diff --git a/research/asynchronous-whole-owners/ADVERSARIAL-REVIEW.md b/research/asynchronous-whole-owners/ADVERSARIAL-REVIEW.md
new file mode 100644
index 0000000000..b0d6afdda4
--- /dev/null
+++ b/research/asynchronous-whole-owners/ADVERSARIAL-REVIEW.md
@@ -0,0 +1,27 @@
+# Adversarial review of the asynchronous construction
+
+Reviewed the actual emitted template, emit_async.py, the complete source execution schedule, the sufficient composition proof, and the independent complex lane audit_async.py / ASYNC-AUDIT.json. The latter passes all40,320 physical owner intervals/charts,72 complete invocations,9,615 remainders, and18 mutation controls. Reviewed template SHA-256:276b69e3fc79a211daaf39776d91b3a6f9c262c415cbd199ab02d5e0ccb9bf4b.
+
+## Event scope
+
+The source has30 replica-local events and two whole-stock events. Projection of the emitted schedule onto EACH of the eight replicas is exactly source events0..29, in order. Replica-local events are local cover calls, pending idle completions, bridges, terminal Y translations, and the terminal signed exchange. The new event's replica / replicas=[replica] explicitly restrict every such event to that replica's data families; it must not be interpreted by an old decoder that silently ignores these fields. The independent checker compares every full event dictionary against this restriction of its source event. There are72 local sweeps,72 one-replica bridge sweeps, eight terminal-translation events and eight terminal signed exchanges.
+
+The empty bank-padding operation and the full-stock correction remain exactly once after all replicas finish. The correction still covers all7,680 live families. It is not duplicated per replica. Private centers/tableau/coefficient streams can be shared because each complete local program restores them before another invocation begins.
+
+## Actual intervals, including bridges
+
+The independent checker derives each owner window from the last preceding touch of its (replica,pair), counting both local calls and every individual bridge, then uses the literal idle-completion event as its deadline. It does not trust the optimizer's stage-window metadata. Every use lies strictly between those physical event positions. In particular, the narrow rank8 windows open after a forward bridge and close before its inverse bridge; final long windows open after the last earlier inverse bridge and close before the final bridge cascade. Initial windows have no preceding touch. The emitter's stage blocks place all source nonlocal events after their local call and before any subsequent call, so its coarser block-time convention agrees with these exact touch intervals.
+
+A foreign replica may use the same pair number while the owner's pair is idle; pair numbers are not physical owners. All800 physical families per complete call are distinct, so this freedom cannot alias an active source/target. No pending block is reused; disjoint blocks plus the explicit remainder exactly cover each original idle child.
+
+## Full-cover composition
+
+The proof uses the admitted endpoint of a COMPLETE normalized invocation, including its whole cover sweep. It never cancels or commutes gates through an unfinished scalar program. Each actual73-column chart is orthogonal; right multiplication by its inverse permutes the cover group, so a unique physical family has one corresponding stream per cover vertex. Thus the retained800-column arbitrary-dirt theorem applies without assuming fresh helper values. Borrowed spectators are restored. The only persistent helper action is the checked residual on its assigned pending coordinates.
+
+After replacing complete invocations by their admitted endpoints, each data replica retains its original data/bridge/terminal order. The only reordered factors between consecutive touches of a family are residuals on disjoint coordinate blocks. These commute and multiply with the remainder to the original pending child. This gives the original endpoint exactly. It relies on the same explicit normalized-invocation, all-size compiler and analytic contracts as PR496; it does not establish those inherited contracts anew.
+
+## Invoice caveat and conclusion
+
+The former192-bit prefix charge cannot simply be inherited: the nine synchronized bridge rounds became72 ordered one-replica sweeps. A sufficient bound is20+37+72+72+4=205 bits, using the retained local transient envelope and a factor2 per complete invocation/bridge. The parent is charging512. Total scalar bridge additions do not increase; only their order changes. Maximum child48 still satisfies73^2>2*48^2.
+
+No additional mathematical admission gap was found in the reviewed finite scheduling change. Final success still requires the parent's independently regenerated coefficient invoice and exact outer assembly. The positive statement is the sufficient endpoint-preserving asynchronous construction, not a claim that a packing relaxation alone proves an improved kappa.
diff --git a/research/asynchronous-whole-owners/EXPECTED.json b/research/asynchronous-whole-owners/EXPECTED.json
new file mode 100644
index 0000000000..0696052f0c
--- /dev/null
+++ b/research/asynchronous-whole-owners/EXPECTED.json
@@ -0,0 +1,8 @@
+{
+  "kappa": "67885087881447/50000000000000000",
+  "kappa_decimal": "0.001357701757628940",
+  "complex_lower": "679773808909616785409/500000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "276b69e3fc79a211daaf39776d91b3a6f9c262c415cbd199ab02d5e0ccb9bf4b",
+  "scope": "Conditional whole-owner finite derivative; unchanged PR493 bit supplier is cited, not reverified."
+}
diff --git a/research/asynchronous-whole-owners/LICENSE b/research/asynchronous-whole-owners/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/asynchronous-whole-owners/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/asynchronous-whole-owners/MANIFEST.json b/research/asynchronous-whole-owners/MANIFEST.json
new file mode 100644
index 0000000000..1146a94a9b
--- /dev/null
+++ b/research/asynchronous-whole-owners/MANIFEST.json
@@ -0,0 +1,66 @@
+{
+  ".gitattributes": "4ce4b6e6b8435f8c3a8387387732964a2ebf0183e8d77b8247ae8061b033e462",
+  "ADVERSARIAL-REVIEW.md": "6c8f69452df88c2082568d83ff3692176d391fd1e1db6533d071049ec873163c",
+  "code/assemble.py": "9db68cad2738d76052b25c8bdf6485edd6f14025bf47107d2425b10a2bdf69e0",
+  "code/audit_async.py": "d01ad6a70c4d3132bcd631f175d23bbee44fecc15f2a80a0f14d0d1d2b0a7206",
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+  "code/emit_async.py": "3dca3efbce0e1b775801d072e64995472749553f6f7f3250bb6a898cfe117fbc",
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+  "evidence/EXACT-ASSEMBLY.json": "b50c77f8089f9697844dbfb3ad2fb6d954e2bb71bfd544fa970da35cf21b25d0",
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+  "vendor/complex/split-centres-global/code/complex_phases_full.py": "0f2795aaffafe0c64d77f3748ef2109a3c42c58da867e4cf269a0a8cb6109466",
+  "vendor/complex/split-centres-global/vendor/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+  "verify.py": "5f36c115ba65135b95117229cba7ca78ad2bc47032036d88d8ee25bbcde1a084",
+  "verify.sh": "2b1b51f757d8ddf81941c8c96007a2256336856c2e017bcf6c3a37576c82bc8b"
+}
diff --git a/research/asynchronous-whole-owners/NOTICE.md b/research/asynchronous-whole-owners/NOTICE.md
new file mode 100644
index 0000000000..a810ab684e
--- /dev/null
+++ b/research/asynchronous-whole-owners/NOTICE.md
@@ -0,0 +1,18 @@
+# Attribution
+
+New asynchronous scheduler, independent audits, mathematical composition proof,
+and package integration: OpenAI Codex assistance. Apache-2.0; see LICENSE.
+Original authorship notices in every vendored source are preserved.
+
+Direct dependencies: CrocSwap/integer-mult-bounds PR496 whole-owner pooling and
+independent invoice/assembly; PR484 gauge80-kernel42 complex local circuit and
+wrappers; PR493 unchanged R489 bit supplier. The PR493 relevant attribution excerpt is saved
+in references/PR493-NOTICE.md and describes that upstream package, not new files here.
+PR433/425/370 supply the retained geometry and scalar/phase compiler ancestry;
+PR458 supplies whole-owner entrance/spectator wrappers; PR361/315 supply the
+exact moment and outer arithmetic ancestry. PR434/417/435/440 and
+PR401/408-416 supply kernel and gauge ancestry through PR484.
+
+OpenAI math source inspection informed the new scheduling argument and the
+separate matroid/sparse-shear searches. No Lean source is vendored or claimed
+freshly kernel-checked in this package. See RESEARCH.md and SOURCES.json.
diff --git a/research/asynchronous-whole-owners/PROOF.md b/research/asynchronous-whole-owners/PROOF.md
new file mode 100644
index 0000000000..6eeb5171ae
--- /dev/null
+++ b/research/asynchronous-whole-owners/PROOF.md
@@ -0,0 +1,42 @@
+# Asynchronous whole-owner replica scheduling
+
+## Sufficient construction
+
+Start with any admitted complete-invocation supplier with the following literal properties. Each invocation is an arbitrary-dirt-valid shear on its two active data banks; each helper belongs to a distinct full physical family, distinct from every active data family; its paid entry/exit wrappers restore all borrowed spectator coordinates and leave exactly its prescribed residual transform on its assigned pending coordinate block. The retained PR484/496 complex supplier provides these properties. No split residual or interleaved incomplete invocation is used here.
+
+Take T independent copies of the complete nine-stage controller. Their data banks are disjoint. A schedule is any shuffle of the T per-replica controller event lists that preserves each list's order and keeps every complete cover invocation indivisible. A pending idle child of replica r becomes available after its previous data/bridge touch and must be completed before its own next touch. A helper may use a disjoint block of that child whenever its complete invocation falls in this actual open interval. It does not matter whether the helper invocation and owner replica currently have the same stage number.
+
+The correctness proof is induction over the shuffled event list. At a local invocation its active data action is exactly the retained shear. Arbitrary dirty state in each borrowed family is allowed by the full local theorem. Its only persistent helper action is the specified residual transform on a previously unconsumed pending block; borrowed spectators are restored. These residual blocks are disjoint within each idle child, so their product with the paid leftover transform is exactly the retained full idle transform. Complete that product by the child's deadline. At a bridge or terminal event, its own replica is therefore in exactly its retained controller state. Different replicas have disjoint active data banks. After every replica completes, apply the retained full-stock correction. Thus the resulting global operator is unchanged.
+
+This is a sufficient finite scheduling theorem under the SAME retained complete-invocation/compiler/analytic contracts. It is not an unconditional integer-multiplication theorem, a split-owner lift, or permission to commute scalar gates through unfinished invocations. The new scheduler requires a fresh global prefix bound because intermediate dirty states may pass between replicas.
+
+## Constructive packing and exact ownership
+
+ASYNC-3.json freezes the order sorted by (stage + 3*replica/7, stage, replica). It also freezes an integer pattern nomination for each (owner replica, pending child):120 actual port families, each with a list of consecutive residual block widths. The local widths remain {5:4,7:14,8:104,9:438}. There are 72 calls and 40320 helper occurrences.
+
+The initial aggregate time assignment is only a nomination. It is replaced by a joint integer flow assigning each pattern's width slots to legal call times. For a pattern used on n families, at most n slots may be assigned to one time. For each pattern, form a bipartite multigraph between call times and its width-slot positions. Each slot position has degree n and each call time has degree at most n. Pad with dummy vertices and edges to an n-regular bipartite graph, then remove n perfect matchings. Each matching is one physical port family: it receives exactly the selected width pattern and at most one helper at any call time. This produces literal family, port, child, offset, width and call records. Existing arbitrary dirty helpers can then be assigned by matching width.
+
+The actual ASYNC-OWNERS.json.gz passes all 40320 occurrences, all 72 calls,560 distinct helper families per call, and no active-data overlap. This is an exact finite witness; floating MILP pricing is not its correctness evidence. The replay consumes the frozen witness and needs no optimizer.
+
+## Changed paid profile
+
+Ambient73, live7680, deficit 2496, physical8258 remain. The exact integer paid profile is:
+
+    1:148240, 2:66816, 3:7032, 4:19728, 5:26109,
+    6:144, 7:2209, 8:1224, 16:1, 48:408.
+
+Its exact admitted moment lower bound, including the inherited bad-cover allowance, is0.001359547617819233570818. The exact composed kappa is0.001357701757628940. Independent literal chronology, chart, scalar/prefix invoice and 47-inequality checks pass. The maximum child increases to48, but73^2=5329>2*48^2=4608, so depth2 remains sufficient.
+
+## Research provenance and scope
+
+PR496 supplies whole-owner pooling, exact normalization and the original matching-based owner construction. PR484 supplies the gauge/kernel local word; PR493 supplies the nonbinding stronger bit side. The new contribution is removing replica lockstep while retaining complete invocation boundaries and owner-relative pending windows. Generic bipartite matching is inherited mathematics, not a claimed new theorem.
+
+The downloaded OpenAI common-integer-polymatroid work (problem114), especially the tight-set augmentation/base calculus in its preprint, motivated looking for exchanges of capacity across previously fixed stage partitions. The actual finite feasible family is not asserted to be a matroid or M-convex set; no FPRAS theorem is imported as a packing certificate. The sufficient construction above is direct and the final ownership witness is exact.
+
+## Other bounded screens preserved
+
+Uniform stage counts K3,K6,K7, stage-selective local kernel component portfolios, optional paid whole banks, and the siblings' joint gauge/kernel variants did not beat PR496 under the tested lockstep packing. The component words remain valid local constructions but are not kappa gains. Their failures are restricted screens, not universal impossibility theorems. No Lean certification or publication was performed.
+
+## Finite prefix and explicit retained conditions
+
+The completed invocation/bridge L2 argument gives 20+37+72+72+4=205bits; charge512bits. The two-level row coefficient includes another2*512 and is16467<20161. The new schedule is sufficient under the unchanged PR493 bit supplier and PR484/496 all-size compiler, mutable-basis/common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts. This is not a proof of those inherited contracts.
diff --git a/research/asynchronous-whole-owners/README.md b/research/asynchronous-whole-owners/README.md
new file mode 100644
index 0000000000..635bc7d961
--- /dev/null
+++ b/research/asynchronous-whole-owners/README.md
@@ -0,0 +1,81 @@
+# Asynchronous whole-owner replicas
+
+Conditional kappa = **0.001357701757628940**, or `67885087881447/50000000000000000`,
+from complex saving b = `679773808909616785409/500000000000000000000000` and the unchanged PR493 bit
+saving c = `391360506745414227149/250000000000000000000000`. This is **1.923642% above PR496**
+under the same whole-owner supplier assumptions.
+
+The new mechanism removes replica lockstep. Eight replicas retain their own
+nine-stage order, but run in an order sorted by `(stage + 3*replica/7, stage, replica)`.
+Each complete cover invocation is indivisible. This exposes additional legal
+pending-child intervals on other replicas, including 4,539 uses of the same
+pair number on a different physical replica. No helper is split between owners.
+The frozen map names all 40,320 whole helper uses. No optimizer runs in verification.
+
+## What changes
+
+The gauge80-kernel42 local word, both scalar orientations, Gaussian phases,
+wrappers and data routes are unchanged. Only the order of complete replica
+blocks, whole-helper placement, and exact idle remainders change. The source
+controller has 30 replica-local events and two final global events. Every
+replica's projection is exactly those 30 events in order; the two final events
+run once. New `replica` fields restrict bridges, idle completion, and terminal
+events to the named replica. Old decoders that ignore those fields are invalid
+for this new template version.
+
+The paid profile is:
+
+```
+rank      1      2     3      4      5    6     7     8  16  48
+count 148240  66816  7032  19728  26109  144  2209  1224   1 408
+```
+
+Ambient dimension 73, live families 7680, physical families 8258, rank mass 558144,
+and deficit 2496 are unchanged. There are 3,194 actual orthogonal73-column maps,
+9,615 explicit remainder children, and 33,114 cross-replica helper uses.
+The maximum child rises to48, still satisfying `73^2 > 2*48^2`.
+
+The old192-bit prefix allowance is replaced. Count 72 full local sweeps and 72
+individual bridge sweeps: `20+37+72+72+4=205` bits suffice;512 are charged.
+The two-level row invoice charges an additional `2*512` and remains16467<20161.
+Both exact rational moment engines agree on the adjacent10^-24 endpoints.
+Six bootstrap steps and all 47 strict outer inequalities pass on the 10^-18
+kappa grid; the next grid point and three degenerate-parameter controls fail.
+
+## Reproduce offline
+
+Python3.11 or later, standard library only. No C++ compiler, optimizer, network,
+Lean, shell extension, or external package is needed. From this directory:
+
+```
+python -B verify.py --work /absolute/path/to/a-new-output-directory
+```
+
+On Windows use an available drive path for `--work`. The output directory must
+not already exist; prior outputs are preserved. POSIX users may run
+`bash verify.sh`; its temporary output directory is printed through the result.
+The verifier reconstructs the required parent local word and phase data, emits
+the new asynchronous program, independently checks its literal chronology and
+charts, recounts the scalar/prefix invoice, and performs exact composition.
+It rejects19 corrupt controller variants. See RESULT.json in the work directory.
+No external absolute data paths occur in the verifier.
+
+The unchanged bit operator is reused from the pinned PR493 publication. Its
+published profile is independently repriced here, but its C++ operator replay
+is deliberately not rerun. That distinction is explicit in every result.
+
+## Scope and comparison
+
+This is a conditional finite witness under the inherited all-size compiler,
+mutable-basis/common-label, PR484 Lemma A realization, restored-row,
+precision/tape and analytic-transfer contracts. Finite replay does not prove
+those contracts, and this is not a new unconditional multiplication theorem.
+The positive mathematical statement is the sufficient endpoint-preserving
+asynchronous construction in PROOF.md, with independently checked hypotheses.
+
+PR conversations were downloaded through 497, then the public snapshot was
+frozen for packaging. PR496 is the comparable whole-owner frontier. PR494's
+larger0.001435468764627892 computation was explicitly under review because its
+split-residual operator interface was disputed; that interface is not used.
+This package does not claim to surpass that number or reach0.0014.
+No submission, fork change, or publication is performed by this package.
diff --git a/research/asynchronous-whole-owners/RESEARCH.md b/research/asynchronous-whole-owners/RESEARCH.md
new file mode 100644
index 0000000000..65f689de17
--- /dev/null
+++ b/research/asynchronous-whole-owners/RESEARCH.md
@@ -0,0 +1,62 @@
+# Research appendix: corpus reuse, the achieved mechanism, and preserved candidates
+
+The delivered conditional bound is **kappa = 0.001357701757628940**. Its new contribution is asynchronous scheduling of complete replica invocations. The local gauge/kernel word is unchanged from PR484/496; the stronger bit supplier comes from PR493. The package's final receipts, physical audit and exact assembly are the evidence for the numerical claim. The inherited complete-invocation, compiler and analytic contracts remain explicit conditions; this is not a new Lean certification of integer multiplication.
+
+## The mechanism that improved the bound
+
+Earlier packing advanced all eight replicas in lockstep. The new schedule preserves each replica's nine-stage controller order while allowing replicas to occupy different stages. A helper may then use an idle block whenever its entire invocation lies between consecutive touches on the **owner's** timeline. The selected order sorts calls by `(stage + 3*replica/7, stage, replica)`.
+
+Correctness uses completed invocation endpoints. Each invocation restores arbitrary dirty workspace and borrowed spectators, and leaves only its specified residual on its assigned pending block. Different residual blocks of an idle child are disjoint; their product with the paid remainder is the original child. Completing that product before the owner's next touch preserves each replica's original controller. No scalar gate is commuted through an unfinished invocation, and no residual is split between owners.
+
+A flow nomination is converted to literal owners using bipartite edge coloring. There are 72 calls and 40,320 helper occurrences, with 560 distinct helper families per call. Ambient dimension 73, live stock7680 and deficit 2496 stay fixed. The changed paid profile is:
+
+    1:148240, 2:66816, 3:7032, 4:19728, 5:26109,
+    6:144, 7:2209, 8:1224, 16:1, 48:408.
+
+The complete schedule needs its own physical chart checks and prefix invoice. Its gain does not follow from the floating packing objective alone.
+
+## What was actually reused from the OpenAI corpus
+
+The inspected snapshot is `adc7f1241b42e322a6451854ab7e4b4c146bf78a` of [openai/math](https://github.com/openai/math). `APPENDIX-SOURCES.json` records repository-relative source paths and hashes. Direct source inspection and Git consistency checks are distinct from compiling these modules in this round; no claim is made that every paper in the collection is formalized.
+
+- [FourierCircuit/WordScheduling.lean](https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/Computability/FourierCircuit/WordScheduling.lean): `scheduledStep_product` and `scheduledLayer_product` preserve products under order-preserving schedules on fixed disjoint supports. `Word.matrix_substitute` and `Word.weight_substitute` preserve semantics and account for substituted calls. These supplied the structural template for scheduling complete normalized invocations. The new owner-relative interval argument is stated and checked separately; the fixed-support theorem is not silently applied to aliased unfinished programs.
+- [MatroidCounting/CommonBases.lean](https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/Combinatorics/MatroidCounting/CommonBases.lean): `greedyOracle_correct`, `greedyOracle_rank`, and the parallel/nonparallel pair-rank lemmas motivated response-matroid basis and circuit-component selection. The common-integer-polymatroid preprint, problem114, also suggested moving capacity across fixed stage partitions. The actual packing family is not asserted to be a matroid, and no counting FPRAS is used as a packing certificate.
+- `FourierCircuit/TensorTools.lean`, `RowCompression.sparse_row_compression`, and `SparseShear.lean`, `cancellation_identity`, provide explicit row-basis changes and cancellation of a shared exterior block. Independent dirty replica coordinates cannot be deleted merely by compressing a displayed response matrix. No additional gain was obtained from this route.
+- `FourierCircuit/PivotJoin.lean`, `PivotJoin.of_join`, and `MonomialFeedback.lean`, `Dense2x2.price`, suggested alternative local compositions. The latter's abstract normalized price bound is not a literal bounded-coefficient routine in this model. The exact-Fourier documentation also limits its theorem to a subsequence; it does not supply the missing all-length bit-complexity implementation.
+- `Topology/ArtinGroups/Cancellation/BlockPivot.lean`, `homotopy_square`, `homotopy_retract`, `remainder_retained`, and `NumberTheory/TwoPoint/Walks/ColumnRankRelations.lean`, `columnDifference_disjoint_minor`, were inspected for simultaneous elimination and donor/pivot separation. They did not produce another priced gain in this round.
+
+## Three checked local constructions, not added to the achieved gain
+
+For a common entrance frame, choose a basis of a response-matroid component as donors. Each remaining column is an exact rational donor combination. Prepending its cancelling donor shears makes that pivot's dirty response zero; reverse cleanup restores the helper state. All required frame nesting and source spans must still hold.
+
+The following concrete words passed exact rational reconstruction, all 800 arbitrary-dirt columns in both forward and inverse-transpose orientations, and every individual pivot-correction omission control:
+
+| Candidate | Local profile change from PR484/496 | Residual counts (width:count) | Omission controls |
+|---|---|---|---:|
+| COMPONENT | -10 rank 1, -14 rank 2, +14 rank 3 | 5:4, 7:14, 8:100, 9:442 | 38 |
+| JOINT-47 | -14 rank 1, -2 rank 2, -4 rank 3, +4 rank 4, +4 rank 5 | 5:4, 7:12, 8:102, 9:442 | 48 |
+| JOINT-51 | -14 rank 1, -4 rank 2, +8 rank 3, -2 rank 4, +2 rank 5 | 5:4, 7:14, 8:100, 9:442 | 40 |
+
+These improve selected local objectives but lose scarce narrow residual inventory. Their tested lockstep allocations, including stage-selective portfolios and paid banks, did not improve the full bound. None is counted in the delivered kappa. They remain useful sufficient constructions for future schedules.
+
+The companion base, three selections and `REBUILD.json` permit source-bound reconstruction through `rebuild_candidate.py`; `audit_component_scalar.py` checks each reconstructed word independently. `LOCAL-CANDIDATE-AUDITS.json` preserves the three exact scalar receipts. The constructor reuses the retained, hash-pinned `gk_word.py` and `gk_common.py` with their attribution.
+
+## Other bounded lessons
+
+All14,851 subspaces contained in first-touch frames were screened. Under the fixed80 gauge exclusions, only 14 classes had positive response nullity, all dimension 1. Allowing excluded gauge helpers exposed63 additional components, still dimension 1. A catalogue of 646 components from deletion minors up to depth two did not beat the inherited42-pivot width budget. These are finite-search results, not global impossibility theorems.
+
+The proposed gauged-donor ordering is algebraically sufficient when original dirt compensation precedes the kernel update. Adding individual donors while retaining the current palette failed exact target/centre nesting in all 86 tested cases; geometric admissibility alone was insufficient. Whole-palette replacements remain a separate route.
+
+Native frame-retiming searches on the full joint gauge word and its cleanup extension found no better profile. A direct lift of PR493's bit skeleton to the complex side also failed a specific structural test: all 14,400 port pairs obey complemented adjacency. An even-parity-frame repair and the identity `G Hadamard G + A_orth - J = 3 I` are constructive leads, but require extra paid copies and a different decoder; they are not achieved improvements.
+
+The productive change was therefore at the scheduling level: reuse the already checked local engine, remove replica lockstep, and reconstruct the complete physical ownership and prefix bill.
+
+
+Portable companion files are under `research-notes/kernel/`. From the package root, rebuild a local candidate with:
+
+```
+python -B research-notes/kernel/rebuild_candidate.py vendor/complex/e8-complex-gauge-kernel/code research-notes/kernel JOINT-47 /new/output-word.json.gz
+python -B research-notes/kernel/audit_component_scalar.py /new/output-word.json.gz research-notes/kernel/JOINT-47-SELECTION.json /new/scalar-receipt.json
+```
+
+These separate local identities are not added to the achieved kappa.
diff --git a/research/asynchronous-whole-owners/SCHEDULING-LEMMA.md b/research/asynchronous-whole-owners/SCHEDULING-LEMMA.md
new file mode 100644
index 0000000000..9328fb1ee5
--- /dev/null
+++ b/research/asynchronous-whole-owners/SCHEDULING-LEMMA.md
@@ -0,0 +1,25 @@
+# Sufficient asynchronous whole-owner scheduling lemma
+
+This is a mathematical composition proof, not Lean certification. It applies to the complete-call interfaces already retained by PR496. It does not permit splitting a residual across physical owners or stopping before dirty workspace restoration.
+
+Let physical families be mutually independent vector spaces. A local invocation is an explicitly implemented finite word whose COMPLETE endpoint factors as its intended data operation on one replica and one prescribed residual operator on each distinct helper owner; all private workspace and borrowed spectator coordinates are restored. A pending idle child on a family factors into commuting coordinate residuals on disjoint coordinate blocks and its complementary remainder.
+
+A finite schedule is sufficient if:
+
+1. For each data replica it preserves the order of all of that replica's data operations, including bridges and recipe phases.
+2. Every helper use occurs inside the pending child's interval on the OWNER replica's timeline, and that owner is not an active data family in the invocation.
+3. Pending coordinate blocks allocated to different uses are disjoint; all blocks and the one complementary remainder cover the original pending child exactly.
+4. Every complete invocation has distinct physical helper owners and finishes its entry wrappers, scalar body, cleanup, exit wrappers and full cover sweep before the next invocation. It restores spectators even when later calls will use those coordinates actively.
+5. All allocated residuals and the remainder finish before the owner replica's next operation that depends on completion of that pending child.
+
+Then the schedule has exactly the same complete endpoint as the original controller. Proof: replace each completed local invocation by its established block-diagonal endpoint. This is valid on arbitrary dirty input, hence remains valid after any preceding invocation. On each family, data operations occur in their original order. Between two consecutive such operations, the only newly ordered factors are residuals on disjoint coordinate blocks; they commute, and their product with the remainder is the original pending child. Regroup these factors inside each family interval. Their product is unchanged, so the overall controller endpoint is unchanged. No operation is commuted through an unfinished scalar body, and no independent-dirt claim is inferred merely from a logical alias. The full-cover right-translation bijection and actual owner maps remain premises of each complete invocation.
+
+Replica lockstep is therefore unnecessary for this sufficient composition argument. The construction still needs an explicit schedule, owner injection, full maps, interval checks, and paid profile.
+
+## Prefix bill
+
+The old synchronized prefix bound cannot be copied without checking its batching premise. If nine bridge rounds become as many as seventy-two ordered bridge sweeps, a safe logarithmic envelope should count those sweeps individually, alongside the seventy-two complete local sweeps, exact local transient norm, and conversion from entry sup norm to full-family L2. Enlarging the finite coefficient allowance is allowed if the outer assembly pays it. Alternatively an independent argument can retain a tighter norm bound by tracking disjoint active replicas. This is an invoice issue, not an extra recursive child count.
+
+## Structural source
+
+OpenAI FourierCircuit/WordScheduling.lean gives fixed-support scheduling and substitution identities. The proof above uses the same support-sensitive mechanism, with completed normalized invocations as its indivisible units. SparseShear's whole-call-index constructions reinforce why physical supports, not just abstract row dimensions, must remain explicit.
diff --git a/research/asynchronous-whole-owners/SNAPSHOT.md b/research/asynchronous-whole-owners/SNAPSHOT.md
new file mode 100644
index 0000000000..a48fecee1f
--- /dev/null
+++ b/research/asynchronous-whole-owners/SNAPSHOT.md
@@ -0,0 +1,17 @@
+# Frozen public comparison
+
+Downloaded all 497 PR conversation pages (all-state pagination), then froze the
+snapshot before packaging. Changed relevant source heads were pinned locally.
+This is a retrieval snapshot, not an independent certification of every PR.
+
+| PR | Reported kappa | Treatment |
+|---|---:|---|
+| 493 | bit supplier c=0.001565442026981656908596 | Unchanged cited bit dependency; no duplicate operator replay |
+| 494 | 0.001435468764627892 | Retitled under review: disputed split-residual interface; not adopted |
+| 495 | 0.001307044366925301 | Below comparable frontier |
+| 496 | 0.001332077359286333 | Comparable whole-owner parent; changed complex dependency reconstructed |
+| 497 | 0.001325117552367841 | Moment-directed placement inspiration; no arithmetic addition of its gain |
+
+The new 0.001357701757628940 improves496 by 1.9236419089 percent. It neither
+claims to surpass494's disputed number nor to reach0.0014. See SOURCES.json
+for direct dependency heads. The withdrawn491 GL sampling argument is unused.
diff --git a/research/asynchronous-whole-owners/SOURCE-FILES.json b/research/asynchronous-whole-owners/SOURCE-FILES.json
new file mode 100644
index 0000000000..0d1b538113
--- /dev/null
+++ b/research/asynchronous-whole-owners/SOURCE-FILES.json
@@ -0,0 +1,148 @@
+[
+  {
+    "path": "vendor/complex/e8-complex-gauge-kernel/code/gk_word.py",
+    "sha256": "f027a9273bcf4e0971258c160b7d3b3c196366b32a529cff6e6a0e666b03826b",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/e8-complex-gauge-kernel/code/gk_common.py",
+    "sha256": "e68d190fd436b2f3955decb590adb53344d5d4ea0a19d62d86df1e4b55ecd198",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py",
+    "sha256": "cb79c6b788333a031e14c7f134823f5f6147d7f1dcc6e5e3b1420743c32f8ebc",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py",
+    "sha256": "4e415bff1d9f154496ed38e6889929b600aa0f3d583a375e8ca257ad8f51fa23",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py",
+    "sha256": "a8d6d9ccf20c261cb0b216baa9906f2f7689e1bb1dca070313a60b2cb6d3043c",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py",
+    "sha256": "2e807893180a3716b36a81f1a7d933bd55f2299489b6f236ba5c644d87739209",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py",
+    "sha256": "2422b44fc2fb4742bb575572337158a15fb6831630f8746a1c7ee3133e0ee2e3",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py",
+    "sha256": "416b318c1b6b8c7b72e24713b1b18d8772ec368e042a321b4418c63a74711590",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/split-centres-global/code/complex_phases_full.py",
+    "sha256": "0f2795aaffafe0c64d77f3748ef2109a3c42c58da867e4cf269a0a8cb6109466",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/split-centres-global/vendor/clifford_exact.py",
+    "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json",
+    "sha256": "436e4acadee227dbfcb66386c9ccaa38e68054e8ed4870bb174eeb41363375bb",
+    "origin": "PR496 pinned vendor of PR484; unchanged"
+  },
+  {
+    "path": "inputs/work/complex-network/hamming/PACKET-PROGRAMS.json.gz",
+    "sha256": "d833ae0390d165d7da0c639a3c7aeb77156c2ddb52447087cb49b9d03b19e9b9",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/work/complex-network/hamming/PROTOTYPE.json",
+    "sha256": "b155f101a2b7ec8cfc4e7b6e7147b2d51f0dc31d3ea3499bdfa79d399a76be47",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/work/complex-nine-native/DATA-PHASES.json",
+    "sha256": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz",
+    "sha256": "1b84904a31a733aab9bfdda3f528c06719f590d2133a43687a8bded955dc991e",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz",
+    "sha256": "77b0c0fa19ef3da1c7316010e13493aa5eea1a50c3506eddc08f7480e659878b",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/work/odd-stages/clifford_exact.py",
+    "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/work/pr361/code/engines/base_two_moment.py",
+    "sha256": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/work/pr361/code/engines/moment.py",
+    "sha256": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/work/pr361/code/engines/outer.py",
+    "sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz",
+    "sha256": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55",
+    "origin": "Pinned parent reconstruction input, inherited PR433/425/370/361"
+  },
+  {
+    "path": "inputs/BASE-WORD.json.gz",
+    "sha256": "da4c5007092fd9456403179ef2a4391aef9fc5310e3eec5f2ab6c49b24147387",
+    "origin": "PR433 base before gauge80-kernel42; preserved cached input"
+  },
+  {
+    "path": "inputs/ASYNC-3.json",
+    "sha256": "8d16c05f4b3239fb5f9ec93958c9436c0cc0c76f6d4899a12bce5b84007d0893",
+    "origin": "New frozen asynchronous witness; optimizer not trusted"
+  },
+  {
+    "path": "inputs/ASYNC-OWNERS.json.gz",
+    "sha256": "52cb8c2b5869b429e3fe3b7a8b061792f020f6fad9f402dc4e4656110b9af068",
+    "origin": "New frozen asynchronous witness; optimizer not trusted"
+  },
+  {
+    "path": "code/emit_async.py",
+    "sha256": "3dca3efbce0e1b775801d072e64995472749553f6f7f3250bb6a898cfe117fbc",
+    "origin": "New emitter"
+  },
+  {
+    "path": "inputs/PR493-EXPECTED.json",
+    "sha256": "3494ba83280cc86548fe0cc6695c50d23e6b6ffca85aeb1a33337c1196e280cb",
+    "origin": "PR493 c3a9a436b84fe44fdc223a5784d84736d1c2d3c7 published unchanged bit supplier"
+  },
+  {
+    "path": "vendor/audit_scalar_invoice.py",
+    "sha256": "652eed65fe8f72ab486dcdbe761f401f8a2d43530f2fb0c5c7777be488cd4648",
+    "origin": "PR496 independent scalar invoice; unchanged"
+  },
+  {
+    "path": "references/PR496-PROOF.md",
+    "sha256": "144f1bf6952b3e31e99cf372a2cae9a13f96c9988808fe8a57ec70b09ee2007c",
+    "origin": "PR496 original conditional scope"
+  },
+  {
+    "path": "PROOF.md",
+    "sha256": "1fd10bedaf12f5221c1f22f4e508279ca1a16af7d0733dfdaac6a2a02a8a668a",
+    "origin": "New asynchronous sufficient composition argument; adapted in final package",
+    "source_snapshot_sha256": "a892161a798f2dd482cf77c9c6d7e8e405aeebf9f075fe1fc26101ab73a14937"
+  }
+]
diff --git a/research/asynchronous-whole-owners/SOURCES.json b/research/asynchronous-whole-owners/SOURCES.json
new file mode 100644
index 0000000000..48abd471c4
--- /dev/null
+++ b/research/asynchronous-whole-owners/SOURCES.json
@@ -0,0 +1,46 @@
+{
+  "snapshot": "PR conversations through497; no live refresh during packaging",
+  "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"
+    }
+  ],
+  "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
+  ],
+  "excluded": {
+    "494": "under-review split-residual interface not used",
+    "491": "withdrawn GL sampling argument not used"
+  }
+}
diff --git a/research/asynchronous-whole-owners/code/assemble.py b/research/asynchronous-whole-owners/code/assemble.py
new file mode 100644
index 0000000000..de2a375d13
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/code/audit_async.py b/research/asynchronous-whole-owners/code/audit_async.py
new file mode 100644
index 0000000000..f3a6693920
--- /dev/null
+++ b/research/asynchronous-whole-owners/code/audit_async.py
@@ -0,0 +1,137 @@
+"""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
+"""
+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');width=[9-len(canon['frames'][canon['start'][240+h]])for h in range(560)];prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=7680
+
+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)]
+
+def audit(t):
+ assert(t['live'],t['physical'])==(7680,8258)
+ 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':[7680,7696],'reserved_tableau':[7696,8256],'coefficient':[8256,8258]}
+ # 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)==800 and len({f for f,rt in own})==800 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(560)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==40320
+ 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']})==40320
+ 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=40320,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',8257))
+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=40320,physical=8258,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=8258,rank_mass=r['mass'],deficit=2496,hosted_residuals=40320,banked_residuals=0,all_800_owners_per_call_distinct=True,actual_helper_owner_charts=40320,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/asynchronous-whole-owners/code/audit_async_invoice.py b/research/asynchronous-whole-owners/code/audit_async_invoice.py
new file mode 100644
index 0000000000..d6b5d21e2b
--- /dev/null
+++ b/research/asynchronous-whole-owners/code/audit_async_invoice.py
@@ -0,0 +1,99 @@
+"""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')
+N=800;M=73;R=560;L=9;T=8;VV=120;K=4
+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==20 and bridge_sweeps==72 and required_prefix==205 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='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 costs20bits, initial sup-to-L2 conversion37bits, primitive margin4bits: total205<512. 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/asynchronous-whole-owners/code/emit_async.py b/research/asynchronous-whole-owners/code/emit_async.py
new file mode 100644
index 0000000000..e73fa798d1
--- /dev/null
+++ b/research/asynchronous-whole-owners/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 Counter(widths)==Counter({9:438,8:104,7:14,5:4})
+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/asynchronous-whole-owners/evidence/ASYNC-AUDIT.json b/research/asynchronous-whole-owners/evidence/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..0e22d24cf6
--- /dev/null
+++ b/research/asynchronous-whole-owners/evidence/ASYNC-AUDIT.json
@@ -0,0 +1,59 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "276b69e3fc79a211daaf39776d91b3a6f9c262c415cbd199ab02d5e0ccb9bf4b",
+  "complex_template_sha256": "276b69e3fc79a211daaf39776d91b3a6f9c262c415cbd199ab02d5e0ccb9bf4b",
+  "complex_live": 7680,
+  "complex_profile": {
+    "1": 148240,
+    "2": 66816,
+    "3": 7032,
+    "4": 19728,
+    "5": 26109,
+    "6": 144,
+    "7": 2209,
+    "8": 1224,
+    "16": 1,
+    "48": 408
+  },
+  "complex_hosted_residuals": 40320,
+  "physical": 8258,
+  "rank_mass": 558144,
+  "deficit": 2496,
+  "entering_helper_roles": 8784,
+  "cross_replica_helper_roles": 33114,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 40320,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 3194,
+  "actual_sigma_stream_sha256": "f2e2f8346abac2d6eb8f51877644f271791cf0385823f2c0be72628063a2c1ee",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 9615,
+  "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": {
+    "5": 4,
+    "7": 14,
+    "8": 104,
+    "9": 438
+  },
+  "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/asynchronous-whole-owners/evidence/EXACT-ASSEMBLY.json b/research/asynchronous-whole-owners/evidence/EXACT-ASSEMBLY.json
new file mode 100644
index 0000000000..584df13533
--- /dev/null
+++ b/research/asynchronous-whole-owners/evidence/EXACT-ASSEMBLY.json
@@ -0,0 +1,127 @@
+{
+  "status": "PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY",
+  "complex_lower": "679773808909616785409/500000000000000000000000",
+  "complex_decimal": "0.001359547617819233570818",
+  "next_b_rejected": "1359547617819233570819/1000000000000000000000000",
+  "exact_moment_receipts": [
+    {
+      "endpoint": "679773808909616785409/500000000000000000000000",
+      "mercator": [
+        "-24701029572391194233163396454784816194406099/13479973333575319897333507543509815336818572211270286240551805124608",
+        "-12350514786195597116581698227392408097203049/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "-4581062751698854583809/2500000000000000000000000000000000000000000000",
+        "-18324241006795418335121/10000000000000000000000000000000000000000000000"
+      ],
+      "accept": true
+    },
+    {
+      "endpoint": "1359547617819233570819/1000000000000000000000000",
+      "mercator": [
+        "39093084283798609982256402899859243863127849/26959946667150639794667015087019630673637144422540572481103610249216",
+        "39093084283798609982256402899859243863127851/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
+        "7250214496780752717751/5000000000000000000000000000000000000000000000",
+        "453138718548797044863/312500000000000000000000000000000000000000000"
+      ],
+      "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": "67885087881447/50000000000000000",
+  "kappa_decimal": "0.001357701757628940",
+  "binding_component": "complex",
+  "strict_outer_constraints": {
+    "bit_positive": "10621465764212762196210268477770276461723499661738917254091303764940482784625241058990440193116685451709011434821012853854051728646922354068764110240451788082301425101506809984537459990353093448305054158108924126790768824207046981816251961458553922111479604919294584678617563063070334752769/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "75805356522229723538276500338261082745908696235059517215374758941009559806883314548290988565178987146145948271353077645931235889759548211917698574898493190015462540009646906551694945841891075873209231175792953018183748038541446077888520395080705415321382436936929665247231/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "14945226191090383214591/500000000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "65183890758016961266260875338261082745908696235059517215374758941009559806883314548290988565178987146145948271353077645931235889759548211917698574898493190015462540009646906551694945841891075873209231175792953018183748038541446077888520395080705415321382436936929665247231/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "5310732882106381087483668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "10621465764212762196210268477770276461723499661738917254091303764940482784625241058990440193116685451709011434821012853854051728646922354068764110240451788082301425101506809984537459990353093448305054158108924126790768824207046981816251961458553922111479604919294584678617563063070334752769/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "43213411143221242829340706146900817834677847779268675861778683235445262688066898333135934475706179024781985570497551676819669673526696460027613397689698383090032695106330263260384932911298631384909669746005400635882642843477770020760512158998906629772170823387759417302233063063070334752769/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "5310732882106382064046168474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "3900939267117893617935953831525327623965348518646900817834677847779268675861778683235445262688066898333135934475706179024781985570497551676819669673526696460027613397689698383090032695106330263260384932911298631384909669746005400635882642843477770020760512158998906629772170823387759417302233063063070334752769/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "10621465764212762196210268477770276461723499661738917254091303764940482784625241058990440193116685451709011434821012853854051728646922354068764110240451788082301425101506809984537459990353093448305054158108924126790768824207046981816251961458553922111479604919294584678617563063070334752769/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "86426822286442485734486768816031359207632195896798434469466062705950042591508555607281428758295672597854959706174090499785287618406470565986462685138944978097763965111153716536232405832244169321514285333901877144974516862748493059704772356539259337432862041856224249925848563063070334752769/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "10621465764212762196210268477770276461723499661738917254091303764940482784625241058990440193116685451709011434821012853854051728646922354068764110240451788082301425101506809984537459990353093448305054158108924126790768824207046981816251961458553922111479604919294584678617563063070334752769/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "10621465764212762196210268477770276461723499661738917254091303764940482784625241058990440193116685451709011434821012853854051728646922354068764110240451788082301425101506809984537459990353093448305054158108924126790768824207046981816251961458553922111479604919294584678617563063070334752769/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "43213411143221242829340706146900817834677847779268675861778683235445262688066898333135934475706179024781985570497551676819669673526696460027613397689698383090032695106330263260384932911298631384909669746005400635882642843477770020760512158998906629772170823387759417302233063063070334752769/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "5310732882106381087483668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "epsilon_positive": "3906249999999999996093750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/3911560732882106381087483668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231",
+    "epsilon_below_one": "5310732882106384993733668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231/3911560732882106381087483668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231",
+    "guard_width": "5310732882106384993733668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231/3911560732882106381087483668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231",
+    "K_geometry": "2934998232882106382064046168474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231/3911560732882106381087483668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231000000000000000000",
+    "K_dominates_log": "5310732882106382058735435592565993970605312878426806130670670867632141972899164543823413173711784902309328212360719308353948905208627347962315896970855216792056275836998076937580702583368119829647762195031631875475263165293230749027026902527630615122130684478863390988341335611147212469937760324689082549464063063070334752769/3911560732882106381087483668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231000000000000000000",
+    "record_suffix": "5310732882106384993733668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231/3911560732882106381087483668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231",
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+    "gamma_sublinear": "1/2000000000000000000",
+    "cell_above_band": "7812499999999999988275939267117893618912516331525327623965348518646900817834677847779268675861778683235445262688066898333135934475706179024781985570497551676819669673526696460027613397689698383090032695106330263260384932911298631384909669746005400635882642843477770020760512158998906629772170823387759417302233063063070334752769/15646242931528425524349934673898689504138605925412396728661288608882925296552885267058218949247732406667456262097175283900872057718009793292721321305893214159889546409241206467639869219574678946958460268354805474460361321015978397456469428626088919916957951364004373480911316706448962330791067747747718660988924000000000000000000",
+    "prime_interval_packing": "5310732882106384993733668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231/3911560732882106381087483668474672376034651481353099182165322152220731324138221316764554737311933101666864065524293820975218014429502448323180330326473303539972386602310301616909967304893669736739615067088701368615090330253994599364117357156522229979239487841001093370227829176612240582697766936936929665247231",
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+    "delta_positive": "1/8000000000000000000",
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+    "small_field_exposure": "1/1000000000000000000",
+    "artificial_boundary": "219089886904454808432583636981025351209480145812022364786684572186186102291342130729593697160378382456972964405490603847414545120061038155609195184182798771527773733527279214102155067320125768002065266208357896801584626337521758465148781848779406516763679293293636665632299530826186677403340571493800220323916084810810788995741693/31292485863056851048699869347797379008277211850824793457322577217765850593105770534116437898495464813334912524194350567801744115436019586585442642611786428319779092818482412935279738439149357893916920536709610948920722642031956794912938857252177839833915902728008746961822633412897924661582135495495437321977848000000000000000000",
+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
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+    "Gaussian_arithmetic_above_kappa": "650945904092364114458106277473001586542067723911959094143958356887989784732290494273066504489257848992363144694209814326063870847959615716223786623908677348746588810825640057995006903698509685417446122459737571309936249653083497808129198400219535817156080215410849226584383915837421308774117748640855519601709/1251699434522274041947994773911895160331088474032991738292903088710634023724230821364657515939818592533396500967774022712069764617440783463417705704471457132791163712739296517411189537565974315756676821468384437956828905681278271796517554290087113593356636109120349878472905336515916986463285419819817492879113920000000000000000",
+    "scalar_work_above_kappa": "31919890533837528385802591610723729167690299023211374082260247531082669914860147623884881561479178631476534879452420642052468828917000186198315986903610147878554266679882207917515041812037421082394613329848244757208767562343065842659699388631577315345859956749275604145520914602384495050144011463769106651031649/31292485863056851048699869347797379008277211850824793457322577217765850593105770534116437898495464813334912524194350567801744115436019586585442642611786428319779092818482412935279738439149357893916920536709610948920722642031956794912938857252177839833915902728008746961822633412897924661582135495495437321977848000000000000000000",
+    "dimension_above_kappa": "195046963355894680778947386993264098491330396427335050540014833042491391695748744682418520878143150795715773591229757283385342684629342977764026254591976288760732652572506490520293217769019697753175553626384249188834410968156183318193243970905516263686880269125567489770480069858617330338541301771883114442899565004412726976743/195578036644105319054374183423733618801732574067654959108266107611036566206911065838227736865596655083343203276214691048760900721475122416159016516323665176998619330115515080845498365244683486836980753354435068430754516512699729968205867857826111498961974392050054668511391458830612029134888346846846483262361550000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "449020414922846710689433426655558230469635792154792303094639231241802755297281/250000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "11159644099234"
+    },
+    {
+      "gap": "305232317730280040825308835590987929903916022046304981461323310497994616857940652573544720024451785628400210621827071/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "6037560531089891199"
+    },
+    {
+      "gap": "207488935225822819707329944397914542017357247747950207874090506920289069740932634230320647467086765522447186084241700065543015944786272931178754706685992961/62500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "3266424703371836125114550"
+    },
+    {
+      "gap": "141045543805058336212649010292305025939820708534171267604518810486058306439990756026263446106135360755810503860317998166184340480573013333355654103297932838083993074527887268756892915247978493951/31250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1767192277055604162917945126478"
+    },
+    {
+      "gap": "95879066542092708925688584119303870977398057083360511006259925303938427875169627138804769682491484367184212664343124194508853936496116207677240233614616406658790651905415671420236414749865832511242765726328404100094386838726228439041/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "956081596144316677228711405955568612"
+    },
+    {
+      "gap": "65176078258016961266260875338261082745908696235059517215374758941009559806883314548290988565178987146145948271353077645931235889759548211917698574898493190015462540009646906551694945841891075873209231175792953018183748038541446077888520395080705415321382436936929665247231/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "517256684716205688376238722884845576914065"
+    }
+  ],
+  "complex_template_sha256": "276b69e3fc79a211daaf39776d91b3a6f9c262c415cbd199ab02d5e0ccb9bf4b",
+  "owner_audit_sha256": "c091ef330ae4566838b3a6c214d57847ce7c9962d5fc161f4ad155cd6bc69b21",
+  "invoice_sha256": "3d38891f6db3fd70728f1bcba7d1f1356250903a15f3916ca91ae1ad98a24c73",
+  "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/asynchronous-whole-owners/evidence/GLOBAL-PREFIX.json b/research/asynchronous-whole-owners/evidence/GLOBAL-PREFIX.json
new file mode 100644
index 0000000000..a957679ed7
--- /dev/null
+++ b/research/asynchronous-whole-owners/evidence/GLOBAL-PREFIX.json
@@ -0,0 +1,13 @@
+{
+  "status": "PASS_ASYNC_GLOBAL_PREFIX",
+  "template_sha256": "276b69e3fc79a211daaf39776d91b3a6f9c262c415cbd199ab02d5e0ccb9bf4b",
+  "global_prefix_bits": 205,
+  "retained_payload_bits": 512,
+  "complete_invocation_cover_sweeps": 72,
+  "bridge_factor_two_sweeps": 72,
+  "local_scalar_coefficient_work_prefix_bits": 20,
+  "stream_input_sup_to_l2_bits": 37,
+  "primitive_arithmetic_margin_bits": 4,
+  "controller_audit_sha256": "e3f3c8dd3d9ead17031574f86fe7c7887f5f08ead36877b0baa93def9db58431",
+  "proof": "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 costs20bits, initial sup-to-L2 conversion37bits, primitive margin4bits: total205<512. All-size child/compiler and precision/tape interfaces remain inherited."
+}
diff --git a/research/asynchronous-whole-owners/evidence/OWNERS-AND-PROFILE.json b/research/asynchronous-whole-owners/evidence/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..f7283dfdb8
--- /dev/null
+++ b/research/asynchronous-whole-owners/evidence/OWNERS-AND-PROFILE.json
@@ -0,0 +1,36 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "276b69e3fc79a211daaf39776d91b3a6f9c262c415cbd199ab02d5e0ccb9bf4b",
+  "paid_profile": {
+    "1": 148240,
+    "2": 66816,
+    "3": 7032,
+    "4": 19728,
+    "5": 26109,
+    "6": 144,
+    "7": 2209,
+    "8": 1224,
+    "16": 1,
+    "48": 408
+  },
+  "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": 3194,
+  "cross_replica_helper_roles": 33114,
+  "explicit_idle_remainder_children": 9615,
+  "source_idle_children_charged": 17280,
+  "source_artifacts": {
+    "split-centres/CANONICAL-WORD.json.gz": "aff71d7ca599f34a695f96d3b6ad4ba8038b0a5719653e2a6076f9477775261a",
+    "split-centres/LOCAL-PROGRAMS.json.gz": "6cb91d27f03650b67dd72cc441c6a49ae429abee6fb8ea3ec814078ba629e563",
+    "split-centres/LOCAL-CHECKS.json": "d36cce576a03faec3005f15cc0b8f5e7f3890e50c5d85bdd12794f3979e33462",
+    "split-centres/RESIDUAL-ADAPTERS.json": "a4cec4b3ccaebb33cf169b50230c4033eb956f9e75fad64cf6647a3f794c5cca",
+    "work/complex-nine-native/DATA-PHASES.json": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a"
+  },
+  "controller_audit_sha256": "e3f3c8dd3d9ead17031574f86fe7c7887f5f08ead36877b0baa93def9db58431"
+}
diff --git a/research/asynchronous-whole-owners/evidence/PREFIX-AND-INVOICE.json b/research/asynchronous-whole-owners/evidence/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..c1caf19da3
--- /dev/null
+++ b/research/asynchronous-whole-owners/evidence/PREFIX-AND-INVOICE.json
@@ -0,0 +1,69 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "276b69e3fc79a211daaf39776d91b3a6f9c262c415cbd199ab02d5e0ccb9bf4b",
+  "global_prefix_bits": 205,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "local": {
+    "backward": {
+      "events": 25082,
+      "macros": 19708,
+      "real_component_primitives": 221516,
+      "prefix_l1": "1039266",
+      "prefix_bits": 20,
+      "coefficient_work_primitive_count": 109970,
+      "all_exact_columns": 800,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    },
+    "forward": {
+      "events": 25082,
+      "macros": 19708,
+      "real_component_primitives": 221420,
+      "prefix_l1": "32209",
+      "prefix_bits": 15,
+      "coefficient_work_primitive_count": 109906,
+      "all_exact_columns": 800,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    }
+  },
+  "entering_helpers": 122,
+  "entrance_rank": 148,
+  "local_adapters": 391344,
+  "local_primitive_bound": 10149247009100,
+  "wrapper_elementary_factors_charged": 2529792,
+  "compiler": 25934336,
+  "unhosted_pervertex": 1299225185815824,
+  "hosted_rebased_pervertex": 1299225185483184,
+  "conservative_pervertex_used": 1299225185815824,
+  "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/asynchronous-whole-owners/evidence/RESULT.json b/research/asynchronous-whole-owners/evidence/RESULT.json
new file mode 100644
index 0000000000..4eea6e65cc
--- /dev/null
+++ b/research/asynchronous-whole-owners/evidence/RESULT.json
@@ -0,0 +1,68 @@
+{
+  "status": "PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE",
+  "kappa": "67885087881447/50000000000000000",
+  "kappa_decimal": "0.001357701757628940",
+  "complex_lower": "679773808909616785409/500000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "276b69e3fc79a211daaf39776d91b3a6f9c262c415cbd199ab02d5e0ccb9bf4b",
+  "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": "construct",
+      "exit": 0,
+      "seconds": 0.7339999999967404
+    },
+    {
+      "stage": "scalar",
+      "exit": 0,
+      "seconds": 5.046999999991385
+    },
+    {
+      "stage": "emit-local",
+      "exit": 0,
+      "seconds": 3.9679999999934807
+    },
+    {
+      "stage": "phases",
+      "exit": 0,
+      "seconds": 208.375
+    },
+    {
+      "stage": "adapters",
+      "exit": 0,
+      "seconds": 1.3910000000032596
+    },
+    {
+      "stage": "parent-integration",
+      "exit": 0,
+      "seconds": 1.7339999999967404
+    },
+    {
+      "stage": "parent-replay",
+      "exit": 0,
+      "seconds": 9.594000000011874
+    },
+    {
+      "stage": "emit-async",
+      "exit": 0,
+      "seconds": 4.953000000008615
+    },
+    {
+      "stage": "independent-async",
+      "exit": 0,
+      "seconds": 26.062000000005355
+    },
+    {
+      "stage": "invoice",
+      "exit": 0,
+      "seconds": 2.437999999994645
+    },
+    {
+      "stage": "two-moments-assembly",
+      "exit": 0,
+      "seconds": 0.5940000000118744
+    }
+  ],
+  "package_manifest_sha256": null
+}
diff --git a/research/asynchronous-whole-owners/evidence/STEPS.json b/research/asynchronous-whole-owners/evidence/STEPS.json
new file mode 100644
index 0000000000..70df4595dd
--- /dev/null
+++ b/research/asynchronous-whole-owners/evidence/STEPS.json
@@ -0,0 +1,57 @@
+[
+  {
+    "stage": "construct",
+    "exit": 0,
+    "seconds": 0.7339999999967404
+  },
+  {
+    "stage": "scalar",
+    "exit": 0,
+    "seconds": 5.046999999991385
+  },
+  {
+    "stage": "emit-local",
+    "exit": 0,
+    "seconds": 3.9679999999934807
+  },
+  {
+    "stage": "phases",
+    "exit": 0,
+    "seconds": 208.375
+  },
+  {
+    "stage": "adapters",
+    "exit": 0,
+    "seconds": 1.3910000000032596
+  },
+  {
+    "stage": "parent-integration",
+    "exit": 0,
+    "seconds": 1.7339999999967404
+  },
+  {
+    "stage": "parent-replay",
+    "exit": 0,
+    "seconds": 9.594000000011874
+  },
+  {
+    "stage": "emit-async",
+    "exit": 0,
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diff --git a/research/asynchronous-whole-owners/inputs/ASYNC-3.json b/research/asynchronous-whole-owners/inputs/ASYNC-3.json
new file mode 100644
index 0000000000..930a44dfcd
--- /dev/null
+++ b/research/asynchronous-whole-owners/inputs/ASYNC-3.json
@@ -0,0 +1,13195 @@
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diff --git a/research/asynchronous-whole-owners/inputs/ASYNC-OWNERS.json.gz b/research/asynchronous-whole-owners/inputs/ASYNC-OWNERS.json.gz
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index 0000000000..037f694889
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diff --git a/research/asynchronous-whole-owners/inputs/BASE-WORD.json.gz b/research/asynchronous-whole-owners/inputs/BASE-WORD.json.gz
new file mode 100644
index 0000000000..2b406b9409
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diff --git a/research/asynchronous-whole-owners/inputs/PR493-EXPECTED.json b/research/asynchronous-whole-owners/inputs/PR493-EXPECTED.json
new file mode 100644
index 0000000000..973aaf30f1
--- /dev/null
+++ b/research/asynchronous-whole-owners/inputs/PR493-EXPECTED.json
@@ -0,0 +1,91 @@
+{
+ "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",
+  "local_histogram": {
+   "1": 1200,
+   "2": 1440,
+   "4": 180,
+   "6": 120,
+   "8": 18
+  },
+  "source_destination_gates_A": 577,
+  "sources_rewritten": 117,
+  "five_stage_payload_bits": 100
+ },
+ "eleven": {
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "bit_lower_decimal": "0.001565442026981656908596",
+  "profile": {
+   "1": 105600,
+   "2": 130560,
+   "4": 19680,
+   "6": 14400,
+   "7": 7680,
+   "8": 1584,
+   "48": 2,
+   "56": 2628
+  },
+  "bit": {
+   "live": 9600,
+   "physical": 9609,
+   "maxchild": 56,
+   "rank_mass": 745536,
+   "hosted_residuals": 43032,
+   "prefix_bits": 2119,
+   "charged_prefix_bits": 2176,
+   "coefficient_bits": 2119,
+   "three_level_coefficient_bits": 6411,
+   "charged_three_level_coefficient_bits": 6464,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "e37b52e4861c39154b5891460fb45df8651c92cd68961078f8f06596f057c822",
+  "kappa": {
+   "pr484": {
+    "kappa": "662515748707749/500000000000000000",
+    "kappa_decimal": "0.001325031497415498",
+    "binding_component": "complex",
+    "complex_lower": "663394767670133/500000000000000000",
+    "role": "primary"
+   },
+   "pr471": {
+    "kappa": "260706019542937/200000000000000000",
+    "kappa_decimal": "0.001303530097714685",
+    "binding_component": "complex",
+    "complex_lower": "1305231506267591/1000000000000000000",
+    "role": "control (complex supplier of the current whole-residual frontier)"
+   },
+   "pr458": {
+    "kappa": "323880830669511/250000000000000000",
+    "kappa_decimal": "0.001295523322678044",
+    "binding_component": "complex",
+    "complex_lower": "1297203880559577927527/1000000000000000000000000",
+    "role": "control"
+   },
+   "pr448": {
+    "kappa": "358867191156973/250000000000000000",
+    "kappa_decimal": "0.001435468764627892",
+    "binding_component": "complex",
+    "complex_lower": "718766148669433/500000000000000000",
+    "role": "information only"
+   }
+  }
+ },
+ "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"
+  }
+ }
+}
diff --git a/research/asynchronous-whole-owners/inputs/work/complex-network/hamming/PACKET-PROGRAMS.json.gz b/research/asynchronous-whole-owners/inputs/work/complex-network/hamming/PACKET-PROGRAMS.json.gz
new file mode 100644
index 0000000000..e98ce5d879
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diff --git a/research/asynchronous-whole-owners/inputs/work/complex-network/hamming/PROTOTYPE.json b/research/asynchronous-whole-owners/inputs/work/complex-network/hamming/PROTOTYPE.json
new file mode 100644
index 0000000000..b8ad698417
--- /dev/null
+++ b/research/asynchronous-whole-owners/inputs/work/complex-network/hamming/PROTOTYPE.json
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diff --git a/research/asynchronous-whole-owners/inputs/work/complex-nine-native/DATA-PHASES.json b/research/asynchronous-whole-owners/inputs/work/complex-nine-native/DATA-PHASES.json
new file mode 100644
index 0000000000..6f128ce2d2
--- /dev/null
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+        {
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+          "orthogonal_axes": [],
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+        }
+      ],
+      "terminal_Y_translation": 127
+    }
+  ],
+  "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/asynchronous-whole-owners/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz b/research/asynchronous-whole-owners/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz
new file mode 100644
index 0000000000..975ce5c0df
Binary files /dev/null and b/research/asynchronous-whole-owners/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz differ
diff --git a/research/asynchronous-whole-owners/inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz differ
diff --git a/research/asynchronous-whole-owners/inputs/work/odd-stages/clifford_exact.py b/research/asynchronous-whole-owners/inputs/work/odd-stages/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/inputs/work/pr361/code/engines/base_two_moment.py b/research/asynchronous-whole-owners/inputs/work/pr361/code/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/inputs/work/pr361/code/engines/moment.py b/research/asynchronous-whole-owners/inputs/work/pr361/code/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/inputs/work/pr361/code/engines/outer.py b/research/asynchronous-whole-owners/inputs/work/pr361/code/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz differ
diff --git a/research/asynchronous-whole-owners/references/PR493-NOTICE.md b/research/asynchronous-whole-owners/references/PR493-NOTICE.md
new file mode 100644
index 0000000000..d9e0c531bc
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/references/PR496-PROOF.md b/research/asynchronous-whole-owners/references/PR496-PROOF.md
new file mode 100644
index 0000000000..aa8230f063
--- /dev/null
+++ b/research/asynchronous-whole-owners/references/PR496-PROOF.md
@@ -0,0 +1,105 @@
+# Whole-owner pooling of the complex supplier
+
+This construction is conditional on the all-size compiler, common-label,
+restored-row, precision/tape and analytic-transfer contracts retained by the
+pinned PR493 bit and PR484 complex packages. It also retains PR484's explicit
+Lemma A realization contract for paid residual wrappers with borrowed spectators.
+Its Lemma G schedule/conjugation identities are checked on the serialized local
+programs, with independent pre-operation integer bounds. Finite verification
+alone does not establish the inherited all-size contracts.
+
+## Placement
+
+Keep PR484's gauge80-kernel42 local word, its exact Gaussian phases, both
+orientations, and all entry/exit wrappers. There are 560 helper roles in each of
+72 complete local invocations, indexed by nine stages and eight replicas. A
+helper of entrance rank e has one residual of width 9-e. No residual is split.
+
+Pool the idle coordinates of all eight physical replicas. A frozen allocation
+places every whole residual in a single pending idle child, and a frozen
+bipartite edge coloring assigns that slot to its invocation replica. Left
+vertices are physical families; right vertices are actual helpers. Each helper
+has degree eight and every physical family has degree at most eight at the
+stage. The eight matching colors give each invocation exactly one of every
+helper and at most one helper on any family. The verifier reads every actual
+role, rather than trusting existence of a coloring or the optimizer status.
+
+Every host is an idle pair at that stage. Thus no host is an active data wire,
+even if its physical replica differs from its invocation replica. The literal
+loop order is retained: recipe phase, replica, cover class, complete local
+invocation. Entry wrapper, local word and exit wrapper all finish before the
+next replica or cover class. This is necessary when spectators are borrowed
+from coordinates that another invocation later uses.
+
+## Actual maps and restoration
+
+For each physical port q, take the pinned orthogonal 73-column basis B_q. A
+helper's first w columns are precisely its pending residual coordinates. Its
+next 9-w columns are the canonical unused spectator coordinates. Append every
+remaining B_q column in increasing basis-index order. The resulting full
+matrix is an orthogonal coordinate permutation of B_q, with inverse its
+transpose. Both reflected local programs use this same whole-family chart.
+
+The fresh PR484 local check establishes the normalized helper action
+L_E^-1 S_E R_E^-1 = C_[w] tensor I on all 512 local address columns, including
+spectators, with all global phases. Its emitted scalar word restores arbitrary
+dirty helper inputs and its private work. Unique physical owners within a
+complete invocation let the scalar/common-label identity be transported through
+these full charts without aliasing. Because that invocation restores the
+borrowed work before the next, reusing the physical family in a later replica
+is allowed under the same whole-invocation realization contract.
+
+Across all calls, occupied cells of each pending idle child are disjoint. The
+explicit remainder child uses that family's actual replica, starts at the
+recorded pending offset, and executes once. The old `replicas=8` shorthand is
+not applied to these heterogeneous remainders. The independent controller audit
+checks these cells, execution windows, full charts, source-program hashes,
+private-family rebase and cover correction. Deliberately corrupted programs
+must fail the controller audit.
+
+## Paid profile and finite charge
+
+All 40,320 whole residuals fit on the 7,680 existing data families. There are no
+bank families. The physical stock is 8,258, including unchanged private centres,
+reserved tableau and two coefficient registers. The complete paid profile is
+
+```
+rank   1       2      3     4      5     6    7     8
+count 148440  66816  7472  19728  25664  144  1800  4120
+```
+
+Its rank mass is 558,144, and 73*7680 - 558144 = 2496. Both exact moment engines
+include the inherited bad-cover fallback. The complete invoice counts unchanged
+local primitives, wrappers and selectors, and rebases stock, private families,
+idle remainders, routing and final correction to the actual emitted program.
+No new factor is hidden in a cached coefficient. For the global prefix, use
+maximum stream L2 norm over every physical family and cover class. Each
+completed helper endpoint is unitary; each completed data shear or bridge has
+at most two unitary summands. For each actual orthogonal chart, right
+multiplication permutes the cover classes, so an active stream is visited once
+per complete call sweep. The bound uses all 72 ordered call sweeps and nine
+bridges, without assuming replica independence. The local scalar/Horner envelope
+costs 20 bits; conversion from the initial supremum norm to L2 on 2^73 entries
+costs 37 bits; four bits cover primitive arithmetic. Thus 142 bits suffice,
+within the retained 192-bit allowance. The verifier checks the actual matrices,
+complete-call endpoints, scalar envelope and controller premises used here. Each remainder is at most
+rank eight, so the degree-two halving inequality is 73^2 > 2*8^2.
+
+The bit side is reconstructed from PR493 with real Boost. Its physical prefix,
+charged three-level coefficient and row coefficient are read from the fresh
+receipt. Six bootstrap levels and all 47 strict outer inequalities use the
+fresh complex exponent, common row allowance, and C0=2^210000. The next grid
+point and zero-eta, zero-beta and unit-beta controls must all fail.
+
+## Provenance and limits
+
+The selection is a finite nomination, not an optimality theorem. Search used
+floating-point MILP objectives and matching only to propose the frozen map;
+certification uses the actual scalar words, complete emitted role map, exact
+integer/rational checks and fresh source replays. The earlier unpooled padding
+experiment is retained as provenance, not a separately published record.
+
+This does not use the cross-family split of PR448/480/494. Those submissions
+carry a distinct disputed operator interface. This package makes a conditional
+whole-owner claim only and does not claim the largest number among all draft
+submissions under different assumptions.
diff --git a/research/asynchronous-whole-owners/research-notes/kernel/APPENDIX-MANIFEST.json b/research/asynchronous-whole-owners/research-notes/kernel/APPENDIX-MANIFEST.json
new file mode 100644
index 0000000000..0d911fff2f
--- /dev/null
+++ b/research/asynchronous-whole-owners/research-notes/kernel/APPENDIX-MANIFEST.json
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+  "REBUILD.json": "e18727e4191e18838382948ced1c7506d74b3d43caa3853ce751684eef52d8d6",
+  "COMPONENT-SELECTION.json": "b682f7cff6de4f40bdadfc64a9ecb9b03a8d77dbf29be3748fa9d742dc894071",
+  "JOINT-47-SELECTION.json": "89ca715918bfbb04fad2eaee8a95a40324859cd0955512eb13077502e7d950e3",
+  "JOINT-51-SELECTION.json": "7094bb647cc9951a5385660a9ec5f012a427fd118baacaf3d5e9f28cb436acc7",
+  "rebuild_candidate.py": "f8063d539f772fb63712bed787a1c472da28c9baf38b88e3ae14806632d4afb7",
+  "audit_component_scalar.py": "feab9aa6dbcd8f9fffa6dbdb981d15ffc850402ae91cf45f946ff069cac54037"
+}
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new file mode 100644
index 0000000000..8f51ec043c
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+[
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diff --git a/research/asynchronous-whole-owners/research-notes/kernel/JOINT-51-SELECTION.json b/research/asynchronous-whole-owners/research-notes/kernel/JOINT-51-SELECTION.json
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diff --git a/research/asynchronous-whole-owners/research-notes/kernel/LOCAL-CANDIDATE-AUDITS.json b/research/asynchronous-whole-owners/research-notes/kernel/LOCAL-CANDIDATE-AUDITS.json
new file mode 100644
index 0000000000..bfef2c4569
--- /dev/null
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+      "441": "REJECTED_OMITTED_KERNEL_CORRECTION",
+      "466": "REJECTED_OMITTED_KERNEL_CORRECTION",
+      "467": "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/asynchronous-whole-owners/research-notes/kernel/REBUILD.json b/research/asynchronous-whole-owners/research-notes/kernel/REBUILD.json
new file mode 100644
index 0000000000..a20e7b3889
--- /dev/null
+++ b/research/asynchronous-whole-owners/research-notes/kernel/REBUILD.json
@@ -0,0 +1,26 @@
+{
+  "base_sha256": "8b91151043fd61afe379314e4fb1e647cf9cd3cfe98462920d3faba5b1f268f2",
+  "base_parent_kernel79_sha256": "2e13b2dd1e1b0dfa341dbd57b91ee1758ad041cd5ce2e734bf2f9fd0bac155cb",
+  "base_derivation": "Remove the229 entering gauge-prefix gates from parent kernel79.A, empty start_extra and target_levels, rebuild cleanup as inverse of remaining A+B non-target gates. These exact base bytes are retained.",
+  "gk_sources": {
+    "gk_word.py": "f027a9273bcf4e0971258c160b7d3b3c196366b32a529cff6e6a0e666b03826b",
+    "gk_common.py": "e68d190fd436b2f3955decb590adb53344d5d4ea0a19d62d86df1e4b55ecd198"
+  },
+  "candidates": {
+    "COMPONENT": {
+      "selection": "COMPONENT-SELECTION.json",
+      "selection_sha256": "b682f7cff6de4f40bdadfc64a9ecb9b03a8d77dbf29be3748fa9d742dc894071",
+      "word_sha256": "8cd4987c01252cfa0adcc21b083d84aac89e7b25966299d7f8c26446043627de"
+    },
+    "JOINT-47": {
+      "selection": "JOINT-47-SELECTION.json",
+      "selection_sha256": "89ca715918bfbb04fad2eaee8a95a40324859cd0955512eb13077502e7d950e3",
+      "word_sha256": "f42a6761ec00798d75669b77006260bcaa75606dd652f802174c9e2b503dc98a"
+    },
+    "JOINT-51": {
+      "selection": "JOINT-51-SELECTION.json",
+      "selection_sha256": "7094bb647cc9951a5385660a9ec5f012a427fd118baacaf3d5e9f28cb436acc7",
+      "word_sha256": "b880f20ece93a26eaa649e3b895c76b224b5052775ad8dea9f2239825d36ce10"
+    }
+  }
+}
diff --git a/research/asynchronous-whole-owners/research-notes/kernel/RESEARCH-APPENDIX.md b/research/asynchronous-whole-owners/research-notes/kernel/RESEARCH-APPENDIX.md
new file mode 100644
index 0000000000..6748d26366
--- /dev/null
+++ b/research/asynchronous-whole-owners/research-notes/kernel/RESEARCH-APPENDIX.md
@@ -0,0 +1,52 @@
+# Research appendix: corpus reuse, the achieved mechanism, and preserved candidates
+
+The delivered conditional bound is **kappa = 0.001357701757628940**. Its new contribution is asynchronous scheduling of complete replica invocations. The local gauge/kernel word is unchanged from PR484/496; the stronger bit supplier comes from PR493. The package's final receipts, physical audit and exact assembly are the evidence for the numerical claim. The inherited complete-invocation, compiler and analytic contracts remain explicit conditions; this is not a new Lean certification of integer multiplication.
+
+## The mechanism that improved the bound
+
+Earlier packing advanced all eight replicas in lockstep. The new schedule preserves each replica's nine-stage controller order while allowing replicas to occupy different stages. A helper may then use an idle block whenever its entire invocation lies between consecutive touches on the **owner's** timeline. The selected order sorts calls by `(stage + 3*replica/7, stage, replica)`.
+
+Correctness uses completed invocation endpoints. Each invocation restores arbitrary dirty workspace and borrowed spectators, and leaves only its specified residual on its assigned pending block. Different residual blocks of an idle child are disjoint; their product with the paid remainder is the original child. Completing that product before the owner's next touch preserves each replica's original controller. No scalar gate is commuted through an unfinished invocation, and no residual is split between owners.
+
+A flow nomination is converted to literal owners using bipartite edge coloring. There are 72 calls and 40,320 helper occurrences, with 560 distinct helper families per call. Ambient dimension73, live stock7680 and deficit2496 stay fixed. The changed paid profile is:
+
+    1:148240, 2:66816, 3:7032, 4:19728, 5:26109,
+    6:144, 7:2209, 8:1224, 16:1, 48:408.
+
+The complete schedule needs its own physical chart checks and prefix invoice. Its gain does not follow from the floating packing objective alone.
+
+## What was actually reused from the OpenAI corpus
+
+The inspected snapshot is `adc7f1241b42e322a6451854ab7e4b4c146bf78a` of [openai/math](https://github.com/openai/math). `APPENDIX-SOURCES.json` records repository-relative source paths and hashes. Direct source inspection and Git consistency checks are distinct from compiling these modules in this round; no claim is made that every paper in the collection is formalized.
+
+- [FourierCircuit/WordScheduling.lean](https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/Computability/FourierCircuit/WordScheduling.lean): `scheduledStep_product` and `scheduledLayer_product` preserve products under order-preserving schedules on fixed disjoint supports. `Word.matrix_substitute` and `Word.weight_substitute` preserve semantics and account for substituted calls. These supplied the structural template for scheduling complete normalized invocations. The new owner-relative interval argument is stated and checked separately; the fixed-support theorem is not silently applied to aliased unfinished programs.
+- [MatroidCounting/CommonBases.lean](https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/Combinatorics/MatroidCounting/CommonBases.lean): `greedyOracle_correct`, `greedyOracle_rank`, and the parallel/nonparallel pair-rank lemmas motivated response-matroid basis and circuit-component selection. The common-integer-polymatroid preprint, problem114, also suggested moving capacity across fixed stage partitions. The actual packing family is not asserted to be a matroid, and no counting FPRAS is used as a packing certificate.
+- `FourierCircuit/TensorTools.lean`, `RowCompression.sparse_row_compression`, and `SparseShear.lean`, `cancellation_identity`, provide explicit row-basis changes and cancellation of a shared exterior block. Independent dirty replica coordinates cannot be deleted merely by compressing a displayed response matrix. No additional gain was obtained from this route.
+- `FourierCircuit/PivotJoin.lean`, `PivotJoin.of_join`, and `MonomialFeedback.lean`, `Dense2x2.price`, suggested alternative local compositions. The latter's abstract normalized price bound is not a literal bounded-coefficient routine in this model. The exact-Fourier documentation also limits its theorem to a subsequence; it does not supply the missing all-length bit-complexity implementation.
+- `Topology/ArtinGroups/Cancellation/BlockPivot.lean`, `homotopy_square`, `homotopy_retract`, `remainder_retained`, and `NumberTheory/TwoPoint/Walks/ColumnRankRelations.lean`, `columnDifference_disjoint_minor`, were inspected for simultaneous elimination and donor/pivot separation. They did not produce another priced gain in this round.
+
+## Three checked local constructions, not added to the achieved gain
+
+For a common entrance frame, choose a basis of a response-matroid component as donors. Each remaining column is an exact rational donor combination. Prepending its cancelling donor shears makes that pivot's dirty response zero; reverse cleanup restores the helper state. All required frame nesting and source spans must still hold.
+
+The following concrete words passed exact rational reconstruction, all800 arbitrary-dirt columns in both forward and inverse-transpose orientations, and every individual pivot-correction omission control:
+
+| Candidate | Local profile change from PR484/496 | Residual counts (width:count) | Omission controls |
+|---|---|---|---:|
+| COMPONENT | -10 rank1, -14 rank2, +14 rank3 | 5:4, 7:14, 8:100, 9:442 | 38 |
+| JOINT-47 | -14 rank1, -2 rank2, -4 rank3, +4 rank4, +4 rank5 | 5:4, 7:12, 8:102, 9:442 | 48 |
+| JOINT-51 | -14 rank1, -4 rank2, +8 rank3, -2 rank4, +2 rank5 | 5:4, 7:14, 8:100, 9:442 | 40 |
+
+These improve selected local objectives but lose scarce narrow residual inventory. Their tested lockstep allocations, including stage-selective portfolios and paid banks, did not improve the full bound. None is counted in the delivered kappa. They remain useful sufficient constructions for future schedules.
+
+The companion base, three selections and `REBUILD.json` permit source-bound reconstruction through `rebuild_candidate.py`; `audit_component_scalar.py` checks each reconstructed word independently. `LOCAL-CANDIDATE-AUDITS.json` preserves the three exact scalar receipts. The constructor reuses the retained, hash-pinned `gk_word.py` and `gk_common.py` with their attribution.
+
+## Other bounded lessons
+
+All14,851 subspaces contained in first-touch frames were screened. Under the fixed80 gauge exclusions, only14 classes had positive response nullity, all dimension1. Allowing excluded gauge helpers exposed63 additional components, still dimension1. A catalogue of646 components from deletion minors up to depth two did not beat the inherited42-pivot width budget. These are finite-search results, not global impossibility theorems.
+
+The proposed gauged-donor ordering is algebraically sufficient when original dirt compensation precedes the kernel update. Adding individual donors while retaining the current palette failed exact target/centre nesting in all86 tested cases; geometric admissibility alone was insufficient. Whole-palette replacements remain a separate route.
+
+Native frame-retiming searches on the full joint gauge word and its cleanup extension found no better profile. A direct lift of PR493's bit skeleton to the complex side also failed a specific structural test: all14,400 port pairs obey complemented adjacency. An even-parity-frame repair and the identity `G Hadamard G + A_orth - J = 3 I` are constructive leads, but require extra paid copies and a different decoder; they are not achieved improvements.
+
+The productive change was therefore at the scheduling level: reuse the already checked local engine, remove replica lockstep, and reconstruct the complete physical ownership and prefix bill.
diff --git a/research/asynchronous-whole-owners/research-notes/kernel/audit_component_scalar.py b/research/asynchronous-whole-owners/research-notes/kernel/audit_component_scalar.py
new file mode 100644
index 0000000000..df3f46411c
--- /dev/null
+++ b/research/asynchronous-whole-owners/research-notes/kernel/audit_component_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/asynchronous-whole-owners/research-notes/kernel/rebuild_candidate.py b/research/asynchronous-whole-owners/research-notes/kernel/rebuild_candidate.py
new file mode 100644
index 0000000000..fc15fc255e
--- /dev/null
+++ b/research/asynchronous-whole-owners/research-notes/kernel/rebuild_candidate.py
@@ -0,0 +1,13 @@
+"""Rebuild one checked local candidate from a pinned pre-gauge base and selection.
+python rebuild_candidate.py GK_CODE_DIR LANE_DATA CANDIDATE OUTPUT_WORD
+CANDIDATE is COMPONENT, JOINT-47 or JOINT-51. Uses retained Apache-2.0 upstream
+code with original attribution. Physical hosting and pricing are separate.
+"""
+import sys,json,gzip,hashlib
+from pathlib import Path
+code,data,name,out=Path(sys.argv[1]),Path(sys.argv[2]),sys.argv[3],Path(sys.argv[4])
+assert not out.exists();r=json.loads((data/'REBUILD.json').read_bytes());sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+for f,h in r['gk_sources'].items():assert sha(code/f)==h,(f,'source hash')
+assert sha(data/'BASE-WORD.json.gz')==r['base_sha256'];c=r['candidates'][name];assert sha(data/c['selection'])==c['selection_sha256']
+sys.dont_write_bytecode=True;sys.path.insert(0,str(code.resolve()));import gk_word as g
+word=g.build(json.loads(gzip.decompress((data/'BASE-WORD.json.gz').read_bytes())),json.loads((data/c['selection']).read_bytes()));raw=g.dump(word);assert hashlib.sha256(raw).hexdigest()==c['word_sha256'];out.write_bytes(raw);print('PASS_SOURCE_BOUND_RECONSTRUCTION',name,c['word_sha256'])
diff --git a/research/asynchronous-whole-owners/vendor/audit_scalar_invoice.py b/research/asynchronous-whole-owners/vendor/audit_scalar_invoice.py
new file mode 100644
index 0000000000..b03fdf510f
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py
new file mode 100644
index 0000000000..252ca9393d
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py
new file mode 100644
index 0000000000..e80ca6b8b3
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py
new file mode 100644
index 0000000000..0dd1853bb5
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py
new file mode 100644
index 0000000000..0e5fde920d
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py
new file mode 100644
index 0000000000..15782ba625
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py
new file mode 100644
index 0000000000..df261063e1
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py
new file mode 100644
index 0000000000..220cc7a2f5
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py
new file mode 100644
index 0000000000..b2e08a30c9
--- /dev/null
+++ b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py
@@ -0,0 +1,271 @@
+# 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)
+for name,mut in [('missing_padding',lambda t:t['bank_padding']['families'].pop()),
+                 ('aliased_owner',lambda t:t['calls'][0]['owners'][241].__setitem__(1,[2,0])),
+                 ('missing_cover_phase',lambda t:t['cover_final_correction'].__setitem__('charged_calls_per_cover',0))]:
+    t=copy.deepcopy(ir);mut(t)
+    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)
+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/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json
new file mode 100644
index 0000000000..cf624433f0
--- /dev/null
+++ b/research/asynchronous-whole-owners/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json
@@ -0,0 +1,470 @@
+{
+ "gauge": {
+  "134": [
+   510
+  ],
+  "135": [
+   510
+  ],
+  "136": [
+   510
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+  "137": [
+   510
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+   510
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+   510
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+   510
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+   102
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+   102
+  ],
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+  "542": [
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+   24
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+  "546": [
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+  "547": [
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+  "549": [
+   408,
+   102
+  ],
+  "550": [
+   408,
+   102
+  ],
+  "551": [
+   408,
+   102
+  ],
+  "552": [
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+  "553": [
+   510
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+  "554": [
+   510
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+  "555": [
+   510
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+  "556": [
+   510
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+  "557": [
+   510
+  ],
+  "558": [
+   510
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+  "559": [
+   510
+  ]
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+  {
+   "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/asynchronous-whole-owners/vendor/complex/split-centres-global/code/complex_phases_full.py b/research/asynchronous-whole-owners/vendor/complex/split-centres-global/code/complex_phases_full.py
new file mode 100644
index 0000000000..b5a5bd64b4
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/vendor/complex/split-centres-global/vendor/clifford_exact.py b/research/asynchronous-whole-owners/vendor/complex/split-centres-global/vendor/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/asynchronous-whole-owners/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/asynchronous-whole-owners/verify.py b/research/asynchronous-whole-owners/verify.py
new file mode 100644
index 0000000000..c0d540ffd3
--- /dev/null
+++ b/research/asynchronous-whole-owners/verify.py
@@ -0,0 +1,49 @@
+"""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
+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 not W.exists(),'Choose a new output directory; existing outputs are preserved.'
+mf=P/'MANIFEST.json'
+if mf.exists():
+ for n,h in json.loads(mf.read_text()).items():assert hashlib.sha256((P/n).read_bytes()).hexdigest()==h,n
+W.mkdir(parents=True);V=W/'base';V.mkdir();(V/'split-centres').mkdir();shutil.copytree(P/'inputs/work',V/'work')
+shutil.copy2(P/'inputs/BASE-WORD.json.gz',V/'BASE-WORD.json.gz')
+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))
+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(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('construct',G/'code/gk_word.py',V/'BASE-WORD.json.gz',G/'data/selections/gauge80-kernel42.json',V/'split-centres/FULL-WORD.json.gz')
+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',P/'inputs/ASYNC-3.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/asynchronous-whole-owners/verify.sh b/research/asynchronous-whole-owners/verify.sh
new file mode 100644
index 0000000000..275570d71e
--- /dev/null
+++ b/research/asynchronous-whole-owners/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