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index 0000000000..ddf88093f5
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+}
diff --git a/research/partial-kernel92-async/LICENSE b/research/partial-kernel92-async/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/partial-kernel92-async/LICENSE
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diff --git a/research/partial-kernel92-async/MANIFEST.json b/research/partial-kernel92-async/MANIFEST.json
new file mode 100644
index 0000000000..77aa9de44b
--- /dev/null
+++ b/research/partial-kernel92-async/MANIFEST.json
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+      "sha256": "2e807893180a3716b36a81f1a7d933bd55f2299489b6f236ba5c644d87739209"
+    },
+    "vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py": {
+      "mode": "lf-text",
+      "sha256": "416b318c1b6b8c7b72e24713b1b18d8772ec368e042a321b4418c63a74711590"
+    },
+    "vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py": {
+      "mode": "lf-text",
+      "sha256": "2f064890bdde1eb9ea2c9a339e8ae9713dcffe0274be4b1ef6208ad2b7ba5a2a"
+    },
+    "vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json": {
+      "mode": "lf-text",
+      "sha256": "436e4acadee227dbfcb66386c9ccaa38e68054e8ed4870bb174eeb41363375bb"
+    },
+    "vendor/complex/split-centres-global/code/complex_phases_full.py": {
+      "mode": "lf-text",
+      "sha256": "0f2795aaffafe0c64d77f3748ef2109a3c42c58da867e4cf269a0a8cb6109466"
+    },
+    "vendor/complex/split-centres-global/vendor/clifford_exact.py": {
+      "mode": "lf-text",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    },
+    "verify.py": {
+      "mode": "lf-text",
+      "sha256": "ae9b5763e656696add6d106fe70d90facb5d2700fb8e66e4eea678c46b1d5720"
+    },
+    "verify.sh": {
+      "mode": "lf-text",
+      "sha256": "2b1b51f757d8ddf81941c8c96007a2256336856c2e017bcf6c3a37576c82bc8b"
+    },
+    "evidence/PORTABLE-REPLAY.json": {
+      "mode": "lf-text",
+      "sha256": "d307e5f71b148454c5be5575d0f93650fa494fd307564cd679b47892bf39e958"
+    },
+    "evidence/TRANSPORT-CONTROLS.json": {
+      "mode": "lf-text",
+      "sha256": "af70924e999305938a693718e34b1f3a4e7199e4050bde193a416426df755bae"
+    },
+    "research-notes/REPLAY-REPAIRS.md": {
+      "mode": "lf-text",
+      "sha256": "0ad48be86ec6c5b3617b3ef9e728587c57f549aac9826041665d0d04c21c561c"
+    }
+  }
+}
diff --git a/research/partial-kernel92-async/NOTICE.md b/research/partial-kernel92-async/NOTICE.md
new file mode 100644
index 0000000000..1a413bfa41
--- /dev/null
+++ b/research/partial-kernel92-async/NOTICE.md
@@ -0,0 +1,9 @@
+# Scoped attribution
+
+Prepared with OpenAI Codex assistance. Apache-2.0; see LICENSE. Original authorship notices in included vendor code are retained.
+
+PR507 directly supplies the partial-own factory, 84-pivot reference and its retiming map. PR484 supplies the gauge/kernel construction and wrappers; PR496 supplies whole-owner pooling and invoice ancestry. PR493 supplies the unchanged cited bit operator. PR495 supplies body-frame retiming, with PR501 and PR502 integrating it. PR473's single-gauge proposal inspired our coordinated four-gauge collapse; its updated schedule was also considered. PR505 contains our prior asynchronous complete-invocation scheduling. PR506 supplies a related public comparison and portability feedback. PR477's experiment log informed bounded route selection.
+
+Earlier retained ancestry includes PR433/425/370 for geometry and the scalar/phase compiler, PR458 for whole-owner spectator wrappers, PR361/315 for exact moments and outer arithmetic, and PR434/417/435/440/401/408/416 for response-kernel and gauge methods. SOURCES.json separates direct ingredients, ancestry, comparisons and excluded interfaces; credits do not mean their gains were added independently.
+
+Our contribution here is the actual combined reconstructed 92-pivot word and literal whole-owner allocation, with complete fresh checks of the changed complex program. OpenAI math, the Problem 1.8 implementation and the installed machine compiler sources informed the documented research adaptations. No fresh Lean certification is claimed.
diff --git a/research/partial-kernel92-async/PORTABILITY.md b/research/partial-kernel92-async/PORTABILITY.md
new file mode 100644
index 0000000000..c5c9dd7743
--- /dev/null
+++ b/research/partial-kernel92-async/PORTABILITY.md
@@ -0,0 +1,11 @@
+# Portable replay and browser uploads
+
+No hidden file is required. MANIFEST.json binds every included file except itself. Each entry declares either exact raw-byte hashing (gzip and other binary inputs) or SHA-256 after converting CRLF to LF (recognized text files). This accepts only the platform newline distinction; it does not ignore whitespace, JSON values, source code or any other content. An omitted file or changed token still fails.
+
+verify.py copies static work inputs into its new output directory, canonicalizes recognized text there, and creates an LF copy of the frozen asynchronous plan. Only those canonical copies enter runtime raw-byte template hashes. Each child executes through code/run_portable.py, which preserves argv, import path and working directory while forcing generated Path.write_text output to UTF-8/LF. Generated adapter JSON therefore has the same embedded hash on Windows and Linux.
+
+Gzip transport bytes are manifest-bound. Newly generated gzip container headers can vary across Python versions; the expected final template hash binds decompressed canonical content instead. Mathematical input fields are checked independently. The normalized local word omits only two irrelevant inherited display floats and a checked redundant dimension field.
+
+The package is tested locally with assertions enabled. Optimized Python is rejected. The final portability test changes every recognized package text file to CRLF and runs the complete verifier against the frozen expected result. This is a Windows line-ending test, not a claim that Linux or Python 3.14 ran locally.
+
+Upload batches contain at most 40 files each, have no hidden files, and reproduce the same research/partial-kernel92-async directory. Upload each batch's research folder at your fork's repository root, on one fresh branch. Do not upload the part folder itself. After all batches are committed, open one PR from that branch. Nothing in the verifier publishes, deletes files or modifies a fork.
diff --git a/research/partial-kernel92-async/PROOF.md b/research/partial-kernel92-async/PROOF.md
new file mode 100644
index 0000000000..b0b27963f7
--- /dev/null
+++ b/research/partial-kernel92-async/PROOF.md
@@ -0,0 +1,27 @@
+# Sufficient composition and complete cost
+
+## Reconstructed local operator
+
+Start with PR507's pinned partial-own factory. Reconstruct its 84-pivot reference and check every old frame in the frozen retiming map before replacing any frame. Scalar operands and coefficients must remain identical. Transfer the resulting scalar-body frames back to the factory, then reconstruct the four coordinated rank-two gauges and the selected 92 exact rational response relations. Donor relations and dirty compensation are recomputed from the actual word.
+
+The local recursive profile is 2,539 rank-one, 160 rank-two, 530 rank-three, 88 rank-four, 298 rank-five, 68 rank-six, one rank-seven and 17 rank-eight children. The residual widths are 18 at seven, 154 at eight and 388 at nine. The normalized complete word has SHA-256 `c6e758b324d3566e8443b3fd3d739c4d01e1928eadbee40f5c36973404b0640b`. Normalization removes only two unused display floats and an independently checked redundant dimension field.
+
+The verifier separately checks every arbitrary-dirt input column in both orientations, all 92 correction-omission controls, Gaussian phases, frame legality and paid spectator wrappers. A clean-input identity alone is insufficient.
+
+## Sufficient global schedule
+
+Assume the inherited complete normalized invocation contract: one complete call has its declared active data shear on arbitrary dirt, uses distinct whole helper owners, restores borrowed spectators and private workspace, and leaves exactly the declared residual transform on each assigned pending block.
+
+Execute eight replicas of the nine-stage controller in order (7*stage+6*replica, stage, replica). Preserve each replica's complete source-event order; finish each call and its wrappers before the next starts. Assign disjoint subspaces of each owner's actual pending child to helpers strictly within that owner's idle interval. Execute the exact complementary remainder before the next active or bridge touch.
+
+Induct on emitted events. The invocation contract preserves spectators; the disjoint residual factors commute and compose with the explicit remainder to exactly the original pending child. Each owner therefore has the original state when next touched. The data projections preserve each replica's original operator, and the common final correction completes the original global endpoint. No helper is split between owners, and no scalar gate is moved through an unfinished invocation.
+
+The independent checker verifies all 40,320 assignments, simultaneous injection, actual idle intervals, orthogonal charts, paid adapters and residual coverage. The witness is literal; no optimization oracle enters replay.
+
+## Cost and exponent
+
+The global paid profile is `{1: 182808, 2: 11520, 3: 41233, 4: 6336, 5: 25173, 6: 4896, 7: 195, 8: 1224, 16: 1, 32: 1, 39: 1, 48: 766}`. Its rank sum is 73*7,680 - 2,496. The maximum recursive rank is 48 and 73^2 > 2*48^2. The independent finite invoice recounts all prefix, row and physical costs.
+
+Two rational moment engines accept b = `139346249534416215349/100000000000000000000000` and reject the adjacent upper endpoint. The published PR493 bit histogram is independently repriced while its unchanged operator remains a cited dependency. Six bootstrap steps and all 47 strict outer constraints give kappa = `1391523459591829/1000000000000000000`; the next kappa grid point and the three invalid parameter controls are rejected.
+
+This is sufficient for the stated conditional bound under exactly the retained interfaces, not a proof of those interfaces themselves. Complete numerical evidence is in evidence/EXACT-ASSEMBLY.json.
diff --git a/research/partial-kernel92-async/README.md b/research/partial-kernel92-async/README.md
new file mode 100644
index 0000000000..892f660f33
--- /dev/null
+++ b/research/partial-kernel92-async/README.md
@@ -0,0 +1,38 @@
+# Partial-own factory, 92 kernel pivots and asynchronous whole owners
+
+Conditional kappa = **0.001391523459591829**, exactly `1391523459591829/1000000000000000000`. This is **1.381994% above our previous checked construction**, 0.001372554837726243. The complex supplier binds, with b = `139346249534416215349/100000000000000000000000`; the unchanged cited PR493 bit supplier has c = `391360506745414227149/250000000000000000000000`.
+
+This package combines PR507's partial-own factory, our coordinated four-gauge rank reduction, a newly selected 92-pivot response kernel, public body retiming and our asynchronous complete-invocation schedule. It reconstructs and prices their combined program; it does not add headline gains.
+
+## Reproduce
+
+Python 3.11 or later, standard library only:
+
+```
+python -B verify.py --work /absolute/path/to/a-new-output-directory
+```
+
+The output directory must be new and outside this package. Keep assertions enabled. No network, optimizer, C++ compiler or Lean installation is required for replay. Thirteen stages reconstruct the changed factory and word, check arbitrary-dirt scalar columns and exact Gaussian phases, emit paid wrappers and actual physical owners, recount costs, and run two exact rational moment engines plus all 47 strict outer inequalities. Logs and RESULT.json appear in the requested directory. The unchanged bit operator is a pinned dependency, not freshly reconstructed here.
+
+## Concrete changes
+
+- PR507 changes the factory and supplies the 84-pivot reference construction.
+- Helpers 540 through 543 use the rank-two plane spanned by 408 and 102; target frame labels 81, 82, 84 and 87 are reduced together.
+- A frozen exact rational selection raises the kernel count to 92 pivots. All 800 input columns pass in both orientations, and all 92 omitted-correction controls fail as intended.
+- The resulting 560 helpers have widths 7, 8 and 9 with multiplicities 18, 154 and 388.
+- Eight replicas execute 72 complete invocations in order (7*stage+6*replica, stage, replica). Every one of the 40,320 helper uses has an explicit whole physical owner.
+- Ambient dimension 73, live stock 7,680, physical stock 8,258 and rank deficit 2,496 are unchanged.
+
+The complete global profile is `{1: 182808, 2: 11520, 3: 41233, 4: 6336, 5: 25173, 6: 4896, 7: 195, 8: 1224, 16: 1, 32: 1, 39: 1, 48: 766}`. It includes every paid idle remainder.
+
+## Machine research: what did and did not contribute
+
+We inspected actual Word RAM, Turing-machine and workspace implementations from OpenAI math, our Problem 1.8 library and the installed compiler libraries. We constructed or tested old-state snapshots, first-read frontiers, frame-preserving register coalescing, fused entry/return and deferred modulo-four normalization. These are documented with sufficient applicability rules and source hashes in RESEARCH.md and research-notes/.
+
+**We did not obtain three new machine-derived numerical gains.** The winning 92-pivot selection uses the existing response-kernel method on the changed factory. Machine-inspired alternatives were explicitly priced and did not beat it. They are research records, not hidden ingredients of this exponent.
+
+## Scope
+
+This is a checked finite conditional construction. The inherited all-size compiler, common-label/mutable-basis interface, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain assumptions. No unconditional faster multiplication theorem, new Lean certification or universal optimality claim is made. It does not claim to exceed larger submissions using disputed split-residual interfaces.
+
+The public snapshot was frozen through PR507 before packaging. See SOURCES.json and NOTICE.md for direct PR credits. See PORTABILITY.md for text and upload handling. Nothing is published or pushed by this package.
diff --git a/research/partial-kernel92-async/RESEARCH.md b/research/partial-kernel92-async/RESEARCH.md
new file mode 100644
index 0000000000..6602e30042
--- /dev/null
+++ b/research/partial-kernel92-async/RESEARCH.md
@@ -0,0 +1,16 @@
+# Machine-source research ledger
+
+The deliverable's numerical improvement comes from the reconstructed factory, coordinated gauges, 92-pivot kernel and complete asynchronous allocation. None of the following is credited with an additional gain in the selected program.
+
+| Source concept | Concrete adaptation | Outcome |
+| --- | --- | --- |
+| Word RAM reads operands before overwriting a destination | Capture a pair sum and the still-old second operand between two shears, then decode the changed basis | Constructed; the best snapshot candidate reached 88 pivots but lost to the selected 92-pivot program |
+| Machine execution preserves locations outside an injective live-register renaming | Reuse retired factory storage for own-output rows, with exact frame restoration | Later retired rows do not fit the output frames; the explicit downward transitions cost more rank than the available deficit |
+| Exact Turing return/restoration and word substitution with additive cost | Merge an exterior pending factor into a helper's first or final recursive call | A sufficient rule is proved; the tested coordinated-rank2 baseline has no eligible entry or exit site |
+| Reversible finite-state normalization | Track repeated pending axes modulo four and emit the explicit parity remainder and translation | Sufficient identity proved; the paid finite-stock screen selected no overlaps |
+| Persistent reserved workspace and continuation composition | Shorter controllers with paid spills; larger finite replica pipelines | The tested programs did not improve the complete price |
+| Actual machine read dependency | Recompute entrance eligibility at the first observer after retiming | A valid 89-pivot candidate lost to the selected program |
+
+These are bounded outcomes, not universal barriers. The useful sufficient transformations, exact coalescing gate and source hashes are retained in research-notes/. Missing typed DAG ports are reported; reading a Lean source is not kernel certification. A polynomial RAM-to-Turing simulation alone cannot preserve an improvement to this near-linear exponent, so no such simulation is used as a free speedup.
+
+For a future successful machine-derived change, emit the actual modified arbitrary-dirt operator, pay restoration and routing, rebuild the literal physical assignment and compare the complete rank moment. Saving a register or a local instruction alone does not establish a larger kappa.
diff --git a/research/partial-kernel92-async/SNAPSHOT.md b/research/partial-kernel92-async/SNAPSHOT.md
new file mode 100644
index 0000000000..f03803d38d
--- /dev/null
+++ b/research/partial-kernel92-async/SNAPSHOT.md
@@ -0,0 +1,5 @@
+# Frozen public snapshot
+
+The discovery refresh retrieved 81 recent or updated PR conversations through PR507. Relevant newly downloaded heads are pinned in SOURCES.json. PR507 supplies the changed factory. PR506 and the updated PR473 provide comparable scheduling developments; PR477 provides research records. Its archive contains 46 missing changed-file paths and is not claimed complete. No missing file is a replay dependency.
+
+The snapshot was frozen before packaging. No claim is made to outrank moving heads after that snapshot, or larger bounds using disputed split-residual interfaces.
diff --git a/research/partial-kernel92-async/SOURCES.json b/research/partial-kernel92-async/SOURCES.json
new file mode 100644
index 0000000000..95e55066e6
--- /dev/null
+++ b/research/partial-kernel92-async/SOURCES.json
@@ -0,0 +1,92 @@
+{
+  "snapshot": "81 recent or updated conversation pages retrieved, frozen through PR507; no refresh during packaging. PR477 changed-file download had 46 missing paths and is not a complete source archive or a proof dependency.",
+  "direct": [
+    {
+      "pr": 496,
+      "head": "00cf70efd6a8637531deafef698157ca83e249ee",
+      "role": "whole-owner parent, invoice and assembly ancestry"
+    },
+    {
+      "pr": 484,
+      "head": "035845ce95f31d0a2dcfb42b8c8e13411271fa5f",
+      "role": "PR496 pinned gauge80-kernel42 parent, not newer moving head"
+    },
+    {
+      "pr": 493,
+      "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7",
+      "role": "unchanged cited R489 bit supplier"
+    },
+    {
+      "pr": 502,
+      "head": "4d30b8322184598e65e90a92389e17e1baedd9eb",
+      "role": "retiming transfer constructor and PR495 schedule fixture"
+    },
+    {
+      "pr": 501,
+      "head": "1dc056496fdbbc74073ed26d948a2dc235dbf356",
+      "role": "parallel retiming integration; credited, no duplicated gain"
+    },
+    {
+      "pr": 473,
+      "head": "628b454d3df00367d2d4f78de7d4eb9cbcbd47ca",
+      "role": "single-helper gauge withdrawal inspiration"
+    },
+    {
+      "pr": 507,
+      "head": "8d4444cf8a16d500cbb94add6e4fa8bcfb9c7d5e",
+      "role": "partial-own factory, 84-pivot reference and retiming map"
+    },
+    {
+      "pr": 505,
+      "head": "4ee769c8e28837482272b5f4742497da8e2fc9d4",
+      "role": "our prior complete-invocation asynchronous scheduling"
+    },
+    {
+      "pr": 506,
+      "head": "a4948baee6c7ea35323db74ff636620c6af2925a",
+      "role": "public asynchronous retiming comparison and portability feedback"
+    }
+  ],
+  "openai_math": {
+    "repository": "https://github.com/openai/math",
+    "revision": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
+    "status": "source inspection and mathematical adaptation; no new Lean audit"
+  },
+  "other_inspirations": [
+    497,
+    458,
+    442,
+    434,
+    433,
+    425,
+    417,
+    435,
+    440,
+    401,
+    408,
+    416,
+    370,
+    361,
+    315,
+    495,
+    503,
+    504
+  ],
+  "excluded": {
+    "494": "under-review split-residual interface not used",
+    "491": "withdrawn GL sampling argument not used",
+    "499": "larger claim inherits disputed split-residual interface; not used"
+  },
+  "related_updated": [
+    {
+      "pr": 473,
+      "head": "94b3c908fb7628142817d995155368aba2eae841",
+      "role": "new nonuniform scheduling comparison; earlier pinned gauge proposal remains a separate source"
+    },
+    {
+      "pr": 477,
+      "head": "2f23f46f1f9e4599168d40096fbacce4973a2978",
+      "role": "experiment log consulted to avoid repeating old searches"
+    }
+  ]
+}
diff --git a/research/partial-kernel92-async/code/assemble.py b/research/partial-kernel92-async/code/assemble.py
new file mode 100644
index 0000000000..de2a375d13
--- /dev/null
+++ b/research/partial-kernel92-async/code/assemble.py
@@ -0,0 +1,42 @@
+"""Two exact moment engines and strict outer composition of a new PR484 rehosting
+with the unchanged published PR493 bit supplier. Prepared by OpenAI Codex; arithmetic
+engines are pinned inherited PR361/Mercator and independent base-two code.
+Usage: assemble_candidate.py AUDIT_OUT PARENT_VARIANT HOSTED BIT_RESULT
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+import json,gzip,sys,hashlib,importlib.util
+O,V,H,B=map(Path,sys.argv[1:5]);sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+def load(n):
+ p=V/'work/pr361/code/engines'/(n+'.py');s=importlib.util.spec_from_file_location('candidate_'+n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,Other,Outer=[load(n)for n in ['moment','base_two_moment','outer']]
+owner=json.loads((O/'OWNERS-AND-PROFILE.json').read_text());inv=json.loads((O/'PREFIX-AND-INVOICE.json').read_text());host=json.loads((H/'HOSTED.json').read_text());bit=json.loads(B.read_text())["eleven"];P={int(r):n for r,n in owner['paid_profile'].items()};m,W=73,owner['live'];assert m*W-sum(r*n for r,n in P.items())==2496
+rc=M.certify(P,m,W,True);b=Q(rc['lower']);bp=Q(rc['upper']);assert bp-b==Q(1,10**24)
+fallback=32*m*m*sum(P.values());receipts=[]
+for z,accept in[(b,True),(bp,False)]:
+ ml,mh=M.moment(P,m,W,z,True);a,c=Other.moment(m,W,list(P.items()),z);d,e=Other.moment(m,W,[(1,fallback)],z);a+=d/10**16;c+=e/10**16
+ assert (mh<1 and c<1)if accept else(ml>1 and a>1)
+ receipts.append(dict(endpoint=str(z),mercator=[str(ml-1),str(mh-1)],base_two=[str(a-1),str(c-1)],accept=accept))
+# Reprice the cited unchanged bit histogram, clearly separate from bit operator verification.
+bitP={int(r):n for r,n in bit['profile'].items()};bitc=Q(bit['bit_lower']);bitnext=bitc+Q(1,10**24)
+for zz,accepted in [(bitc,True),(bitnext,False)]:
+ bl,bh=M.moment(bitP,78,9600,zz,True)
+ ol,oh=Other.moment(78,9600,list(bitP.items()),zz)
+ fl,fh=Other.moment(78,9600,[(1,32*78*78*sum(bitP.values()))],zz)
+ assert (bh<1 and oh+fh/10**16<1) if accepted else (bl>1 and ol+fl/10**16>1)
+c=Q(bit['bit_lower']);eta=beta=Q(1,10**18);grid=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24)
+assert 0<s<c and s<(1-beta)*b
+coeff=int(bit['bit']['charged_three_level_coefficient_bits']);row=max(20161,int(bit['bit']['row_coefficient']),inv['finite']['physical_row_coefficient']);chain=[Q(384599,10**10)];cuts=[]
+def ceil(x):return -(-x.numerator//x.denominator)
+for i in range(6):
+ old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+ cut=max(ceil(36/gap**2),ceil(2*(4+coeff)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+coeff);cuts.append(dict(gap=str(gap),cutoff_log2=str(cut)));chain.append(a)
+q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;kap=grid*((ticks.numerator-1)//ticks.denominator)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*row,25)}}
+a=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta);assert len(a['strict_constraints'])==47 and all(x>0 for x in a['strict_constraints'].values());controls=[]
+for name,k,e,be in [('next_grid',kap+grid,eta,beta),('zero_eta',kap,Q(0),beta),('zero_beta',kap,eta,Q(0)),('unit_beta',kap,eta,Q(1))]:
+ try:Outer.assembly(chain[-1],b,bridge,k,eta=e,beta=be)
+ except AssertionError:controls.append(name)
+ else:raise AssertionError(name)
+res=dict(status='PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY',complex_lower=str(b),complex_decimal=rc['lower'],next_b_rejected=str(bp),exact_moment_receipts=receipts,bit_lower=str(c),bit_result_sha256=sha(B),bit_template_sha256=bit['emitted_program_sha256'],bit_prefix_bits=bit['bit']['charged_prefix_bits'],bit_charged_three_level_coefficient_bits=coeff,external_row_allowance=row,kappa=str(kap),kappa_decimal=f'{float(kap):.18f}',binding_component='bit'if c<(1-beta)*b else'complex',strict_outer_constraints={k:str(v)for k,v in a['strict_constraints'].items()},outer_controls=controls,bootstrap=cuts,complex_template_sha256=host['template_sha256'],owner_audit_sha256=sha(O/'OWNERS-AND-PROFILE.json'),invoice_sha256=sha(O/'PREFIX-AND-INVOICE.json'),bit_scope='PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.',scope='Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately.')
+(O/'EXACT-ASSEMBLY.json').write_text(json.dumps(res,indent=2)+'\n');print(res['status'],'b',res['complex_decimal'],'kappa',res['kappa_decimal'],flush=True)
diff --git a/research/partial-kernel92-async/code/audit_async.py b/research/partial-kernel92-async/code/audit_async.py
new file mode 100644
index 0000000000..43642d1aa0
--- /dev/null
+++ b/research/partial-kernel92-async/code/audit_async.py
@@ -0,0 +1,149 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: VERIFIED_VARIANT POOLED_HOSTED OUT.json
+The local provider is read from VERIFIED_VARIANT, never from a baseline width histogram.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json');V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers']);assert V==120 and canon['h']==9; width=[9-len(canon['frames'][canon['start'][2*V+h]])for h in range(R)];prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=7680;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(120)]
+# Bind the selected provider's actual normalization recipes, including newly
+# selected entrance frames; a baseline recipe registry cannot silently survive.
+required_artifacts={'split-centres/CANONICAL-WORD.json.gz','split-centres/LOCAL-PROGRAMS.json.gz','split-centres/LOCAL-CHECKS.json','split-centres/RESIDUAL-ADAPTERS.json','work/complex-nine-native/DATA-PHASES.json'}
+assert required_artifacts <= set(summary['source_artifacts'])
+adapter_path=BASE/'split-centres/RESIDUAL-ADAPTERS.json'
+assert hashlib.sha256(adapter_path.read_bytes()).hexdigest()==parent['residual_adapter_sha256']
+adapters=read(adapter_path)['recipes']
+for h,w in enumerate(width):
+ if w<9:
+  f=canon['start'][240+h];a=adapters[str(f)]
+  assert a['frame']==f and a['vectors']==canon['frames'][f] and a['rank']==w and a['entrance_rank']==9-w
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_programs']==parent['local_programs']and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert len(t['calls'])==72 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','exact_local_clifford_recipe_sha256','residual_adapter_sha256','adapter_policy'):assert t[key]==parent[key]
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==72
+ all_local=[];perrep={r:[]for r in range(8)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<8 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   assert e==expected
+   assert 0<=e['time']<72 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[7680,7680]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,7680],charged_calls_per_cover=7680)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,7680],charged_calls_per_cover=7680)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time')}=={k:v for k,v in old.items()if k!='owners'}
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:240]==old['owners'][:240]
+  for h,(family,route)in enumerate(own[240:]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,960);fampair,sub=divmod(sub,240);side,port=divmod(sub,120)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*120+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(8)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*960+(2*pairs[i]+sides[i])*120+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*7680-mass;assert assert73==2496 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+reject('wrong call time',lambda q:q['calls'][0].__setitem__('time',71))
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][240:]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][240].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][240].__setitem__(0,7680))
+reject('unbound change of owner replica',lambda q:q['calls'][0]['owners'][240].__setitem__(0,(q['calls'][0]['owners'][240][0]+960)%7680))
+reject('omit complete invocation',lambda q:q['calls'].pop())
+reject('reorder invocation replicas',lambda q:q['calls'].__setitem__(0,q['calls'][1]))
+reject('interleave local invocations',lambda q:q.__setitem__('loop_order','interleaved local instructions'))
+reject('change local instruction stream',lambda q:q['local_programs']['forward'].pop())
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit spectator route',lambda q:enter(q).__setitem__(1,enter(q)[1][:3]))
+reject('overlap residual footprint',lambda q:q['calls'][0]['owners'][240][1].__setitem__(2,100))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('underpay idle remainder',lambda q:q['idle_children'][0].__setitem__('rank',0))
+reject('omit bridge touch',lambda q:q['execution_schedule'].pop(next(i for i,e in enumerate(q['execution_schedule'])if e['kind']=='bridge')))
+reject('remove one-owner rule',lambda q:q['hosting'].pop('max_helpers_per_physical_family_per_call'))
+reject('duplicate frozen role',lambda q:q['hosting']['pooled_slots'].__setitem__(1,q['hosting']['pooled_slots'][0]))
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=7680,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2496,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,widths=dict(sorted(Counter(width).items())),scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses unchanged source local program and normalized residual-wrapper identities; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=7680,physical=PHYSICAL,rank_mass=r['mass'],deficit=2496,hosted_residuals=HOSTED,banked_residuals=0,all_800_owners_per_call_distinct=True,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
diff --git a/research/partial-kernel92-async/code/audit_async_invoice.py b/research/partial-kernel92-async/code/audit_async_invoice.py
new file mode 100644
index 0000000000..568edf53a0
--- /dev/null
+++ b/research/partial-kernel92-async/code/audit_async_invoice.py
@@ -0,0 +1,100 @@
+"""Async PR484 scalar/prefix lowering and finite overcharge recount. OpenAI Codex.
+Reads emitted programs, canonical word and raw routes, importing no supplier code.
+Inherited all-size compiler admissibility is a condition, not inferred here.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import gzip,json,math,hashlib
+import sys
+O=Path(sys.argv[1]);V=Path(sys.argv[2]);HOSTED=Path(sys.argv[3])
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+w=read(V/'split-centres/CANONICAL-WORD.json.gz');p=read(V/'split-centres/LOCAL-PROGRAMS.json.gz');old=read(V/'split-centres/GLOBAL-TEMPLATE.json.gz');new=read(HOSTED/'GLOBAL-TEMPLATE.json.gz');integ=read(V/'split-centres/INTEGRATION.json');checks=read(V/'split-centres/LOCAL-CHECKS.json');prior=read(V/'split-centres/INDEPENDENT-REPLAY.json');owners=read(O/'OWNERS-AND-PROFILE.json')
+VV=w['v'];R=w['R'];N=2*VV+R;M=73;L=9;T=8;K=4
+assert VV==120 and w['h']==9
+PAYLOAD=512
+control=read(O/'ASYNC-AUDIT.json')
+raw=gzip.decompress((HOSTED/'GLOBAL-TEMPLATE.json.gz').read_bytes());th=hashlib.sha256(raw).hexdigest()
+assert th==control['complex_template_sha256']==owners['template_sha256']
+assert control['one_owner_per_complete_invocation'] and control['complete_invocations']==72
+assert new['local_programs']==old['local_programs'] and new['recipe']==old['recipe']
+assert Counter(c['orientation']for c in new['calls'])==Counter(c['orientation']for c in old['calls'])
+local={}
+for ori,evs in p.items():
+ rows={('L',i):{i:F(1)}for i in range(N)};env={('L',i):F(1)for i in range(N)};peak=F(1);real=macros=0;paid=Counter();workops=0
+ for e in evs:
+  if e[0]=='climb':paid[e[5]]+=1
+  elif e[0]=='center':paid[e[4]]+=1
+  elif e[0]=='scalar':
+   macros+=1;x=e[1];op=x[0];a=tuple(x[1]);count=0
+   if op=='clear':rows[a]={};env[a]=F(0);count=1
+   elif op=='copy':rows[a]=dict(rows[tuple(x[2])]);env[a]=env[tuple(x[2])];count=1
+   elif op=='scale':
+    q=F(x[2],x[3]);num,den=abs(q.numerator),q.denominator
+    assert num and num&(num-1)==0 and den&(den-1)==0
+    rows[a]={j:q*v for j,v in rows[a].items()};env[a]*=abs(q)
+    count=abs(num.bit_length()-den.bit_length())+int(q<0)
+   elif op=='add':
+    b=tuple(x[2]);q=F(x[3],x[4]);num,den=abs(q.numerator),q.denominator
+    assert a!=b and num>0 and den&(den-1)==0
+    # Lower actual coefficient to cleared Horner work. Every intermediate
+    # magnitude envelope is explicitly included, before denominator halvings.
+    acc=0;count=1
+    for i,ch in enumerate(bin(num)[2:]):
+     if i:acc*=2;count+=1;peak=max(peak,acc*env[b])
+     if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b])
+    v=F(acc)
+    for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b])
+    assert v==abs(q);count+=2 # signed accumulation and private work clear
+    env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{})
+    for j,z in list(rows[b].items()):
+     value=rr.get(j,F(0))+q*z
+     if value:rr[j]=value
+     else:rr.pop(j,None)
+    workops+=count
+   else:raise AssertionError(op)
+   real+=2*count;peak=max(peak,env[a])
+ assert all(not row for reg,row in rows.items()if reg[0]=='C')
+ for i in range(N):
+  expected={i:F(1)}
+  if ori=='forward'and 120<=i<240:expected[i-120]=F(1)
+  if ori=='backward'and i<120:expected[i+120]=F(-1)
+  assert rows['L',i]==expected
+ assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192
+ assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros']
+ assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()}
+ local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True)
+centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][240:]];enter=sum(x<9 for x in widths)
+children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3
+adapters=16*(macros+children+N+centres)+64*M
+primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler
+bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;assert sum(e['kind']=='bridge'for e in new['execution_schedule'])==T*bridges
+shifts=K*VV*T;moves=2*K*VV*T
+oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L
+scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls'])
+nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144
+outside=8*nonlocal_items+64*M
+pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP
+invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler'])
+# Independent hosted stock rebase, retaining the larger unhosted operation
+# overcharge; only the stock and mass in the common router/literal change.
+W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile']
+assert M*W-mass==2496 and P==W+R+centres+2
+rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex)
+r=M//2;group=2**(r*r)
+for i in range(1,r+1):group*=2**(2*i)-1
+stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2
+G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252+2*PAYLOAD;maxchild=max(map(int,profile))
+ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router<G,literal=literal<E,mass=B<2**100001,precision=32*M*B*B<C0,tape=2*B+18<C0,row=row<20161,halving=M*M>2*maxchild*maxchild)
+assert all(ineq.values())
+localbits=max(x['prefix_bits']for x in local.values());input_l2_bits=(M+1)//2
+bridge_sweeps=sum(e['kind']=='bridge'for e in new['execution_schedule'])
+required_prefix=localbits+input_l2_bits+len(new['calls'])+bridge_sweeps+4
+assert localbits==21 and bridge_sweeps==72 and required_prefix==206 and required_prefix<PAYLOAD
+assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged']
+assert new['physical']<=old['physical'] and new['live']<=old['live'] and not new['bank_padding']['families']
+out=dict(status='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',template_sha256=th,global_prefix_bits=required_prefix,charged_prefix_bits=PAYLOAD,complete_invocation_sweeps=72,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*PAYLOAD,local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound.')
+(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True)
+
+prefix=dict(status='PASS_ASYNC_GLOBAL_PREFIX',template_sha256=th,global_prefix_bits=required_prefix,retained_payload_bits=PAYLOAD,complete_invocation_cover_sweeps=len(new['calls']),bridge_factor_two_sweeps=bridge_sweeps,local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,primitive_arithmetic_margin_bits=4,controller_audit_sha256=hashlib.sha256((O/'ASYNC-AUDIT.json').read_bytes()).hexdigest(),proof=f'Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Distinct full orthogonal owner charts act by right-translation bijections on the retained cover group. Thus the maximum full-stream L2 norm grows by at most2per complete local cover sweep and individual bridge. All72local sweeps and72individual bridge sweeps are counted. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently replayed scalar/Horner envelope costs {localbits} bits, initial sup-to-L2 conversion {input_l2_bits} bits, primitive margin 4 bits: total {required_prefix} < {PAYLOAD}. All-size child/compiler and precision/tape interfaces remain inherited.')
+(O/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
diff --git a/research/partial-kernel92-async/code/audit_kernel_scalar.py b/research/partial-kernel92-async/code/audit_kernel_scalar.py
new file mode 100644
index 0000000000..4373bb9bd5
--- /dev/null
+++ b/research/partial-kernel92-async/code/audit_kernel_scalar.py
@@ -0,0 +1,55 @@
+"""Independent exact scalar witness for a selected complex kernel word.
+Uses immutable correct-word compensation for omission controls; no repaired
+compensation is silently supplied to a mutant. No physical-hosting claim.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+p=Path(__file__).resolve().parent
+path=Path(sys.argv[1]);selection=Path(sys.argv[2]);out=Path(sys.argv[3]);w=json.loads(gzip.decompress(path.read_bytes()));sel=json.loads(selection.read_text());n=240+w['report']['R']
+def ident():return[{r:Q(1)}for r in range(n)]
+def apply(e,rows):
+ if e[0]=='scale':
+  _,t,a,b,*_=e;q=Q(a,b);rows[t]={j:q*x for j,x in rows[t].items()};return
+ _,t,s,a,b,*_=e;q=Q(a,b)
+ for j,x in list(rows[s].items()):
+  z=rows[t].get(j,Q(0))+q*x
+  if z:rows[t][j]=z
+  else:rows[t].pop(j,None)
+def inv(e,dual=False):
+ e=copy.deepcopy(e)
+ if e[0]=='add':
+  e[3]*=-1
+  if dual:e[1],e[2]=e[2],e[1]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def replay(es):
+ rows=ident()
+ for e in es:apply(e,rows)
+ return rows
+main=w['A']+w['cut']+w['B'];mx=replay(main);dirty=[{}for _ in range(n)]
+for r in range(120,240):dirty[r]={j:x for j,x in mx[r].items()if j>=240}
+for e in w['precondition']:apply(e,dirty)
+comp=[]
+for r in range(120,240):
+ for j,x in sorted(dirty[r].items()):
+  assert not w.get('start_extra',{}).get(str(j)),('nonzero-frame compensation',j)
+  comp.append(['add',r,j,-x.numerator,x.denominator,[]])
+cleanup=[inv(e)for e in reversed(w['A']+w['B'])if not 120<=e[1]<240]
+assert[e[:-1]for e in cleanup]==[e[:-1]for e in w['cleanup']]
+program=w['precondition']+comp+main+cleanup;expected=ident()
+for t in range(120):expected[120+t][t]=Q(1)
+assert replay(program)==expected
+back=ident()
+for t in range(120):back[t][120+t]=Q(-1)
+assert replay([inv(e,True)for e in program])==back
+controls={}
+for cl in sel['kernel']:
+ for h in cl['pivots']:
+  aa=[e for e in w['A']if not(e[0]=='add'and e[2]==240+h and e[1]>=240 and e[-1]==cl['E'])]
+  assert len(aa)<len(w['A']);cc=[inv(e)for e in reversed(aa+w['B'])if not 120<=e[1]<240]
+  assert replay(w['precondition']+comp+aa+w['cut']+w['B']+cc)!=expected
+  controls[str(h)]='REJECTED_OMITTED_KERNEL_CORRECTION'
+r=dict(status='PASS_EXACT_RATIONAL_FORWARD_AND_INVERSE_TRANSPOSE',word_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),selection_sha256=hashlib.sha256(selection.read_bytes()).hexdigest(),columns_each_orientation=n,compensations=len(comp),program_operations=len(program),kernel_pivots=len(controls),controls=controls,scope='Exact local scalar identity and preserved frame-zero compensation; physical owner routing, complete invoice and outer kappa separate.')
+out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],n,len(controls))
diff --git a/research/partial-kernel92-async/code/build_kernel92.py b/research/partial-kernel92-async/code/build_kernel92.py
new file mode 100644
index 0000000000..f5e68e01f9
--- /dev/null
+++ b/research/partial-kernel92-async/code/build_kernel92.py
@@ -0,0 +1,42 @@
+"""Reconstruct the selected 92-pivot partial-own complex word.
+Apache-2.0. Prepared with OpenAI Codex assistance; retain PR507/484 notices.
+Usage: python -B build_kernel92.py GK_CODE PARTIAL_BASE KERNEL84_SELECTION
+       RETIME_MAP KERNEL92_SELECTION NEW_OUTPUT_DIR
+No discovery search runs. Actual physical allocation is independently checked.
+"""
+from pathlib import Path
+import json,gzip,sys,copy,hashlib
+from collections import Counter
+if not __debug__:raise RuntimeError('Assertions must remain enabled')
+code,basefile,s84file,mapfile,s92file,out=map(Path,sys.argv[1:]);assert not out.exists();sys.dont_write_bytecode=True;sys.path.insert(0,str(code));import gk_word as g
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+base=read(basefile);s84=read(s84file);s92=read(s92file);fm=read(mapfile)
+assert base['report']['R']==560 and len(base['A'])==2680 and len(base['B'])==840
+assert sum(len(c['pivots'])for c in s84['kernel'])==84
+assert sum(len(c['pivots'])for c in s92['kernel'])==92
+wanted=copy.deepcopy(s84['gauge'])
+for h in ['540','541','542','543']:wanted[h]=[408,102]
+assert s92['gauge']==wanted
+w84=g.build(base,s84);r=copy.deepcopy(w84)
+for part in ['A','B']:
+ seen=set()
+ for i,old,new in fm[part]:
+  assert i not in seen and r[part][i][-1]==old,(part,i);seen.add(i);r[part][i][-1]=new
+ assert [e[:-1]for e in r[part]]==[e[:-1]for e in w84[part]]
+assert r['A'][:671]==w84['A'][:671]
+assert g.profile(r)==Counter({int(k):v for k,v in fm['expected_local_profile'].items()})
+ret=copy.deepcopy(base)
+for part in ['A','B']:
+ tail=r[part][-len(base[part]):];assert [e[:-1]for e in tail]==[e[:-1]for e in base[part]];ret[part]=copy.deepcopy(tail)
+ret['cleanup']=[g.inverse(e,g.FULL)for e in reversed(ret['A']+ret['B'])if not 120<=e[1]<240]
+w=g.build(ret,s92);H=g.profile(w);widths=g.widths_of(w)
+assert H=={1:2539,2:160,3:530,4:88,5:298,6:68,7:1,8:17}
+assert Counter(widths)=={7:18,8:154,9:388}
+# Normalize only the established inherited floating display fields and redundant R.
+norm=copy.deepcopy(w);assert norm.get('R',norm['report']['R'])==norm['report']['R']==560;norm.pop('R',None)
+for k in ['complex_coarse_float','gain_percent_float']:norm['report'].pop(k,None)
+semantic=hashlib.sha256(json.dumps(norm,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+assert semantic=='c6e758b324d3566e8443b3fd3d739c4d01e1928eadbee40f5c36973404b0640b'
+out.mkdir(parents=True);(out/'FULL-WORD.json.gz').write_bytes(g.dump(w));(out/'SELECTION.json').write_text(json.dumps(s92,indent=2)+'\n');(out/'RETIMED-BASE.json.gz').write_bytes(g.dump(ret))
+receipt=dict(status='PASS_EXACT_SOURCE_BOUND_KERNEL92_RECONSTRUCTION',sources={label:hashlib.sha256(path.read_bytes()).hexdigest()for label,path in [('partial_base',basefile),('kernel84_selection',s84file),('frame_map',mapfile),('kernel92_selection',s92file),('gk_word.py',code/'gk_word.py'),('gk_common.py',code/'gk_common.py')]},normalized_word_sha256=semantic,word_sha256=hashlib.sha256((out/'FULL-WORD.json.gz').read_bytes()).hexdigest(),profile=dict(H),widths=dict(Counter(widths)),widths_ordered=widths,pivots=92,entrance_rank=sum(9-x for x in widths),scope='Exact local source construction; arbitrary-dirt scalar, physical phases/owners and final outer assembly checked separately.')
+(out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n');print(receipt['status'])
diff --git a/research/partial-kernel92-async/code/construct_partial.py b/research/partial-kernel92-async/code/construct_partial.py
new file mode 100644
index 0000000000..69500f6513
--- /dev/null
+++ b/research/partial-kernel92-async/code/construct_partial.py
@@ -0,0 +1,309 @@
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        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 inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+def alloc():
+    n=len(cur);cur.append(());rows.append({});return n
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# All original-source loads precede source borrowing.
+own={};fl={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    for s in ids:
+        own[s]=alloc()
+
+packets={};retired={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)})
+    for event_index,(e,F) in enumerate(zip(z['events'],z['event_frames'])):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        # 16 source copies and 24 two-shear operations precede face assembly.
+        if event_index==39:
+            for parity in (0,1):
+                tet=sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity)
+                matching=[[(tet[0],tet[1]),(tet[2],tet[3])],[(tet[0],tet[2]),(tet[1],tet[3])],[(tet[0],tet[3]),(tet[1],tet[2])]][(1,1)[parity]]
+                for pair in matching:
+                    rs=sorted(r for r in mp.values() if set(rows[r])==set(pair))
+                    assert len(rs)==2,(pair,rs)
+                    for s,r in zip(pair,rs):
+                        assert len(cur[r])==2
+                        add(own[s],r,1,cur[r])
+    keys=[(p,epsilon) for p in it.combinations(c,2) for epsilon in (-1,1)]
+    for key,(reg,alpha) in zip(keys,z['outputs']):
+        a=mp[reg];alpha=Q(alpha);F=cur[a]
+        b=alloc();add(b,a,1,F)
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,rr in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(rr,alpha)
+    retired[c]=[mp[r] for r in z['dead_registers']]
+
+# Four coordinate sums per code block, reconstructed in the retired register
+# stock at its legal rank-four frame. The remaining eight rows retain a basis.
+block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];regs=retired[c];F=basis([P[s] for s in ids])
+    assert len(regs)==12 and len(F)==4
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    assert all(not rows[r] for r in regs[8:])
+    for i,reg in zip(c,regs[8:]):
+        for j,s in enumerate(ids):add(reg,regs[j],R[s][i],F)
+        block_totals[c,i]=reg
+
+# Eight global coordinate sums, with a single copy each for the centers. The
+# other copy is exactly the correction needed by the eight frame-line targets.
+global_totals={};centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    global_totals[i]=a
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+
+# Own-block and coordinate-frame corrections, one stream per code target.
+own_out={};tetrads={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        sources=tet[1-parity];xs=[own[s] for s in sources]
+        F=basis([P[s] for s in sources])
+        # Current own registers are an invertible pair-partial basis T*x.
+        T=[[rows[x].get(s,Q(0)) for s in sources] for x in xs]
+        n=len(T);aug=[r+[Q(i==j) for j in range(n)] for i,r in enumerate(T)]
+        for col in range(n):
+            k=next(i for i in range(col,n) if aug[i][col]);aug[k],aug[col]=aug[col],aug[k]
+            q=aug[col][col];aug[col]=[x/q for x in aug[col]]
+            for i in range(n):
+                if i!=col:
+                    q=aug[i][col];aug[i]=[a-q*b for a,b in zip(aug[i],aug[col])]
+        inv=[r[n:] for r in aug]
+        M=[[sum(Q(G[t][s])*inv[k][j] for k,s in enumerate(sources)) for j in range(n)] for t in targets]
+        assert all(q.denominator&(q.denominator-1)==0 for row in M for q in row)
+        linear(xs,M,F)
+        for t,x in zip(targets,xs):own_out[t]=x
+
+# Cross-block M packets, shared by four targets, then two-output pair transforms.
+Ms={};consumers=defaultdict(list);pairs=[]
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for epsilon in (-1,1):
+            (a,alpha),(b,beta)=[packets[d,p,epsilon,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,epsilon]=(a,alpha)
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    for parity,tet in enumerate(tetrads[c]):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in tet:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                assert len(ts)==2;a,b=sorted(ts)
+                e2=R[a][q[0]]*R[a][q[1]]
+                assert e2==R[b][q[0]]*R[b][q[1]]
+                keys=[(c,p,eps),(c,q,e2)];pid=len(pairs)
+                selected=(pi==parity)  # different first partitions in the two tetrads
+                pairs.append({'targets':(a,b),'keys':keys,'selected':selected,
+                              'matrix':[[R[t][p[0]],R[t][q[0]]] for t in (a,b)]})
+                for key in keys:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    a,alpha=Ms[key];ordinary=[i for i in uses if not pairs[i]['selected']]
+    for j,pid in enumerate(ordinary):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+
+assert len(cur)-240==560,(len(cur)-240)
+
+# The selected target pairs borrow Y as the first packet destination. Their
+# two-shear output basis is compensated at frame zero and in the scatter table.
+phase=B;selected=[];output_basis=[]
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=Ms[key1],Ms[key2]
+    add(v+t,a,-Q(mat[0][0],2)*alpha,cur[a])
+    add(v+u,b,-Q(mat[0][1],2)*beta,cur[b])
+    selected.append((pid,t,u,mat))
+for pid,t,u,mat in selected:
+    F=basis(cur[v+t]+cur[v+u]);assert all((P[s]&p).bit_count()%2==0 for s in (t,u) for p in F)
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F)
+    output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+for t,r in own_out.items():add(v+t,r,-Q(1,2),hyper(P[t]))
+
+side=[dict(rows[v+t]) for t in range(v)]
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert side[t]==expected,('side identity',t)
+
+# Correct the eight-center scatter through the inverse two-output basis.
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8;by['c'][8]+=8;by['c'][1]+=8
+n=len(cur);Rcount=n-240
+assert sum(r*z for r,z in H.items())==9*Rcount+240*8+72
+
+def apply(event,matrix):
+    if event[0]=='add':
+        _,t,s,a,b,*_=event;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=event;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e,F=None):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    if F is not None:e[-1]=list(F)
+    return e
+cut=[]
+for t,rr in enumerate(scatter):
+    for i,q in enumerate(rr):
+        if q:cut.append(['add',v+t,centers[i],q.numerator,q.denominator,None])
+cleanup=[inverse(e,FULL) for e in reversed(A+B) if not v<=e[1]<2*v]
+
+# Exact clean replay checks the changed decoder and restored source basis.
+matrix=[{r:Q(1)} if r<v else {} for r in range(n)]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(n))
+
+m=73;T=8;L=9;W=7680+L*Rcount;globalH=Counter({r:z*L*T for r,z in H.items()})
+for r in (16,8,32,8,48,8,48,32,16):globalH[r]+=240*T
+globalH[1]+=L*Rcount
+assert m*W-sum(r*z for r,z in globalH.items())==2496
+# Discovery-only approximate display annotations use explicit left-to-right
+# accumulation for stable results across Python sum() implementations. These
+# floats are not acceptance inputs; complete profiles receive exact pricing.
+low,high=0.,.003
+for _ in range(60):
+    q=(low+high)/2
+    moment=0.0
+    for r,z in globalH.items():moment+=r*z/(m*W)*(m/r)**q
+    moment+=32*m*sum(globalH.values())/(10**16*W)*m**q
+    if moment<1:low=q
+    else:high=q
+report={'status':'EXACT_CLEAN_FULL_WORD_DISCOVERY_NOT_ADMITTED',
+        'h':9,'v':120,'R':Rcount,'cst':72,'local_profile':dict(sorted(H.items())),
+        'global_profile':dict(sorted(globalH.items())),'m':m,'W':W,
+        'complex_coarse_float':(low+high)/2,'baseline_b':0.000999388595603943,
+        'gain_percent_float':100*((low+high)/2/0.000999388595603943-1),
+        'scalar_operations_A':len(A),'scalar_operations_B':len(B),
+        'borrowed_output_pairs':len(output_basis),'centre_ranks':list(map(len,center_frames)),'source_columns_exact':120,
+        'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'retained_center_rows_exact':True,
+        'remaining':['full arbitrary-dirt program and independent replay','exact complex phases and global template','finite invoice and coefficient lowering','two rational prices and outer assembly']}
+full={'report':report,'ports':P,'root_lines':R,'A':A,'B':B,'centers':centers,'scatter':[[str(x) for x in r] for r in scatter],
+      'cut':cut,'cleanup':cleanup,'precondition':precondition,'center_frames':center_frames}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(full,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'FULL-DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/partial-kernel92-async/code/emit_async.py b/research/partial-kernel92-async/code/emit_async.py
new file mode 100644
index 0000000000..9ffe035202
--- /dev/null
+++ b/research/partial-kernel92-async/code/emit_async.py
@@ -0,0 +1,89 @@
+"""OpenAI Codex whole-owner cross-replica derivative of pinned PR484.
+CLI: SOURCE484_PACKAGE VERIFIED_VARIANT ASYNC-OWNERS.json.gz ASYNC-PLAN.json OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+SOURCE,BASE,MAP,PLAN,OUT=map(lambda p:Path(p).resolve(),sys.argv[1:6]);assert not OUT.exists();OUT.mkdir(parents=True)
+sys.path.insert(0,str(SOURCE/'code'));import onehost_gk as OH
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+plan=read(PLAN);call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==72;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);DATA=7680;T=8;V=120;M=73;R=560
+assert(len(roles),len(canon['start']),len(ph['recipes']))==(40320,800,120)
+widths=[9-len(canon['frames'][canon['start'][240+h]])for h in range(R)];assert widths==plan['baseline_widths'], 'source-bound selected provider widths'
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==widths[h] and 0<=orp<T
+ assert f==orp*960+(2*pairs[i]+side[i])*120+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:240]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==800 and all(f<DATA for f,r in c['owners'])
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in checks[c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*960+(2*pairs[i]+side[i])*120+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==2496
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='complex484-asynchronous-replica-whole-owner-v1',live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes()).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert t['local_programs']==parent['local_programs']
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',template_sha256=hashlib.sha256(raw).hexdigest(),parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),rank_mass=sum(r*n for r,n in paid.items()),deficit=2496,maxchild=max(paid),hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),source_artifacts={p.relative_to(BASE).as_posix():hashlib.sha256(p.read_bytes()).hexdigest()for p in [BASE/'split-centres/CANONICAL-WORD.json.gz',BASE/'split-centres/LOCAL-PROGRAMS.json.gz',BASE/'split-centres/LOCAL-CHECKS.json',BASE/'split-centres/RESIDUAL-ADAPTERS.json',BASE/'work/complex-nine-native/DATA-PHASES.json']},scope='New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/partial-kernel92-async/code/run_portable.py b/research/partial-kernel92-async/code/run_portable.py
new file mode 100644
index 0000000000..dcfe7128e1
--- /dev/null
+++ b/research/partial-kernel92-async/code/run_portable.py
@@ -0,0 +1,15 @@
+"""Run one retained verifier with UTF-8/LF text outputs on every platform.
+This changes output serialization only; no mathematical operation is replaced.
+"""
+from pathlib import Path
+import runpy,sys
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+original_write_text=Path.write_text
+def write_text_lf(self,data,encoding=None,errors=None,newline=None):
+    return original_write_text(self,data,encoding=encoding or 'utf-8',errors=errors,newline='\n')
+Path.write_text=write_text_lf
+script=Path(sys.argv[1]).resolve()
+sys.argv=sys.argv[1:]
+sys.path.insert(0,str(script.parent))
+runpy.run_path(str(script),run_name='__main__')
diff --git a/research/partial-kernel92-async/evidence/ASYNC-AUDIT.json b/research/partial-kernel92-async/evidence/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..f80e9bf1d7
--- /dev/null
+++ b/research/partial-kernel92-async/evidence/ASYNC-AUDIT.json
@@ -0,0 +1,60 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "complex_template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "complex_live": 7680,
+  "complex_profile": {
+    "1": 182808,
+    "2": 11520,
+    "3": 41233,
+    "4": 6336,
+    "5": 25173,
+    "6": 4896,
+    "7": 195,
+    "8": 1224,
+    "16": 1,
+    "32": 1,
+    "39": 1,
+    "48": 766
+  },
+  "complex_hosted_residuals": 40320,
+  "physical": 8258,
+  "rank_mass": 558144,
+  "deficit": 2496,
+  "entering_helper_roles": 12384,
+  "cross_replica_helper_roles": 30804,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 40320,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 3024,
+  "actual_sigma_stream_sha256": "7e47b83098762619fea0e3c018d49245810b198c3b1f1c6ba7cfdb02a2d94638",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 7682,
+  "mutations_rejected": [
+    "wrong call time",
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "unbound change of owner replica",
+    "omit complete invocation",
+    "reorder invocation replicas",
+    "interleave local invocations",
+    "change local instruction stream",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit spectator route",
+    "overlap residual footprint",
+    "omit idle remainder",
+    "underpay idle remainder",
+    "omit bridge touch",
+    "remove one-owner rule",
+    "duplicate frozen role",
+    "understate physical reserve"
+  ],
+  "widths": {
+    "7": 18,
+    "8": 154,
+    "9": 388
+  },
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses unchanged source local program and normalized residual-wrapper identities; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/partial-kernel92-async/evidence/EXACT-ASSEMBLY.json b/research/partial-kernel92-async/evidence/EXACT-ASSEMBLY.json
new file mode 100644
index 0000000000..f7d322e865
--- /dev/null
+++ b/research/partial-kernel92-async/evidence/EXACT-ASSEMBLY.json
@@ -0,0 +1,127 @@
+{
+  "status": "PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY",
+  "complex_lower": "139346249534416215349/100000000000000000000000",
+  "complex_decimal": "0.00139346249534416215349",
+  "next_b_rejected": "1393462495344162153491/1000000000000000000000000",
+  "exact_moment_receipts": [
+    {
+      "endpoint": "139346249534416215349/100000000000000000000000",
+      "mercator": [
+        "-54703880107433440999858104301338860500009803/26959946667150639794667015087019630673637144422540572481103610249216",
+        "-54703880107433440999858104301338860500009801/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
+        "-253635052727043702191/125000000000000000000000000000000000000000000",
+        "-20290794218163496175163/10000000000000000000000000000000000000000000000"
+      ],
+      "accept": true
+    },
+    {
+      "endpoint": "1393462495344162153491/1000000000000000000000000",
+      "mercator": [
+        "3955425413759435303055253810238845835062729/3369993333393829974333376885877453834204643052817571560137951281152",
+        "15821701655037741212221015240955383340250917/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "2934296445549106059021/2500000000000000000000000000000000000000000000",
+        "5868597891098212118101/5000000000000000000000000000000000000000000000"
+      ],
+      "accept": false
+    }
+  ],
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "bit_result_sha256": "3494ba83280cc86548fe0cc6695c50d23e6b6ffca85aeb1a33337c1196e280cb",
+  "bit_template_sha256": "e37b52e4861c39154b5891460fb45df8651c92cd68961078f8f06596f057c822",
+  "bit_prefix_bits": 2176,
+  "bit_charged_three_level_coefficient_bits": 6464,
+  "external_row_allowance": 20161,
+  "kappa": "1391523459591829/1000000000000000000",
+  "kappa_decimal": "0.001391523459591829",
+  "binding_component": "complex",
+  "strict_outer_constraints": {
+    "bit_positive": "139346249534416214217553383528807406988201842235985269562593616994374883176325351545829800050429344047484846426471962634480675851340231000985418679656055660447565031173172526170877892483672155340646824791401221649410742227102573112433696521168170535806582087578860429744142643857309949/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "1131446616471192593011798157764014730437406383005625116823674648454170199949570655952515153573528037365519324148659768999014581320343944339552434968826827473829122107516327844659353175208598778350589257772897426887566303478831829464193417912421139570255857356142690051/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "2985653750465583784651/100000000000000000000000",
+    "beta_positive": "1/1000000000000000000",
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+    {
+      "gap": "51088277973342530064709504142360074753095393237306993768328581701371906956085334590272978494013829595435240096477880475149811069460617262201940246023188989863375509502243781694754392215148251/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1379303925895103678503547601120"
+    },
+    {
+      "gap": "7118959930757007712774322746735797722169090993444286417182192513622708903511320575381343782299321394696018700852959327704134175684211981733197710759142043227679727880703224338037250835232500394362704238819472564425224153623295401/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "710345124099563582273849559553093478"
+    },
+    {
+      "gap": "992000366936776377662798157764014730437406383005625116823674648454170199949570655952515153573528037365519324148659768999014581320343944339552434968826827473829122107516327844659353175208598778350589257772897426887566303478831829464193417912421139570255857356142690051/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "365829594086429480022029191003211743321777"
+    }
+  ],
+  "complex_template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "owner_audit_sha256": "031a05f7394934f17b02b4f758d905b90100b614530888dfa13c2f731f9fc396",
+  "invoice_sha256": "953b07409f98216378ea5b95a3194d09b6b26c5847568e824c467ddded71e158",
+  "bit_scope": "PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.",
+  "scope": "Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately."
+}
diff --git a/research/partial-kernel92-async/evidence/INDEPENDENT-NOMINATION-REVIEW.json b/research/partial-kernel92-async/evidence/INDEPENDENT-NOMINATION-REVIEW.json
new file mode 100644
index 0000000000..0148856744
--- /dev/null
+++ b/research/partial-kernel92-async/evidence/INDEPENDENT-NOMINATION-REVIEW.json
@@ -0,0 +1,35 @@
+{
+  "status": "PASS_INDEPENDENT_LITERAL_OWNER_AND_PROFILE_REVIEW",
+  "calls": 72,
+  "roles": 40320,
+  "remainder_profile": {
+    "3": 3073,
+    "5": 3717,
+    "7": 123,
+    "16": 1,
+    "32": 1,
+    "39": 1,
+    "48": 766
+  },
+  "profile": {
+    "1": 182808,
+    "2": 11520,
+    "3": 41233,
+    "4": 6336,
+    "5": 25173,
+    "6": 4896,
+    "7": 195,
+    "8": 1224,
+    "16": 1,
+    "32": 1,
+    "39": 1,
+    "48": 766
+  },
+  "deficit": 2496,
+  "source_hashes": {
+    "KERNEL92-FOCUS-O6.json": "7a30db32ad8fc54bd5e7060febf4f8ff7747b8287c057ae926efc736e2b9f800",
+    "KERNEL92-OWNERS.json.gz": "9c6bd9793db16d599d3c7f9493350d2359681d19eb170ec7239e8d568090e745",
+    "CONSTRUCTION.json": "a1210ff603b5d73330d9f94e718101c808ebddfd0fb03336593a87b3cd976108"
+  },
+  "scope": "Exact nomination-level chronology, original child lifetimes, complete-family uniqueness, disjoint pending-coordinate offsets, source-bound widths, all remainders. Full physical maps, phases and scalar invoice remain separate checks."
+}
diff --git a/research/partial-kernel92-async/evidence/KERNEL-SCALAR.json b/research/partial-kernel92-async/evidence/KERNEL-SCALAR.json
new file mode 100644
index 0000000000..8289fcf492
--- /dev/null
+++ b/research/partial-kernel92-async/evidence/KERNEL-SCALAR.json
@@ -0,0 +1,104 @@
+{
+  "status": "PASS_EXACT_RATIONAL_FORWARD_AND_INVERSE_TRANSPOSE",
+  "word_sha256": "92d156d50398b06e28231b42ff56e878a391d73a963d033d9e1888c8c081f143",
+  "selection_sha256": "c8e6400a8f4780be3aef6a643d856f956e97447161d33493ae651070e2f033fb",
+  "columns_each_orientation": 800,
+  "compensations": 12094,
+  "program_operations": 19800,
+  "kernel_pivots": 92,
+  "controls": {
+    "46": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "43": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "158": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "214": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "103": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "65": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "271": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "215": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "510": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "527": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "24": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "87": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "467": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "26": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "83": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "68": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "518": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "159": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "14": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "8": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "85": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "40": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "508": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "517": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "361": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "416": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "472": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "98": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "66": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "30": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "161": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "56": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "52": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "383": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "36": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "530": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "51": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "521": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "162": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "35": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "160": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "32": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "54": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "468": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "529": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "528": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "34": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "76": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "59": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "520": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "90": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "512": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "514": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "93": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "94": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "217": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "16": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "515": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "95": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "216": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "0": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "3": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "105": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "212": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "505": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "6": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "213": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "106": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "108": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "104": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "332": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "380": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "329": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "502": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "498": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "381": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "437": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "445": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "441": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "384": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "324": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "436": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "156": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "157": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "446": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "334": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "474": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "475": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "132": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "133": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "244": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "189": "REJECTED_OMITTED_KERNEL_CORRECTION"
+  },
+  "scope": "Exact local scalar identity and preserved frame-zero compensation; physical owner routing, complete invoice and outer kappa separate."
+}
diff --git a/research/partial-kernel92-async/evidence/OWNERS-AND-PROFILE.json b/research/partial-kernel92-async/evidence/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..a830b54213
--- /dev/null
+++ b/research/partial-kernel92-async/evidence/OWNERS-AND-PROFILE.json
@@ -0,0 +1,38 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "paid_profile": {
+    "1": 182808,
+    "2": 11520,
+    "3": 41233,
+    "4": 6336,
+    "5": 25173,
+    "6": 4896,
+    "7": 195,
+    "8": 1224,
+    "16": 1,
+    "32": 1,
+    "39": 1,
+    "48": 766
+  },
+  "live": 7680,
+  "physical": 8258,
+  "rank_mass": 558144,
+  "deficit": 2496,
+  "hosted_residuals": 40320,
+  "banked_residuals": 0,
+  "all_800_owners_per_call_distinct": true,
+  "actual_helper_owner_charts": 40320,
+  "actual_73column_sigmas": 3024,
+  "cross_replica_helper_roles": 30804,
+  "explicit_idle_remainder_children": 7682,
+  "source_idle_children_charged": 17280,
+  "source_artifacts": {
+    "split-centres/CANONICAL-WORD.json.gz": "c57e6494e047e924a02051c0401778e967c16bf2d7724441b74f721fd9d6e5ef",
+    "split-centres/LOCAL-PROGRAMS.json.gz": "ad5526bcf6d93f0d7ca6bbfd0f4d971406f0e879b49d6b439e3d93eb24e96f56",
+    "split-centres/LOCAL-CHECKS.json": "fc8d796e3be50be7d7ec270ecc4e5bc4d600d7eef0182b77ac84e3793b7bbc84",
+    "split-centres/RESIDUAL-ADAPTERS.json": "0e19e861b824ae229be801b98a64b4dd476618adf57c582782fcec0c97ada147",
+    "work/complex-nine-native/DATA-PHASES.json": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a"
+  },
+  "controller_audit_sha256": "2b501debc401c623615ff4429cdf11a82e0b5ea572c1709c5cdedb013550ed26"
+}
diff --git a/research/partial-kernel92-async/evidence/PORTABLE-REPLAY.json b/research/partial-kernel92-async/evidence/PORTABLE-REPLAY.json
new file mode 100644
index 0000000000..af3f21362d
--- /dev/null
+++ b/research/partial-kernel92-async/evidence/PORTABLE-REPLAY.json
@@ -0,0 +1,78 @@
+{
+  "status": "PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE",
+  "kappa": "1391523459591829/1000000000000000000",
+  "kappa_decimal": "0.001391523459591829",
+  "complex_lower": "139346249534416215349/100000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "strict_constraints": 47,
+  "scope": "New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.",
+  "stages": [
+    {
+      "stage": "partial-factory",
+      "exit": 0,
+      "seconds": 0.6089999999967404
+    },
+    {
+      "stage": "construct-kernel92",
+      "exit": 0,
+      "seconds": 2.062999999994645
+    },
+    {
+      "stage": "kernel-scalar-controls",
+      "exit": 0,
+      "seconds": 26.796999999991385
+    },
+    {
+      "stage": "scalar",
+      "exit": 0,
+      "seconds": 2.2969999999913853
+    },
+    {
+      "stage": "emit-local",
+      "exit": 0,
+      "seconds": 1.3440000000118744
+    },
+    {
+      "stage": "phases",
+      "exit": 0,
+      "seconds": 199.21799999999348
+    },
+    {
+      "stage": "adapters",
+      "exit": 0,
+      "seconds": 1.0160000000032596
+    },
+    {
+      "stage": "parent-integration",
+      "exit": 0,
+      "seconds": 1.2179999999934807
+    },
+    {
+      "stage": "parent-replay",
+      "exit": 0,
+      "seconds": 9.51600000000326
+    },
+    {
+      "stage": "emit-async",
+      "exit": 0,
+      "seconds": 4.375
+    },
+    {
+      "stage": "independent-async",
+      "exit": 0,
+      "seconds": 25.030999999988126
+    },
+    {
+      "stage": "invoice",
+      "exit": 0,
+      "seconds": 2.360000000015134
+    },
+    {
+      "stage": "two-moments-assembly",
+      "exit": 0,
+      "seconds": 0.6719999999913853
+    }
+  ],
+  "package_manifest_sha256": "4d30fb450a7a17f0ee06b340c2d74b5733e527659f1f298ceb4a9c622c940256"
+}
diff --git a/research/partial-kernel92-async/evidence/PREFIX-AND-INVOICE.json b/research/partial-kernel92-async/evidence/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..c212e28678
--- /dev/null
+++ b/research/partial-kernel92-async/evidence/PREFIX-AND-INVOICE.json
@@ -0,0 +1,69 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "global_prefix_bits": 206,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "local": {
+    "backward": {
+      "events": 25330,
+      "macros": 19848,
+      "real_component_primitives": 222442,
+      "prefix_l1": "1048913",
+      "prefix_bits": 21,
+      "coefficient_work_primitive_count": 110377,
+      "all_exact_columns": 800,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    },
+    "forward": {
+      "events": 25330,
+      "macros": 19848,
+      "real_component_primitives": 222346,
+      "prefix_l1": "57339",
+      "prefix_bits": 16,
+      "coefficient_work_primitive_count": 110313,
+      "all_exact_columns": 800,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    }
+  },
+  "entering_helpers": 172,
+  "entrance_rank": 190,
+  "local_adapters": 394512,
+  "local_primitive_bound": 10231406986474,
+  "wrapper_elementary_factors_charged": 3566592,
+  "compiler": 25934336,
+  "unhosted_pervertex": 1520250460705152,
+  "hosted_rebased_pervertex": 1520250460372512,
+  "conservative_pervertex_used": 1520250460705152,
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7984,
+    "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": "Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound."
+}
diff --git a/research/partial-kernel92-async/evidence/RESULT.json b/research/partial-kernel92-async/evidence/RESULT.json
new file mode 100644
index 0000000000..744d930acb
--- /dev/null
+++ b/research/partial-kernel92-async/evidence/RESULT.json
@@ -0,0 +1,78 @@
+{
+  "status": "PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE",
+  "kappa": "1391523459591829/1000000000000000000",
+  "kappa_decimal": "0.001391523459591829",
+  "complex_lower": "139346249534416215349/100000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "strict_constraints": 47,
+  "scope": "New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.",
+  "stages": [
+    {
+      "stage": "partial-factory",
+      "exit": 0,
+      "seconds": 0.6559999999881256
+    },
+    {
+      "stage": "construct-kernel92",
+      "exit": 0,
+      "seconds": 2.10999999998603
+    },
+    {
+      "stage": "kernel-scalar-controls",
+      "exit": 0,
+      "seconds": 27.312000000005355
+    },
+    {
+      "stage": "scalar",
+      "exit": 0,
+      "seconds": 2.360000000015134
+    },
+    {
+      "stage": "emit-local",
+      "exit": 0,
+      "seconds": 1.4219999999913853
+    },
+    {
+      "stage": "phases",
+      "exit": 0,
+      "seconds": 199.60899999999674
+    },
+    {
+      "stage": "adapters",
+      "exit": 0,
+      "seconds": 1.0469999999913853
+    },
+    {
+      "stage": "parent-integration",
+      "exit": 0,
+      "seconds": 1.3440000000118744
+    },
+    {
+      "stage": "parent-replay",
+      "exit": 0,
+      "seconds": 9.421999999991385
+    },
+    {
+      "stage": "emit-async",
+      "exit": 0,
+      "seconds": 4.594000000011874
+    },
+    {
+      "stage": "independent-async",
+      "exit": 0,
+      "seconds": 26.187000000005355
+    },
+    {
+      "stage": "invoice",
+      "exit": 0,
+      "seconds": 2.1710000000020955
+    },
+    {
+      "stage": "two-moments-assembly",
+      "exit": 0,
+      "seconds": 0.6410000000032596
+    }
+  ],
+  "package_manifest_sha256": null
+}
diff --git a/research/partial-kernel92-async/evidence/TRANSPORT-CONTROLS.json b/research/partial-kernel92-async/evidence/TRANSPORT-CONTROLS.json
new file mode 100644
index 0000000000..75e9772036
--- /dev/null
+++ b/research/partial-kernel92-async/evidence/TRANSPORT-CONTROLS.json
@@ -0,0 +1,14 @@
+[
+  {
+    "control": "modified_text_content",
+    "rejected": true
+  },
+  {
+    "control": "missing_upload_file",
+    "rejected": true
+  },
+  {
+    "control": "optimized_python",
+    "rejected": true
+  }
+]
diff --git a/research/partial-kernel92-async/inputs/ASYNC-6.json b/research/partial-kernel92-async/inputs/ASYNC-6.json
new file mode 100644
index 0000000000..896cf316ba
--- /dev/null
+++ b/research/partial-kernel92-async/inputs/ASYNC-6.json
@@ -0,0 +1,12123 @@
+{
+  "status": "EXACT_INTEGER_ASYNC_NOMINATION_PHYSICAL_SLOT_MATCHING_PENDING",
+  "mode": "offset6",
+  "K": 4,
+  "T": 8,
+  "M": 73,
+  "L": 9,
+  "live": 7680,
+  "deficit": 2496,
+  "profile": {
+    "1": 182808,
+    "2": 11520,
+    "3": 41233,
+    "4": 6336,
+    "5": 25173,
+    "8": 1224,
+    "6": 4896,
+    "7": 195,
+    "48": 766,
+    "39": 1,
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diff --git a/research/partial-kernel92-async/inputs/PR493-EXPECTED.json b/research/partial-kernel92-async/inputs/PR493-EXPECTED.json
new file mode 100644
index 0000000000..973aaf30f1
--- /dev/null
+++ b/research/partial-kernel92-async/inputs/PR493-EXPECTED.json
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+{
+ "note": "Exact values that verify.sh must reproduce. The bit c is on the 10^-24 grid of PR #472's assembly (largest grid point admitted by both PR #315 moment engines with the inherited 10^-16 bad-branch allowance; the next grid point is rejected); kappa values are on the 10^-18 grid of the six-level, 47-inequality outer assembly.",
+ "word": {
+  "R": 489,
+  "content_sha256": "88435b75b8d6e5c722eb2aa1449f3a5e8e9601a9ffe243839ce1ec932ab76547",
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+   "48": 2,
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+   "hosted_residuals": 43032,
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+   "charged_prefix_bits": 2176,
+   "coefficient_bits": 2119,
+   "three_level_coefficient_bits": 6411,
+   "charged_three_level_coefficient_bits": 6464,
+   "row_coefficient": 19431,
+   "halving_depth": 3
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+    "kappa_decimal": "0.001325031497415498",
+    "binding_component": "complex",
+    "complex_lower": "663394767670133/500000000000000000",
+    "role": "primary"
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+    "binding_component": "complex",
+    "complex_lower": "1305231506267591/1000000000000000000",
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+    "complex_lower": "718766148669433/500000000000000000",
+    "role": "information only"
+   }
+  }
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+ "controls": {
+  "pr472": {
+   "bit_lower": "323442810173099014031/250000000000000000000000",
+   "kappa": "646049779721139/500000000000000000",
+   "published": "research/e8-r715-whole-hosted/EXPECTED.json at 259c684: bit_lower 323442810173099014031/250000000000000000000000, kappa 646049779721139/500000000000000000"
+  },
+  "pr445": {
+   "bit_lower": "316240894019344628547/250000000000000000000000",
+   "published": "research/r740-hosted-eleven README at 40ab91d: 1264963576077378514188/10^24"
+  },
+  "pr451": {
+   "bit_lower": "158442042752174644233/125000000000000000000000",
+   "published": "PR #451 body at f3a3815: c = 0.001267536342017397153864"
+  }
+ }
+}
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new file mode 100644
index 0000000000..9efe30ee10
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new file mode 100644
index 0000000000..6f128ce2d2
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+    }
+  ],
+  "cover_correction": {
+    "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.",
+    "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.",
+    "mandatory": true,
+    "complete_small_cover_checks": [
+      {
+        "n": 1,
+        "orthogonal_matrices": 1,
+        "nonzero_full_kernel_corrections": 0
+      },
+      {
+        "n": 2,
+        "orthogonal_matrices": 2,
+        "nonzero_full_kernel_corrections": 0
+      },
+      {
+        "n": 3,
+        "orthogonal_matrices": 6,
+        "nonzero_full_kernel_corrections": 0
+      },
+      {
+        "n": 4,
+        "orthogonal_matrices": 48,
+        "nonzero_full_kernel_corrections": 24
+      },
+      {
+        "n": 5,
+        "orthogonal_matrices": 720,
+        "nonzero_full_kernel_corrections": 600
+      }
+    ]
+  },
+  "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 well.",
+  "scope": "All compressed data boundary operators, idle children, terminal X_q and all-live cover correction. Internal arbitrary-subspace canonical labels are checked separately."
+}
\ No newline at end of file
diff --git a/research/partial-kernel92-async/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz b/research/partial-kernel92-async/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz
new file mode 100644
index 0000000000..975ce5c0df
Binary files /dev/null and b/research/partial-kernel92-async/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz differ
diff --git a/research/partial-kernel92-async/inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz b/research/partial-kernel92-async/inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz
new file mode 100644
index 0000000000..ccbdc0596c
Binary files /dev/null and b/research/partial-kernel92-async/inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz differ
diff --git a/research/partial-kernel92-async/inputs/work/odd-stages/clifford_exact.py b/research/partial-kernel92-async/inputs/work/odd-stages/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/partial-kernel92-async/inputs/work/odd-stages/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/partial-kernel92-async/inputs/work/pr361/code/engines/base_two_moment.py b/research/partial-kernel92-async/inputs/work/pr361/code/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/partial-kernel92-async/inputs/work/pr361/code/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/partial-kernel92-async/inputs/work/pr361/code/engines/moment.py b/research/partial-kernel92-async/inputs/work/pr361/code/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/partial-kernel92-async/inputs/work/pr361/code/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/partial-kernel92-async/inputs/work/pr361/code/engines/outer.py b/research/partial-kernel92-async/inputs/work/pr361/code/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/partial-kernel92-async/inputs/work/pr361/code/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/partial-kernel92-async/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz b/research/partial-kernel92-async/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz
new file mode 100644
index 0000000000..8bec1751f7
Binary files /dev/null and b/research/partial-kernel92-async/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz differ
diff --git a/research/partial-kernel92-async/references/PR493-NOTICE.md b/research/partial-kernel92-async/references/PR493-NOTICE.md
new file mode 100644
index 0000000000..ac7d789262
--- /dev/null
+++ b/research/partial-kernel92-async/references/PR493-NOTICE.md
@@ -0,0 +1,11 @@
+# Attribution for the included PR493 material
+
+Apache-2.0. Prepared by eumemic with substantial Anthropic Claude assistance.
+The only copied PR493 payload in this package is its published EXPECTED.json.
+Its R489 bit operator is cited, not vendored or freshly reconstructed here.
+
+The original complete notice is available with the pinned source:
+https://github.com/CrocSwap/integer-mult-bounds/blob/c3a9a436b84fe44fdc223a5784d84736d1c2d3c7/research/e8-bit-carrier-skeleton/NOTICE.md
+
+This attribution excerpt omits sections for code and historical receipt files
+that are not included in this package. It does not modify any upstream file.
diff --git a/research/partial-kernel92-async/research-notes/COALESCING-GATE.json b/research/partial-kernel92-async/research-notes/COALESCING-GATE.json
new file mode 100644
index 0000000000..7c704edbf7
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/COALESCING-GATE.json
@@ -0,0 +1,3174 @@
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+          "compatible_retired": []
+        },
+        {
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+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 83,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 84,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 85,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 86,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 87,
+          "compatible_packets": [],
+          "compatible_retired": []
+        }
+      ]
+    },
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+      ],
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+        [
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+      ],
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+        [],
+        []
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+      "direct": [
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+        },
+        {
+          "target": 105,
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+          "compatible_retired": []
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+        {
+          "target": 106,
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+          "compatible_retired": []
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+          "target": 107,
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+        {
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+          "compatible_retired": []
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+          "compatible_retired": []
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+        {
+          "target": 110,
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+          "compatible_retired": []
+        },
+        {
+          "target": 111,
+          "compatible_packets": [],
+          "compatible_retired": []
+        }
+      ]
+    },
+    {
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+        4,
+        5
+      ],
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+        [
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+          265,
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+        [
+          137,
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+          6
+        ]
+      ],
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+          ],
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+          }
+        },
+        {
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+          }
+        },
+        {
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+          }
+        },
+        {
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+          "frame": [
+            265,
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+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 663,
+          "frame": [
+            271,
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+          ],
+          "row": {
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+          }
+        },
+        {
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+          ],
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+          }
+        },
+        {
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+          ],
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+          }
+        },
+        {
+          "register": 103,
+          "frame": [
+            265,
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+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 100,
+          "frame": [
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+          ],
+          "row": {
+            "100": "1/2",
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+          }
+        },
+        {
+          "register": 101,
+          "frame": [
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+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 673,
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+          "row": {
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+          }
+        },
+        {
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+            6
+          ],
+          "row": {
+            "99": "1/2",
+            "96": "-1/2"
+          }
+        }
+      ],
+      "eligible": [
+        [],
+        []
+      ],
+      "direct": [
+        {
+          "target": 96,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 97,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 98,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 99,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 100,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 101,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 102,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 103,
+          "compatible_packets": [],
+          "compatible_retired": []
+        }
+      ]
+    },
+    {
+      "block": [
+        2,
+        3,
+        6,
+        7
+      ],
+      "tetrads": [
+        [
+          88,
+          91,
+          93,
+          94
+        ],
+        [
+          89,
+          90,
+          92,
+          95
+        ]
+      ],
+      "own_frames": [
+        [
+          73,
+          49,
+          6
+        ],
+        [
+          425,
+          120,
+          6
+        ]
+      ],
+      "retired": [
+        {
+          "register": 697,
+          "frame": [
+            408,
+            49,
+            6
+          ],
+          "row": {
+            "92": "1",
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+          }
+        },
+        {
+          "register": 88,
+          "frame": [
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+            6
+          ],
+          "row": {
+            "88": "1",
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+          }
+        },
+        {
+          "register": 693,
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+          ],
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+          }
+        },
+        {
+          "register": 688,
+          "frame": [
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+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 691,
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+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 689,
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+          ],
+          "row": {
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+        },
+        {
+          "register": 698,
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+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 95,
+          "frame": [
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+            55
+          ],
+          "row": {
+            "95": "1/2",
+            "89": "-1/2"
+          }
+        },
+        {
+          "register": 92,
+          "frame": [
+            414,
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+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 93,
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+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 701,
+          "frame": [
+            465,
+            49,
+            6
+          ],
+          "row": {
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+            "93": "-1/2"
+          }
+        },
+        {
+          "register": 91,
+          "frame": [
+            425,
+            73,
+            6
+          ],
+          "row": {
+            "91": "1/2",
+            "88": "-1/2"
+          }
+        }
+      ],
+      "eligible": [
+        [],
+        []
+      ],
+      "direct": [
+        {
+          "target": 88,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 89,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 90,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 91,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 92,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 93,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 94,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 95,
+          "compatible_packets": [],
+          "compatible_retired": []
+        }
+      ]
+    },
+    {
+      "block": [
+        4,
+        5,
+        6,
+        7
+      ],
+      "tetrads": [
+        [
+          56,
+          59,
+          61,
+          62
+        ],
+        [
+          57,
+          58,
+          60,
+          63
+        ]
+      ],
+      "own_frames": [
+        [
+          161,
+          24,
+          6
+        ],
+        [
+          289,
+          24,
+          6
+        ]
+      ],
+      "retired": [
+        {
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+          "frame": [
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+            6
+          ],
+          "row": {
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+          }
+        },
+        {
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+            6
+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 721,
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+          ],
+          "row": {
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+        },
+        {
+          "register": 716,
+          "frame": [
+            289,
+            161,
+            24
+          ],
+          "row": {
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+          }
+        },
+        {
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+          "frame": [
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+            30
+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 717,
+          "frame": [
+            295,
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+            30
+          ],
+          "row": {
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+          }
+        },
+        {
+          "register": 726,
+          "frame": [
+            295,
+            161,
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+          ],
+          "row": {
+            "61": "1/2",
+            "59": "-1/2"
+          }
+        },
+        {
+          "register": 63,
+          "frame": [
+            289,
+            167,
+            30
+          ],
+          "row": {
+            "63": "1/2",
+            "57": "-1/2"
+          }
+        },
+        {
+          "register": 60,
+          "frame": [
+            289,
+            167,
+            24
+          ],
+          "row": {
+            "60": "1/2",
+            "57": "-1/2"
+          }
+        },
+        {
+          "register": 61,
+          "frame": [
+            295,
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+            24
+          ],
+          "row": {
+            "61": "1/2",
+            "56": "-1/2"
+          }
+        },
+        {
+          "register": 729,
+          "frame": [
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+            6
+          ],
+          "row": {
+            "62": "1/2",
+            "61": "-1/2"
+          }
+        },
+        {
+          "register": 59,
+          "frame": [
+            313,
+            185,
+            6
+          ],
+          "row": {
+            "59": "1/2",
+            "56": "-1/2"
+          }
+        }
+      ],
+      "eligible": [
+        [],
+        []
+      ],
+      "direct": [
+        {
+          "target": 56,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 57,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 58,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 59,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 60,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 61,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 62,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 63,
+          "compatible_packets": [],
+          "compatible_retired": []
+        }
+      ]
+    }
+  ],
+  "scope": "Unchanged packet assembly, current retired checkpoint; no assertion against a redesigned packet network.",
+  "nonmonotone_excess_per_local": 224,
+  "nonmonotone_excess_global": 16128,
+  "baseline_deficit": 2496
+}
diff --git a/research/partial-kernel92-async/research-notes/COALESCING-PROOF.md b/research/partial-kernel92-async/research-notes/COALESCING-PROOF.md
new file mode 100644
index 0000000000..a16a31eac7
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/COALESCING-PROOF.md
@@ -0,0 +1,19 @@
+# Register coalescing with explicit frame restoration
+
+This is a sufficient compiler transformation, not an achieved kappa gain.
+
+Let an existing verified frame transition from E to F, E contained in F, implement the exact invertible operator U(F) U(E)^(-1) with one rank-d recursive child and its existing coordinate/monomial wrappers, where d=dim(F)-dim(E). The reverse transition is implemented by reversing that exact circuit and replacing its rank-d child by its inverse. For the normalized complex child C, C^(-1)=X C since C^2=X and X^2=I; therefore the inverse uses one rank-d child plus an explicitly charged translation and reversed wrappers. This does not make a downward frame change free. The exact all-column equation is U(E) U(F)^(-1), so composing it with the forward prefix changes the frame label correctly on arbitrary register contents.
+
+Any scalar elementary operation at a common frame remains legal after this restoration. A proposed register coalescing must additionally provide an invertible change of basis on the reused registers, preserve every still-live source, rebuild both forward and dual dirty-data compensation from the actual scalar word, and pay all reverse wrappers and translations. Those are concrete finite circuit checks, not consequences of a clean-input row calculation alone.
+
+For a frame path with total upward dimension u and downward dimension d, the sum of recursive ranks is u+d = (final dimension - initial dimension)+2d. Thus 112 independent dimension-one descents incur 224 additional local rank units. Across 72 invocations this is 16,128 units. Removing a logical helper ordinarily returns its formerly hosted pending coordinates to the idle remainder; it does not by itself create rank deficit. Against the inherited deficit 2,496, the naive 112-descent substitution is not a viable profile without additional genuine rank savings.
+
+## Exact restricted gate
+
+`coalescing_gate.py` replays the pinned PR507 constructor to the checkpoint immediately before coordinate totals. `COALESCING-GATE.json` preserves every retired row and frame, every intended own tetrad, and the target access tests.
+
+All fourteen blocks have twelve retired rows already at rank-three face frames. None of those 168 frames is contained in either corresponding own-output tetrad frame. More strongly, none of the current packet output frames or retired frames is contained in any of the eight own-target hyperplanes of its block. The apparent rank-two opportunity exists earlier, at the snapshot point, before the face assembly raises these rows. Therefore deleting snapshots and merely reusing the later retired stock is invalid without a paid nonmonotone transition. This test does not exclude a redesigned packet assembly or a different early live-range allocation.
+
+## Reusable source connections
+
+The precise analogue is injective live-register renaming with a frame invariant, rather than reuse based on equal clean values alone. OpenAI `WLIdentification/WordCommands.lean`, `StackModel.Command.Exec.rename`, and P18 `Problem18IMPAssignments20261002.run_framed` were identified and source-inspected by the kernel lane; their hashes and audit scope are in that lane's `KERNEL-SOURCE-HASHES.json`. They do not automatically certify the new complex circuit. Our earlier inspected `Slots.restoreMemory`, `effects_argsCode`, and `Word.matrix_substitute` similarly supply the structural pattern: exact state restoration, preserved outside state, and additive replacement cost.
diff --git a/research/partial-kernel92-async/research-notes/COMPLEX-SOURCE-HASHES.json b/research/partial-kernel92-async/research-notes/COMPLEX-SOURCE-HASHES.json
new file mode 100644
index 0000000000..e3bf72b4f6
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/COMPLEX-SOURCE-HASHES.json
@@ -0,0 +1,41 @@
+{
+  "registered_search": "Shared source_catalogs and live DAG were queried across their federated registrations; source files then inspected directly. This is not a claim that every indexed declaration was read or kernel-certified.",
+  "sources": [
+    {
+      "path": "Mathproof/Meta/Problem18ConcreteSlotTransport20261002.lean",
+      "sha256": "2b436d58c0f28a98cba11c2ffe20858062b1cd05d567cd7f2f9c29b6851fbdeb",
+      "declarations": "Slots.transport; Slots.restoreMemory",
+      "statement_summary": "A decoded workspace invariant is preserved when the relevant layout registers and backing memory agree, even if unrelated scratch differs.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    },
+    {
+      "path": "Mathproof/Meta/Problem18ConcreteAutoRestore20261002.lean",
+      "sha256": "16076d909a7ca6d957cb68f7455832979e9b4df25b8f3f5a43705858aa5e0c02",
+      "declarations": "run; extract_run",
+      "statement_summary": "An actual restoration program composes with extraction, with exact additive run cost and unchanged input/output.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    },
+    {
+      "path": "leanlibs/formal-math-3sum-apsp/ThreeSumApsp/Lang/Compiler/CallFrames.lean",
+      "sha256": "cf7f74321dc79b952663a253f5537640f6460748a97eb951fe714ad271f90553",
+      "declarations": "Light.Compiler.effects_argsCode",
+      "statement_summary": "Argument evaluation writes its designated temporaries and satisfies AgreeOutside for all other locations.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    },
+    {
+      "path": "openai-math/lean/OAI/Combinatorics/VariableWL/MachineSimulation.lean",
+      "sha256": "d2148836dc632a9a4fd68adf029f1f47c33a0b0168a1fb7266dd994016aa45ac",
+      "declarations": "drain_stage; drain_both",
+      "statement_summary": "Two explicit Turing stack draining runs compose with additive step counts and an exactly tracked accumulated answer.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    },
+    {
+      "path": "openai-math/lean/OAI/Computability/FourierCircuit/WordScheduling.lean",
+      "sha256": "0f1b0c89091f6acc5310e95c07102792749a38b0e35a760b7feae25682ef2713",
+      "declarations": "Word.matrix_substitute; Word.weight_substitute",
+      "statement_summary": "Substitution of a word implementing the same matrix preserves the full word matrix, and its weight equals the sum of actual substituted weights.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    }
+  ],
+  "dag_observation": "Selected external declarations are present under source-catalog operation identities, with no typed ports or axiom audit in the returned records. No source-only hit was promoted to certification."
+}
diff --git a/research/partial-kernel92-async/research-notes/HOSTING-RESEARCH.md b/research/partial-kernel92-async/research-notes/HOSTING-RESEARCH.md
new file mode 100644
index 0000000000..9b551054fe
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/HOSTING-RESEARCH.md
@@ -0,0 +1,40 @@
+# Machine-derived allocation routes
+
+Source-only inspection, not new Lean certification. Exact source declarations consulted:
+
+- Mathproof/Meta/Problem18RecursiveWorkspaceChain20261002.lean: program, cost, run, code_uniform. The run theorem keeps one physical reservation and preserves array lengths through an arbitrarily long sequence of verified calls.
+- Mathproof/Meta/Problem18P34Subfield20261003NRecursiveWorkspaceRestore.lean: run. The entire reserved concrete memory image is restored, not merely a candidate-local prefix; restoration itself has an explicit cost.
+- Mathproof/Meta/Problem18ConcreteSelectedChildContinuation20261002.lean: program, cost, run. Composes a concrete selected continuation with a disjoint-reservation precondition and additive counted cost.
+- Mathproof/Meta/Problem18P351PolynomialWorkspaceFrameClose20261003.lean: gcd_ws_safe, quotient_ws_safe. Workspace-base ABI registers are excluded from scalarWrites.
+
+## Sufficient adaptation
+
+Treat each complete arbitrary-dirt cover invocation as a continuation that preserves the caller's reserved arrays outside its exact endpoint. A finite schedule is sufficient only when each pending child receives its full intended factor exactly once, every borrowed physical family is restored before its next data/bridge touch, distinct simultaneously interpreted local registers have distinct full owners, and all remaining children are explicitly charged. Composition then follows from equality of endpoints and per-replica event projection; neither shared workspace nor a different dispatch order introduces a free mathematical operation. This is an applicability theorem, not by itself a kappa improvement.
+
+## Bounded new screens
+
+1. Paid register spills for shorter K=3 controllers: rejected before expensive search. Current provider demands 7*4900=34300 helper-rank units per replica, while initial plus final pending children supply only26880. Shortage7420 already exceeds total positive rank deficit216. Any implementation must pay missing residual transformations and restore its full reserve. No private-reserve or LIVE increase is silently assumed.
+2. Finite steady-state amortization at T=16: exact integer allocations for offsets6 and12 both reproduce twice the T=8 histogram and the same nominal b=0.0013744413363825925, with zero solver gap. No improvement claimed.
+3. K=5,T=8,offset6: bounded feasible candidate b=0.0013680017192500558, worse than current. Solver reached time limit with tiny nonzero gap; this is not a universal no-gain theorem.
+
+These screens use actual coordinated-rank2 local paid profile and widths (18 rank7,104 rank8,438 rank9), complete paid remainders, and finite fixed T. They do not merely score local savings. Literal owner matching and full scalar invoice would still be required for a positive nominee; no negative nominee was promoted.
+
+## Public507 composition and literal owner witness
+
+The new PR507 partial-own factory combines constructively with our previous coordinated rank-two gauge collapse. Kernel lane reconstructed its exact local word. The changed local profile is {1:2493,2:208,3:516,4:88,5:298,6:68,7:1,8:17}; widths are 18 rank7,146 rank8,396 rank9. Our complete offset6 allocation has nominal b=0.0013910579397602985 with every remainder paid. Its literal owner witness passes all40320 role assignments,72 calls,560 distinct helpers per call. Files RANK2-PARTIAL-O6.json and RANK2-PARTIAL-OWNERS.json.gz bind the construction. This is a positive composed supplier nomination; it still needs fresh emitted full orthogonal maps, scalar prefix and outer assembly. Its gain does not establish that three entirely new machine concepts improved the exponent.
+
+## Repeated-axis modulo-four gate
+
+The proposed sufficient algebraic extension tracks multiplicity of each pending coordinate modulo4: C squared equals translation X, so an even repeated factor can be compensated explicitly without another recursive Fourier call. Overlapping factors must still obey actual owner lifetime, full-family injection and scalar routing. For a rank-r pending bin hosting roles with total width s, a best-case leftover has size r-s if s<=r, otherwise parity(r-s). The latter is an optimistic capacity relaxation: every loss of odd coverage reduces the actual rank deficit and cannot be hidden as a free bank.
+
+Native integer screens allowing aggregate width excess0,1,2,4 and16 per pending bin all selected the same disjoint pattern optimum, nominal b=0.001391135951042288, zero reported integer-solver gap. No overlap selected; therefore no positive candidate promoted from this bounded route. This is not a proof that every possible modulo-four physical compiler is unhelpful. It is a cheap full-profile gate with all repeated-rank loss charged.
+
+## New kernel-92 candidate
+
+Kernel lane supplied exact source-based variants after broadening availability at concrete instruction boundaries. Full controller pricing ranks them as follows: kernel-partial-base with 92 pivots, b approximately 0.0013934624979634045; latefirst-partial-base with 89 pivots, b approximately 0.0013927996101125715; snapshot-even, b approximately 0.0013926403309490465; snapshot-both, b approximately 0.0013914512506201793. All are floating nominations, not outer assembled kappa values.
+
+The selected 92-pivot local profile is {1:2539,2:160,3:530,4:88,5:298,6:68,7:1,8:17}, with 18 width-7,154 width-8 and388 width-9 helpers. Selected plan KERNEL92-FOCUS-O6.json has SHA256 7a30db32ad8fc54bd5e7060febf4f8ff7747b8287c057ae926efc736e2b9f800. KERNEL92-OWNERS.json.gz has SHA256 9c6bd9793db16d599d3c7f9493350d2359681d19eb170ec7239e8d568090e745. Literal matching passes all40320 helper roles,72 invocations and560 distinct helper families per invocation. The emitted full physical maps and prefix invoice remain parent/independent-auditor responsibilities.
+
+The complete selected paid histogram is {1:182808,2:11520,3:41233,4:6336,5:25173,6:4896,7:195,8:1224,16:1,32:1,39:1,48:766}. Live stock7680, ambient73, rank deficit2496, maximum child48.
+
+An optimistic static stock allocation gives b approximately 0.0013943119744464494, but its fixed optimal patterns were infeasible under tested offset4,6,8,12 schedules with eight replicas and offset6 with sixteen replicas. That stronger number is not a delivered candidate. The limited failure is retained as a concrete search result, not a universal scheduling barrier.
diff --git a/research/partial-kernel92-async/research-notes/KERNEL-MACHINE-SOURCES.md b/research/partial-kernel92-async/research-notes/KERNEL-MACHINE-SOURCES.md
new file mode 100644
index 0000000000..a216cdd1f8
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/KERNEL-MACHINE-SOURCES.md
@@ -0,0 +1,35 @@
+# Machine-source transfer ledger
+
+These are direct source inspections, not new Lean compilation or certification. A machine optimization counts toward the exponent only when its complete child-rank profile and physical inventory improve.
+
+## Old-state operand capture: constructed and tested
+
+OpenAI math, `lean/OAI/Computability/WeisfeilerLeman/RAMInstruction.lean`, defines `WLTime.SparseRAM.execute`: a load evaluates its address/read from the old configuration and only then updates the destination register. The theorem `execute_forget` states
+
+    A.execute I (forget A n C) = forget A n (execute I C).
+
+`SparseStore.lean`, theorem `WLTime.WordMemory.read_prepend`, states that a prepended address/value pair implements exactly `Function.update` of the abstract memory. This makes the distinction between an old value and its overwritten successor explicit.
+
+The P18 source `Mathproof/Meta/Problem18IMPAssignments20261002.lean`, `run_assignments`, proves a static assignment sequence correct from original-environment right-hand-side values under `Independent xs`; `run_framed` adds preservation of untouched variables, arrays and external tapes. This is a sufficient independence hypothesis, not permission to merge aliased live registers. `Problem18P351PairSnapshot20261003.lean`, theorem `run`, gives an exact snapshot into a separate bank while preserving every other array and external tape.
+
+Concrete transfer: PR507 captures both pair intermediates after their two-shear basis change. We implemented a triangular snapshot between the two shears: capture the new pair sum and the still-unmodified second operand. The resulting pair basis remains invertible; the later own-tetrad decoder is recomputed exactly. Three variants change one or both tetrad parities. All pass clean scalar algebra; after retiming and exact rational kernel construction, the best snapshot-even candidate has88 pivots and an improved full supplier compared with the simple84-pivot composition. It nevertheless loses to the separately found92-pivot word. Therefore old-state capture is a real tested mechanism but is not counted as an ingredient of the selected92-pivot construction.
+
+## Actual first-read frontier: bounded test
+
+The exact frame immediately before the first observer, rather than the pre-retiming source layout, determines which incoming cancellation subspaces are legal. We recomputed these first-read frontiers from the emitted retimed body and reran a bounded native C++ response search. A valid89-pivot word resulted, but its full supplier price was below the92-pivot word. No gain from this representation is counted in the winner.
+
+## Ambient frame preservation
+
+OpenAI math, `WLIdentification/WordCommands.lean`, theorem `StackModel.Command.Exec.rename`, transports execution through an injective register renaming while preserving every ambient location outside the image. This is the correct local rule for reusing a physical region whose other live contents must survive. It requires injectivity on simultaneously live registers; it does not by itself justify identifying two live helpers or erasing their dirty state.
+
+The parent/complex lane uses this distinction while testing lifetime-based coalescing of own-helper storage with retired factory rows. The actual paid transitions and arbitrary-dirt restoration must be constructed before claiming an exponent gain. A literal rank4-to-rank3 descent adds total variation; dropping a helper count alone is not a price argument.
+
+## Selected fallback and honest attribution
+
+The selected fallback has92 kernel pivots with profile
+
+    1:2539, 2:160, 3:530, 4:88, 5:298, 6:68, 7:1, 8:17
+
+and residual inventory18 width7,154 width8,388 width9. It combines PR507's changed factory with the prior coordinated rank2 gauges, public frame retiming, asynchronous whole-owner packing, and an improved response-basis selection. The92-pivot improvement is an application of our existing algebraic response selector; it is not relabeled as one of three new machine techniques. Its exact local scalar audit passes all800 columns in both orientations and92 omission controls. The parent's complete physical and arithmetic replay remains the authority for the final exponent.
+
+DAG coverage note: a direct `Shape-DAG.ps1 sig Mathproof.Problem18IMPAssignments20261002.run_framed` query loaded the registered compiled overlays but returned `ERR no such declaration`. The source file and its statement were available and inspected. Thus this lane records that item as source evidence, not a retrieved typed-DAG certificate; no second catalog or compilation was created to hide the missing port.
diff --git a/research/partial-kernel92-async/research-notes/KERNEL-SOURCE-HASHES.json b/research/partial-kernel92-async/research-notes/KERNEL-SOURCE-HASHES.json
new file mode 100644
index 0000000000..625d50de57
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/KERNEL-SOURCE-HASHES.json
@@ -0,0 +1,49 @@
+[
+  {
+    "repository": "openai-math",
+    "path": "lean/OAI/Computability/WeisfeilerLeman/RAMInstruction.lean",
+    "sha256": "5ca836a29da196f6140a948b593a7463d7395b1d59842913ebd3fbee59feee7c",
+    "declarations": [
+      "WLTime.SparseRAM.execute",
+      "WLTime.SparseRAM.execute_forget"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  },
+  {
+    "repository": "openai-math",
+    "path": "lean/OAI/Computability/WeisfeilerLeman/SparseStore.lean",
+    "sha256": "0e51415ad2e954588789a54dd1713a3b988ba84233797303840656eddc974e7f",
+    "declarations": [
+      "WLTime.WordMemory.read_prepend"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  },
+  {
+    "repository": "openai-math",
+    "path": "lean/OAI/Computability/WLIdentification/WordCommands.lean",
+    "sha256": "687f9e465ad37124a7a5c1bde32e4657b37f69610cf22f3c30375f22141ca8af",
+    "declarations": [
+      "StackModel.Command.Exec.rename"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  },
+  {
+    "repository": "Mathproof",
+    "path": "Mathproof/Meta/Problem18IMPAssignments20261002.lean",
+    "sha256": "5bb547049c7c6d622fbe6547e5d7b45b39842942091ebaf89e2cf4c85c765cfc",
+    "declarations": [
+      "Mathproof.Problem18IMPAssignments20261002.run_assignments",
+      "Mathproof.Problem18IMPAssignments20261002.run_framed"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  },
+  {
+    "repository": "Mathproof",
+    "path": "Mathproof/Meta/Problem18P351PairSnapshot20261003.lean",
+    "sha256": "c5535c358ee3a7d63f8d8a18e0f5e3fe45be85f1f22303b37e8dc6d2690cdcb3",
+    "declarations": [
+      "Mathproof.Problem18P351PairSnapshot20261003.run"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  }
+]
diff --git a/research/partial-kernel92-async/research-notes/MACHINE-TRANSFORMATIONS.md b/research/partial-kernel92-async/research-notes/MACHINE-TRANSFORMATIONS.md
new file mode 100644
index 0000000000..f4c39e557c
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/MACHINE-TRANSFORMATIONS.md
@@ -0,0 +1,31 @@
+# Machine-inspired sufficient transformations
+
+This note records constructive transformations with exact applicability tests. It does not claim an achieved kappa improvement from the three bounded pilot screens below. The source provenance and current evidence level are in COMPLEX-SOURCE-HASHES.json.
+
+## 1. Fused restoration return or entry
+
+Suppose a complete normalized invocation has arbitrary-dirt endpoint (data transformation D, helper operator S on a whole owner, identity on spectators). Suppose S and all final monomial normalizers act inside a fixed local9-coordinate factor. Let Q be a product of C_v on orthogonal pending axes outside this full local9 factor.
+
+If a helper's final recursive child C_r occurs after its last scalar observation or update, replace that child by C_(r+q) on its r coordinates and q of these additional axes, using an explicit full owner chart. No later scalar observation can expose the extra factor. The resulting complete invocation endpoint is (D,Q S), so remove exactly those q axes from its later idle remainder. The exact paid-profile replacement is -[r]-[q]+[r+q]. The larger child must satisfy the existing halving and compiler conditions; all new routing is billed.
+
+There is an entry version: if the selected child occurs before the helper's first scalar observation/update, insert Q at the beginning of the complete invocation, then commute it through the untouched prefix to the selected child. The arbitrary-dirt endpoint theorem makes the data output independent of this changed initial helper value; S Q=Q S gives the same completed pending factor. Initial normalizers must preserve the exterior factor. This is the matrix analogue of an AgreeOutside frame invariant and a fused machine return/entry.
+
+The pilot checks actual emitted scalar operands, not nominal labels. In the current coordinated rank2 word, all 560 helpers are observed in the frame-zero dirty precondition and updated/read again in FULL cleanup. Both prologue and epilogue inventories are empty in both orientations. Do not manufacture a positive tail from the endpoint formula alone. A follow-up must first change compensation/cleanup, prove the same all-column endpoint, and then reprice the complete global profile.
+
+## 2. Deferred normalization with a finite residue ledger
+
+For C_v=((1+i)I+(1-i)X_v)/2, direct expansion gives C_v^2=X_v and C_v^4=I. Allow several different complete invocations to borrow the same pending axis of one whole owner. Let k_v be its actual multiplicity. Choose e_v in {0,1} so k_v+e_v is odd, execute C_v only on the missing-parity axes e_v=1, and emit X_v^((1-k_v-e_v)/2). The final product is exactly C_v. All factors commute, and the sign of the translation exponent is immaterial modulo2.
+
+Every invocation must still use distinct whole owners, complete before the next begins, restore spectators, and occur inside the physical idle interval. Use actual pending vectors, not different charts' coincident coordinate indices. Emit an explicit chart for the possibly noncontiguous remainder and charge the final translation. This is a reversible-machine deferred-normalization invariant; it is not permission to split one residual among owners.
+
+Repeated use does not automatically save rank: it can reduce odd-parity coverage and increase the final remainder. The hosting lane's early paid screen selected disjoint use on the current stock. No numerical gain is assigned here. The rule remains a sufficient way to compile a future positively priced overlapping assignment.
+
+## 3. Recursive common-subexpression substitution
+
+At a proposed recursive call sending a register from frame E to F, suppose a simultaneously live register already equals the same exact logical linear form at frame F on every independent input column. Then a proved copy/scale sequence can supply that output instead of executing the recursive call. Its old value may be overwritten only under the exact reachable-state relation; all private copies must later be cleared correctly. Equality of frame labels alone, equality on test inputs, or equality of response columns without dirty columns is insufficient.
+
+This is a machine checkpoint/common-subexpression rule, with the same matrix-substitution and actual-weight accounting structure as OpenAI WordScheduling. The pilot compares exact rational logical rows and frames at all 3,635 positive recursive sites in each orientation of the existing provider. It finds zero exact matches. This does not rule out proportional forms, a redesigned checkpoint schedule, or a changed provider. A positive follow-up must emit the copy/erase path and pass the all-column physical audit before any saved child is credited.
+
+## What the library reuse establishes
+
+P18's transport/restoration lemmas explain exactly which machine state can be forgotten and which memory must be preserved. Anthropic's AgreeOutside rule provides the footprint criterion. OpenAI's explicit machine-run composition and word substitution explain how to compose complete endpoints and charge the actual replacement. None of these imported source statements by itself proves a new multiplication bound. The mathematical specializations above must be applied to an actual construction and pass the full paid-profile gate.
diff --git a/research/partial-kernel92-async/research-notes/REPEATED-AXIS-LEMMA.md b/research/partial-kernel92-async/research-notes/REPEATED-AXIS-LEMMA.md
new file mode 100644
index 0000000000..9e3ee8bc5d
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/REPEATED-AXIS-LEMMA.md
@@ -0,0 +1,27 @@
+# Sufficient repeated-axis normalization rule
+
+Let C_v=((1+i)I+(1-i)X_v)/2 for a binary translation X_v. Direct expansion gives
+C_v^2=X_v and C_v^4=I; translations and all C_v commute. Suppose a physical
+owner remains idle between its actual previous touch and next touch. Each
+complete normalized helper invocation has one distinct whole owner and leaves
+exactly its declared C factors on that owner's assigned axes while restoring
+borrowed spectators and all private workspace, for arbitrary initial dirt.
+
+Axis v may occur k_v times across different completed invocations in that idle
+window. Choose e_v in {0,1} so k_v+e_v is odd. Emit a residual child on all axes
+with e_v=1 and an explicit translation X_v to the power (1-k_v-e_v)/2. Then
+C_v^(k_v+e_v) X_v^((1-k_v-e_v)/2)=C_v exactly. Apply this independently to every
+axis of the original pending child. The result is its original endpoint; no
+physical owner is split, and no invocation is interleaved internally.
+
+All actual axes, charts, multiplicities, parity-complement remainder and final
+translations must be serialized and charged. Scalar and prefix invoices must
+include the added translations. A repeated even pair loses two units of covered
+rank relative to disjoint placement, so the original fixed deficit cannot be
+assumed. The existing audit's disjointness rule must be replaced by this exact
+ledger only for a new explicitly versioned program.
+
+This is a sufficient new construction rule, independently reviewed by the
+complex lane under the same normalized-invocation contract. A bounded full-stock
+screen chose no overlaps, so this note claims no achieved kappa gain. It is not
+permission to treat repeated calls or translations as free.
diff --git a/research/partial-kernel92-async/research-notes/REPLAY-REPAIRS.md b/research/partial-kernel92-async/research-notes/REPLAY-REPAIRS.md
new file mode 100644
index 0000000000..e4eb71418e
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/REPLAY-REPAIRS.md
@@ -0,0 +1,7 @@
+# Repairs exercised by the final replay
+
+The first run exposed an inherited negative control that set a pure helper route to the route it already had. The repaired test chooses two distinct width-nine owners, copies the complete owner entry to create a real collision, asserts that the mutation changed the input, and requires the direct ownership rule to reject overlapping physical footprints. No mathematical validity check was removed.
+
+The new response kernel raises the backward scalar prefix envelope to 1,048,913, requiring 21 bits rather than the old fixture's 20. The independent invoice now derives its local prefix requirement from the exact replay. The global total is 206 bits; the retained 512-bit charge and row allowance remain sufficient. All strict finite and outer inequalities are checked anew.
+
+After these repairs and the manifest/input newline changes, all 13 stages passed from scratch on a copy where every recognized text file had CRLF line endings. This is the delivered program, with the same exact exponent and canonical final template as the discovery replay. Original failed logs remain in the local research archive rather than being represented as successful runs.
diff --git a/research/partial-kernel92-async/research-notes/RESTORATION-AND-CSE-SCREEN.json b/research/partial-kernel92-async/research-notes/RESTORATION-AND-CSE-SCREEN.json
new file mode 100644
index 0000000000..51b57aed25
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/RESTORATION-AND-CSE-SCREEN.json
@@ -0,0 +1,22 @@
+{
+  "status": "EXACT_SOURCE_SCALAR_AND_FRAME_PILOT",
+  "source_sha256": {
+    "CANONICAL-WORD.json.gz": "e88cd2b8a34a012542ab126a12518ab16888435ec42c4065ee63c7a85b5ec9f2",
+    "LOCAL-PROGRAMS.json.gz": "7f59bfbfc174adac07ae70afe290d6a41e9d8aa4e2550edb45e0004788c99d98"
+  },
+  "orientations": {
+    "backward": {
+      "prologue": [],
+      "epilogue": [],
+      "exact_row_frame_reuse_candidates": [],
+      "recursive_sites_screened": 3635
+    },
+    "forward": {
+      "prologue": [],
+      "epilogue": [],
+      "exact_row_frame_reuse_candidates": [],
+      "recursive_sites_screened": 3635
+    }
+  },
+  "scope": "Nomination screen only. A matched logical row would still require explicit copy/erase lowering, independent physical phase audit and complete global profile. No new kappa claimed."
+}
diff --git a/research/partial-kernel92-async/research-notes/coalescing_gate.py b/research/partial-kernel92-async/research-notes/coalescing_gate.py
new file mode 100644
index 0000000000..196474567b
--- /dev/null
+++ b/research/partial-kernel92-async/research-notes/coalescing_gate.py
@@ -0,0 +1,26 @@
+from pathlib import Path
+import sys,json,hashlib
+from fractions import Fraction
+src=Path(sys.argv[1]); inp=Path(sys.argv[2]); out=Path(sys.argv[3])
+s=src.read_text().split("# Four coordinate sums")[0].replace("OUT.mkdir(parents=True,exist_ok=False);","")
+old=sys.argv;sys.argv=[str(src),str(inp),"unused"];d={};exec(compile(s,str(src),"exec"),d);sys.argv=old
+report=[]
+for c,z in sorted(d["blocks"].items()):
+ ids=z["receipt"]["source_lines"]
+ tet=[sorted(t for t in ids if sum(d["R"][t][i]<0 for i in c)%2==parity) for parity in (0,1)]
+ Fs=[d["basis"]([d["P"][t] for t in a]) for a in tet]
+ retired=[dict(register=r,frame=d["cur"][r],row={str(k):str(x) for k,x in d["rows"][r].items()}) for r in d["retired"][c]]
+ eligible=[[r for r in d["retired"][c] if d["inside"](d["cur"][r],F)] for F in Fs]
+ direct=[]
+ for t in ids:
+  F=d["hyper"](d["P"][t])
+  packetregs=sorted({r for key,(r,a) in d["packets"].items() if key[0]==c})
+  direct.append(dict(target=t,compatible_packets=[r for r in packetregs if d["inside"](d["cur"][r],F)],compatible_retired=[r for r in d["retired"][c] if d["inside"](d["cur"][r],F)]))
+ report.append(dict(block=c,tetrads=tet,own_frames=Fs,retired=retired,eligible=eligible,direct=direct))
+assert len(report)==14
+assert all(len(r["frame"])==3 for b in report for r in b["retired"])
+assert all(not e for b in report for e in b["eligible"])
+assert all(not x["compatible_packets"] and not x["compatible_retired"] for b in report for x in b["direct"])
+result=dict(status="EXACT_RESTRICTED_GATE_NO_COALESCING",source_sha256=hashlib.sha256(src.read_bytes()).hexdigest(),blocks=report,scope="Unchanged packet assembly, current retired checkpoint; no assertion against a redesigned packet network.",nonmonotone_excess_per_local=224,nonmonotone_excess_global=16128,baseline_deficit=2496)
+out.write_text(json.dumps(result,indent=2)+"\n",encoding="utf-8")
+print(json.dumps({k:v for k,v in result.items() if k!="blocks"}))
diff --git a/research/partial-kernel92-async/vendor/audit_scalar_invoice.py b/research/partial-kernel92-async/vendor/audit_scalar_invoice.py
new file mode 100644
index 0000000000..b03fdf510f
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/audit_scalar_invoice.py
@@ -0,0 +1,82 @@
+"""Fresh PR484 scalar/prefix lowering and finite overcharge recount. OpenAI Codex.
+Reads emitted programs, canonical word and raw routes, importing no supplier code.
+Inherited all-size compiler admissibility is a condition, not inferred here.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import gzip,json,math,hashlib
+import sys
+O=Path(sys.argv[1]);V=Path(sys.argv[2]);HOSTED=Path(sys.argv[3])
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+w=read(V/'split-centres/CANONICAL-WORD.json.gz');p=read(V/'split-centres/LOCAL-PROGRAMS.json.gz');old=read(V/'split-centres/GLOBAL-TEMPLATE.json.gz');new=read(HOSTED/'GLOBAL-TEMPLATE.json.gz');integ=read(V/'split-centres/INTEGRATION.json');checks=read(V/'split-centres/LOCAL-CHECKS.json');prior=read(V/'split-centres/INDEPENDENT-REPLAY.json');owners=read(O/'OWNERS-AND-PROFILE.json')
+N=800;M=73;R=560;L=9;T=8;VV=120;K=4
+local={}
+for ori,evs in p.items():
+ rows={('L',i):{i:F(1)}for i in range(N)};env={('L',i):F(1)for i in range(N)};peak=F(1);real=macros=0;paid=Counter();workops=0
+ for e in evs:
+  if e[0]=='climb':paid[e[5]]+=1
+  elif e[0]=='center':paid[e[4]]+=1
+  elif e[0]=='scalar':
+   macros+=1;x=e[1];op=x[0];a=tuple(x[1]);count=0
+   if op=='clear':rows[a]={};env[a]=F(0);count=1
+   elif op=='copy':rows[a]=dict(rows[tuple(x[2])]);env[a]=env[tuple(x[2])];count=1
+   elif op=='scale':
+    q=F(x[2],x[3]);num,den=abs(q.numerator),q.denominator
+    assert num and num&(num-1)==0 and den&(den-1)==0
+    rows[a]={j:q*v for j,v in rows[a].items()};env[a]*=abs(q)
+    count=abs(num.bit_length()-den.bit_length())+int(q<0)
+   elif op=='add':
+    b=tuple(x[2]);q=F(x[3],x[4]);num,den=abs(q.numerator),q.denominator
+    assert a!=b and num>0 and den&(den-1)==0
+    # Lower actual coefficient to cleared Horner work. Every intermediate
+    # magnitude envelope is explicitly included, before denominator halvings.
+    acc=0;count=1
+    for i,ch in enumerate(bin(num)[2:]):
+     if i:acc*=2;count+=1;peak=max(peak,acc*env[b])
+     if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b])
+    v=F(acc)
+    for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b])
+    assert v==abs(q);count+=2 # signed accumulation and private work clear
+    env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{})
+    for j,z in list(rows[b].items()):
+     value=rr.get(j,F(0))+q*z
+     if value:rr[j]=value
+     else:rr.pop(j,None)
+    workops+=count
+   else:raise AssertionError(op)
+   real+=2*count;peak=max(peak,env[a])
+ assert all(not row for reg,row in rows.items()if reg[0]=='C')
+ for i in range(N):
+  expected={i:F(1)}
+  if ori=='forward'and 120<=i<240:expected[i-120]=F(1)
+  if ori=='backward'and i<120:expected[i+120]=F(-1)
+  assert rows['L',i]==expected
+ assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192
+ assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros']
+ assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()}
+ local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True)
+centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][240:]];enter=sum(x<9 for x in widths)
+children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3
+adapters=16*(macros+children+N+centres)+64*M
+primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler
+bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;shifts=K*VV*T;moves=2*K*VV*T
+oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L
+scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls'])
+nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144
+outside=8*nonlocal_items+64*M
+pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP
+invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler'])
+# Independent hosted stock rebase, retaining the larger unhosted operation
+# overcharge; only the stock and mass in the common router/literal change.
+W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile']
+assert M*W-mass==2496 and P==W+R+centres+2
+rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex)
+r=M//2;group=2**(r*r)
+for i in range(1,r+1):group*=2**(2*i)-1
+stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2
+G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252;maxchild=max(map(int,profile))
+ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router<G,literal=literal<E,mass=B<2**100001,precision=32*M*B*B<C0,tape=2*B+18<C0,row=row<20161,halving=M*M>2*maxchild*maxchild)
+assert all(ineq.values())
+out=dict(status='PASS_INDEPENDENT_SCALAR_PREFIX_AND_HOSTED_FINITE_INVOICE',local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention.')
+(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True)
diff --git a/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py
new file mode 100644
index 0000000000..252ca9393d
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py
@@ -0,0 +1,59 @@
+"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.  The wrapper construction follows PR #458
+(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first);
+S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers  R_E^-1  before the whole local invocation and  L_E^-1  after its
+full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically.
+usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json
+Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive
+constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that  L_E^-1 S_E R_E^-1  has exactly the
+tableau and zero-state vector (global phase included) of  fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong
+translation, wrong width) must be rejected."""
+import copy, gzip, json, sys
+from pathlib import Path
+R = Path(__file__).resolve().parent.parent.parent
+sys.path.insert(0, str(R / 'split-centres-global/vendor'))
+from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity
+n = 9; FULL = tuple(1 << i for i in range(n))
+def monomial_op(rec):
+    """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)"""
+    out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset']))
+    return out.then(Op(n, identity(n), [('phase', rec['phase'])]))
+def S_of(U):
+    return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, FULL))
+def wrapped_ok(U, rec):
+    """exactly: L^-1 S R^-1 = C_[w] x I  (apply order: R^-1, S, L^-1)"""
+    w = n - len(U); S = S_of(U); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left'])
+    net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w))
+    return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state()
+def main():
+    c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v']
+    starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0})
+    recipes = {}
+    for f in starts:
+        U = frames[f]; rec, compiled = lower_child(S_of(U))
+        recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right'])
+    Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes), sort_keys=True, separators=(',', ':')) + '\n')
+    # ---- independent decode of the serialized file
+    data = json.loads(Path(sys.argv[2]).read_text())['recipes']
+    dot = lambda a, b: bin(a & b).count('1') & 1
+    detail = []
+    for f in starts:
+        rec = data[str(f)]; U = frames[f]
+        assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f)
+        detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U),
+                           totally_isotropic=all(dot(a, b) == 0 for a in U for b in U)))
+    controls = []
+    def reject(name, fn):
+        f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec)
+        if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name)
+        controls.append(name)
+    reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4))
+    reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1))
+    reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4))
+    reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left'])))
+    reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1))
+    res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail),
+               all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail)
+    Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n')
+    print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight'])
+if __name__ == '__main__': main()
diff --git a/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py
new file mode 100644
index 0000000000..e80ca6b8b3
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py
@@ -0,0 +1,189 @@
+# GK: modified copy of PR #433's complex_audit.py (icekylinx with Codex; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:"; with a word that has no start_extra / target_levels the
+# behaviour and the written files are PR #433's.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Read-back audit, independent of the Hamming producer and its row state."""
+import copy,gzip,hashlib,importlib.util,json,math,time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');p=OUT/'FULL-WORD.json.gz'
+word=json.load(gzip.open(p));v=120;n=240+word['report']['R'];start=time.monotonic()
+def apply(e,rows):
+    if e[0]=='scale':
+        _,t,a,b,*_=e;q=Q(a,b);assert q
+        rows[t]={j:q*x for j,x in rows[t].items()}
+    else:
+        _,t,s,a,b,*_=e;q=Q(a,b);assert t!=s
+        for j,x in list(rows[s].items()):
+            z=rows[t].get(j,Q(0))+q*x
+            if z:rows[t][j]=z
+            else:rows[t].pop(j,None)
+def ident():return [{r:Q(1)} for r in range(n)]
+def inv(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=inv(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1]
+    return e
+
+main=word['A']+word['cut']+word['B']
+assert all(not 120<=e[2]<240 for e in word['A']+word['B'] if e[0]=='add' and not 120<=e[1]<240)
+matrix=ident()
+for e in main:apply(e,matrix)
+print('full main columns',n,'replayed',flush=True)
+# Compute -A_Y^-1 B_S using only rows of the explicit main operator.
+dirty=[{} for r 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)
+comp=[]
+for r in range(v,2*v):
+    for j,q in sorted(dirty[r].items()):comp.append(['add',r,j,-q.numerator,q.denominator,[]])
+
+cleanup=[inv(e) for e in reversed(word['A']+word['B']) if not v<=e[1]<2*v]
+assert [e[:-1] for e in cleanup]==[e[:-1] for e in word['cleanup']]
+program=word['precondition']+comp+main+cleanup
+actual=ident()
+for e in program:apply(e,actual)
+expected=ident()
+for t in range(v):expected[v+t][t]=Q(1)
+assert actual==expected
+print('PASS exact arbitrary dirt and restored sources/helpers',flush=True)
+back=ident()
+for e in program:apply(dual(e),back)
+expected_back=ident()
+for t in range(v):expected_back[t][v+t]=Q(-1)
+assert back==expected_back
+print('PASS exact inverse-transpose on every column',flush=True)
+# Independent sparse vector controls avoid repeating a dense full replay.
+def vector(es,x):
+    x=list(map(Q,x))
+    for e in es:
+        if e[0]=='scale':x[e[1]]*=Q(e[2],e[3])
+        else:x[e[1]]+=Q(e[3],e[4])*x[e[2]]
+    return x
+sample=[((i*137+13)%101)-50 for i in range(n)]
+want=vector(program,sample)
+controls={
+    'missing_dirty_compensation':word['precondition']+main+cleanup,
+    'missing_Y_inverse_basis':comp+main+cleanup,
+    'missing_source_cleanup':word['precondition']+comp+main,
+    'wrong_dual_event_order':[dual(e) for e in reversed(program)],
+}
+for name,es in controls.items():
+    expected_sample=vector([dual(e) for e in program],sample) if name=='wrong_dual_event_order' else want
+    assert vector(es,sample)!=expected_sample,name
+
+# Orthogonal transvection and a port permutation bring the new geometry onto
+# the already fixed 120-port routing family. Every incidence is transformed.
+old=json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))
+def tau(x):return x^(43 if (x&43).bit_count()%2 else 0)
+assert 43 .bit_count()%2==0
+assert set(map(tau,word['ports']))==set(old['ports'])
+mapping={i:old['ports'].index(tau(q)) for i,q 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)})
+def basis(vs):
+    b={}
+    for x in vs:
+        for k in sorted(b,reverse=True):
+            if x>>k&1:x^=b[k]
+        if x:
+            k=x.bit_length()-1
+            for j in b:
+                if b[j]>>k&1:b[j]^=x
+            b[k]=x
+    return tuple(b[k] for k in sorted(b,reverse=True))
+def perp(x):return basis([z for z in range(1,512) if not (x&z).bit_count()%2])
+full=tuple(1<<i for i in range(8,-1,-1));frames=[(),full];fi={f:i for i,f in enumerate(frames)}
+def fid(f):
+    f=basis(f)
+    if f not in fi:fi[f]=len(frames);frames.append(f)
+    return fi[f]
+def canonical(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
+can={key:[canonical(e) for e in word[key]] for key in ('A','B','cut','cleanup','precondition')}
+can['compensation']=[canonical(e) for e in comp]
+can['start']=[fid([q]) for q in old['ports']]+[0]*(v+word['report']['R'])
+for _r,_E in word.get('start_extra',{}).items():
+    assert 2*v<=int(_r)<2*v+word['report']['R'],('an entrance (residual wrapper, spectators, bank footprint) is defined for helper registers only',_r)   # GK
+    can['start'][int(_r)]=fid([tau(x) for x in _E])   # GK: helper entrances
+can['final']=[1]*v+[fid(perp(q)) for q in old['ports']]+[1]*word['report']['R']
+can['ports']=old['ports'];can['centers']=[mapping[r] for r in word['centers']]
+can['center_frames']=[fid([tau(x) for x in f]) for f in word['center_frames']]
+tlev={}   # GK: nonzero-frame compensation raises targets before the centre scatter
+for _t,_E in word.get('target_levels',{}).items():tlev[mapping[v+int(_t)]-v]=fid([tau(x) for x in _E])
+if tlev:can['target_levels']=tlev
+can['h']=9;can['v']=v;can['R']=word['report']['R'];can['frames']=frames
+cur=list(can['start']);paid=Counter();edges=set();incidences=0
+def climb(r,f):
+    old=cur[r]
+    assert basis(frames[old]+frames[f])==frames[f]
+    if old!=f:
+        delta=len(frames[f])-len(frames[old]);assert delta>0
+        edges.add((old,f));paid[delta]+=1;cur[r]=f
+for part in ('A','B'):
+    if part=='B':
+        assert all(cur[r]==f for r,f in zip(can['centers'],can['center_frames']))
+        assert all(cur[r]==tlev.get(r-v,0) for r in range(v,2*v))   # GK: targets sit at their level
+        for r_c,f in zip(can['centers'],can['center_frames']):
+            # GK: a centre copy descends cf -> served levels (descending chain) -> lowest served level; at the defaults the
+            # only served level is 0 and this is PR #433's single child of rank |cf|
+            served={tlev.get(e[1]-v,0) for e in can['cut'] if e[2]==r_c}
+            o=f
+            for Lv in sorted(served,key=lambda x:-len(frames[x])):
+                assert basis(frames[Lv]+frames[o])==tuple(frames[o]),('centre level outside the previous frame',r_c)
+                if Lv!=o:
+                    paid[len(frames[o])-len(frames[Lv])]+=1
+                    if not(o==f and Lv==0):edges.add((o,Lv));edges.add((Lv,o))   # (cf,0),(0,cf) are added by the phase script
+                    o=Lv
+    for e in can[part]:
+        rs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        for r in rs:climb(r,e[-1]);incidences+=1
+for r,f in enumerate(can['final']):climb(r,f)
+assert dict(paid)=={int(r):x for r,x in word['report']['local_profile'].items()}
+# GK: entrances lower the helper climb by their rank; centre descents may stop above frame zero
+if not word.get('start_extra') and not word.get('target_levels'):assert sum(r*x for r,x in paid.items())==9*can['R']+240*8+72
+else:assert sum(r*x for r,x in paid.items())==sum(int(r)*x for r,x in word['report']['local_profile'].items())
+can['local_profile']=dict(sorted(paid.items()));can['edges']=sorted(edges)
+cp=OUT/'CANONICAL-WORD.json.gz';cp.write_bytes(gzip.compress(json.dumps(can,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+
+def engine(name):
+    p=Path('work/pr361/code/engines')/(name+'.py');s=importlib.util.spec_from_file_location('hamming_'+name,p)
+    m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,M2=engine('moment'),engine('base_two_moment');m,W=73,word['report'].get('live',12720)   # GK: unhosted stock of the word
+HG={int(r):z for r,z in word['report']['global_profile'].items()}
+root=M.certify(HG,m,W,True);b=Q(int(Q(root['lower'])*10**18),10**18);grid=Q(1,10**18)
+assert M.moment(HG,m,W,b,True)[1]<1<M.moment(HG,m,W,b+grid,True)[0]
+fallback=32*m*m*sum(HG.values())
+def second(a):
+    lo,hi=M2.moment(m,W,list(HG.items()),a)
+    l2,h2=M2.moment(m,W,[(1,fallback)],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert second(b)[1]<1<second(b+grid)[0]
+coeff=Counter(str(Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])) for e in program)
+report={'status':'PASS_EXACT_SCALAR_AND_FRAME_RESEARCH_CANDIDATE_NOT_YET_ADMITTED',
+        'full_word_sha256':hashlib.sha256(p.read_bytes()).hexdigest(),
+        'canonical_word_sha256':hashlib.sha256(cp.read_bytes()).hexdigest(),
+        'live_columns_each_orientation':n,'arbitrary_helper_columns':can['R'],
+        'all_live_source_and_helper_rows_restored':True,'all_target_rows_correct':True,
+        'negative_controls_rejected':list(controls),'old_response_additions':len(comp),
+        'complete_forward_scalar_operations':len(program),'coefficient_histogram':dict(coeff),
+        'frames':len(frames),'nested_directed_edges':len(edges),'common_frame_incidences':incidences,
+        'orthogonal_transport_vector':43,'transported_ports_exactly_match_fixed_routes':True,
+        'local_profile':dict(sorted(paid.items())),
+        'prospective_complex_b':str(b),'prospective_b_float':float(b),
+        'prospective_gain_percent':float(100*(b/Q(999388595603943,10**18)-1)),
+        'two_rational_moment_engines':True,'next_b_grid_rejected':True,
+        'remaining':['new general scalar-interface proof integration','exact phase and emitted local/global program','finite invoice and outer assembly'],
+        'scope':'Substantial new scalar-network candidate. All parameter values remain prospective until the expanded scalar interface and complete phase-aware supplier are admitted.',
+        'seconds':time.monotonic()-start}
+(OUT/'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(report,indent=2)+'\n')
+print('PASS prospective b',float(b),'gain',report['prospective_gain_percent'],'percent; seconds',report['seconds'],flush=True)
diff --git a/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py
new file mode 100644
index 0000000000..0dd1853bb5
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py
@@ -0,0 +1,156 @@
+# GK: modified copy of PR #433's complex_emit.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted from PR425 by icekylinx with Codex assistance.
+"""Emit both local programs, integrate the fixed nine-stage geometry, and bill.
+
+The expanded scalar interface is justified in PROOF.txt. This script does not
+claim a Lean proof or discharge the inherited all-size/analytic interfaces.
+"""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp))
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def basis(vs):
+    b={}
+    for x in vs:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def dual(e):
+    e=list(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def scalar(e,back):
+    e=dual(e) if back else list(e)
+    if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]]
+    return ['scale',['L',e[1]],e[2],e[3]]
+def primitive_bound(e):
+    if e[0] in ('clear','copy'):return 1
+    q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])
+    a,b=abs(q.numerator),q.denominator
+    assert b&(b-1)==0
+    if e[0]=='scale':
+        assert a&(a-1)==0
+        return abs(a.bit_length()-b.bit_length())+int(q<0)
+    # Exact binary Horner multiplication on a cleared private stream, repeated
+    # halving, signed accumulation into the target, then clear the private stream.
+    return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1)
+
+def emit(back):
+    out=[];cur=c['start'].copy()
+    def event(e):out.append(e)
+    def scal(e,f):event(['scalar',e,f])
+    event(['phase','zero_frame_precondition'])
+    for e in c['precondition']+c['compensation']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['start'][r]==0 for r in regs)
+        scal(scalar(e,back),0)
+    event(['phase','entry_adapters'])
+    # GK: a helper that starts at a nonzero entrance frame has NO entry adapter; its paid wrapper R_E^-1 (Lemma A) precedes every gate
+    # that touches it and L_E^-1 follows the full-frame cleanup.  Words without entrances emit PR #433's events.
+    entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+    for r,f in enumerate(c['start']):
+        if r in entering:event(['residual_adapter','pre',r,f])
+        else:event(['adapter','old_to_new',r,f])
+    def climb(r,f,part):
+        old=cur[r]
+        if old==f:return
+        assert basis(frames[old]+frames[f])==tuple(frames[f])
+        rank=len(frames[f])-len(frames[old]);assert rank>0
+        event(['climb',part,r,old,f,rank]);cur[r]=f
+    for part in ('A','centers','B','final'):
+        event(['phase',part])
+        if part in ('A','B'):
+            for e in c[part]:
+                regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+                for r in regs:climb(r,e[-1],part)
+                scal(scalar(e,back),e[-1])
+        elif part=='centers':
+            # GK: targets sit at their nonzero-frame-compensation level (0 at the defaults); a centre copy descends
+            # cf -> served levels (descending chain) -> lowest served level and scatters into each target at its level
+            lv=lambda r:c.get('target_levels',{}).get(str(r-v),0)
+            assert all(cur[r]==lv(r) for r in range(v,2*v))
+            for k,r in enumerate(c['centers']):
+                cf=c['center_frames'][k];assert cur[r]==cf
+                terms=[e for e in c['cut'] if e[2]==r]
+                path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x]))
+                C=['C',k]
+                if not back:
+                    scal(['clear',C],cf);scal(['copy',C,['L',r]],cf)
+                    for a in range(len(path)):
+                        if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])])
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a])
+                    scal(['clear',C],path[-1])
+                else:
+                    scal(['clear',C],path[-1])
+                    for a in range(len(path)-1,-1,-1):
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a])
+                        if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])])
+                    scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf)
+        else:
+            for r,f in enumerate(c['final']):climb(r,f,part)
+    event(['phase','exit_adapters'])
+    for r,f in enumerate(c['final']):event(['adapter','new_to_old',r,f])
+    event(['phase','full_frame_cleanup'])
+    for e in c['cleanup']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['final'][r]==1 for r in regs)
+        scal(scalar(e,back),1)
+    for r in entering:event(['residual_adapter','post',r,c['start'][r]])   # GK: L_E^-1 after the full-frame cleanup
+    event(['phase','done'])
+    return out
+
+def check_local(events,back):
+    # Literal scalar replay of the emitted stream, including center lifetimes.
+    state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0
+    for e in events:
+        if e[0]=='climb':assert not live;paid[e[5]]+=1
+        elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1
+        elif e[0]=='scalar':
+            op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op)
+            if tag=='clear':
+                state[t]={}
+                if t[0]=='C' and t[1] in live:live.remove(t[1])
+            elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1])
+            elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()}
+            else:
+                s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{})
+                if t[0]=='C' and t[1] not in live:live.append(t[1])
+                for j,x in list(state.get(s,{}).items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+    assert not live and all(not row for r,row in state.items() if r[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert state['L',r]==expected,('emitted column mismatch',back,r)
+    assert dict(paid)=={int(r):z for r,z in c['local_profile'].items()}
+    return {'sha256':digest(events),'events':len(events),'scalar_macros':macros,
+            'real_component_primitive_bound':prims,'paid_profile':dict(sorted(paid.items())),
+            'all_columns':n,'private_centers_cleared':True,'private_coefficient_stream_cleared_after_each_macro':True}
+
+programs={};checks={}
+for name,back in [('forward',False),('backward',True)]:
+    programs[name]=emit(back);checks[name]=check_local(programs[name],back)
+    print('PASS emitted',name,checks[name]['events'],'events',flush=True)
+
+
+(OUT/'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(json.dumps(programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'LOCAL-CHECKS.json').write_text(json.dumps(checks,indent=2)+'\n')
diff --git a/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py
new file mode 100644
index 0000000000..0e5fde920d
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py
@@ -0,0 +1,94 @@
+"""Shared helpers for the complex shared-donor-kernel / entrance-gauge word.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+
+A "gk word" is PR #433's FULL-WORD.json.gz with optional extension keys (absent in #433's word, so every default is
+#433's behaviour):
+  start_extra   {register: entrance frame (list of F2^9 vectors)}  helpers that start at a nonzero frame (width 9 - dim)
+  target_levels {target: frame}                                    frame a target reaches through nonzero-frame compensation
+Entrance gauges are ordinary gates at the head of A (target += c * helper at the entrance frame); kernel updates are
+ordinary gates at the head of A (donor += q * pivot at the entrance frame).
+"""
+import math
+from collections import Counter
+
+V, K, T, L, M = 120, 4, 8, 9, 73
+DATA = 2 * K * V * T          # 7680
+FULL = tuple(1 << i for i in range(8, -1, -1))
+
+
+def basis(vs):
+    b = {}
+    for x in vs:
+        for p in sorted(b, reverse=True):
+            if x >> p & 1: x ^= b[p]
+        if x:
+            p = x.bit_length() - 1
+            for q in b:
+                if b[q] >> p & 1: b[q] ^= x
+            b[p] = x
+    return tuple(b[p] for p in sorted(b, reverse=True))
+
+
+def widths_of(word):
+    """residual width of every helper: 9 - dim(entrance frame); 9 when the word has no extension"""
+    R = word['report']['R'] if 'R' not in word else word['R']
+    w = [L] * R
+    for r, E in word.get('start_extra', {}).items():
+        assert 2 * V <= int(r) < 2 * V + R
+        w[int(r) - 2 * V] = L - len(basis(E))
+    return w
+
+
+def split_pad(p):
+    """a pad of rank p is paid as nested commuting children of rank <= 51 (so that 73^2 > 2*child^2); rank 1 stays 1"""
+    if p == 0: return []
+    n = -(-p // 51); return [p // n + (1 if i < p % n else 0) for i in range(n)]
+
+
+def tile(items):
+    """Bank tiling of unhosted residuals.  items: list of (rep, helper, width); a bank has M = 73 cells.
+    * width-9 residuals (no wrapper acts on them): first fit in the given order, packed from offset 0, eight per bank, pad rank 1
+      (PR #433/#442's tiling and routes [2, slot]);
+    * ENTERING residuals (width w < 9, paid wrappers, e = 9 - w spectators): banks of their own in which every entering helper is the ONLY
+      owner of its bank family in its invocation (the one-helper rule of PR #458 extended to banks): bank j holds the j-th entering
+      helper of each replica, residuals packed from offset 0 in replica order (at most one helper per replica, hence per invocation).
+      The spectators of an entering helper are the first e cells of the bank beyond every residual cell of the bank (the pad, which no call
+      uses for a residual, is paid as before: rank 73 - sum of widths; the spectators are borrowed inside it and not deducted).
+    Returns (assign, banks, pads): assign[(rep, helper)] = (bank, offset, width, pure, spectators) with pure = the bank holds only width-9
+    residuals and spectators = () for width 9; pads = Counter of pad ranks (split into children of rank <= 51)."""
+    assign = {}; pads = Counter(); fill = []
+    for z, (rep, h, w) in enumerate(items):             # width 9: first fit, as PR #433 (all widths 9 reproduces it exactly)
+        if w != L: continue
+        for b, f in enumerate(fill):
+            if f + w <= M: break
+        else:
+            b = len(fill); fill.append(0)
+        assign[(rep, h)] = (b, fill[b], w, True, ()); fill[b] += w
+    nwide = len(fill); byrep = {}
+    for rep, h, w in items:
+        if w < L: byrep.setdefault(rep, []).append((h, w))
+    cells = [0] * max((len(v) for v in byrep.values()), default=0); emax = [0] * len(cells); place = {}
+    for rep in sorted(byrep):                           # the j-th entering helper of every replica goes to entering bank j
+        for j, (h, w) in enumerate(byrep[rep]):
+            place[(rep, h)] = (nwide + j, cells[j], w); cells[j] += w; emax[j] = max(emax[j], L - w)
+    for j in range(len(cells)): assert cells[j] + emax[j] <= M, ('entering bank without room for its spectators', j)
+    for (rep, h), (b, off, w) in place.items():
+        assign[(rep, h)] = (b, off, w, False, tuple(range(cells[b - nwide], cells[b - nwide] + L - w)))
+    fill += cells
+    for f in fill:
+        for part in split_pad(M - f): pads[part] += 1
+    return assign, len(fill), pads
+
+
+def route(off, w, pure, sp=()):
+    """owner route of a banked helper residual: PR #433's [2, slot] for width 9 (pure width-9 bank); an entering helper (w < 9) is
+    [2, offset, width, [spectator cells]] with e = 9 - w spectators"""
+    if w == L: assert pure and not sp; return [2, off // L]
+    assert not pure and len(sp) == L - w; return [2, off, w, list(sp)]
+
+
+def unhosted_stock(widths):
+    """live stock and padding histogram of the unhosted (parent) template, per stage x nine"""
+    R = len(widths)
+    _, nb, pads = tile([(rep, h, widths[h]) for rep in range(T) for h in range(R)])
+    return DATA + L * nb, Counter({r: z * L for r, z in pads.items()})
diff --git a/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py
new file mode 100644
index 0000000000..15782ba625
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py
@@ -0,0 +1,194 @@
+"""Apply a frozen selection (shared-donor kernel + entrance gauges) to PR #433's complex word.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+usage: gk_word.py BASE_FULL-WORD.json.gz SELECTION.json OUT_FULL-WORD.json.gz
+An empty selection ({}) copies the input byte for byte (regression anchor).
+
+selection = {"kernel": [{"E": [x], "donors": [h..], "pivots": [h..]}..], "gauge": {"h": [x..]}}   (h = helper index 0..R-1)
+Kernel (PR #417/#435/#434/#440): a pivot starts at E; every donor receives  donor += -q * pivot  at frame E before the main
+word, where col(pivot) = sum q_d col(d) are the exact dirty-response columns; the pivot's frame-zero compensation vanishes.
+Gauge (#401/#408-#416): the compensation  target += -C[t,h] * helper  of helper h is executed at frame E_h as the first gates
+of the main word; h starts at E_h and its targets climb to the level L_t = largest E over their entering helpers.
+The exact verification is the arbitrary-dirt replay of audit_gk.py; this module also checks the structural conditions."""
+import copy, gzip, hashlib, json, sys
+from collections import Counter, defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from gk_common import *
+
+
+def apply_op(e, rows):
+    if e[0] == 'scale':
+        _, t, a, b, *_ = e; q = Q(a, b); rows[t] = {j: q * x for j, x in rows[t].items()}
+    else:
+        _, t, s, a, b, *_ = e; q = Q(a, b)
+        for j, x in list(rows[s].items()):
+            z = rows[t].get(j, Q(0)) + q * x
+            if z: rows[t][j] = z
+            else: rows[t].pop(j, None)
+
+
+def inverse(e, F):
+    e = copy.deepcopy(e)
+    if e[0] == 'add': e[3] *= -1
+    else: e[2], e[3] = e[3], e[2]
+    e[-1] = list(F); return e
+
+
+def responses(word):
+    """dirty-response columns col[h] = {target: coefficient} of the unmodified word (after the frame-zero preconditioner)"""
+    R = word['report']['R']; n = 2 * V + R
+    rows = [{r: Q(1)} for r in range(n)]
+    for e in word['A'] + word['cut'] + word['B']: apply_op(e, rows)
+    dirty = [{} for _ in range(n)]
+    for r in range(V, 2 * V): dirty[r] = {j: x for j, x in rows[r].items() if j >= 2 * V}
+    for e in word['precondition']: apply_op(e, dirty)
+    col = [{} for _ in range(R)]
+    for r in range(V, 2 * V):
+        for j, x in dirty[r].items(): col[j - 2 * V][r - V] = x
+    return col
+
+
+def first_frames(word):
+    first = {}
+    for seq in (word['A'], word['B']):
+        for e in seq:
+            F = basis(e[-1])
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []):
+                if r >= 2 * V: first.setdefault(r - 2 * V, F)
+    return first
+
+
+def solve_relation(col, donors, p):
+    """exact rational c with col[p] = sum_d c_d col[d]; None if p is not in the span"""
+    ts = sorted({t for d in donors for t in col[d]} | set(col[p]))
+    idx = {t: i for i, t in enumerate(ts)}
+    Mx = [[Q(0)] * (len(donors) + 1) for _ in ts]
+    for ci, d in enumerate(donors):
+        for t, x in col[d].items(): Mx[idx[t]][ci] = x
+    for t, x in col[p].items(): Mx[idx[t]][-1] = x
+    piv = []; r = 0
+    for c in range(len(donors)):
+        pr = next((i for i in range(r, len(Mx)) if Mx[i][c]), None)
+        if pr is None: continue
+        Mx[r], Mx[pr] = Mx[pr], Mx[r]; q = Mx[r][c]; Mx[r] = [x / q for x in Mx[r]]
+        for i in range(len(Mx)):
+            if i != r and Mx[i][c]:
+                f = Mx[i][c]; Mx[i] = [a - f * b for a, b in zip(Mx[i], Mx[r])]
+        piv.append(c); r += 1
+    if any(Mx[i][-1] for i in range(r, len(Mx))): return None
+    assert r == len(donors), 'donors must have independent response columns'
+    return {donors[c]: Mx[i][-1] for i, c in enumerate(piv) if Mx[i][-1]}
+
+
+def span(U):
+    s = {0}
+    for b in U: s |= {x ^ b for x in s}
+    return s
+
+
+def perp(x): return basis([z for z in range(1, 512) if not (x & z).bit_count() % 2])
+
+
+def profile(word):
+    """local paid profile of a gk word by direct simulation of the frame chains (second implementation: audit_gk.py)"""
+    R = word['report']['R']; n = 2 * V + R; P = word['ports']
+    cur = {}
+    for r in range(n):
+        cur[r] = (P[r],) if r < V else ((basis(word['start_extra'][str(r)]) if str(r) in word.get('start_extra', {}) else ()) if r >= 2 * V else ())
+    paid = Counter()
+    def climb(r, F):
+        F = basis(F); o = cur[r]
+        assert basis(list(o) + list(F)) == F, ('frame violation', r, o, F)
+        if o != F: paid[len(F) - len(o)] += 1; cur[r] = F
+    lev = {int(t): basis(E) for t, E in word.get('target_levels', {}).items()}
+    for seq, part in ((word['A'], 'A'), (word['B'], 'B')):
+        if part == 'B':
+            for r, f in zip(word['centers'], word['center_frames']):
+                assert cur[r] == basis(f), 'centre frame'
+                served = sorted({lev.get(e[1] - V, ()) for e in word['cut'] if e[2] == r}, key=lambda E: -len(E))
+                o = basis(f)
+                for Lv in served:
+                    assert span(Lv) <= span(o), 'served levels must descend inside the centre frame'
+                    if Lv != o: paid[len(o) - len(Lv)] += 1; o = Lv
+            for t in range(V): assert cur[V + t] == lev.get(t, ()), 'target level at the centre scatter'
+        for e in seq:
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): climb(r, e[-1])
+    for r in range(n): climb(r, FULL if (r < V or r >= 2 * V) else perp(P[r - V]))
+    return paid
+
+
+def global_profile(local, widths):
+    """unhosted nine-stage profile: local x (stages*replicas) + the 240*8 idle children per rank + bank pads"""
+    live, pads = unhosted_stock(widths)
+    g = Counter({r: z * L * T for r, z in local.items()})
+    for r in (16, 8, 32, 8, 48, 8, 48, 32, 16): g[r] += 240 * T
+    g.update(pads)
+    return live, g
+
+
+def build(word, sel, check=True):    # check=False only for the mutation controls that must be caught by the certifying scripts
+    if not sel: return word
+    w = copy.deepcopy(word); R = w['report']['R']
+    col = responses(word); first = first_frames(word)
+    gauge = {int(h): basis(E) for h, E in sel.get('gauge', {}).items()}
+    classes = sel.get('kernel', [])
+    pivots = {p for c in classes for p in c['pivots']}; donors = {d for c in classes for d in c['donors']}
+    assert not (pivots & donors) and not (pivots | donors) & set(gauge) and len(pivots) == sum(len(c['pivots']) for c in classes)
+    # --- structural conditions -------------------------------------------------------------------------------------
+    for h, E in gauge.items():
+        assert not check or span(E) <= span(first[h]), ('gauge entrance outside the first frame', h)
+    levels = defaultdict(list)
+    for h, E in gauge.items():
+        for t in col[h]: levels[t].append(E)
+    for t, Es in levels.items():                                   # pairwise nested comps per target
+        for a in Es:
+            for b in Es: assert not check or span(a) <= span(b) or span(b) <= span(a), ('non-nested gauges at target', t)
+    lev = {t: max(Es, key=len) for t, Es in levels.items()}
+    for k, r in enumerate(w['centers']):                              # chain per centre, inside the centre frame
+        served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == r}
+        for a in served:
+            for b in served: assert not check or span(a) <= span(b) or span(b) <= span(a), ('centre chain', k)
+        top = max(served, key=len)
+        assert not check or span(top) <= span(basis(w['center_frames'][k])), ('level outside centre frame', k)
+    # --- gates ----------------------------------------------------------------------------------------------------------
+    gates = []
+    for h, E in sorted(gauge.items(), key=lambda kv: (len(kv[1]), kv[0])):
+        for t, x in sorted(col[h].items()):
+            c = -x; gates.append(['add', V + t, 2 * V + h, c.numerator, c.denominator, list(E)])
+    pre = []
+    start = {2 * V + h: list(E) for h, E in gauge.items()}
+    for cl in sorted(classes, key=lambda c: (len(c['E']), c['E'])):
+        E = basis(cl['E'])
+        for x in [*cl['donors'], *cl['pivots']]: assert span(E) <= span(first[x]), ('kernel entrance outside the first frame', x)
+        for p in cl['pivots']:
+            rel = solve_relation(col, cl['donors'], p)
+            assert rel is not None, ('pivot response not in the donor span', p)
+            start[2 * V + p] = list(E)
+            for d, c in rel.items():
+                q = -c; pre.append(['add', 2 * V + d, 2 * V + p, q.numerator, q.denominator, list(E)])
+    w['A'] = gates + pre + w['A']
+    w['cleanup'] = [inverse(e, FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V]
+    w['start_extra'] = {str(r): list(E) for r, E in sorted(start.items())}
+    w['target_levels'] = {str(t): list(E) for t, E in sorted(lev.items()) if E}
+    if not check: return w
+    prof = profile(w); widths = widths_of(w)
+    live, g = global_profile(prof, widths)
+    w['report']['local_profile'] = {str(k): z for k, z in sorted(prof.items())}
+    w['report']['global_profile'] = {str(k): z for k, z in sorted(g.items())}
+    w['report']['live'] = live
+    w['report']['entrance_rank'] = sum(L - x for x in widths); w['report']['entering_helpers'] = sum(1 for x in widths if x < L)
+    w['report']['selection_sha256'] = hashlib.sha256(json.dumps(sel, sort_keys=True).encode()).hexdigest()
+    return w
+
+
+def dump(w): return gzip.compress(json.dumps(w, sort_keys=True, separators=(',', ':')).encode(), mtime=0)
+
+
+if __name__ == '__main__':
+    src, selp, out = map(Path, sys.argv[1:4])
+    sel = json.loads(selp.read_text())
+    if not sel: out.write_bytes(src.read_bytes()); print('empty selection: copied byte for byte'); sys.exit(0)
+    word = json.load(gzip.open(src)); w = build(word, sel); out.write_bytes(dump(w))
+    print('gk word: entering helpers', w['report']['entering_helpers'], 'entrance rank', w['report']['entrance_rank'],
+          'local profile', w['report']['local_profile'], 'unhosted live', w['report']['live'])
diff --git a/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py
new file mode 100644
index 0000000000..df261063e1
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py
@@ -0,0 +1,123 @@
+# GK: modified copy of PR #433's complex_integrate.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 for heterogeneous centres by icekylinx, with Codex assistance.
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp));audit=json.loads((OUT/'SCALAR-FRAME-AUDIT.json').read_text())
+phase=json.loads((OUT/'CLIFFORD-REVIEW.json').read_text());sha=lambda p:hashlib.sha256(Path(p).read_bytes()).hexdigest()
+assert phase['canonical_word_sha256']==audit['canonical_word_sha256']==sha(cp)
+assert phase['all_child_equalities_include_global_phase']
+programs=json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'));checks=json.loads((OUT/'LOCAL-CHECKS.json').read_text())
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R;private_centres=len(c['centers'])
+for z in checks.values():z['paid_profile']={int(r):n for r,n in z['paid_profile'].items()}
+old=Path('work/complex-nine-native');template=json.load(gzip.open(old/'GLOBAL-TEMPLATE.json.gz'))
+data_phase=json.loads((old/'DATA-PHASES.json').read_text())
+assert template['exact_data_phase_recipe_sha256']==sha(old/'DATA-PHASES.json')
+assert data_phase['status']=='PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES'
+m,T,L,k=73,8,9,4
+# GK: residual widths 9 - dim(start frame); banks tile per width class (all 9: PR #433's eight residuals + one pad)
+from gk_common import tile,route
+widths=[h-len(frames[c['start'][2*v+i]]) for i in range(R)]
+assign,nb,pads=tile([(rep,i,widths[i]) for rep in range(T) for i in range(R)]);entering0=any(w_<h for w_ in widths)
+W=2*v*k*T+L*nb;physical=W+R+private_centres+2
+template['version']='hamming-mutable-basis-nine-v1';template['live']=W;template['physical']=physical
+template['local_programs']=programs;paid=Counter();assignments=set();event_count=0;scalar_primitives=0
+for call in template['calls']:
+    stage,rep,pair=call['stage'],call['replica'],call['pair'];ori=call['orientation']
+    owners=[[rep*2*k*v+(2*pair+r//v)*v+r%v,[1,stage,r%v]] for r in range(2*v)]
+    for r in range(R):
+        bank,off_,w_,pure_,sp_=assign[rep,r];owners.append([2*v*k*T+stage*nb+bank,route(off_,w_,pure_,sp_)])   # GK: [2,slot] in pure width-9 banks, [2,offset,width,spectators] for entering helpers
+        assignments.add((stage,rep,r,bank,off_))
+    assert len(owners)==n and len({(f,json.dumps(route)) for f,route in owners})==n
+    assert all(f<W for f,route in owners)   # GK: every owner lies in the live stock (none in the private namespace)
+    fam=Counter(f for f,route in owners)   # GK: an entering helper is the only owner of its bank family in the invocation (PR #458's rule, banks included); the data families are the 240 distinct active ones
+    assert all(fam[f]==1 for f,route in owners[:2*v]) and all(fam[owners[2*v+r][0]]==1 for r in range(R) if widths[r]<h),('entering helper shares its bank family',stage,rep)
+    call['owners']=owners;call['local_program_sha256']=checks[ori]['sha256']
+    for r,z in checks[ori]['paid_profile'].items():paid[r]+=z
+    event_count+=checks[ori]['events'];scalar_primitives+=checks[ori]['real_component_primitive_bound']
+assert len(assignments)==L*T*R and len(template['calls'])==72
+for item in template['idle_children']:paid[item['rank']]+=item['replicas']
+for r_,z_ in pads.items():paid[r_]+=z_*L   # GK: bank pads (rank 1 each at width 9 and 8)
+assert dict(paid)=={int(r):z for r,z in json.load(gzip.open(OUT/'FULL-WORD.json.gz'))['report']['global_profile'].items()}
+mass=sum(r*z for r,z in paid.items());assert m*W-mass==2496
+if entering0:template['route_semantics']['helper']+='; entering helpers: paid wrappers R_E^-1 before and L_E^-1 after the invocation; an entering helper is the only owner of its bank family in the invocation, route [2, offset, width, spectator cells] with the spectators the first cells of the bank beyond every residual cell'   # GK
+template['bank_padding']['families']=list(range(7680,W))
+template['cover_final_correction']['families']=[0,W]
+template['cover_final_correction']['charged_calls_per_cover']=W
+for e in template['execution_schedule']:
+    if e['kind']=='bank_padding_cover_sweep':e['families']=[7680,W]
+    elif e['kind']=='translate_every_live_family':e.update(template['cover_final_correction'])
+template['private_namespace']={'centers':[W,W+private_centres],'reserved_tableau':[W+private_centres,W+private_centres+R],
+                               'coefficient':[physical-2,physical]}
+template['exact_local_clifford_recipe_sha256']=sha(OUT/'CLIFFORD-RECIPES.json')
+if (OUT/'RESIDUAL-ADAPTERS.json').exists():template['residual_adapter_sha256']=sha(OUT/'RESIDUAL-ADAPTERS.json')   # GK: paid wrappers of entering helpers (Lemma A)
+template['expanded_scalar_interface']='See PROOF.txt: mutable source basis, frame-zero output preconditioner, explicit dirty compensator, and full-frame inverse source/helper cleanup.'
+blob=json.dumps(template,sort_keys=True,separators=(',',':')).encode()
+(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+
+# Fresh finite overcharge, with the changed stock, scalar counts, coefficient
+# lowering, and private work reserve. No unchanged local invoice is assumed.
+compiler=64*(m+1)**3;macros=max(z['scalar_macros'] for z in checks.values());children=sum(checks['forward']['paid_profile'].values())
+adapters=16*(macros+children+n+private_centres)+64*m
+local_bound=max(z['real_component_primitive_bound'] for z in checks.values())+adapters*compiler
+bridges=[e for e in template['recipe'] if e['kind']=='bridge'];bridge_adds=2*v*T*len(bridges)
+terminal_shifts=k*v*T;terminal_moves=2*k*v*T
+entering=sum(1 for w_ in widths if w_<h)   # GK: entrance adapters (Lemma A): a monomial on 9 bits is at most 81+45+9=135 elementary factors (matrix, quadratic form, translation); charge 144 at entry and at exit of every entering helper in every invocation
+nonlocal_items=4*v*T*L+2*v*T*L+2*L*T*R+sum(e['replicas'] for e in template['idle_children'])+L*nb+bridge_adds+terminal_shifts+terminal_moves+W+physical+2*L*T*entering*144
+outside=8*nonlocal_items+64*m
+pervertex=scalar_primitives+bridge_adds+terminal_shifts+terminal_moves+W+(72*adapters+outside)*compiler+64*physical
+r=m//2;group=2**(r*r)*math.prod(2**(2*i)-1 for i in range(1,r+1));stock=group*physical
+smass=group*mass;logical=group*pervertex+64;router=compiler*(logical+1)*(stock+1)**2
+GG,EE,C0=1<<30000,1<<100000,1<<210000;BB=smass+EE
+literal=2*GG*stock**2+8*smass+4*stock+4+32*m
+maxchild=max(paid);depth=2;assert m**depth>2*maxchild**depth
+assert local_bound<1<<48 and logical<1<<6050 and router<GG and literal<EE and BB<1<<100001
+assert 32*m*BB*BB<C0 and 2*BB+18<C0
+row=depth*stock.bit_length()+9909+252;assert row<20161
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('hamming_integrate_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    mod=importlib.util.module_from_spec(sp);sp.loader.exec_module(mod);return mod
+Outer=load('outer');b=Q(audit['prospective_complex_b']);bit=Q(json.loads(Path('BIT-PRICE.json').read_text())['lower'])
+eta=Q(1,10**12);beta=Q(1,10**9);grid=Q(1,10**18)
+s=Q(int(((1-beta)*min(b,bit)-grid)*10**18),10**18);assert s<bit
+chain=[Q(384599,10**10)];cutoffs=[]
+for _ in range(3):
+    a=chain[-1];z=(1-s)*s+s*a;gap=min(s-z,1-z-s,1-z-s*(1-a),1-s)
+    assert a<z<s<1-z and gap>0
+    bound=max(math.ceil(36/gap**2),math.ceil(2*(4+512)/gap))
+    assert bound*gap**2>=36 and bound*gap>=2*(4+512)
+    cutoffs.append(str(bound));chain.append(z)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},
+        'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+q=chain[-1]*(1-2*eta);ticks=(1-eta)*q/(1+q)/grid;kap=Q((ticks.numerator-1)//ticks.denominator,10**18)
+assembly=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta)
+try:Outer.assembly(chain[-1],b,bridge,kap+grid,eta=eta,beta=beta)
+except AssertionError:pass
+else:raise AssertionError('next kappa grid accepted')
+result={'status':'PASS_NEW_STRUCTURAL_PROGRAM_AND_FINITE_ASSEMBLY_PENDING_REPLAY',
+        'canonical_word_sha256':sha(cp),'scalar_audit_sha256':sha(OUT/'SCALAR-FRAME-AUDIT.json'),
+        'exact_phase_receipt_sha256':sha(OUT/'CLIFFORD-REVIEW.json'),'global_template_sha256':hashlib.sha256(blob).hexdigest(),
+        'local_program_checks':checks,'R':R,'m':m,'live':W,'physical':physical,
+        'bank_assignments':len(assignments),'rank_mass':mass,'deficit':2496,
+        'global_profile':dict(sorted(paid.items())),'emitted_local_events_all_calls':event_count,
+        'finite_invoice':{'local_primitive_bound':local_bound,'local_adapters':adapters,
+                          'pervertex':pervertex,'physical_stock_bits':stock.bit_length(),
+                          'router_bits':router.bit_length(),'literal_bits':literal.bit_length(),
+                          'physical_row_coefficient':row,'retained_row_coefficient':20161,
+                          'compiler':compiler,'G_exponent':30000,'E_exponent':100000,'C0_exponent':210000,
+                          'required_C0_bits':(32*m*BB*BB).bit_length(),'halving_degree':depth,
+                          'halving_integer_inequality':[m**depth,2*maxchild**depth]},
+        'complex_b':str(b),'bit_c':str(bit),'prospective_kappa':str(kap),'kappa_float':float(kap),
+        'log2_kappa':math.log2(float(kap)),
+        'kappa_gain_percent':float(100*(kap/Q(998390813251625,10**18)-1)),
+        'strict_outer_constraints':{name:str(z) for name,z in assembly['strict_constraints'].items()},
+        'next_kappa_grid_rejected':True,'bootstrap_cutoffs_log2':cutoffs,
+        'scope':'New finite scalar interface with a written conjugation proof, conditional on inherited all-size compiler, precision/tape and analytic transfer. Independent emitted-program replay and fresh package replay still required before final promotion.'}
+(OUT/'INTEGRATION.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS prospective kappa',float(kap),'gain',result['kappa_gain_percent'],'percent',flush=True)
diff --git a/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py
new file mode 100644
index 0000000000..220cc7a2f5
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py
@@ -0,0 +1,111 @@
+"""Whole-residual idle-axis hosting with at most ONE helper per physical family per invocation (the rule of PR #458), plus the exact
+host chart with explicit spectator coordinates.  Apache-2.0.  Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+A copy (port) of an idle child hosts a PATTERN: residuals of pairwise distinct stages inside the child's window, offsets 0, w1, w1+w2, ...
+(a residual is whole: one slot in one family).  The children of one (pair, side) have pairwise disjoint windows (checked), so the
+families they share never host two helpers of one invocation, and the integer programme needs only the distinct-stage condition.
+Chart: for the host's port q the parent's idle basis is B_q = U_q (+) I (PR #433 geometry; the construction is that of PR #458).  A hosted
+residual of width w occupies the pending vectors b_off..b_(off+w-1) of its child; the other e = 9 - w coordinates of the local nine are
+SPECTATORS: the first e basis indices of B_q not occupied by the residual, in increasing order.  The paid wrappers (adapters_gk.py) act on
+these nine coordinates and restore the spectators identically."""
+import math
+from collections import Counter
+
+H, M = 9, 73
+
+
+def cost(r, m): return r * math.log(m / r) if r else 0.0
+
+
+def patterns(rank, stages, widths):
+    out = [()]
+    ws = sorted(widths, reverse=True)
+    def rec(i, cur, tot):
+        for j in range(i, len(stages)):
+            for w in ws:
+                if tot + w <= rank:
+                    c = cur + [(stages[j], w)]; out.append(tuple(c)); rec(j + 1, c, tot + w)
+    rec(0, [], 0)
+    return out
+
+
+def solve(win, copies, avail, m, pad_value, time_limit=600):
+    """win {idx: (pair, rank, stages)}, avail {(stage, width): helpers per replica}.  Maximise saved idle cost (+ pad_value per hosted residual)."""
+    import numpy as np
+    from scipy.optimize import milp, LinearConstraint, Bounds
+    widths = sorted({w for (_, w) in avail}); var = []
+    for idx, (p, r, st) in sorted(win.items()):
+        for pat in patterns(r, sorted(st), widths): var.append((idx, pat))
+    n = len(var); c = np.zeros(n)
+    for j, (idx, pat) in enumerate(var):
+        r = win[idx][1]; c[j] = -(cost(r, m) - cost(r - sum(w for _, w in pat), m) + pad_value * len(pat))
+    rows, lo, hi = [], [], []
+    by = {}
+    for j, (idx, pat) in enumerate(var): by.setdefault(idx, []).append(j)
+    for idx, js in by.items():
+        row = np.zeros(n); row[js] = 1; rows.append(row); lo.append(copies); hi.append(copies)
+    for (s, w), a in sorted(avail.items()):
+        row = np.zeros(n)
+        for j, (idx, pat) in enumerate(var): row[j] = sum(1 for sw in pat if sw == (s, w))
+        rows.append(row); lo.append(0); hi.append(a)
+    res = milp(c, constraints=LinearConstraint(np.array(rows), lo, hi), integrality=np.ones(n), bounds=Bounds(np.zeros(n), np.full(n, np.inf)),
+               options=dict(time_limit=time_limit, disp=False))
+    assert res.x is not None, res.message
+    x = [int(round(t)) for t in res.x]
+    return [[idx, [list(sw) for sw in pat], x[j]] for j, (idx, pat) in enumerate(var) if x[j]], -res.fun
+
+
+def save(path, key, sel, val):
+    import json
+    from pathlib import Path
+    p = Path(path); d = json.loads(p.read_text()) if p.exists() else {}
+    d[key] = dict(rule='one-helper-per-family', patterns=sorted(sel), proxy_saving=val)
+    p.write_text(json.dumps(d, indent=1, sort_keys=True) + '\n')
+
+
+def load(path, key):
+    import json
+    from pathlib import Path
+    d = json.loads(Path(path).read_text())[key]; assert d['rule'] == 'one-helper-per-family'
+    return d['patterns'], d['proxy_saving']
+
+
+def check_disjoint_groups(win, pair_of, side_of):
+    """children of one (pair, side) share their physical families; their windows must be disjoint"""
+    seen = {}
+    for idx, (p, r, st) in win.items():
+        for s in st:
+            k = (pair_of[idx], side_of[idx], s); assert k not in seen, ('windows of two children of one family group overlap', idx, seen[k], k); seen[k] = idx
+
+
+def expand(win, sel, widths, V):
+    """-> slots [idx, port, off, w, s, h] (one replica), rem {(idx, port): remaining pending rank}"""
+    R = len(widths); pool = {}
+    for h in sorted(range(R)): pool.setdefault(widths[h], []).append(h)
+    pool = {(s, w): list(hs) for s in range(9) for w, hs in pool.items()}
+    slots = []; rem = {}; used = Counter()
+    for idx, pat, copies in sorted(sel, key=lambda e: (e[0], e[1])):
+        r = win[idx][1]
+        for _ in range(copies):
+            cp = used[idx]; used[idx] += 1; assert cp < V; off = 0
+            assert len({s for s, w in pat}) == len(pat)
+            for s, w in pat:
+                assert s in win[idx][2] and off + w <= r
+                slots.append([idx, cp, off, w, s, pool[s, w].pop(0)]); off += w
+            rem[idx, cp] = r - off
+    assert all(n == V for n in used.values()) and len(used) == len(win)
+    return slots, rem
+
+
+def idle_basis(q):
+    """PR #433 / #458: the parent's orthonormal idle basis U_q (+) I for port q (H = 9 local coordinates, M = 73)"""
+    z = next(i for i in range(H) if not (q >> i & 1)); a = q ^ (1 << z); order = list(range(H)); order[0], order[z] = order[z], order[0]
+    return [(1 << i) ^ (a if a >> i & 1 else 0) for i in order] + [1 << i for i in range(H, M)]
+
+
+def spectators(q, pending, off, w):
+    """indices (into B_q) of the e = 9 - w spectator coordinates of a residual at pending[off:off+w]"""
+    B = idle_basis(q); occ = [B.index(x) for x in pending[off:off + w]]
+    assert len(set(occ)) == w
+    sp = [j for j in range(M) if j not in occ][:H - w]
+    assert len(sp) == H - w
+    return sp
diff --git a/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py
new file mode 100644
index 0000000000..629de3b6ce
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py
@@ -0,0 +1,280 @@
+# GK: modified copy of PR #433's complex_replay.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 for heterogeneous centres by icekylinx with Codex assistance.
+"""Independent read-back of the serialized local/global instruction stream."""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');P=OUT/'GLOBAL-TEMPLATE.json.gz'
+ir=json.load(gzip.open(P));c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'))
+integration=json.loads((OUT/'INTEGRATION.json').read_text())
+assert hashlib.sha256(gzip.decompress(P.read_bytes())).hexdigest()==integration['global_template_sha256']
+assert c['ports']==json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))['ports']
+v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames']
+from gk_common import tile   # GK
+widths=[h-len(frames[c['start'][2*v+i]]) for i in range(R)]
+assign,nb,pads=tile([(rep,i,widths[i]) for rep in range(8) for i in range(R)]);W=7680+9*nb
+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)}   # GK
+def contains(a,b):
+    for x in a:
+        for y in b:
+            if x>>(y.bit_length()-1)&1:x^=y
+        if x:return False
+    return True
+def local(events,back):
+    rows={('L',r):{r:Q(1)} for r in range(n)}
+    norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={}
+    hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256();chain={};wrappers=[]
+    allowed=['zero_frame_precondition','entry_adapters','A','centers','B','final','exit_adapters','full_frame_cleanup','done']
+    for event in events:
+        tag=event[0]
+        if tag=='phase':
+            phases.append(event[1]);assert phases==allowed[:len(phases)]
+            if event[1]=='A':assert entry==[(r,f) for r,f in enumerate(c['start']) if r in plain] and sorted(r for k_,r,f_ in wrappers if k_=='pre')==entering   # GK
+            if event[1]=='centers':assert all(cur[r]==levels.get(r-v,0) for r in range(v,2*v))   # GK
+            if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==list(enumerate(c['final']))
+            assert not private
+        elif tag=='residual_adapter':   # GK: paid wrappers of entering helpers: R_E^-1 before the invocation, L_E^-1 after the full-frame cleanup
+            _,kind,r,f=event;assert r in entering and f==c['start'][r] and kind in ('pre','post')
+            assert (kind=='pre' and phases[-1]=='entry_adapters') or (kind=='post' and phases[-1]=='full_frame_cleanup')
+            assert (kind,r) not in {(k,x) for k,x,_ in wrappers};wrappers.append((kind,r,f))
+        elif tag=='adapter':
+            assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]]
+            (entry if event[1]=='old_to_new' else exit).append((event[2],event[3]))
+        elif tag=='climb':
+            _,part,r,a,b,rank=event
+            assert not private and phases[-1]==part and cur[r]==a
+            assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0
+            hist[rank]+=1;cur[r]=b
+        elif tag=='center':
+            _,k,a,b,rank=event
+            assert phases[-1]=='centers' and private=={('C',k):a}
+            cf=c['center_frames'][k];cr=len(frames[cf])
+            # GK: stepwise descent cf -> served levels -> lowest (forward), reversed ascent (backward); each step is a nested child
+            assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a])
+            assert rank==abs(len(frames[a])-len(frames[b]))>0
+            chain.setdefault(k,[]).append((a,b))
+            private['C',k]=b;hist[rank]+=1;centers.append(k)
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None
+            if target[0]=='C' and op=='clear':
+                assert private.get(target,f)==f
+                private.pop(target,None)
+            else:
+                for r in (target,source):
+                    if r is None:continue
+                    if r[0]=='L':assert cur[r[1]]==f,('common frame',r,cur[r[1]],f)
+                    else:
+                        if r==target and r not in private:private[r]=f
+                        assert private[r]==f
+            if op=='clear':rows[target]={};norm[target]=Q(0)
+            elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source]
+            elif op=='scale':
+                q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator
+                assert a&(a-1)==0 and b&(b-1)==0
+                rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q)
+            else:
+                q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator
+                assert source!=target and b&(b-1)==0
+                # Independent symbolic replay of the cleared coefficient work.
+                w=0
+                for bit in bin(a)[2:]:w=2*w+int(bit)
+                assert Q(w,b)*(1 if q>0 else -1)==q
+                prefix=max(prefix,Q(a)*norm[source])
+                norm[target]=norm.get(target,Q(0))+abs(q)*norm[source]
+                row=rows.setdefault(target,{})
+                for j,x in list(rows[source].items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+            prefix=max(prefix,norm[target])
+        else:raise AssertionError(tag)
+    assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private
+    assert sorted(r for k,r,_ in wrappers if k=='pre')==entering and sorted(r for k,r,_ in wrappers if k=='post')==entering   # GK
+    for k,st in chain.items():   # GK: the steps of each centre chain link up and end at the centre frame
+        cf=c['center_frames'][k]
+        if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+        else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+    assert all(not row for reg,row in rows.items() if reg[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert rows['L',r]==expected
+    # A 192-bit local payload allowance vastly dominates even coefficient work.
+    assert prefix<2**192
+    return hist,{'all_exact_columns':n,'prefix_l1_upper':str(prefix),
+                 'prefix_bits_upper':prefix.numerator.bit_length()-prefix.denominator.bit_length()+1,
+                 'charged_payload_bits':192,'private_work_erased':True}
+
+profiles={};checks={}
+for name in ('forward','backward'):
+    profiles[name],checks[name]=local(ir['local_programs'][name],name=='backward')
+    assert dict(profiles[name])=={int(r):z for r,z in c['local_profile'].items()}
+    print('independent emitted replay PASS',name,flush=True)
+controls=[]
+for name,mut in [
+    ('wrong_scale',lambda es:next(e for e in es if e[0]=='scalar' and e[1][0]=='scale')[1].__setitem__(2,3)),
+    ('missing_center',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center'))),
+    ('wrong_common_frame',lambda es:next(e for e in es if e[0]=='scalar' and e[2]!=0).__setitem__(2,0)),
+    ('wrong_child_rank',lambda es:next(e for e in es if e[0]=='climb').__setitem__(5,99)),
+]+([
+    ('missing_pre_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre'))),
+    ('missing_post_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post'))),
+    ('wrapper_with_wrong_frame',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(3,0)),
+    ('wrapper_in_wrong_phase',lambda es:es.insert(es.index(['phase','A']),es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post')))),
+    ('wrapper_on_a_data_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,3)),
+    ('wrapper_on_a_target_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,v+3)),
+    ('wrapper_on_a_centre_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,['C',0])),
+] if entering else [])+([
+    ('centre_step_not_nested',lambda es:next(e for e in es if e[0]=='center').__setitem__(3,next(f for f in range(len(frames)) if not contains(frames[f],frames[next(e for e in es if e[0]=='center')[2]]) and not contains(frames[next(e for e in es if e[0]=='center')[2]],frames[f])))),
+    ('centre_descent_step_skipped',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center' and e[3]!=0))),
+] if levels else []):
+    es=copy.deepcopy(ir['local_programs']['forward']);mut(es)
+    try:local(es,False)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('mutation accepted: '+name)
+
+def residual_cells(route):
+    """cells of a bank family occupied by a helper residual (independent of tile): a width-9 slot or [offset, offset + width)"""
+    return set(range(route[1]*9,route[1]*9+9)) if len(route)==2 else set(range(route[1],route[1]+route[2]))
+def bank_rule(owners,occ,sole=True):
+    """GK: the one-helper rule of PR #458 on EVERY register class of one invocation (owners: 240 active data owners, then the 560 helpers).
+    data class (family < 7680): only the active wires, each the sole owner of its family; bank class (7680 <= family < W): helpers only; an ENTERING
+    helper (width < 9) is the sole owner of its bank family, its route is [2, offset, width, spectators] with the spectators the first
+    cells of the bank beyond every residual cell of it (occ[family] = those cells, over all invocations); width-9 helpers share a pure bank in
+    disjoint 9-cell slots (no wrapper acts on them); nobody owns a family of the private namespace (family >= W).  sole=False skips only the
+    sole-owner assertion (used by a control to show that the footprints themselves are fine)."""
+    fam=Counter(f for f,_ in owners);foot={}
+    for i,(f,route) in enumerate(owners):
+        assert f<W,('owner in the private namespace',f)
+        if f<7680:
+            assert i<240 and route[0]==1 and fam[f]==1,('data class: only the active wires, each alone on its family',i,f)
+        else:
+            assert i>=240 and route[0]==2,('bank class: helpers only',i,f);w=widths[i-240]
+            if w==9: assert len(route)==2,('width-9 helper in a pure bank',i)
+            else:
+                if sole: assert fam[f]==1,('entering helper shares its bank family in one invocation',i,f)
+                assert len(route)==4 and route[2]==w and len(set(route[3]))==9-w==len(route[3]),('entering helper without a spectator record',i)
+                assert route[3]==list(range(len(occ[f]),len(occ[f])+9-w)) and len(occ[f])+9-w<=73,('spectators are not the first cells beyond the residuals',i,f)
+            cells=residual_cells(route)|(set(route[3]) if len(route)==4 else set())
+            assert len(cells)==9 and not cells&foot.setdefault(f,set()),('footprints overlap on a bank family',i,f);foot[f]|=cells
+def global_check(t):
+    assert t['live']==W and t['physical']==W+R+len(c['centers'])+2   # GK
+    occ={}
+    for call in t['calls']:
+        for fam,route in call['owners'][240:]:occ.setdefault(fam,set()).update(residual_cells(route))
+    assert all(cs==set(range(len(cs))) for cs in occ.values()),'bank residuals are packed from cell 0'
+    # Eight data-wire scalar columns, independently recomposed.
+    matrix=[[int(i==j) for j in range(8)] for i in range(8)]
+    for e in t['recipe']:
+        if e['kind']=='local':
+            a=2*e['pair'];b=a+1;dst,src,q=(a,b,-1) if e['reverse'] else (b,a,1)
+            matrix[dst]=[x+q*y for x,y in zip(matrix[dst],matrix[src])]
+        elif e['kind']=='bridge':
+            i,j,q=e['dst'],e['src'],e['coefficient']
+            matrix[2*i]=[x+q*y for x,y in zip(matrix[2*i],matrix[2*j])]
+            matrix[2*j+1]=[x-q*y for x,y in zip(matrix[2*j+1],matrix[2*i+1])]
+        else:
+            assert e['kind']=='terminal';old=copy.deepcopy(matrix)
+            for i in range(4):matrix[2*i]=old[2*i+1];matrix[2*i+1]=[-x for x in old[2*i]]
+    assert matrix==[[int(i==j) for j in range(8)] for i in range(8)]
+    seen=set();hist=Counter();pairs={e['stage']:e for e in t['recipe'] if e['kind']=='local'}
+    for call in t['calls']:
+        stage,rep,pair=call['stage'],call['replica'],call['pair']
+        assert (stage,rep) not in seen;seen.add((stage,rep))
+        assert pair==pairs[stage]['pair']
+        assert call['orientation']==('backward' if pairs[stage]['reverse'] else 'forward')
+        assert len(call['owners'])==800
+        for r,(fam,route) in enumerate(call['owners']):
+            if r<240:assert fam==rep*960+(2*pair+r//120)*120+r%120 and route==[1,stage,r%120]
+            else:
+                bk,off_,w_,pure_,sp_=assign[rep,r-240];assert fam==7680+stage*nb+bk and route==([2,off_//9] if (w_==9 and pure_) else [2,off_,w_,list(sp_)])   # GK
+        assert len(set((f,json.dumps(r)) for f,r in call['owners']))==800
+        bank_rule(call['owners'],occ)   # GK: the rule on every register class, stated independently of tile()
+        for r,z in profiles[call['orientation']].items():hist[r]+=z
+    assert seen=={(s,r) for s in range(9) for r in range(8)}
+    for child in t['idle_children']:hist[child['rank']]+=child['replicas']
+    assert t['bank_padding']=={'families':list(range(7680,W)),'axis':72,'child_rank':1}
+    for r_,z_ in pads.items():hist[r_]+=z_*9   # GK
+    assert t['cover_final_correction']['families']==[0,W]
+    assert t['cover_final_correction']['charged_calls_per_cover']==W
+    assert t['execution_schedule'][-1]=={'kind':'translate_every_live_family',**{k:v for k,v in t['cover_final_correction'].items() if k!='kind'}}
+    assert 73*W-sum(r*z for r,z in hist.items())==2496
+    return hist
+H=global_check(ir)
+# Derivative repair: select two genuine width-9 owners; a fixed route may already match.
+pure_alias=[r for r in range(240,800) if widths[r-240]==9 and len(ir['calls'][0]['owners'][r][1])==2]
+assert len(pure_alias)>=2
+alias_src,alias_dst=pure_alias[:2]
+assert ir['calls'][0]['owners'][alias_src]!=ir['calls'][0]['owners'][alias_dst]
+def alias_owner(owners):
+    owners[alias_dst]=copy.deepcopy(owners[alias_src])
+for name,mut in [('missing_padding',lambda t:t['bank_padding']['families'].pop()),
+                 ('aliased_owner',lambda t:alias_owner(t['calls'][0]['owners'])),
+                 ('missing_cover_phase',lambda t:t['cover_final_correction'].__setitem__('charged_calls_per_cover',0))]:
+    t=copy.deepcopy(ir);mut(t)
+    assert t!=ir,('vacuous global mutation',name)
+    try:global_check(t)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('global mutation accepted: '+name)
+# GK: controls of the rule itself, one per register class, run on bank_rule (not on the equality with tile()); only for words with entering
+# helpers (the anchor's INDEPENDENT-REPLAY.json must stay byte-identical to PR #433's)
+occ_all={}
+for call in ir['calls']:
+    for fam_,route_ in call['owners'][240:]:occ_all.setdefault(fam_,set()).update(residual_cells(route_))
+def rule_control(name,mut,must):
+    o=copy.deepcopy(ir['calls'][0]['owners']);mut(o)
+    try:bank_rule(o,occ_all)
+    except AssertionError as e:
+        assert must in str(e),(name,str(e));controls.append(name)
+    else:raise AssertionError('rule mutation accepted: '+name)
+bank_rule(ir['calls'][0]['owners'],occ_all)
+rule_control('same_width_pure_helper_alias',alias_owner,'footprints overlap')
+ent=[r for r in range(240,800) if widths[r-240]<9]
+if entering:
+    a_,b_=ent[0],ent[1]
+    def to_one_bank(o):   # bank class: b joins a's bank family at the next free cells, with a spectator of its own
+        fa=o[a_][0];free=len(occ_all[fa]);o[b_]=[fa,[2,free,widths[b_-240],[free+widths[b_-240]]]]
+    rule_control('two_entering_helpers_on_one_bank_family',to_one_bank,'shares its bank family')
+    rule_control('bank_spectator_is_a_residual_cell',lambda o:o[a_][1].__setitem__(3,[o[a_][1][1]]+o[a_][1][3][1:]),'first cells beyond')
+    rule_control('bank_spectator_shifted',lambda o:o[a_][1].__setitem__(3,[x+1 for x in o[a_][1][3]]),'first cells beyond')
+    rule_control('bank_spectator_record_dropped',lambda o:o[a_].__setitem__(1,o[a_][1][:3]),'without a spectator record')
+    rule_control('bank_spectator_count_wrong',lambda o:o[a_][1].__setitem__(3,o[a_][1][3]*2),'without a spectator record')
+    rule_control('second_owner_on_an_active_data_family',lambda o:o.__setitem__(241,[o[0][0],[1,0,0]]),'data class')
+    rule_control('helper_owner_on_an_active_data_family',lambda o:o.__setitem__(250,[o[3][0],[2,0]]),'data class')
+    rule_control('active_wire_on_a_bank_family',lambda o:o.__setitem__(5,[7680,[1,0,5]]),'bank class')
+    C_=len(c['centers'])
+    rule_control('owner_in_the_private_namespace_centres',lambda o:o.__setitem__(300,[W+3,[2,0]]),'private namespace')
+    rule_control('owner_in_the_private_namespace_reserved_tableau',lambda o:o.__setitem__(300,[W+C_+5,[2,0]]),'private namespace')
+    rule_control('owner_in_the_private_namespace_coefficient',lambda o:o.__setitem__(300,[W+C_+R+1,[2,0]]),'private namespace')
+    t=copy.deepcopy(ir);t['calls'][0]['owners'][0][0]+=960   # copies: an active owner of replica 0's invocation on a family of replica 1
+    try:global_check(t)
+    except (AssertionError,KeyError):controls.append('active_owner_on_the_family_of_another_replica')
+    else:raise AssertionError('global mutation accepted: active_owner_on_the_family_of_another_replica')
+assert dict(H)=={int(r):z for r,z in integration['global_profile'].items()}
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('replay_hamming_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m
+M,B=load('moment'),load('base_two_moment');b=Q(integration['complex_b']);grid=Q(1,10**18)
+assert M.moment(H,73,W,b,True)[1]<1<M.moment(H,73,W,b+grid,True)[0]
+def other(a):
+    lo,hi=B.moment(73,W,list(H.items()),a)
+    l2,h2=B.moment(73,W,[(1,32*73**2*sum(H.values()))],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert other(b)[1]<1<other(b+grid)[0]
+result={'status':'PASS_INDEPENDENT_NEW_STRUCTURAL_IR_REPLAY',
+        'template_sha256':integration['global_template_sha256'],'local':checks,
+        'mutation_controls_rejected':controls,'all_eight_global_scalar_columns':True,
+        'bank_owners_and_padding_exact':True,'paid_profile':dict(sorted(H.items())),
+        'two_rational_moment_engines':True,'complex_b':str(b),
+        'next_b_grid_rejected':True,
+        'scope':'Independent finite replay; retains the written generic scalar-interface lemma and inherited all-size/analytic assumptions.'}
+(OUT/'INDEPENDENT-REPLAY.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS independent local/global replay and two exact moments',flush=True)
diff --git a/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json
new file mode 100644
index 0000000000..cf624433f0
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json
@@ -0,0 +1,470 @@
+{
+ "gauge": {
+  "134": [
+   510
+  ],
+  "135": [
+   510
+  ],
+  "136": [
+   510
+  ],
+  "137": [
+   510
+  ],
+  "138": [
+   510
+  ],
+  "139": [
+   510
+  ],
+  "164": [
+   510
+  ],
+  "165": [
+   510
+  ],
+  "166": [
+   510
+  ],
+  "167": [
+   510
+  ],
+  "190": [
+   408,
+   102
+  ],
+  "191": [
+   408,
+   102
+  ],
+  "192": [
+   510
+  ],
+  "193": [
+   510
+  ],
+  "194": [
+   510
+  ],
+  "195": [
+   510
+  ],
+  "220": [
+   510
+  ],
+  "221": [
+   510
+  ],
+  "222": [
+   510
+  ],
+  "223": [
+   510
+  ],
+  "246": [
+   408,
+   102
+  ],
+  "247": [
+   408,
+   102
+  ],
+  "248": [
+   510
+  ],
+  "249": [
+   510
+  ],
+  "250": [
+   510
+  ],
+  "251": [
+   510
+  ],
+  "274": [
+   408,
+   102
+  ],
+  "275": [
+   408,
+   102
+  ],
+  "276": [
+   510
+  ],
+  "277": [
+   510
+  ],
+  "278": [
+   510
+  ],
+  "279": [
+   510
+  ],
+  "304": [
+   510
+  ],
+  "305": [
+   510
+  ],
+  "306": [
+   510
+  ],
+  "307": [
+   510
+  ],
+  "326": [
+   408
+  ],
+  "327": [
+   408
+  ],
+  "330": [
+   408
+  ],
+  "331": [
+   408
+  ],
+  "408": [
+   408
+  ],
+  "409": [
+   408
+  ],
+  "414": [
+   408
+  ],
+  "415": [
+   408
+  ],
+  "464": [
+   408
+  ],
+  "465": [
+   408
+  ],
+  "470": [
+   408
+  ],
+  "471": [
+   408
+  ],
+  "492": [
+   408
+  ],
+  "493": [
+   408
+  ],
+  "494": [
+   408
+  ],
+  "495": [
+   408
+  ],
+  "532": [
+   510
+  ],
+  "533": [
+   510
+  ],
+  "534": [
+   510
+  ],
+  "535": [
+   510
+  ],
+  "536": [
+   408,
+   102
+  ],
+  "537": [
+   408,
+   102
+  ],
+  "538": [
+   408,
+   102
+  ],
+  "539": [
+   408,
+   102
+  ],
+  "540": [
+   291,
+   163,
+   102,
+   24
+  ],
+  "541": [
+   291,
+   163,
+   102,
+   24
+  ],
+  "542": [
+   291,
+   163,
+   102,
+   24
+  ],
+  "543": [
+   291,
+   163,
+   102,
+   24
+  ],
+  "544": [
+   510
+  ],
+  "545": [
+   510
+  ],
+  "546": [
+   510
+  ],
+  "547": [
+   510
+  ],
+  "548": [
+   408,
+   102
+  ],
+  "549": [
+   408,
+   102
+  ],
+  "550": [
+   408,
+   102
+  ],
+  "551": [
+   408,
+   102
+  ],
+  "552": [
+   510
+  ],
+  "553": [
+   510
+  ],
+  "554": [
+   510
+  ],
+  "555": [
+   510
+  ],
+  "556": [
+   510
+  ],
+  "557": [
+   510
+  ],
+  "558": [
+   510
+  ],
+  "559": [
+   510
+  ]
+ },
+ "kernel": [
+  {
+   "E": [
+    504
+   ],
+   "donors": [
+    334,
+    335,
+    362,
+    363
+   ],
+   "pivots": [
+    390,
+    391,
+    418,
+    419
+   ]
+  },
+  {
+   "E": [
+    390
+   ],
+   "donors": [
+    324,
+    325,
+    328,
+    329,
+    380,
+    384,
+    440,
+    444
+   ],
+   "pivots": [
+    381,
+    385,
+    441,
+    445,
+    498,
+    499,
+    500,
+    501
+   ]
+  },
+  {
+   "E": [
+    6
+   ],
+   "donors": [
+    128,
+    129
+   ],
+   "pivots": [
+    156,
+    157
+   ]
+  },
+  {
+   "E": [
+    414
+   ],
+   "donors": [
+    218,
+    219,
+    302,
+    303
+   ],
+   "pivots": [
+    358,
+    359,
+    386,
+    387
+   ]
+  },
+  {
+   "E": [
+    384
+   ],
+   "donors": [
+    162,
+    163,
+    240,
+    241,
+    300,
+    352,
+    353,
+    356,
+    360,
+    361,
+    412,
+    416,
+    417,
+    438,
+    442
+   ],
+   "pivots": [
+    301,
+    357,
+    413,
+    436,
+    437,
+    439,
+    443,
+    496,
+    497,
+    502,
+    503
+   ]
+  },
+  {
+   "E": [
+    126
+   ],
+   "donors": [
+    160,
+    161
+   ],
+   "pivots": [
+    242,
+    243
+   ]
+  },
+  {
+   "E": [
+    102
+   ],
+   "donors": [
+    188,
+    189
+   ],
+   "pivots": [
+    244,
+    245
+   ]
+  },
+  {
+   "E": [
+    30
+   ],
+   "donors": [
+    132,
+    133
+   ],
+   "pivots": [
+    268,
+    269
+   ]
+  },
+  {
+   "E": [
+    96
+   ],
+   "donors": [
+    186,
+    187
+   ],
+   "pivots": [
+    216,
+    217
+   ]
+  },
+  {
+   "E": [
+    120
+   ],
+   "donors": [
+    158,
+    159
+   ],
+   "pivots": [
+    214,
+    215
+   ]
+  },
+  {
+   "E": [
+    480
+   ],
+   "donors": [
+    272,
+    273,
+    298
+   ],
+   "pivots": [
+    299
+   ]
+  },
+  {
+   "E": [
+    24
+   ],
+   "donors": [
+    130,
+    131
+   ],
+   "pivots": [
+    212,
+    213
+   ]
+  }
+ ]
+}
\ No newline at end of file
diff --git a/research/partial-kernel92-async/vendor/complex/split-centres-global/code/complex_phases_full.py b/research/partial-kernel92-async/vendor/complex/split-centres-global/code/complex_phases_full.py
new file mode 100644
index 0000000000..b5a5bd64b4
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/split-centres-global/code/complex_phases_full.py
@@ -0,0 +1,39 @@
+# Adapted from PR425 for heterogeneous centres by icekylinx with Codex assistance.
+"""Exact phase-aware lowering of every used edge of the new structural word."""
+import gzip,hashlib,json,sys,time
+from collections import Counter
+from pathlib import Path
+sys.path.insert(0,str(Path('work/odd-stages').resolve()))
+from clifford_exact import *
+
+OUT=Path('split-centres');P=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(P));n=c['h'];frames=c['frames'];start=time.monotonic();ops=[]
+for U in frames:
+    op=canonical_frame(n,U)
+    L=[u|(u<<n) for u in U]+[v<<n for v in nullspace(U,n)]
+    pre=[x|(z<<n) for x,z,p in inverse(op.tab)[n:]]
+    assert rank(L)==n and rank(L+pre)==n
+    assert rank([x for x,z,p in op.tab[n:]])==len(U)
+    ops.append(op)
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))};recipes=[];hist=Counter()
+for i,(a,b) in enumerate(sorted(edges)):
+    op=ops[a].adjoint().then(ops[b]);rec,compiled=lower_child(op)
+    assert rec['rank']==abs(len(frames[a])-len(frames[b]))
+    hist[rec['rank']]+=1;recipes.append({'old':a,'new':b,**rec})
+    if i%200==0:print('exact phase edges',i,'/',len(edges),'seconds',time.monotonic()-start,flush=True)
+adapters=[];F=fourier(n)
+for i,q in enumerate(c['ports']):
+    for role,old,f in [('source',cgate(n,q),c['start'][i]),
+                       ('target',cgate(n,q).adjoint().then(F),c['final'][c['v']+i])]:
+        rec,compiled=lower_child(old.adjoint().then(ops[f]));assert rec['rank']==0
+        adapters.append({'port':i,'role':role,'frame':f,**rec})
+raw=json.dumps({'children':recipes,'endpoint_adapters':adapters},sort_keys=True,separators=(',',':')).encode()
+(OUT/'CLIFFORD-RECIPES.json').write_bytes(raw)
+result={'status':'PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES',
+        'canonical_word_sha256':hashlib.sha256(P.read_bytes()).hexdigest(),
+        'frames':len(frames),'directed_edges':len(edges),'ranks':dict(hist),
+        'endpoint_adapters':len(adapters),'all_child_equalities_include_global_phase':True,
+        'recipe_sha256':hashlib.sha256(raw).hexdigest(),'seconds':time.monotonic()-start,
+        'scope':'Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations.'}
+(OUT/'CLIFFORD-REVIEW.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS exact local phases',result['seconds'],'seconds',flush=True)
diff --git a/research/partial-kernel92-async/vendor/complex/split-centres-global/vendor/clifford_exact.py b/research/partial-kernel92-async/vendor/complex/split-centres-global/vendor/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/partial-kernel92-async/vendor/complex/split-centres-global/vendor/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/partial-kernel92-async/verify.py b/research/partial-kernel92-async/verify.py
new file mode 100644
index 0000000000..1d3b08899f
--- /dev/null
+++ b/research/partial-kernel92-async/verify.py
@@ -0,0 +1,62 @@
+"""Offline, stdlib-only reconstruction of the asynchronous complex derivative.
+The unchanged PR493 bit operator is a cited dependency, not freshly verified here.
+"""
+from pathlib import Path
+import argparse,hashlib,json,os,shutil,subprocess,sys,time,gzip
+if not __debug__:raise RuntimeError('Assertions must remain enabled; do not use -O or PYTHONOPTIMIZE.')
+sys.dont_write_bytecode=True
+if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0)
+P=Path(__file__).resolve().parent
+a=argparse.ArgumentParser();a.add_argument('--work',type=Path,required=True);args=a.parse_args()
+W=args.work.resolve();assert P not in W.parents and W!=P,'Output must be outside this package.';assert not W.exists(),'Choose a new output directory; existing outputs are preserved.'
+mf=P/'MANIFEST.json'
+if mf.exists():
+ manifest=json.loads(mf.read_text());assert manifest['format']=='sha256-lf-text-v1'
+ for n,entry in manifest['files'].items():
+  data=(P/n).read_bytes()
+  assert entry['mode'] in ['raw','lf-text'],n
+  if entry['mode']=='lf-text':data=data.replace(b'\r\n',b'\n')
+  assert hashlib.sha256(data).hexdigest()==entry['sha256'],n
+W.mkdir(parents=True);V=W/'base';V.mkdir();shutil.copytree(P/'inputs/work',V/'work')
+# Canonicalize generated copies, never edit immutable checked-out inputs.
+for f in (V/'work').rglob('*'):
+ if f.is_file() and f.suffix in {'.json','.txt','.md','.py','.sh'}:
+  f.write_bytes(f.read_text(encoding='utf-8').encode('utf-8'))
+(V/'ASYNC-6.json').write_bytes((P/'inputs/ASYNC-6.json').read_text(encoding='utf-8').encode('utf-8'))
+bit=json.loads((P/'inputs/PR493-EXPECTED.json').read_text())['eleven']
+(V/'BIT-PRICE.json').write_text(json.dumps({'lower':bit['bit_lower'],'scope':'PR493 cited published supplier'}))
+C=P/'vendor/complex';G=C/'e8-complex-gauge-kernel';A=W/'audit';A.mkdir();H=W/'hosted'
+env=dict(os.environ,PYTHONUTF8='1',PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0',TEMP=str(W),TMP=str(W))
+env.pop('PYTHONOPTIMIZE',None)
+steps=[]
+def run(name,script,*argv):
+ start=time.monotonic();print('RUN',name,flush=True)
+ with (W/(name+'.log')).open('w',encoding='utf-8') as log:
+  result=subprocess.run([sys.executable,'-B',str(P/'code/run_portable.py'),str(script),*map(str,argv)],cwd=V,env=env,stdout=log,stderr=subprocess.STDOUT)
+ steps.append({'stage':name,'exit':result.returncode,'seconds':time.monotonic()-start})
+ (W/'STEPS.json').write_text(json.dumps(steps,indent=2)+'\n')
+ if result.returncode:
+  print((W/(name+'.log')).read_text()[-5000:]);raise SystemExit(result.returncode)
+ print('PASS',name,flush=True)
+run('partial-factory',P/'code/construct_partial.py',V/'work/complex-network/hamming',V/'partial-base')
+run('construct-kernel92',P/'code/build_kernel92.py',G/'code',V/'partial-base/FULL-WORD.json.gz',P/'inputs/KERNEL84-SELECTION.json',P/'inputs/RETIME-FRAMES.json.gz',P/'inputs/KERNEL92-SELECTION.json',V/'split-centres')
+run('kernel-scalar-controls',P/'code/audit_kernel_scalar.py',V/'split-centres/FULL-WORD.json.gz',V/'split-centres/SELECTION.json',A/'KERNEL-SCALAR.json')
+run('scalar',G/'code/audit_gk.py')
+run('emit-local',G/'code/emit_gk.py')
+run('phases',C/'split-centres-global/code/complex_phases_full.py')
+run('adapters',G/'code/adapters_gk.py',V/'split-centres/CANONICAL-WORD.json.gz',V/'split-centres/RESIDUAL-ADAPTERS.json',V/'LEMMA-A.json')
+run('parent-integration',G/'code/integrate_gk.py')
+run('parent-replay',G/'code/replay_gk.py')
+run('emit-async',P/'code/emit_async.py',G,V,P/'inputs/ASYNC-OWNERS.json.gz',V/'ASYNC-6.json',H)
+run('independent-async',P/'code/audit_async.py',V,H,A/'ASYNC-AUDIT.json')
+run('invoice',P/'code/audit_async_invoice.py',A,V,H)
+run('two-moments-assembly',P/'code/assemble.py',A,V,H,P/'inputs/PR493-EXPECTED.json')
+x=json.loads((A/'EXACT-ASSEMBLY.json').read_text());audit=json.loads((A/'ASYNC-AUDIT.json').read_text())
+assert all(z['exit']==0 for z in steps)
+result={'status':'PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE','kappa':x['kappa'],'kappa_decimal':x['kappa_decimal'],'complex_lower':x['complex_lower'],'bit_lower':x['bit_lower'],'template_sha256':x['complex_template_sha256'],'strict_constraints':len(x['strict_outer_constraints']),'scope':'New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.','stages':steps,'package_manifest_sha256':hashlib.sha256(mf.read_bytes()).hexdigest() if mf.exists() else None}
+expected=P/'EXPECTED.json'
+if expected.exists():
+ e=json.loads(expected.read_text())
+ for key in ['kappa','complex_lower','bit_lower','template_sha256']:assert result[key]==e[key],key
+(W/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],'kappa',result['kappa_decimal'],flush=True)
diff --git a/research/partial-kernel92-async/verify.sh b/research/partial-kernel92-async/verify.sh
new file mode 100644
index 0000000000..275570d71e
--- /dev/null
+++ b/research/partial-kernel92-async/verify.sh
@@ -0,0 +1,10 @@
+#!/usr/bin/env bash
+set -euo pipefail
+here="$(cd -- "$(dirname -- "$0")" && pwd)"
+if [ "$#" -eq 0 ]; then
+  out="$(mktemp -d)/run"
+  echo "Output: $out"
+  exec python3 -B "$here/verify.py" --work "$out"
+else
+  exec python3 -B "$here/verify.py" "$@"
+fi