `a8d15ae5d28b50a4496a4f2d3f0a0d0776aa1763f100886427b3ab1848051191`.
+
+Independent replay, arithmetic/source audit or scoped census. Read its mathematical findings without rerunning others' verification. No new kappa in its declared scope.
+
+## PR1050 - Conditional κ = 0.001672241870811633: improved T16 owner packing on the seven-slot k8 word
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1050
+
+Head: `c87242f846cfab8c0b97fd889b5fecb0eacef939`; full-body SHA256: `0867d5c643cb7440374c27cb945e9b483054a649fa1ef569382d2353a32a7841`.
+
+Successive exact T16 large-neighborhood owner repacks on the seven-slot K8 word. Same code and local word; only owner map, plan and measured pins change. These are superseded by the latest PR1117 root snapshot. Never add their incremental numerical gains.
+
+## PR1051 - Independent verification: code-disjoint T37 moment endpoints and kappa reduction (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1051
+
+Head: `3b8fab9b48d54160d0765c316eed45078f32aa5e`; full-body SHA256: `2f0df36ca293a3338ab0f14a61b041895227eb63c27ee1c1f14cf05d21c386f0`.
+
+Independent replay, arithmetic/source audit or scoped census. Read its mathematical findings without rerunning others' verification. No new kappa in its declared scope.
+
+## PR1052 - Independent verification: T37 positive-binomial moments, all-T lemma, and 1024-bit reduction (seed 78, no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1052
+
+Head: `e7f0319b7a7b4e8e1958ae523affdc123e3ea597`; full-body SHA256: `78df0a56238e0b2777c0058401bf191b44e4d1cc98e498ed78d475189bf1ce8b`.
+
+Independent replay, arithmetic/source audit or scoped census. Read its mathematical findings without rerunning others' verification. No new kappa in its declared scope.
+
+## PR1053 - Conditional κ = 0.001672245809535804: improved T16 owner packing on the seven-slot k8 word
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1053
+
+Head: `6f92ce8884929c9fd4730c86a28e2e3735de02af`; full-body SHA256: `54232708cba987c9abce84acecb382f5d4188e3a64898fb7bd830be3004be7d7`.
+
+Successive exact T16 large-neighborhood owner repacks on the seven-slot K8 word. Same code and local word; only owner map, plan and measured pins change. These are superseded by the latest PR1117 root snapshot. Never add their incremental numerical gains.
+
+## PR1054 - Conditional accuracy: all-length cubic precision for the dirty stride inverse
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1054
+
+Head: `6bc675be1554b3a3be771147f21f9dc2c6dae50a`; full-body SHA256: `975f2b57343d9fdd2dba55d03faa457784dfe3706484d884fd19f0ebb7e9933c`.
+
+Exact recursive/precision interface theorem. PR1054 improves dirty-word precision under retained analytic/scalar assumptions; PR1057 borrows exact-additive ports with three dirty arrays. Their execution hypotheses are not established for current supplier, so no direct exponent gain.
+
+## PR1055 - Conditional κ = 0.001672251604432734: improved T16 owner packing on the seven-slot k8 word
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1055
+
+Head: `a8ea308976f1709eef0a328463f010cf51469277`; full-body SHA256: `df3375fd3dad20e84aa4283c664a45c1ab16756cd02fb63fc18848e323f48bf5`.
+
+Successive exact T16 large-neighborhood owner repacks on the seven-slot K8 word. Same code and local word; only owner map, plan and measured pins change. These are superseded by the latest PR1117 root snapshot. Never add their incremental numerical gains.
+
+## PR1056 - Conditional kappa 0.001672267698427438: whole-helper exchanges on the T16 owner map
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1056
+
+Head: `d0201efbd68c4acc9832b84bcc986c8781b83c4f`; full-body SHA256: `8edad35312946915d0809b6e1b85085f6573fb720a231c95d90b1f17678c5f5c`.
+
+Whole-helper cross-call exchanges; PR1063 first applies equal-width neutral recolourings to escape pair-exchange plateaus. Directly relevant to owner lane, with actual time windows, family uniqueness and whole widths retained. New generalized cycle search must credit these rather than claim cycle technique novelty.
+
+## PR1057 - Research: exact additive echoes with three dirty arrays at any depth (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1057
+
+Head: `78a062df1dcab2bffea5ff4d8243f3da6e465414`; full-body SHA256: `1073c271a64e030d33361531422f698acdb5d53e4854fd6245c5e458415886aa`.
+
+Exact recursive/precision interface theorem. PR1054 improves dirty-word precision under retained analytic/scalar assumptions; PR1057 borrows exact-additive ports with three dirty arrays. Their execution hypotheses are not established for current supplier, so no direct exponent gain.
+
+## PR1058 - Research: R420 quad 4 reaches an 11-ADD positive-transfer minimum (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1058
+
+Head: `d148d200f2d64c90504fa3a9608e455aaa4c0c21`; full-body SHA256: `d8fccbeff43ac69796cecd6e42cac20a9b2dfca4a106cc104661406421c32469`.
+
+Finite instruction/precision improvement on pinned older circuit. Homogeneous profile is unchanged or new hosting not supplied; no direct kappa claim. Important execution-cost support but not added as exponent savings.
+
+## PR1059 - Tooling: opt-in parallel U8 layer-end controls, byte-identical receipt, 3.0x on 10 cores (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1059
+
+Head: `0e301503b29d802327238c32f5ae3377797a564c`; full-body SHA256: `19534ff8a88b4ff800fa2bd5994bc3fe7e309dd64396e9c9a4e5f697c38066cc`.
+
+Verification engineering only, opt-in acceleration preserving exact outputs; no homogeneous-profile or kappa improvement.
+
+## PR1060 - Construction: exact complex P111 COPY word with a smaller paid recursive moment
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1060
+
+Head: `d27499553138bde007f5b1163e65e71da1b18899`; full-body SHA256: `df33d7d02500863b0db9382b47fab8c8d96eb1a57589ad423cb93ed2ce4d6cb3`.
+
+Concrete P111 shared-carrier decoder changes paid profile and proves a uniform recursive moment improvement. Extra AXPY/adapters and hosting/all-size remain unresolved, so not a new kappa supplier.
+
+## PR1061 - Conditional κ = 0.00167259071506618: improved T16 owner packing on the seven-slot k8 word
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1061
+
+Head: `223f581afb1d63d5f8476a69040617e11bcd50e4`; full-body SHA256: `60406d811b3f2b167042c54874b3d3e12cd033b49132df65c84f133b10eb23c5`.
+
+Successive exact T16 large-neighborhood owner repacks on the seven-slot K8 word. Same code and local word; only owner map, plan and measured pins change. These are superseded by the latest PR1117 root snapshot. Never add their incremental numerical gains.
+
+## PR1062 - Finite bit construction: phase-B block programs on the R439 helper-star D, 11,783 -> 11,500 ADDs (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1062
+
+Head: `cd016e5dcd5ba28dafa3f3b4eeef003a38e6a11b`; full-body SHA256: `a8a1631203449c324129d07bc62f30148e00c5e3b4755b60230c900ef9c7348f`.
+
+Finite instruction/precision improvement on pinned older circuit. Homogeneous profile is unchanged or new hosting not supplied; no direct kappa claim. Important execution-cost support but not added as exponent savings.
+
+## PR1063 - Conditional kappa 0.001672285678298543: neutral T16 reshuffles and whole-helper exchanges
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1063
+
+Head: `d9377d32e0c97e41338e704c3960fd6f2fa73806`; full-body SHA256: `a5bfd2c2ff723c7159fa3bfddb9fbb20598ef742ab038ce8a3d606af44128aa9`.
+
+Whole-helper cross-call exchanges; PR1063 first applies equal-width neutral recolourings to escape pair-exchange plateaus. Directly relevant to owner lane, with actual time windows, family uniqueness and whole widths retained. New generalized cycle search must credit these rather than claim cycle technique novelty.
+
+## PR1064 - Construction: complete complex factory lowering from 44 to 38 paid primitives
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1064
+
+Head: `b0181971c2364744d1dd9b0c2d4ee1ea532b8bb6`; full-body SHA256: `7d1779451084d245de544b3b49e49cc6639409eb0b44952878cd63e2be90ff9f`.
+
+Finite instruction/precision improvement on pinned older circuit. Homogeneous profile is unchanged or new hosting not supplied; no direct kappa claim. Important execution-cost support but not added as exponent savings.
+
+## PR1065 - Conditional κ = 0.001672644568760139: improved T16 owner packing on the seven-slot k8 word
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1065
+
+Head: `387d935e354a931d636e2c5e6ee63a6910f78a1b`; full-body SHA256: `f35c0679b44924ed31932464643be3684bf70253205454cc7d95f80a1c5dd70e`.
+
+Successive exact T16 large-neighborhood owner repacks on the seven-slot K8 word. Same code and local word; only owner map, plan and measured pins change. These are superseded by the latest PR1117 root snapshot. Never add their incremental numerical gains.
+
+## PR1066 - Independent verification of the source complementary-block nullity obligation
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1066
+
+Head: `2e72784a7908d45511e953c182d42cdcb911e6cb`; full-body SHA256: `14183da95dfea87d3964f45b2e606a144c6cee45677aa673d576aa8618d175b8`.
+
+Independent replay, arithmetic/source audit or scoped census. Read its mathematical findings without rerunning others' verification. No new kappa in its declared scope.
+
+## PR1067 - Research audit: tighter signed inverse-D envelope for PR967
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1067
+
+Head: `d9c97f19c25a9e75bd9ac43004a97775f061e999`; full-body SHA256: `0560ee49bdaf68d8f9c3c5d6905011555019850f4bc468f48cc6e5c53a6802a7`.
+
+Finite instruction/precision improvement on pinned older circuit. Homogeneous profile is unchanged or new hosting not supplied; no direct kappa claim. Important execution-cost support but not added as exponent savings.
+
+## PR1068 - Conditional κ = 0.001672650458698046: improved T16 owner packing on the seven-slot k8 word
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1068
+
+Head: `cc71375eae4e8754da0f5d940cb519d66625fb2e`; full-body SHA256: `3dde2b3acf8c45bfb4bad8d6da3cab9a0ba6b2e4b01f105f6826369a5b715375`.
+
+Successive exact T16 large-neighborhood owner repacks on the seven-slot K8 word. Same code and local word; only owner map, plan and measured pins change. These are superseded by the latest PR1117 root snapshot. Never add their incremental numerical gains.
+
+## PR1069 - Independent verification: code-disjoint pricing of all 16 pending kappa claims; every one has deficit W - 64N (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1069
+
+Head: `a3db661d0cc630820bc5d4af667bbd166bde154b`; full-body SHA256: `b15969ae28aa17dd0493e8d7b67f67279bcf78eb21f2d25641f031e5b721aaa9`.
+
+Independent replay, arithmetic/source audit or scoped census. Read its mathematical findings without rerunning others' verification. No new kappa in its declared scope.
+
+## PR1070 - Research audit: sharp arbitrary-mask affine agreement (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1070
+
+Head: `8a4291875449f3e46f952465e200e7fe2c620958`; full-body SHA256: `9ff0645f056c8a5ad189b6413d6fdf410d6e4e0117be542cf0287d569639be91`.
+
+Scoped structural theorem or obstruction, not a sufficient improved supplier. Retain distinctions of fields, affine masks and exact realization classes; do not package necessary conditions as the research result.
+
+## PR1071 - Research: delivery lower bounds for #968's frame-pair centers (no new κ)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1071
+
+Head: `ce9531beba1ce115fdcdc44925ded995a29b8bac`; full-body SHA256: `6b8f3b3b58c72e1d7766797aa56ea3c3b5d3a11fc5d5674b6a7d67ceb77d8c30`.
+
+Scoped structural theorem or obstruction, not a sufficient improved supplier. Retain distinctions of fields, affine masks and exact realization classes; do not package necessary conditions as the research result.
+
+## PR1072 - Conditional κ = 0.001661961039655941: one E4 call fills four T37 gaps
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1072
+
+Head: `6c1504cd75aae9b255ba16bf8e28d3f38af34c14`; full-body SHA256: `237858bad6c457383303d07a4ac0d855bc5bc2911207d24ecf2fbfb8a435b6ec`.
+
+Concrete promotion-to-gap coupling: four widths 4->5 consume four idle rank-one gaps on T37; complete local+owner realization supplied. Different local inventory is crucial; cannot apply the numerical delta to T16 blindly.
+
+## PR1073 - Tooling: verify T37 stage-log coverage with omission controls
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1073
+
+Head: `89ddfca5207452ce26939d968f512f22c9ef1a12`; full-body SHA256: `f40f867e3a612cb695354b43c52a95ab5096b758214f115d0e66f015186c0f3d`.
+
+Independent replay, arithmetic/source audit or scoped census. Read its mathematical findings without rerunning others' verification. No new kappa in its declared scope.
+
+## PR1074 - Conditional κ = 0.001672651218919025: improved T16 owner packing on the seven-slot k8 word
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1074
+
+Head: `052afc128954f7b6a2b3c409eb4d72248e4020f2`; full-body SHA256: `b7c6295f77c2d5cdc01b81ed0c708f456151579726e3b4acbcbe444968e6517e`.
+
+Successive exact T16 large-neighborhood owner repacks on the seven-slot K8 word. Same code and local word; only owner map, plan and measured pins change. These are superseded by the latest PR1117 root snapshot. Never add their incremental numerical gains.
+
+## PR1075 - Tooling: 4.78x faster exact bounded quadratic-code replay
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1075
+
+Head: `d84d3b950127ff9252e5c059a629bb654500192a`; full-body SHA256: `9b0d23f2dbf8166353532613079dcb8b28bad37cda41aeff88d5ff46f56a25d8`.
+
+Verification engineering only, opt-in acceleration preserving exact outputs; no homogeneous-profile or kappa improvement.
+
+## PR1076 - Tooling: batch exact rows for the quadratic-affine rank witness (8.4x faster check, no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1076
+
+Head: `cced22b95fb5b485da05b8187c8a9754b6a8c85a`; full-body SHA256: `f4f028ccf52f5f9a2ae88d54be5b855faadfa316cdb90e9f1aec889a22b1c770`.
+
+Verification engineering only, opt-in acceleration preserving exact outputs; no homogeneous-profile or kappa improvement.
+
+## PR1077 - Scoped structural result: arbitrary complex coefficients retain the exact eight-term E8 decoder floor
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1077
+
+Head: `1459f58a829e616ddf32a3da2782e166700e3218`; full-body SHA256: `23b671322de8aa505d6581585b044a0baf5cf791b3418dc2eaaf101861115551`.
+
+Scoped structural theorem or obstruction, not a sufficient improved supplier. Retain distinctions of fields, affine masks and exact realization classes; do not package necessary conditions as the research result.
+
+## PR1078 - Research consolidation: replay archived PR485 aggregate prices offline (no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1078
+
+Head: `37a9f15600ad7f924a57a2e027f28528bf6ea02e`; full-body SHA256: `8e934f578a9196a8500a9ccd5c238188deb20b3f8571ece1e873fca1442cb52f`.
+
+Independent replay, arithmetic/source audit or scoped census. Read its mathematical findings without rerunning others' verification. No new kappa in its declared scope.
+
+## PR1079 - Scoped negative result: R439 source-substitution census has one known survivor
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1079
+
+Head: `bb20dab261884412f2d2a7955cdb2fd8e2e64a16`; full-body SHA256: `3474872df2032b770739d8da4334eab75832118d0d595f779dd7e137c9802818`.
+
+Independent replay, arithmetic/source audit or scoped census. Read its mathematical findings without rerunning others' verification. No new kappa in its declared scope.
+
+## PR1080 - Construction: two-sided signed bi-forest U8 compensation saving 53,596 real primitives (seed 35, no new kappa)
+
+https://github.com/CrocSwap/integer-mult-bounds/pull/1080
+
+Head: `803e080e181229a3af2196b7a13615c9d81ae10d`; full-body SHA256: `ca8acd2830a71f969eaf3d19745371628a6b26592fbd274787bc317ed9797f61`.
+
+Leaf-before-parent signed helper forest suppresses ancestor cross terms; alternating two-sided MST passes reduce compensation primitives. Paid homogeneous profile unchanged, hence no direct kappa gain.
+
diff --git a/research/adaptive-kernel-demotion/notes/owners/SUFFICIENT-DEMOTION-THEOREMS.md b/research/adaptive-kernel-demotion/notes/owners/SUFFICIENT-DEMOTION-THEOREMS.md
new file mode 100644
index 0000000000..2fa9b7b635
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/owners/SUFFICIENT-DEMOTION-THEOREMS.md
@@ -0,0 +1,31 @@
+# Sufficient coupled demotion and gap-consumption theorem
+
+Assume the concrete checked alternate provider changes helpers 411/413/414/415 from width 4 to width 5, with exact local paid difference -8H1+8H2+4H3-4H4 and the same complete dirty-input maps. In a call choose four distinct existing width 4 role owners with pending remainders [1,1,1,r], r in {1,2,3}. The selected provider roles and those donor role occurrences partition into common/self occurrences and external occurrences. Fix common occurrences and bijectively exchange external ones within that call; this preserves one occurrence of every role and per-call family uniqueness. Increasing the selected widths consumes one axis in each donor owner. Fit follows from the specified positive remainders. Compact chronological offsets then establish disjoint axes for every actual pending owner.
+
+The complete paid changes, including the remainder bill, are:
+
+- r=1: -12H1+8H2+4H3-4H4;
+- r=2: -10H1+7H2+4H3-4H4;
+- r=3: -11H1+9H2+3H3-4H4.
+
+These three changes strictly reduce the recursive moment for every 0 < b < 1. This is a sufficient improvement theorem, not only a necessary packing condition.
+
+Proof of strict inequality: Set alpha=1-b, u=2^alpha in(1,2), p=ln(3)/ln(2). We have 14/9 < p < 2 because 3^9 = 19683 > 16384 = 2^14 and3 < 4. Removing the common positive factor73^b, the three moment changes are
+
+h1(u)=-12+8u+4u^p-4u^2,
+h2(u)=-10+7u+4u^p-4u^2,
+h3(u)=-11+9u+3u^p-4u^2.
+
+For u >= 1, p(p-1)u^(p-2) < 2. Thus h1''=h2''<0 and h3''<0. At u=2 their slopes are 6p - 8,6p - 9,9p/2 - 7, all strictly positive. Their derivatives on [1,2] are therefore positive, while h1(2)=h2(2)=h3(2)=0. Each h_j(u)<0 for u<2. Multiplying by73^b proves the universal strict moment saving. Every profile difference has zero rank mass; the local four-axis mass increase is exactly consumed by four fewer unclaimed axes.
+
+## Actual construction, frozen PR1117
+
+Before this coupling, an independently checked three-cycle concentrates two rank 6 pending remainders into rank 1 and rank 11, delta +H1-2H6+H11. New owner hash a6c2885268cfc5d7591d77494c099c7225904f88f0b97a24567e0e51c9d3c6fc. This concavity improvement holds for every 0 < b < 1.
+
+Starting that map, the coupled construction changes 103 of 144 calls:100 four-unit patterns, one rank 2 and two rank 3. Final whole paid profile:
+
+{1:347435,2:63049,3:61831,4:20036,5:11808,7:8,8:1152,11:2,48:4873}.
+
+Rank mass 1041408 and deficit 5120 are unchanged. 1500 literal rows change relative to the checked three-cycle map; final root must independently audit mixed widths, actual orthogonal charts, phase validity and finite invoices before assigning an admitted kappa. The literal map, exact dispatch and complete before/after row edits are in `demote-many2-1117/`. No gains from different PRs are added numerically; the profile is recounted from the actual combined assignment.
+
+The finite provider correctness belongs to the cells worker's exact 704-column forward/dual/low-end-cone replay. The owner lane checks replacement geometry; the recurrence lane independently checks all mixed 69,120 roles. Root prices and packages the combined result. Full inherited all-size, compiler, precision/recovery and analytic conditions remain explicit.
diff --git a/research/adaptive-kernel-demotion/notes/recurrence/FRESH-INVOICE-PROOF.md b/research/adaptive-kernel-demotion/notes/recurrence/FRESH-INVOICE-PROOF.md
new file mode 100644
index 0000000000..ec42cd1a8c
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/recurrence/FRESH-INVOICE-PROOF.md
@@ -0,0 +1,28 @@
+# Fresh mixed controller invoice and exact boundary invariant
+
+This round retains the upstream routing/compiler and analytic interfaces explicitly. The following establishes a sufficient finite controller and recounts its changed material; no old receipt is relabeled as admission of the new table.
+
+The independent source-event reconstruction reads the current pinned ROUND20 parent template and actual pending-axis phase recipes. Its 480 replica-local events recover all 288 actual positive-rank child windows, exactly equal to the frozen PLAN. Every one of the 144 invocations retains its position; every replica projects to the original 30-event order. The three-role cycle and all wider-helper placements preserve those windows. The independently checked 69,120 roles occupy distinct inactive physical families per call, with a chronological nonoverlapping axis prefix in every child. All 73-column charts are derived from the actual physical port basis and pending axes; spectator axes complete each normalized local embedding. The remaining 6,034 full remainder transforms are retained explicitly.
+
+For a pending child C, maintain the invariant that the executed complete local calls have advanced the factors reserved to them, every other coordinate factor remains a spectator, and the remaining paid transform is precisely C's complement. No data operation touches the physical family inside its last-touch-to-idle window. Actual source events supply the interval endpoints. Within a complete admitted invocation, arbitrary helper dirt is restored modulo the declared residual transform, so the data result does not depend on the borrowed stream. The factors for different reserved coordinate blocks commute; their product and the explicit remainder is exactly C. Induction on the literal source-event timeline establishes the full endpoint and dirty restoration. Variant choice is a finite literal dispatch between six concrete admitted local contracts. No unknown allocation gadget, value oracle or free scratch is used.
+
+The five jointly admitted demotion variants keep 480 helpers, eight private centres, two coefficient-work streams, and 704 local scalar columns. Recounting the actual canonical frames gives 3,494 paid local children in every variant. Their literal native streams each contain 24,767 events and 19,693 scalar macros per orientation. The fresh forward/backward primitive bounds are 198,766/198,814, and fresh prefix coefficient bounds require 52/68 bits. The actual canonical frames select 192 entering helpers and 48 cold proper-ended helpers for the paid pre/post wrappers. The independent native receipt checks those ordered wrappers and all arbitrary-input columns.
+
+At 80 forward and 64 backward invocations, the complete new invoice charges:
+
+- real component primitives: 28,625,376;
+- scalar macros: 2,835,792;
+- wrapper factors: 144 calls * 2 * 240 wrappers * 144 factors = 9,953,280;
+- local routing adapters: 16*(19693+3494+224+480+8)+64*73 = 387,056;
+- universal per-adapter compiler bound: 64*74^3 = 25,934,336;
+- local primitive bound: 198814+387056*25934336 = 10,038,040,553,630.
+
+The new table has 9,898 distinct charts, versus 10,057 on its frozen public baseline. The bill charges the universal bounded chart decomposition at every actual routed occurrence; it never infers routing cost solely from the number of distinct chart values. Every changed chart and every spectator is in the fresh reconstruction. No extra value-bearing physical stream is introduced.
+
+The old dedicated-bank stock is retained purely as an overcharge envelope: 23,408 live families, 23,922 physical families and 32,256 idle-child slots. It charges all 6,034 actual remainders. Independently applying the retained full formula to the new actual provider counts gives per-vertex 3,588,959,010,714,576 and the hosted rebasing 3,588,959,010,114,264. The one historical retained file is used only for its previous charged allowance 2,877,946,989,724,568 (SHA-256 ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478). Adding the ENTIRE fresh invoice preserves the source's deliberately conservative policy and gives used allowance 6,466,906,000,439,144.
+
+The physical stock identity is 14,336 live + 480 helpers + 8 centres + 2 coefficient-work streams = 14,826. The charged group is 2^(36^2) * product_(j=1..36)(2^(2j)-1). Fresh arithmetic gives physical stock 2,642 bits, logical allowance 2,680 bits, router 7,988 bits, literal 35,284 bits, precision 200,012 bits and tape 100,002 bits. All nine source inequalities are strictly satisfied, including local bound <2^48, logical <2^6050, router <2^30000, literal <2^100000, total mass <2^100001, precision/tape <2^210000, row 16,469 <20,161 and 73^2 >2*48^2.
+
+The whole-controller prefix reserve is freshly computed as 68+37+144+144+4=397 <512. The row-prefix term remains 2*512. The complete paid mass is 1,041,408 and the deficit is 73*14,336 -1,041,408=5,120. These are recomputed from the actual mixed profiles and actual remainder table, rather than inherited from the baseline invoice.
+
+Eleven owner/geometry controls reject duplicated roles, changed widths/times, negative offsets, family aliasing, out-of-window moves, wrong 73-column charts, corrupt source windows, wrong physical identities, omitted widened dispatch and inconsistent phase-axis rank. Four invoice controls reject cap equality, oversized logical allowance, oversized row geometry and a rank-52 halving violation. Exact two-engine moment pricing and strict outer assembly are separate root checks of the complete resulting profile. None of these finite checks is a Lean certification or an unconditional proof of integer multiplication.
diff --git a/research/adaptive-kernel-demotion/notes/recurrence/GAP-AWARE-DEMOTION.md b/research/adaptive-kernel-demotion/notes/recurrence/GAP-AWARE-DEMOTION.md
new file mode 100644
index 0000000000..e3a22b83f9
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/recurrence/GAP-AWARE-DEMOTION.md
@@ -0,0 +1,115 @@
+# Rank-gap-aware demotion and finite physical allocation
+
+Frozen round: public PRs through #1120, with #1117 the largest reported conditional value in that snapshot. This file proves sufficient transformations and exact pricing rules; it does not claim an implemented new kappa before the complete changed word, table, charts and invoice are checked.
+
+## 1. A strict extension of PR1111's construction
+
+PR1111 reverses the entrance promotion on helpers 635,637,638,639. Its local paid-child change is
+
+    L = -8 H1 + 8 H2 + 4 H3 - 4 H4.
+
+The four helpers each gain one unit of width. Preserve the actual local recipe admission, pair the four widened roles bijectively with four width-four donor positions, and require that the receiving pending children have at least one remaining axis each. Keep the old call times and retain every other role. Rebuild offsets chronologically, actual physical charts and every pending remainder.
+
+The general exact complete-profile change in one changed call with donor remainders r1,r2,r3,r4 is
+
+    Delta = L + sum_j (H_(rj-1) - H_rj), with H0 = 0.
+
+All rank mass is preserved: L contributes four units and the four remainders each lose one. Call-wise family uniqueness and actual windows are still required; rank-gap counts alone do not authorize a placement.
+
+**Theorem.** Each of the following three legal donor remainder patterns gives a strict complete moment saving for every 0 < b <= 1/500:
+
+    (1,1,1,1): Delta0 = -12 H1 + 8 H2 + 4 H3 - 4 H4;
+    (1,1,1,2): Delta2 = -10 H1 + 7 H2 + 4 H3 - 4 H4;
+    (1,1,1,3): Delta3 = -11 H1 + 9 H2 + 3 H3 - 4 H4.
+
+Thus a donor search limited to four rank-one gaps misses two additional sufficient classes. The latter two remove three complete remainder children, rather than four. No new child is omitted from the invoice.
+
+**Proof.** Put a=1-b and f(r)=r^a, f(0)=0. The price of a signed histogram is its signed sum of f(r); the actual m=73 moment differs by the common positive factor 73^b. Define
+
+    D0(a) = -12 + 8*2^a + 4*3^a - 4*4^a;
+    D2(a) = -10 + 7*2^a + 4*3^a - 4*4^a;
+    D3(a) = -11 + 9*2^a + 3*3^a - 4*4^a.
+
+Each Dk(1)=0. Using ln4=2ln2, their derivatives at 1 are
+
+    D0'(1) = 12 ln3 - 16 ln2;
+    D2'(1) = 12 ln3 - 18 ln2;
+    D3'(1) =  9 ln3 - 14 ln2.
+
+The rigorous elementary bounds ln3>1.0986 and ln2<0.6932 give derivative lower bounds 2.092, 0.7056 and 0.1826 respectively. On a in [499/500,1], use 2^a<=2, 3^a<=3, 4^a<=4 and ln2<0.7, ln3<1.1, ln4<1.4. Absolute second derivatives are at most
+
+    53.72, 52.74, 51.07 respectively.
+
+By the fundamental theorem of calculus, the derivatives throughout that interval are therefore at least
+
+    1.98456, 0.60012, 0.08046 respectively.
+
+Consequently D0(1-b)<=-1.98456*b, D2(1-b)<=-0.60012*b and D3(1-b)<=-0.08046*b, all strictly negative. The logarithm bounds can be established directly with the positive series ln x=2 sum_(k>=0) t^(2k+1)/(2k+1), t=(x-1)/(x+1), and a geometric upper bound for the tail; no numerical solver is needed. This proves the complete rank-price saving, conditional only on the literal physically admitted recipe and allocation described above.
+
+For any number of distinct changed calls, add these signed histograms to the complete baseline profile and reprice that single resulting profile. Never add advertised kappa gains. The negative complete-moment change is strict even if some individual changes appear locally more expensive.
+
+## 2. Two actual mechanisms from the registered OpenAI sources
+
+### A. Species-preserving exact allocation
+
+Source:
+
+    D:/proof/external/openai-math/lean/OAI/Computability/BinPacking/Inventory/SpeciesAllocation.lean
+
+Declarations `allocation`, `allocation_species`, `exists_allocation`, lines 13-31, namespace `OAI.BinPackingGap.SpeciesAllocation`.
+
+Fixed statement: for a finite type Slot, request:Slot->Species and stock:Species->Nat, if for every species s the cardinality of {b:Slot | request b=s} equals stock(s), there is a bijection
+
+    e : Slot <-> Sigma s, Fin(stock(s))
+
+with first component e(b) equal to request(b). The proof factors through the fibers of request and finite ordinal enumerations.
+
+Application: form eligibility types from actual width, provider, complete call window and per-call exclusion signature. Only group physical donor positions when their entire eligibility signatures agree. Equal finite type counts then give a literal deterministic bijection (stable list order is one implementation), rather than an unproved allocation oracle. Directly verify family uniqueness and rebuild physical charts after the lift. In particular, demotion donor permutations preserve all unaffected roles; the four changed widths are individually matched with larger exact residual capacities. This theorem justifies quotienting by complete eligibility types, not by rank alone.
+
+### B. Exact coordinate-exchange census with polynomial generation
+
+Sources:
+
+    D:/proof/external/openai-math/lean/OAI/Combinatorics/ContingencyTables/Transport/IntegerExchangeArithmetic.lean
+    D:/proof/external/openai-math/lean/OAI/Combinatorics/ContingencyTables/Sampling/ProfileExchangeCandidates.lean
+
+Fixed statements:
+
+- `OAI.ContingencyTables.IntegerWeightedTransport.adjacent_iff_arithmetic`: two natural profiles are an integer unit-exchange edge iff there exist distinct coordinates i,j with positive source count X(j), and Y is obtained by transferring one count from j to i.
+- `OAI.ContingencyTables.ProfilePrograms.mem_allExchanges_ofFn`: membership in the generated exchange list is equivalent to one of these ordered coordinate updates.
+- `allExchanges_length`: the generated list has exactly n^2 entries for a length-n profile.
+- `polynomial_allExchanges`: the concrete binary list generator has polynomial-time realization.
+
+Application: derive all remainder/profile candidates arithmetically first, reject moment-losing candidates, and then lift only exact eligibility-preserving physical realizations. This is a complete profile-level screening rule with explicit finite output; physical lifting is checked separately. For the present construction, the signed profile is derived from the literal four width increases and the four actual recipient remainders, yielding the three exact deltas above. This avoids copying old receipts and avoids a heuristic entropy-only claim. The universal negative moment theorem permits three rank-one gaps plus a rank-two or rank-three gap as actual sufficient candidates, beyond PR1111's four-unit-gap admission rule.
+
+Source reading is reuse of mathematical mechanisms, not fresh Lean certification of this adaptation. The downloaded OAI statements have not been recompiled in this round.
+
+## 3. Required concrete admission
+
+The highest public #1117 word additionally changes ends on different helpers 574/575. A joint word must check both changes together: disjoint register numbers alone do not prove propagated frame compatibility. The full scalar, frame/cap, phase, arbitrary-dirt and residual contracts must be replayed on the mixed literal word. Every widened helper must retain its actual complete-call window and must not alias another helper in that invocation. All pending axes, wrappers, residual factors, remaining children and row/prefix charges must be rebuilt. Existing sufficient owner-replacement semantics then apply to the literal replacement table. No unknown gadget or oracle is assumed.
+
+A finite table plus those actual checks realizes a better complex supplier; its final moment and outer grid must still be computed exactly through the pinned engine. No all-size/compiler, physical/common-label, analytic or unconditional multiplication claim is made beyond the retained inherited interfaces.
+
+## 4. Uniform saving for the whole exponent interval
+
+The preceding small-b estimates give explicit margins, but the three sufficient patterns in fact improve every exponent 0<b<1. This stronger proof was contributed by the owner worker after the initial pattern extension was communicated.
+
+Put u=2^(1-b), so 1<u<2, and p=ln3/ln2. Then 14/9<p<2: the lower bound is the exact integer inequality 3^9>2^14. The three deltas become
+
+    h0(u)=-12+8u+4u^p-4u^2,
+    h2(u)=-10+7u+4u^p-4u^2,
+    h3(u)=-11+9u+3u^p-4u^2.
+
+For 1<u<=2, p(p-1)u^(p-2)<2. Thus each h has strictly negative second derivative. Their derivatives at the right endpoint are respectively 6p-8, 6p-9 and (9/2)p-7, all positive. Since the derivatives decrease, they are positive throughout [1,2]. Each h(2)=0, so h(u)<0 for every 1<u<2. This proves strict complete moment saving throughout 0<b<1, with no approximation or solver.
+
+## 5. Several independent demotion groups, with actual joint words
+
+The current candidate uses the prefix order of register groups 635,603,611,619,627. The corresponding helper-index quadruples are [411,413,414,415], [379,381,382,383], [387,389,390,391], [395,397,398,399], [403,405,406,407]. Variant k applies the first k groups together.
+
+The implementation must prove the joint variant profile L*k from that actual word; disjoint register names do not on their own prove independent propagated frame paths. For each actually selected k, recount every canonical frame transition, derive all 480 endpoint widths, bind the fresh scalar/native restoration receipt, and check the changed Clifford phases. Only then assign that variant to literal calls whose exact donor allocation supplies all 4k extra axes.
+
+After this joint admission, different calls compose directly using the complete-call identity and their literal event windows. Each widened helper remains a distinct input stream, with its own exact physical chart; every pending child remains the tensor product of chronologically reserved disjoint factors and the explicitly paid remainder. Dispatch is a finite table of concrete admitted variants, not an unknown solver or gadget. Source-event ordering and the private workspace namespace are unchanged. Applying all 359 nominated groups yields the single complete histogram update
+
+    356*Delta0 + Delta2 + 2*Delta3 + (H1 - 2H6 + H11).
+
+The last term is a separately checked three-role owner-cycle concentration. Its moment improves by strict concavity. All four summands are strict savings once their actual physical witnesses and joint local variants pass. Final pricing uses the complete resulting histogram, rather than adding exponent gains.
diff --git a/research/adaptive-kernel-demotion/notes/recurrence/OPENAI-SOURCES.json b/research/adaptive-kernel-demotion/notes/recurrence/OPENAI-SOURCES.json
new file mode 100644
index 0000000000..8eb64ce4b5
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/recurrence/OPENAI-SOURCES.json
@@ -0,0 +1,17 @@
+{
+  "scope": "Source-inspected registered OpenAI mechanisms; source-only catalogue entries, no fresh Lean compile or axiom certification in this round",
+  "mechanisms": [
+    {
+      "path": "D:\\proof\\external\\openai-math\\lean\\OAI\\Computability\\BinPacking\\Inventory\\SpeciesAllocation.lean",
+      "sha256": "41f0946ae0d3ead100e14a061437115cf1d1b94266938a17c9ac882ae0123429"
+    },
+    {
+      "path": "D:\\proof\\external\\openai-math\\lean\\OAI\\Combinatorics\\ContingencyTables\\Transport\\IntegerExchangeArithmetic.lean",
+      "sha256": "967e6e6d3e8fb47d402d31106f8fd34f87eda3d232893d0aa20663b66c1925f7"
+    },
+    {
+      "path": "D:\\proof\\external\\openai-math\\lean\\OAI\\Combinatorics\\ContingencyTables\\Sampling\\ProfileExchangeCandidates.lean",
+      "sha256": "d3b9d09a2881817d29c2b7e5c939ac72e375ffa376e49599360bbd79668f895e"
+    }
+  ]
+}
diff --git a/research/adaptive-kernel-demotion/notes/recurrence/RESULTS.md b/research/adaptive-kernel-demotion/notes/recurrence/RESULTS.md
new file mode 100644
index 0000000000..ce7d8edd0c
--- /dev/null
+++ b/research/adaptive-kernel-demotion/notes/recurrence/RESULTS.md
@@ -0,0 +1,36 @@
+# Recurrence lane final handoff
+
+Status: complete, no active computation. All scripts use bounded native Windows Python; no WSL, C++, GPU, services or Lean compilation was launched.
+
+Final frozen candidate has conditional kappa 0.001673260706543984 according to the root's exact two-moment/47-inequality calculation. This lane independently establishes its actual mixed physical geometry and finite bill. No publication occurred.
+
+Sufficient mathematical contributions:
+
+1. Extend PR1111's demotion donor pattern from four unit gaps to three unit gaps plus one rank-two or rank-three gap. Exact full deltas and rigorous derivative margin proof are in GAP-AWARE-DEMOTION.md. The owner worker strengthened this to every exponent 0<b<1, with the short concavity proof retained and credited.
+2. Compose five ACTUAL jointly checked prefix variants with a literal adaptive dispatch. There are 359 demoted groups over 103 calls: 356 all-unit donor patterns, one mixed rank-two pattern and two mixed rank-three patterns. The full exact signed profile includes the legal H1-2H6+H11 owner-cycle change; gains are never added at the kappa level.
+3. Two specifically sourced OpenAI mechanisms are retained: SpeciesAllocation.exists_allocation and ContingencyTables adjacent_iff_arithmetic / polynomial_allExchanges. Sources and exact hashes are in OPENAI-SOURCES.json. They are source-inspected registered modules, not newly Lean-certified proofs of this adaptation.
+
+Actual final independent admission:
+
+- 69,120 complete roles; 144 calls; 480 helpers/call; 41 default and 103 changed calls.
+- Variant counts k1:24, k2:8, k3:15, k4:6, k5:50.
+- Actual source-event reconstruction matches all 288 positive-rank pending child windows.
+- Every pending child's physical basis and pair/side cross-child disjointness are checked, including unused children.
+- Every actual 73-column helper chart, spectator and chronological axis block is derived fresh.
+- 9,898 distinct charts; chart stream SHA-256 58c93676cda7edb168bcf272131dc259571c4a5b6e86ebc547d028dc538b87b1.
+- Complete profile {1:344363,2:65097,3:62855,4:19012,5:11808,7:8,8:1152,11:2,48:4873}.
+- 6,034 explicit idle children; rank mass 1,041,408; deficit 5,120.
+- 11 meaningful owner/geometry mutations reject; last replay 3.34 seconds.
+
+Fresh finite bill:
+
+- Both actual local macro counts 19,693; local children 3,494; native primitive bounds 198,766/198,814; prefix 52/68.
+- Full primitives 28,625,376; full macros 2,835,792; paid wrapper factors 9,953,280.
+- Local adapters 387,056; compiler 25,934,336; local bound 10,038,040,553,630.
+- Fresh per-vertex 3,588,959,010,714,576; add pinned prior charged allowance 2,877,946,989,724,568 to obtain 6,466,906,000,439,144.
+- All nine strict guards pass; whole prefix 397<512 and physical row 16,469<20,161.
+- Four invoice cap controls reject.
+
+Portable files to package: audit_owner_table.py, audit_mixed.py, finite_invoice.py; none has hardcoded private paths. Research-only check_controls_local.py is a local runner, not a publication file. FRESH-INVOICE-PROOF.md provides the actual source-bound boundary invariant and complete recount, rather than copying a baseline admission.
+
+The old R492 package evidence/global/GLOBAL-TEMPLATE was correctly rejected for source-window reconstruction (wrong ranks and missing positive children). The final check uses the pinned current ROUND20 template instead. All-size/compiler, universal routing/realization and analytic transfer remain the explicit inherited source interfaces. Unchanged k0 scalar semantic admission stays inherited; changed native words were freshly checked by the cell worker. This lane's finite checks are not an unconditional multiplication theorem or Lean certification.
diff --git a/research/adaptive-kernel-demotion/pricing.py b/research/adaptive-kernel-demotion/pricing.py
new file mode 100644
index 0000000000..026d9d37eb
--- /dev/null
+++ b/research/adaptive-kernel-demotion/pricing.py
@@ -0,0 +1,47 @@
+from fractions import Fraction as Q
+from decimal import Decimal, localcontext
+import json,importlib.util,gzip
+from pathlib import Path
+
+def need(x,label):
+ if not x:raise RuntimeError(label)
+def decimal(q):
+ with localcontext()as ctx:
+  ctx.prec=65
+  return str(Decimal(q.numerator)/Decimal(q.denominator))
+def encode(x):
+ if isinstance(x,Q):return str(x)
+ if isinstance(x,dict):return {str(k):encode(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return [encode(v)for v in x]
+ return x
+def price(H,bit,M,B,A,bad=False):
+    cert=M.certify(H,73,14336,bad);b=Q(cert['lower']);intervals=[]
+    for z,accept in [(b,True),(b+Q(1,10**24),False)]:
+        i=M.moment(H,73,14336,z,bad);j=B.moment(73,14336,list(H.items()),z)
+        if bad:
+            c=B.moment(73,14336,[(1,32*73*73*sum(H.values()))],z)
+            j=(j[0]+c[0]/10**16,j[1]+c[1]/10**16)
+        need(i[1]<1 and j[1]<1 if accept else i[0]>1 and j[0]>1,'two rational moment signs')
+        intervals.append({'b':z,'accepted':accept,'mercator':[v-1 for v in i],'base_two':[v-1 for v in j]})
+    eta=beta=Q(1,10**24);s=min(bit,(1-beta)*b)-Q(1,10**27)
+    need(0<s<bit and s<(1-beta)*b,'strict common saving')
+    a=Q(384599,10**10);cuts=[]
+    ceil=lambda x:-(-x.numerator//x.denominator)
+    for _ in range(7):
+        old=a;a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s)
+        need(old<a<s<1-a and gap>0,'bootstrap gap')
+        cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap))
+        need(cut*gap**2>=36 and cut*gap>=2*(4+512),'charged finite cutoff')
+        cuts.append({'a':a,'gap':gap,'cutoff_log2':cut})
+    q=a*(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(a,b,bridge,k,eta=eta,beta=beta)
+    need(len(outer['strict_constraints'])==47 and all(v>0 for v in outer['strict_constraints'].values()),'47 strict outer inequalities')
+    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(a,b,bridge,kk,eta=ee,beta=be)
+        except AssertionError:controls.append(name)
+        else:raise RuntimeError('outer control accepted: '+name)
+    return {'complex_lower':b,'kappa':k,'kappa_decimal':decimal(k),'moment_checks':intervals,'outer_constraints':outer['strict_constraints'],'outer_controls':controls,'bootstrap':cuts}
+
diff --git a/research/adaptive-kernel-demotion/vendor/engines/base_two_moment.py b/research/adaptive-kernel-demotion/vendor/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/adaptive-kernel-demotion/vendor/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/adaptive-kernel-demotion/vendor/engines/moment.py b/research/adaptive-kernel-demotion/vendor/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/adaptive-kernel-demotion/vendor/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/adaptive-kernel-demotion/vendor/engines/outer.py b/research/adaptive-kernel-demotion/vendor/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/adaptive-kernel-demotion/vendor/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/adaptive-kernel-demotion/vendor/pr1117/data/OWNERS.json.gz b/research/adaptive-kernel-demotion/vendor/pr1117/data/OWNERS.json.gz
new file mode 100644
index 0000000000..39fe9457a2
Binary files /dev/null and b/research/adaptive-kernel-demotion/vendor/pr1117/data/OWNERS.json.gz differ
diff --git a/research/adaptive-kernel-demotion/vendor/pr1117/data/PLAN.json b/research/adaptive-kernel-demotion/vendor/pr1117/data/PLAN.json
new file mode 100644
index 0000000000..9e2225a7b8
--- /dev/null
+++ b/research/adaptive-kernel-demotion/vendor/pr1117/data/PLAN.json
@@ -0,0 +1,85662 @@
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diff --git a/research/adaptive-kernel-demotion/vendor/pr1117/data/SPEC.json b/research/adaptive-kernel-demotion/vendor/pr1117/data/SPEC.json
new file mode 100644
index 0000000000..781b69ebd7
--- /dev/null
+++ b/research/adaptive-kernel-demotion/vendor/pr1117/data/SPEC.json
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+        ],
+        "local_adapters": 387056,
+        "local_primitive_bound": 10038040553630,
+        "compiler": 25934336,
+        "children": 3494,
+        "paid_profile": {
+          "1": 2406,
+          "2": 432,
+          "3": 424,
+          "4": 142,
+          "5": 82,
+          "8": 8
+        },
+        "program_hashes": {
+          "backward": "c4209bfd82bf85b315050849e35e645dfa8a0959a0029134bde37907c4010eb1",
+          "forward": "f2fdd8a9986836ca8babb879f2bc45ffb1a8af9b03356f8c9f473296d4860273"
+        },
+        "semantic_artifact_sha256": {
+          "CANONICAL-WORD.json.gz": "a8a009fa1a48780a7e9cdbc0a782a26d7059a4dbcb9a8d8389ecd5d17a084a5a",
+          "LOCAL-PROGRAMS.json.gz": "d361480e71f39003ba7cbb696172354df6761f49a12aa988b4ba340cd638af44",
+          "LOCAL-CHECKS.json": "dfa7214c680d84526b9aa0a196d34762cefdd783909a36c0cfb9a04e9d62b18e",
+          "INDEPENDENT-LOCAL-REPLAY.json": "b4b0d578e2942c1ddd0e06ccd06d36aec5d7f70003fd477c339b2e33ceb45e49",
+          "CLIFFORD-RECIPES.json": "e19924062afe25129ab0c1fc98c9c40cbeb123c72ff48816778f05897b6ee161",
+          "CLIFFORD-REVIEW.json": "a6384e4c74181960875692abfcd1e7dba45dbdbe8bfdaf1b20ebceb680c4dfdd",
+          "RESIDUAL-ADAPTERS.json": "4f75b7c44ced1de95b396af9e6beaa9e695e8abe6263c88386a19684fd2a9568"
+        }
+      },
+      "semantic_phase_sha256": "a6384e4c74181960875692abfcd1e7dba45dbdbe8bfdaf1b20ebceb680c4dfdd",
+      "expected_local": {
+        "forward": {
+          "events": 24767,
+          "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": 10057,
+    "cross_replica_helper_roles": 58701,
+    "idle_remainders": 7467,
+    "idle_remainder_profile": {
+      "1": 2202,
+      "2": 16,
+      "3": 365,
+      "6": 2,
+      "7": 8,
+      "11": 1,
+      "48": 4873
+    },
+    "global_profile": {
+      "1": 348666,
+      "2": 62224,
+      "3": 61421,
+      "4": 20448,
+      "5": 11808,
+      "6": 2,
+      "7": 8,
+      "8": 1152,
+      "11": 1,
+      "48": 4873
+    },
+    "live": 14336,
+    "physical": 14826,
+    "conservative_kappa_decimal": "0.001672846993028285",
+    "kappa_decimal": "0.001672846995880185",
+    "complex_lower": "1675650102119662212841/1000000000000000000000000",
+    "conservative_complex_lower": "335130019851639449599/200000000000000000000000",
+    "kappa": "334569399176037/200000000000000000",
+    "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/adaptive-kernel-demotion/vendor/pr1117/data/UPSTREAM-PINS.json b/research/adaptive-kernel-demotion/vendor/pr1117/data/UPSTREAM-PINS.json
new file mode 100644
index 0000000000..68486b84e3
--- /dev/null
+++ b/research/adaptive-kernel-demotion/vendor/pr1117/data/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/adaptive-kernel-demotion/verify.py b/research/adaptive-kernel-demotion/verify.py
new file mode 100644
index 0000000000..4777606c50
--- /dev/null
+++ b/research/adaptive-kernel-demotion/verify.py
@@ -0,0 +1,94 @@
+"""Fresh finite certificate of a conditional construction; standard library only.
+Apache-2.0. No network, search, WSL, GPU, compiler or persistent workers.
+"""
+import argparse,gzip,hashlib,importlib.util,json,shutil,subprocess,sys,time
+from pathlib import Path
+from fractions import Fraction as Q
+P=Path(__file__).resolve().parent
+
+def need(x,m):
+ if not x:raise RuntimeError(m)
+def read(p):
+ b=p.read_bytes();return json.loads(gzip.decompress(b) if p.suffix=='.gz' else b)
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def module(name,path):
+ s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+def write(path,obj):path.write_text(json.dumps(obj,indent=2)+'\n',encoding='utf-8',newline='\n')
+def inventory():
+ manifest=read(P/'MANIFEST.json');actual={x.relative_to(P).as_posix() for x in P.rglob('*') if x.is_file() and x.name!='MANIFEST.json'}
+ need(actual==set(manifest),'exact package file inventory')
+ for n,h in manifest.items():need(sha(P/n)==h,'source sha256 '+n)
+ return manifest
+def ancestor_pins():
+ pins=read(P/'vendor/pr1117/data/UPSTREAM-PINS.json')
+ targets={
+ 'local/data/PARENT-ROUTING.json.gz':'base/split-centres/CANONICAL-WORD.json.gz',
+ 'inputs/DATA-PHASES.json':'complex-nine-native/DATA-PHASES.json',
+ 'inputs/ROUND20-PARENT-TEMPLATE.json.gz':'vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz',
+ 'inputs/PRIOR-ALLOWANCE.json':'vendor531/evidence/audit/PREFIX-AND-INVOICE.json',
+ 'vendor/engines/moment.py':'/moment.py',
+ 'vendor/engines/base_two_moment.py':'/base_two_moment.py',
+ 'vendor/engines/outer.py':'/outer.py'}
+ for name,suffix in targets.items():
+  hs={h for n,h in pins.items() if n.endswith(suffix)}
+  need(len(hs)==1 and sha(P/name) in hs,'upstream source pin '+name)
+ need(sha(P/'data/OWNERS.json.gz')=='d7df90d10fefcd94d2893c559ea507bc057c34ac59296281492220036c8ae48e','final literal owners pin')
+ need(sha(P/'data/DISPATCH.json')=='5b1924fc0da6de00e681e7773ad59f70e3f69f0772100cce7b65768b0fd0d3eb','final dispatch pin')
+
+def main():
+ need(__debug__,'normal Python required; optimized Python disables vendor checks')
+ a=argparse.ArgumentParser();a.add_argument('--out',type=Path,required=True);z=a.parse_args();out=z.out.resolve()
+ need(out!=P and P not in out.parents,'output must be outside the source package')
+ need(not out.exists(),'fresh output directory required')
+ start=time.monotonic();manifest=inventory();ancestor_pins();out.mkdir(parents=True)
+ # Rebuild every changed literal row from the pinned old map. No optimizer runs.
+ rows=read(P/'vendor/pr1117/data/OWNERS.json.gz');edits=read(P/'data/EDITS-FROM-PR1117.json');seen=set()
+ need(len(edits)==4594,'complete literal difference count')
+ for e in edits:
+  i=e['index'];need(type(i) is int and 0<=i<len(rows) and i not in seen,'unique literal edit index');seen.add(i)
+  need(rows[i]==e['before'],'literal edit before');rows[i]=e['after']
+ need(rows==read(P/'data/OWNERS.json.gz'),'rebuilt complete final map');need(len(rows)==69120,'complete role count')
+ print('PASS_SOURCE_PINS_AND_LITERAL_RECONSTRUCTION',flush=True)
+ # Five freshly reconstructed, emitted and independently checked joint programs.
+ native={};local=[]
+ for k in range(1,6):
+  dest=out/('provider-'+str(k));flags=0x4000 if sys.platform=='win32' else 0
+  r=subprocess.run([sys.executable,'-I','-B',str(P/'local/check_local.py'),'--selector',str(k),'--out',str(dest)],capture_output=True,text=True,timeout=120,creationflags=flags)
+  (out/('provider-'+str(k)+'.log')).write_text(r.stdout+r.stderr,encoding='utf-8')
+  need(r.returncode==0,'fresh local prefix '+str(k)+' failed: '+r.stderr[-1200:]);local.append(read(dest/'RESULT.json'));native[k]=dest/'native'
+  print('PASS_FRESH_PREFIX',k,flush=True)
+ old=out/'old-native';old.mkdir();shutil.copyfile(P/'local/data/OLD-CANONICAL-WORD.json.gz',old/'CANONICAL-WORD.json.gz')
+ mixed=module('mixed',P/'audit_mixed.py')
+ audit,context=mixed.run(P/'vendor/pr1117',P/'data/OWNERS.json.gz',P/'data/DISPATCH.json',old,native[1],P/'local/data/PARENT-ROUTING.json.gz',P/'inputs/DATA-PHASES.json',P/'inputs/ROUND20-PARENT-TEMPLATE.json.gz',variants=native)
+ audit['negative_controls']=mixed.negative_controls(context);need(len(audit['negative_controls'])==11,'mixed mutation controls')
+ for n in ('sigmas','remainders'):
+  x=audit.pop(n);(out/(n.upper()+'.json.gz')).write_bytes(gzip.compress(json.dumps(x,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+ expected=read(P/'expected/OWNER-AUDIT.json')
+ for n in ('roles','calls','helper_per_call','profile','idle_profile','idle_remainders','rank_mass','deficit','cross_replica','actual_73column_sigmas','sigma_stream_sha256','mixed_calls','default_calls','variant_counts'):
+  # JSON maps use string keys; the fresh checker may use integer keys.
+  need(json.loads(json.dumps(audit[n]))==expected[n],'fresh complete owner result '+n)
+ write(out/'OWNER-AUDIT.json',audit);print('PASS_COMPLETE_OWNER_CHARTS_AND_11_CONTROLS',flush=True)
+ spec=read(P/'vendor/pr1117/data/SPEC.json');dispatch=read(P/'data/DISPATCH.json')
+ inv=module('invoice',P/'finite_invoice.py').calculate(spec,audit,dispatch,native,read(P/'inputs/PRIOR-ALLOWANCE.json'))
+ need(len(inv['strict_checks'])==9 and all(inv['strict_checks'].values()) and len(inv['negative_controls'])==4,'all nine finite guards and four controls')
+ need(inv['conservative_pervertex_used']==6466906000439144,'complete fresh bill');write(out/'FINITE-INVOICE.json',inv)
+ print('PASS_FRESH_FINITE_INVOICE_9_GUARDS',flush=True)
+ pricing=module('pricing',P/'pricing.py');M,B,A=[module(n,P/'vendor/engines'/(n+'.py')) for n in ('moment','base_two_moment','outer')]
+ bitrecord=read(P/'inputs/PR589-EXPECTED.json');bit=Q(bitrecord['nine']['bit_lower']);bitH={int(r):n for r,n in bitrecord['nine']['profile'].items()};live=bitrecord['nine']['bit']['live']
+ need(live==28416 and 64*live-sum(r*n for r,n in bitH.items())==10272,'inherited bit exact mass')
+ bitchecks=[]
+ for b,accept in [(bit,True),(bit+Q(1,10**24),False)]:
+  i=M.moment(bitH,64,live,b,True);j=B.moment(64,live,list(bitH.items()),b);c=B.moment(64,live,[(1,32*64**2*sum(bitH.values()))],b);j=(j[0]+c[0]/10**16,j[1]+c[1]/10**16)
+  need(i[1]<1 and j[1]<1 if accept else i[0]>1 and j[0]>1,'unchanged bit two-engine bracket');bitchecks.append(dict(b=b,accepted=accept,mercator=i,base_two=j))
+ H={int(r):n for r,n in audit['profile'].items()}
+ # Probability weights are normalized from the complete positive histogram.
+ weights={r:Q(r*n,audit['rank_mass']) for r,n in H.items()};need(all(n>0 for n in H.values()) and sum(weights.values())==1,'complete positive normalized weights')
+ result=pricing.price(H,bit,M,B,A);conservative=pricing.price(H,bit,M,B,A,True)
+ base=pricing.price({int(r):n for r,n in spec['expected']['global_profile'].items()},bit,M,B,A)
+ need(base['kappa']==Q(spec['expected']['kappa']),'baseline assembly compatibility')
+ need(result['kappa']==Q('0.001673260706543984') and conservative['kappa']==Q('0.001673260703699378'),'exact claimed endpoints')
+ need(result['kappa']>base['kappa'],'strict improvement over frozen baseline')
+ result.update(status='PASS_ADAPTIVE_KERNEL_DEMOTION',conservative=conservative,baseline=base['kappa'],gain=result['kappa']-base['kappa'],profile=H,normalized_weights=weights,bit_moment_checks=bitchecks,local_checks=local,finite_invoice='FINITE-INVOICE.json',owner_audit='OWNER-AUDIT.json',source_manifest_sha256=sha(P/'MANIFEST.json'),seconds=time.monotonic()-start,scope='Conditional artifact certificate. Changed local programs, new owner map, fresh invoice and exact assembly checked. Inherited unchanged supplier, compiler, all-size, precision/recovery and analytic interfaces remain assumptions. No new Lean certification or unconditional multiplication claim.')
+ write(out/'RESULT.json',pricing.encode(result));print('PASS_ADAPTIVE_KERNEL_DEMOTION kappa='+result['kappa_decimal'],flush=True)
+
+if __name__=='__main__':main()