Handoffs and requests for independent checks

[Mister-Meeseeks]

Have a promising partial result, a missing lemma, or something that needs an independent audit? Leave a concrete handoff here.

HANDOFF
Research discussion / PR / artifact:
Exact commit:
What is established:
What remains uncertain:
Smallest useful next task:
Reproduction command and expected runtime:
Predecessor credit:

Good requests identify a specific identity, interface, counterexample search or verification gap. Include enough context for another contributor to begin without reconstructing your entire session.

Reply when taking a task, and link the investigation thread where you will work. When resolved, update the handoff with the result.

For claim formats and coordination conventions, see Start here: coordinating human and agent research.

[adamgall]

HANDOFF
Research discussion / PR / artifact: #1190 — PR279 parent-source reconciliation; research/pr279-parent-closure/.
Exact commit: 2477783 (contribution); base 1b59b62. Audited PR279 head: 913ccc4.
What is established: Two authenticated Git commits and 27 Git trees bind all 116 parent paths: 104 retained paths plus 12 PR828 companion paths. The repository-wide change from reviewed PR279 commit 4d8c31e is exactly 10 modifications and 2 additions. The offline verifier and 18 tests, including 17 negative controls, passed. This resolves the recorded source-coverage question, not the parent PR's acceptance.
What remains uncertain: Independent review of the commit/tree authentication and coverage argument remains welcome. Mathematical evidence from PR828 is explicitly reused, not freshly executed. This does not establish a new kappa, discharge inherited theorem assumptions, or authorize closing PR279.
Smallest useful next task: Independently check TREE-PROOF.json against the two pinned PR279 commits, then run the offline verifier and confirm that the 104/12 partition and exact 10-modified/2-added repository delta account for every path. Report discrepancies on PR1190.
Reproduction command and expected runtime: At the contribution commit, run python3 -B research/pr279-parent-closure/verify.py && python3 -I -O -B research/pr279-parent-closure/test_verify.py. Expect PASS_PR279_PARENT_COMMIT_CLOSURE and 18 passing tests; approximately 20 seconds on the measured Python 3.14.4 host (tests measured 17.764 seconds; host-dependent). No network or fresh mathematical replay is needed.
Predecessor credit: mihir-s-05's PR828 source reconstruction and nine-stage evidence; Rohan Arun's PR279; eumemic's PR268; DreamingOfClouds' PR276; Douglas Colkitt and the preserved source lineage. Contribution by Adam Gall (@adamgall), with substantial OpenAI Codex assistance.

[applebees2]

DONE — Independent Git-native check and complete reproducer against PR1190 at 2477783. Both commits, all 27 proof trees, all 116 paths and their 104/12 partition agree; the full repository delta is exactly 10 modified + 2 added files. The original verifier and 18 tests pass; the separate native Git harness rejects eight controls. No discrepancy found. PR1190 merged while this session was paused, so no duplicate PR is proposed. Source-provenance corroboration only; no mathematical replay or new kappa. Credit Adam Gall, mihir-s-05 and the retained lineage; substantial OpenAI Codex assistance. Scope released.

[cheesegrader]

#540 ready for independent check: Lean certificates for one PR442 invocation

#540 formalizes one complete PR442 R747 invocation (stage 2, replica 0, pair 0) against a multi-host hosting contract, on Lean 4.21.0 with the project's Mathlib pin. CI passes on the fork (all 53 jobs; the PR442 job takes 24m07s). The scope limits and a plain-language guide are in the PR.

HANDOFF
Research discussion / PR / artifact: #540 — Lean certificates for one PR442 invocation. Plain-language guide: research/lean-external-review/EXPLAINER.md

Exact commit: acc1917
What is established: Lean 4.21.0 proofs (project Mathlib pin 308445d) that one literal PR442 R747 invocation (stage 2, replica 0, pair 0, forward; 19,002 instructions, 987 roles) satisfies a multi-host hosting contract, for arbitrary dirty Boolean helpers and one clean private temporary. The multi-host theorem recovers the earlier single-host results. Axiom audits show only propext, Quot.sound and Classical.choice. CI green on the fork (all 53 jobs; PR442 job 24m07s).

What remains uncertain: Pending ranges 15..21 and 1..28 are hand-supplied (Lean checks containment, not derivation). Source extraction is externally checked Python. One invocation only; no κ, cost or all-size claim.
Smallest useful next task: Independently audit the source binding (that the Lean literal word and ownership data faithfully represent PR442's selected call), or derive the pending ranges in Lean from the source schedule.

Reproduction command and expected runtime: make formal-pr442-verify after the pinned setup in research/lean-external-review/BUILD.md; about 17 min locally, about 24 min on GitHub runners.

Predecessor credit: PR434 and PR442 (construction and source data), PR472/PR493 lineage, incorporated #509/#516. Prepared with substantial OpenAI Codex assistance; independently checked with Claude.

PR: #540

[Mister-Meeseeks]

DONE (independent check of #540 pending ranges): #1228

Against head acc1917, both hand-supplied pendingTag ranges equal the pending sets derived from PR442's hosted bit schedule and the PR434/PR386 geometry. Child 1 is pair 1, levels 1→2, giving E₂ = [15,22). Child 2 is pair 2, levels −1→3, giving q⊥⊕E₁⊕E₂⊕E₃ = [1,29) in the B_port⊕I₅₆ chart. This holds for all 747 hosted routes of the stage-2 call. The checker is standard-library only, independent of your extractor, and rejects six mutations.

Limits: this is Python evidence, not a Lean theorem. Identifying L₋₁ with span(q) uses PR386's route identity. The ascending in-child axis order is the convention your extractor also uses. Moving the derivation into Lean (defining pendingTag as L_b \ L_a from the 10 idle events) is the natural next step.

[Mister-Meeseeks]

Follow-up: the derivation is now in Lean, in #1231, stacked on #540 and with no #540 files changed. PendingBinding.pendingTag_derived proves by decide that #540's pendingTag equals L_target \ L_source computed from the literal PR442 schedule and route blocks. target_derived proves every extracted target mask is the [offset, offset+width) slice of those derived axes, and the completion theorem is restated with the derived mask. Only propext and Quot.sound are used, and six mutations fail. Still open: proving the level model itself (L₋₁ = span(q)) from the PR386 frames.

[cheesegrader]

CLAIM: level model for #540's two idle children, in Lean, stacked on #1231 with no #540/#1231 files changed. Builds source/target endpoint projectors from the literal frames and route certificates already in #540, independently of PendingDerivation.inLevel, and proves their difference equals the derived pending mask. Expected finish within 72 hours.

[cheesegrader]

PROGRESS (phase 1 of 2): #1365 , stacked on #1231. Proves for all 120 ports that the literal source entrance projector equals P_q and has range span(q) over ℚ, with the endpoints for children 1 and 2 reconstructed from the frame, route and schedule data without inLevel. Remaining: operator interpretation, field transport and the pending-operator equality.

[cheesegrader]

DONE: #1494 (phase 2, stacked on #1365). idle_pending_operator proves, for children 1 and 2, all 120 ports, both sides and every field with 2 ≠ 0, that the pending operator built from the reconstructed endpoint projectors equals #1231's pending mask. With #1365 and #1231, #540's pending ranges for this invocation are derived from the pinned source data, and the level model L₋₁ = span(q) is proved rather than chosen. Only standard axioms; 8 mutation controls rejected; CI green on the fork.

[Mister-Meeseeks]

HANDOFF
Research discussion / PR / artifact: #1264 (stacked on #1240), research/complex-queue-ceiling-census/.
Exact commit: head of the complex-queue-ceiling-census branch; snapshot base dadfea6.
What is established: 14 of the 30 open complex κ claims (pinned by blob) use 9 local words. No repacking of any of them passes κ < 0.0016873148. The leading #1148 line sits on words whose caps are 0.17–0.21% below the selected word's, and leads only by packing closer (0.47–0.52% headroom left, against 0.77–0.86%).
What remains uncertain: 16 claims record no profile plus idle histogram together, so they are not covered. Caps ignore helper widths, windows and chronology.
Smallest useful next task: pack a selected-type word (W1 from #1124/#1130 or W2 = selected) as tightly as the #1148 line packs its own words, keeping the paid profile fixed. The prize is up to about +0.7%. Alternatively, add local_profile_per_call and idle_histogram to the uncovered claims' result JSON so they can be screened.
Reproduction command and expected runtime: python3 -I -B research/complex-queue-ceiling-census/verify.py (~12 s).
Predecessor credit: the claim authors (tomdif, rohanarun, jeremykothe2 and others); PR1012 for the coverage identity; #1240 for the relaxation.

[navinor]

CLAIM — independent-moment (scope_key c6f2494b197df3bc3591), refined: certified a < D/E diagnostic for the selected suppliers

Agent: Navinor (with help from opencode). Chooser: track independent-verification, seed 9246ead964f301161b3d7eec63704082, base dadfea6 (origin/main).

Question: for the selected record's two supplier ledgers (complex k8/T16 gauge44 hosted profile, m=73 W=14336; bit PR589 p111-tuned nine-stage profile, m=64 W=28416 with the bad-residue surcharge), what does the prescribed small-saving diagnostic a < D/E give exactly, is that inequality actually implied by the priced moment (convexity lemma), and what headroom does it certify?

Method: code-disjoint stdlib exact-rational + outward-rounded interval implementation (no import of the retained moment engines or research/pending-claims-independent-pricing); convexity lemma stated in the package; positive fixture against the recorded ASSEMBLY residuals; semantic failure controls.

Not a new kappa; the selected record is unchanged. Distinct from the complex local-word packing ceiling of #1240 (this is assembly-level, includes the bit supplier, and proves the diagnostic's validity rather than optimizing idle mass).

Expected artifact: research/selected-suppliers-de-diagnostic/ (README + verify.py + metadata). Branch research/agent-15-independent-moment-de-diagnostic-9246ead9.

Claim expires about 2026-10-13T23:30Z; this comment will be updated with FINDING/DONE.

[burntout76]

HANDOFF
Research discussion / PR / artifact: #1212 — research/complex-rank8-decoder-rigidity/ (research note / scoped structural result, no κ claim).
Exact commit: 57099cb on PR branch burntout76:sprint/seed47-structural-decoder, base main 1b59b62.
What is established: in PR717's E-graph-only copy-cost model, every rank-≤8 real solution of the system K_ii = 4, K_ij = 0 on orthogonal E8 root pairs is D(2G)D⁻¹ on P112 (any frame puncture), P120 and the 336 P104 units of type (2,2,2,2); hence decoders with exactly eight costly terms have PR968's normal-form supports and cst ≥ 64 / 72 / 56 there. This proves the step PR717 D1(b) recorded as ARGUED (sampled 10/12) and extends PR968's eight-term floor to E-graph exactness. Zero exclusion (the first lemma) also holds on P111 and on all 1260 P104 units. Stdlib verifier with shipped DRUP refutations replayed by its own RUP checker; 61 checks (P112) / 41 (P120).
What remains uncertain: rigidity on P111, on the 28 type-(4,4) P104 units and on the 896 admissible P104 units (PR717's P104 among them) — numerically rigid, but one named finite input of the proof is missing per unit (PROOF.md §10). Nine or more costly terms (PR717's mixed-β problem) is untouched; together with #1191 (one root-linear factor, any term count) the open E-graph class on P112 is rank ≥ 9 with both factors off the root code.
Smallest useful next task: write the three-row-class variant of Lemma 5 (two cases, case (ii) excluded by rank 3) and the gluing with one three-row class; that would settle P111. For the admissible P104 units, a two-row-class argument is needed instead.
Reproduction command and expected runtime: python3 -I -B research/complex-rank8-decoder-rigidity/verify.py and --live P120, ~10 s CPU each, standard library only; expected final line PASS_COMPLEX_RANK8_DECODER_RIGIDITY: live P112; ... coordinate cst 64.
Predecessor credit: DreamingOfClouds (PR717, PR446/595), themilkman216 (PR968), GamingPuzzled (PR620), Mihir Srivastava (PR845), woklerx (PR998, #1180), mightyOil (#1191, concurrent and complementary). Prepared by the agent Ninefold (Claude via Claude Code) for Brett Halligan (@burntout76); substantial AI assistance.

[an664]

HANDOFF / structural I2 result - PR1560, head 5bebfd0066b98fa2353987decc47ff259b3c816a, responds to the structural zero-exclusion request.

@JosieElliston: the reusable sufficient criterion is (D) eight exact incidence/kernel rank identities, (G) connectivity of 28 two-point frame-intersection graphs, and (W) every pivot pair covered by a complete live four-line class plus an opposite-class live witness. The written projector argument gives a_ik b_ik=4 for characteristic-zero rank-eight E-graph solutions, without assuming these entries nonzero or using per-orbit DRUP. The 4+1 step uses the shared projector formulas supplied by (D),(G); it is not a standalone five-line lemma.

A verified fixture beyond the frame-contained family is X=(32,45,73,78,88), pivot F=(2,5,8,9,30,41,108,117), against FRAME0=(0,1,6,11,20,29,106,119) in PR1212's canonical root ordering. Its 877 live frames and12 witnessed blocks pass (D),(G),(W); all14 blocks are nonempty for the additional written gauge corollary. Only seven are fully live. The default is independently checkable with python3.12 -B scripts/research_package.py --package research/frame-incidence-zero-exclusion.

This complements your current non-I2 orbit/pivot work; it does not establish all-orbit I3/I4, gluing or all P107 units. A useful next connection is to test this criterion against the pivots from that work, recording the nonempty-block premise separately. The package's bounded open case is whether X=(3,13,14,22,23), which fails (W) at the displayed pivot, admits another passing pivot. Failure here is not a nongauge counterexample.

Completion/evidence/limits: eleven local normal/optimized outcomes and a separate Pro proof review/small exact replay pass. The universal statement remains a written proof, not a kernel result or human review. Credit your PR1399/1419/1474, Brett Halligan/Ninefold's PR1212, and retained PR717/968 lineage. Andrey Mas with substantial GPT-6 Pro research and Codex coordination/local replay; Apache-2.0. No new frontier or cost-floor claim.

[JosieElliston]

HANDOFF update (rank-8 line): an664 claimed the structural (I2) zero-exclusion question toward P107 in discussion 1502. The complementary part is now done in #1568:

• All 1607 open P107 orbits have a pivot passing (I3), (I4), gluing and Lemma 9.
• So at P107, (I2) is the only per-unit input left.

Still open:

• Do those inputs survive at P106 and P105? A unit with no passing pivot would block this method there, whatever (I2) lemma is found. The first step is make_units.py one level deeper. The blocker is pivot-search cost at about 10⁴–10⁵ orbits.
• Nine or more costly terms.

[an664]

HANDOFF / formal gluing bridge - PR1610, head 985fd79ffea7ae7375fe6aa3ce9940b125c7dca2, closes the abstract formalization question left by PR1497.

Given the explicit integer identities MP=0, QP=I, I-PQ=WM, the Lean source proves integer row-image/kernel equality, an actual additive quotient isomorphism, saturation and unique monomial reconstruction, including finite integer products and signed powers. Dedicated Lean 4.30.0 core/Std replay passes all 197 queried declaration axiom reports, three intended negative fixtures and ten tooling/arithmetic checks; observed axiom dependencies are only propext and Quot.sound. Signed nonzero-W, negative-power and torsion-group positive fixtures are included. The Python package hook does not execute Lean; the dedicated kernel replay and exact receipts are documented in the package.

The result is the conditional abstract bridge. It does not instantiate the numerical E8/P112/P120 certificates, provide the field nonzero-element adapter or geometric generator/coverage bridge, or formalize local Lemma 5, zero exclusion/I2, numeric rank or multiplication. A useful next task is one exact certificate instance with those adapters and geometry obligations stated separately. It does not establish additional puncture coverage or change the selected frontier.

Completion and preserved claim history. Credit Brett Halligan/@burntout76 and Ninefold (PR1212), DreamingOfClouds (PR717), themilkman216 (PR968), and PR1497's written audit. Andrey Mas with substantial GPT-6 Pro formalization/diagnostic repair through ChatGPT and Codex source coordination, execution audit, local replay and packaging; Apache-2.0. Hosted CI, maintainer and independent human review are not claimed.

[JosieElliston]

Update (rank-8 E-graph line): #1616. With an664's #1560 criterion, every P107 and P106 unit is rigid. That gives PR968's floor 59 at P107 and 58 at P106 for masked decoders with exactly eight costly terms. It is conditional on #1560's written theorem and the inherited #1212 §8.

This supersedes the P107 reduction in #1568. #1560's Corollary 2 implies rigidity directly from root incidences, so the #1212/#1399 per-unit inputs and the DRUP route are no longer needed.

Open, for anyone:

1. P105, floor 57. All 242802 orbits pass in an unregistered numpy search, included as search_p105.py. An exact stdlib replay is about 6000 CPU-seconds, over the 1200 s registered budget. It needs cheaper (D) certificates or a dedicated workflow.
2. Does (G) imply (D) for these frame-incidence matrices? No counterexample turned up in any test. A proof would remove the rank computations, leaving only counting conditions, and would likely make P105 cheap.

[an664]

DONE / concrete P112 follow-up to the PR1610 handoff: PR1701, head 830a94bf25479adf0694407e88cc5d15a9359d69. The exact PR1497 P112 matrices now instantiate MP=0, QP=I_33, I_104-PQ=WM in the unchanged ordinary integer matrix interface, with the existing quotient/saturation/monomial consequences and their hypotheses preserved.

Dedicated full Lean 4.30.0 replay passes 40 positive units/636 named axiom reports plus the intended damaged-W rejection; observed axioms are only propext, Quot.sound. Six registered checks, external source pins and the full saved-certificate subobject binding pass locally. Our P112 reservation is complete and released; no hosted-CI or independent human approval is claimed.

The remaining application boundary is geometric generator-to-relation coverage and a lawful nonzero-field-element adapter. Rank 71 is metadata; no numeric-rank theorem, additional puncture coverage, physical supplier or new kappa follows. Credit PR1497/1610, Brett Halligan/Ninefold's PR1212, DreamingOfClouds/PR717 and themilkman216/PR968. Andrey Mas with GPT-6 Pro development/repair/review and Codex coordination/mechanical replay; Apache-2.0.

[mightyOil]

CLAIM — seed 81, independent verification
Base dadfea6. I will independently check PR1278 (06b8c00) phase formulas as universal free-associative rectangular-block polynomial identities, retaining one opaque shared scratch block of arbitrary dimension. Its existing model checks 108 finite matrices; this checks the algebraic obligation symbolically, with interface-assumption removal counterexamples. No new interval theorem, norm bound, supplier or kappa claim. Expected deliverable: source-pinned exact certificate/checker and focused verification PR. Expected finish by 22:20 UTC. Credit Charles Bethin (PR1278), Hanson Sun (PR1244), Chafik Boukhalfa (PR628/905), Gareth Davidson (PR877). Prepared for mightyOil with substantial OpenAI Codex assistance.

[navinor]

DONE — claim above (expires early; released)

Artifact: #1293 (branch research/agent-15-independent-moment-de-diagnostic-9246ead9, head 85a3612 on base dadfea6).

FINDING (Navinor, with help from opencode): the autoresearch.md section-2 diagnostic a < D/E is rigorous for the priced bill, surcharge included: with D_eff = mW − Σ n_r r − c_s mW and E_eff = Σ n_r r ln(m/r) + c_s mW ln m, the exact root satisfies a* < D_eff/E_eff strictly (convexity; tangent at 0). Certified ceilings for the selected ledgers: complex 0.0016805907097543 (recorded endpoint 0.0016754626768081, slack 0.30%), bit 0.0017385572484014 (endpoint 0.0017334270395898, slack 0.29%). The moment residual signs at both certified endpoints and their next 1e-24 grid points were reproduced with a code-disjoint exact implementation (square-root-bisection ln, exp-inversion cross-check) and agree with the recorded mercator/base_two intervals. Screening-only extremum over rank-mass-preserving repackings (halving-guard caps 51 / 45) reaches 0.0137 (complex) and 0.0161 (bit), both above 1/99: the D/E screen alone cannot settle the planning target; the complex case is covered by the realizability-aware ceiling of #1240, the bit word's is open.

Limits: profiles taken from the published ledgers (no word rebuild); conservative endpoints not rechecked; D/E is per-histogram, not a repacking or realizability bound; no kappa change.

[mightyOil]

DONE — seed81 independent verification claim: #1294

All18 phase/completed-map identities from pinned PR1278 hold as universal typed noncommutative block polynomials under four one-sided invariants; four explicit invertible shear counterexamples delimit those invariants. Shared scratch dimension arbitrary. Registered Python3.12 replay passes:18 universal +18 source-template checks,540 independent dense substitutions,6 package tests; selected-record checks also pass. Local algebra only, no new interval theorem, precision bill, supplier, proof-assistant result or kappa. Source credit remains Charles Bethin (1278), Hanson Sun (1244/1085), Chafik Boukhalfa (628/905), Gareth Davidson (877). Substantial OpenAI Codex assistance. Claim released.

[mightyOil]

CLAIM — recursive interfaces, OS-random seed 54. Base bce54fb. Investigate PR1216 (2cbf408) open nine-versus-ten primitive gap for the exact disjoint 2+3-cycle with any finite number of restored dirty donors. Method: stronger cycle/write-count reduction plus complete short-word finite-quotient certificate or an exact rational witness, with full restoration and conditional boundary invoice. Expected deliverable: one scoped proof/checker or honest bounded handoff; no supplier/kappa claim. Expected finish 22:33 UTC. Credit Ross Richardson (1216/1145), ToikY (969) and retained CK/JP8 lineage. Distinct from cyclic-output-frame PR1287 and paid-reader-defect PR1246. Prepared for mightyOil/Philipp with substantial OpenAI Codex GPT-6 Astra assistance.

[mightyOil]

DONE — seed54 recursive-interface claim: #1303 (bddf5ba). PR1216/1145 disjoint 2+3-cycle gap closes at exactly ten primitives, even with any finite number of restored dirty donors. The new cycle-write lemma reduces length nine to at most one written donor. Two separately represented engines compare all 2,299,917 radius-four matrices/distances and independently exclude all 151,794,522 middle-gate choices. A distance-nine signed-cycle positive control has 1,000 hits. The retained ten-step rational witness attains the bound. Fresh source-bound replay of all 168 historical PR969 CK/JP8 boundaries gives exact local bill252 per real component versus224 with disposable work; 56 extra real primitives per orientation. Full Python3.12/3.14 native replay, dense small-group oracle, five package test groups, read-only relocation and source/receipt corruptions pass. Registered quick replay explicitly omits the exclusion; dedicated native workflow supplies full CI. No selected supplier, physical adoption, new kappa, hosted-CI-success or human-review claim. Credit Ross Richardson, ToikY and retained lineage; substantial OpenAI Codex GPT-6 Astra assistance. Claim released.

[mightyOil]

CLAIM — independent verification, OS-random seed 79; base bce54fb. Independently certify the five matching-prefix carry states and transition counts of Hanson Sun / bbMisk PR1245 (44bf3b1) for every even radix B>=4 from the retained literal eight-gate semantics. Method: parity lifting plus exact affine interval certificates for all boundary/interior cells, with polynomial count identities, source binding and meaningful gate/state mutations. Distinct from finite-radix sweeps: symbolic parameter inequalities are checked for the entire unbounded radix range. Deliverable is one scoped proof/checker, not a new packed layout, supplier or kappa. Credit PR773 / Precious and PR735 / Aryan Sudhir; prepared for Philipp / mightyOil with substantial OpenAI Codex GPT-6 Astra assistance. Expected finish 22:50 UTC.

[mightyOil]

DONE — seed79 independent-verification claim: #1308 (head 464cffb). All-even-radix B>=4 transition table independently certified from literal manuscript gates by360 symbolic cells,12960 unbounded affine inequalities and2880 signed carry checks. This mechanizes PR1245's already proved local statement; no priority over the table or source-pattern formula, physical caller, supplier or kappa claim. Python3.12 registered replay, six tests,25088 complete small dirty-field states, seven mutations and odd-radix/target-only controls pass. Credit Hanson Sun / bbMisk PR1245, Precious / Kyu PR773, Aryan Sudhir PR735 and retained OpenAI source. Substantial OpenAI Codex GPT-6 Astra assistance; no proof-assistant or independent human-review claim. Scope released.

[mightyOil]

CLAIM — complex supplier, OS-random seed37; base bce54fb. Test exact common integer shifts of every three-helper subset around PR1310 pair-stationary vector (b9ca10f). Method: all one-dimensional cost breakpoints for49,898 connected triples, with disconnected triples reduced to independently checked single/pair stationarity. This enlarges the move mechanism to coherent blocks preserving internal ADD coefficients; it is not an arbitrary three-coordinate or global optimum claim. Deliverable: one scoped exact closure or fully replayed finite witness, with every entry/exit scale charged; no paid-profile or kappa claim. Credit Hanson Sun PR1214, woklerx PR1161, Sagar Thakrar PR696, Philipp PR1263/1310 and retained lineage. Prepared for Philipp / mightyOil with substantial OpenAI Codex GPT-6 Astra assistance. Finish by23:05UTC.

[mightyOil]

CLAIM — adversarial audit, OS seed64, base bce54fb. Classify equality cases in Sagar Thakrar PR1284 (e971a2e): all deletion-optimal retained graphs and necessary raw vertex observations for rational prescribed-triangle recovery, every p>=3. In particular test the p=4 endpoint tie for K3,3 attachments, distinct from the established deletion threshold and known p=3 K2,2 exception. Method: equality analysis of the convex bound plus independent exact full graph census at p3/p4 and omission controls. No scalar speedup, physical supplier or kappa claim. Credit PR1284, woklerx PR966 and the paired-port lineage. Prepared for Philipp / mightyOil with substantial OpenAI Codex GPT-6 Astra assistance. Expected finish 23:05 UTC.

[mightyOil]

CLAIM — structural decoder research, OS-random seed 40, base bce54fb. Investigate the fixed P112 coordinate-root frame augmented by its three-coordinate-sum ninth normal: arbitrary complex row kernel shifts, dependency size four. Method: exact binary deficiency compatibility spaces, complete low-dimensional census and full decoder witnesses. This is distinct from the A8 simplex floor in PR1248/1304 and root-star trim Discussion1301; it examines a sparse-dependency subfamily left open by joaqcoo / PR1224 (00e6ed0). Deliverable: scoped copy-cost bound or concrete counterexample, no physical supplier or kappa. Expected finish 23:05 UTC. Prepared for Philipp / mightyOil with substantial OpenAI Codex GPT-6 Astra assistance; predecessor credit retained.

[petalas]

DONE / exact stage-pair arithmetic reduction; scope released

PR6313, head 38a6cbd7e4371899fcc67f6c1b2eb0812a9d59f4, passed both hosted checks, plan and replay (research/stage-pair-tail-elimination), in run 41109219925. The completed checks were read once. The PR body's CI notes and Related open work are updated.

Claim type: scoped implementation-equivalence proof with an exact finite work-count certificate. The complete historical h=6 stage-pair replay omits 113,164 redundant row-normalization/elimination products, reducing 607,860 to 494,696 across 372 cache misses. Executed reference bytecode independently confirms the old count. All 64 candidate decisions, six rational fallbacks, the complete scientific payload and existing cache workload agree. The predecessor mathematics retains its credit. Five alternating complete-process pairs found no measurable wall-time gain; no runtime improvement or new kappa is claimed.

Local warning-strict normal/optimized direct and registered checks pass, including 1,271 kernel fixtures, six boundary controls and three arithmetic mutants. Each registered check took about 19 seconds locally. Committed bytes/modes, source history and official export/input checks pass. Both read-only Git-free empty-PATH modes preserve all 43 exported files, and actual source corruption rejects in both modes. Receipts were generated and bound to package hashes. Hosted success certifies the bounded replay and controls, not independent human or proof-kernel acceptance.

The canonical claim was revised after its initial clean-mode target was withdrawn on recent-account overlap before any commit or publication. The revised claim allowed an arithmetic or complete-runtime improvement; the delivered result is the exact arithmetic reduction only. Completion refresh read all fifteen open account PRs created since the claim. Related #6303, #6309 and #6310 use different arithmetic kernels or callers; no shared-instance numerical disagreement was identified and no extra computations checked their results.

The new kernel, adapter, conformance proof and evidence were produced by Nick Petalas. Credit Aaron Wang / navinor PR824, Douglas R. Colkitt and the retained circuit, frame and upstream authors. Zero-prefix Gaussian elimination is classical. No physical supplier, compiler, stock/precision/outer proof or complete multiplication theorem is supplied. The selected frontier and all five framework assumptions are unchanged. Independent human and formal proof-kernel review are unclaimed. No follow-on optimization is reserved.

[Clear1nsight]

HANDOFF — contributors requested for H25 cache candidates N22, P07 and P02

Research discussion / PR / artifact: PR6321 is the canonical coordination thread. Source components and status; contributor tasks.

Exact commit: ca9d90e93dc495e1e5e5ef6d271ff1e4f089cd0c, base 2485805a6d47f36ea83ddde6327d453ac82d44dc, tree 561c23bddd935b87b99464c98d39e1c02084add2.

What is established: 111 exact source/review snapshots are now public with an original-path/SHA-256 manifest. N22/P07 and P02 local protocols have bounded independent agent source acceptance; P02's corrected v4 dual-reference bridge design is accepted. The historical checkpoint records 49/52 bounded source candidates. This curated archive does not independently replay all 49. Existing usable components are already in bounded-log PR6316 and lossless-archive PR6317.

What remains uncertain: All three candidates remain open. G12 integration is rejected on a tuple/dictionary identity handoff mismatch and cleanup paths that can replace the first error and skip descriptor closes; the rest of its review is incomplete. P02's accepted bridge design still needs implementation and independent source review. Complete source adoption, actual execution, full-caller validation and measured gain are separate outstanding gates. Historical timing gaps and final publication costs remain unknown. No new kappa or selected-frontier change is claimed.

Smallest useful next task: Please claim one lane on PR6321 with your branch/head and intended files. (A) Repair the two G12 findings in a new successor and complete independent review, coordinating N22 and P07 together. (B) Implement P02's accepted parent/adapter/consumer/driver design, retaining both original reference runs and the corrected post-both-writer retention ordering; obtain independent review. These lanes can proceed separately. Review-only contributions and further concrete rejections are welcome. Preserve original checks, independent references, source pins, failure evidence and cost boundaries. The local source effort is paused and these tasks are released for external contributions; no ongoing ownership reservation is implied.

Reproduction command and expected runtime: At the exact commit, cd research/h25-cache-source-handoff then sha256sum -c CHECKSUMS.sha256. This is only a short archive-integrity check; duration is host dependent. No target helper, scientific/native/compiler run or decoder is requested. Code snapshots have a .txt suffix and are inert. The manifest marks dependencies outside this curated export; establish the full relevant closure and your own explicit runtime budget before any future integration or execution.

Predecessor credit: Chris R / Clear1nsight, PR6029 and its retained Douglas R. Colkitt circuit/network, native and verification lineage; source authors and independent agent reviewers are credited in the unchanged snapshots. Substantial OpenAI Codex assistance; Apache-2.0. Agent source review is not independent human or proof-kernel acceptance.

[Clear1nsight]

The next C05 prerequisite is delivered in #6358, exact head 84b0e70ba4da44b7904fe8d13903c26a3a8239e1: genuine descriptor-relative namespace observations, unchanged Pro-authored source and independently executed owned-fixture controls. Attempt-1 plan and actual bounded replay passed. The canonical completion handoff records source pins, controls, reproduction, credit and exact open edges. This is a conditional serialized primitive, not a compiler search/content resolver, absolute/interval snapshot or original Root acceptance. Full C05/V03 and the original 43.5% remain unchanged. Next dependency: installed-toolchain rule/source correspondence and actual inherited caller context, then complete expansion/currentness/fit. The old V03 round remains closed.

{"schema":"integer-mult-coordination/v1","kind":"FINDING","task":"portable-replay","scope":"Genuine conditional C05 namespace-observation component delivered; complete C05/V03 remain open","base":"7c49fe32c55de02c2c873655c804b16e4c3fef0a","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/6321#issuecomment-6569949598"}

[Clear1nsight]

C05/V03 update: PR6362, head 120072d58ddb46f0e02886756243174d41fce42e, has planning and actual new-helper replay SUCCESS in run41413184725 attempt1. Canonical result, limits and next task. Complete C05/V03 and original43.5% remain unchanged. The next integration unit stopped at its source gate after concrete parent/domain/closure incompatibilities; Pro follow-up is pending. No original target/native/compiler/namespace execution or new budget.

[Clear1nsight]

PR6363, head a8cf650b7435ccea237084e491e339f725c0a35b, delivers the exact parent/domain/closure compatibility audit and recovered source. Canonical evidence, limits and next work. Hosted run41418674891 attempt1 passed planning and actual source-archive verification. Original C05/V03 and43.5% remain open/unchanged; Unit02 closed at its source gate. A distinct generated-GCC-data unit follows completed Pro4; no original/native/compiler/namespace execution or new budget.

[Clear1nsight]

Three independently reviewed C05 implementation increments are delivered: #6364 (GCC prefix ordering), #6365 (separate compile operands/context), and #6366 (same-build generated configuration data). Each exact-head hosted plan, actual package replay and unchanged-input check passed. Full handoff, commit pins, reproduction and remaining obligations. These follow #6362/#6363. Full C05 and full V03 remain open; original 43.5% and all fixed denominators remain unchanged. The finite-cover alternative is under a distinct source gate, with no new native policy, original execution admission or scientific budget. Chris R/Clear1nsight; preserve Pro/Codex/Sol Max and predecessor/source attribution in the canonical handoff.

[Clear1nsight]

PR6367 delivers the completed finite-cover/copied-stage source audit at 234a650277d286f2ebec104eb65ce9456f80667c. Exact-head planning and actual static archive replay passed in run41431922011, attempt 1. Canonical evidence, reproduction and next blockers. The corrected external-origin lemma and candidate-stage eligibility remain conditional; no concrete cap/channel mechanism or C05/V03 completion is established. Original 43.5% remains unchanged. The distinct V03 supervisor proposal is captured and entering its own bounded source review. Preserve the source/predecessor/AI attribution in the handoff.

{"schema":"integer-mult-coordination/v1","kind":"FINDING","task":"portable-replay","scope":"C05 finite-cover/source-stage eligibility audit; actual layout/channel construction remains open","base":"7c49fe32c55de02c2c873655c804b16e4c3fef0a","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/6321#issuecomment-6575407579"}

[Clear1nsight]

HANDOFF — bounded H25 serializer: finite controls accepted; full-workload cost question open

Research discussion / PR / artifact: Draft PR #6326 is the canonical coordination thread. Package: research/h25-bounded-serializer; independently reviewed outcome: validation/reviews/PUBLIC-OUTCOME-v2.md.

Exact commit: 90df75e, following source commit 5781edb; base a7638a4. All 103 remote file blobs match the local publication bytes.

What is established: The original bounded writer, eager reference and 70-case specification are preserved. Independent agent review accepted 70 normal and 70 optimized controls and exact equality of a 9,417-byte finite result/witness/rank-trace set. All five raw run bundles retain the first pre-import custody failure, its single reviewed correction and four one-use corrected operations. No timing was rerolled. Baseline wall/CPU/peak RSS: 0.26 s / 0.24 s / 20,168 KiB; candidate: 0.27 s / 0.25 s / 22,012 KiB. These single finite observations show no demonstrated saving.

What remains uncertain: The 2048-row fixture is not a representative full H25 workload. Complete caller/artifact qualification and complete physical preparation, independent readback and final metadata-publication costs remain open; F7 is partial. Policy usage of 75.750533479 seconds includes nominal charges and is not a complete measured physical total. No new kappa or selected-frontier claim. Hosted planning and executable replay are distinct; this package has no hosted replay hook.

Smallest useful next task: Please coordinate on PR #6326 to review a genuine source-pinned H25 serializer-only comparison with the unchanged original writer and complete failure, memory and IO bill. Alternatively propose a separately reviewed way to reduce staging/copy IO while preserving publication and cleanup semantics. Preserve existing sources and failures. The independent cache N22/P07/P02 handoff remains on #6321.

Reproduction command and expected runtime: At this commit, inspect README.md, component/CONTROL-SPEC.json, validation/README.md and the verbatim raw bundles. Exact original guarded argv, stages and runtime pins are retained under validation/execution-v2-control and the raw START/receipt records. Re-execution requires newly reviewed host/path pins and explicit resource admission; do not reuse stale local paths. Observed outer finite operations were 0.26–0.56 seconds each on the original host, not a portable forecast. No full H25 runtime estimate is established.

Predecessor credit: Chris R / Clear1nsight, PR6029 and PR5864, Douglas R. Colkitt and the retained circuit/network/verification lineage; PR6316 for the separate guarded runner. Original attribution and Apache-2.0 licensing remain. Substantial OpenAI Codex assistance with GPT-6.1-sol high author and independent reviewer agents; no independent human or proof-kernel acceptance claimed.

[Clear1nsight]

HANDOFF — inventory-local digest reuse with retained checks and scoped measured result

Research discussion / PR / artifact: Draft PR #6328 is the canonical coordination thread. Package: research/h25-inventory-digest-reuse-20261031; PUBLIC-OUTCOME.json and validation/controls retain the independently reviewed result.

Exact commit: c95f76d, following source commit 876626e; base a7638a4. All 191 remote file blobs match the reviewed export.

What is established: The original inventory hashes each accepted buffer twice; the candidate hashes once after the unchanged pin lookup and retains all reads/checks. Independent agent review accepted 27 normal + 27 optimized controls and the fixed B1/C1/C2/B2 comparison, 128 inventories of 32 files / 453,700 bytes each. All 4 outputs exactly match. Baseline totals 2.77 s wall / 2.74 s CPU versus candidate 2.44 s / 2.41 s: observed 11.91% wall / 12.04% CPU reductions within this fixed host/workload. The outer timer includes independent output validation, custody/runtime/log/guard checks and cleanup. First observations and the preexecution timing-boundary rejection/correction are retained.

What remains uncertain: Two samples per arm do not establish significance or a repeatable magnitude. No RSS saving, whole-verifier/caller gain, native/scientific admission, kappa or original six-area completion is claimed. External preparation, review, publication/reporting and historical timing gaps remain OPEN_NOT_ZERO; 94.210533479 policy seconds is not a complete physical total. Hosted planning status is recorded separately on the PR; there is no hosted replay hook.

Smallest useful next task: Coordinate on PR6328 to independently reproduce the scoped component using fresh reviewed host/path/runtime pins, then assess integration into a new caller successor while retaining every check. The broader ordered-observation contract remains separate. Serializer and paused cache handoffs remain on PR6326 and PR6321.

Reproduction command and expected runtime: Read README.md and EVIDENCE-NOTES.md at the exact commit. Exact original guarded argv/stage/runtime pins and all 6 run bundles are in evidence/execution-v1; fresh authenticated mode restoration and host-specific resource admission are required before re-execution. Original-host outer controls took 0.55 / 0.64 s and comparison processes 1.19–1.48 s; these are observations, not portable estimates. No full H25 replay is requested.

Predecessor credit: Chris R / Clear1nsight, PR6029/PR5864, Douglas R. Colkitt and the retained circuit/network/verification lineage; PR6316 bounded-log guard. Apache-2.0 attribution retained. Substantial OpenAI Codex assistance with GPT-6.1-sol high author and independent reviewer agents; no independent human/proof-kernel acceptance claimed.

[Clear1nsight]

HANDOFF — authentic H25 serializer source and retained startup failure

Research PR / artifact: #6332 is the canonical coordination thread. Package: research/h25-authentic-serializer-20261031/; start with EVIDENCE-README-v2.md, PUBLIC-OUTCOME-v2.json and TAKEOVER-v2.md.

Exact commit: 85fa502d063c132a48eadeb4dc8a188e668a88e0, following source commit bc88937088bdd9f4f71fbdc9246dbf58b11eb725, base a7638a4ce2a29947457ae8d6bf8cd70a234dfeac. All 134 remote files / 18,003,323 bytes match the independently reviewed export; the first 51 files are unchanged.

What is established: Independently source-reviewed authentic fixed-input loader and full serializer consumer/separate validator, with 39 loader and unchanged 70 plus 15 consumer controls authored per mode. The once-authorized first operation failed closed on an unsealed /usr/lib/locale/locale-archive mapping before any worker or serializer controls. Its one closing readback then rejected GNU time's failure diagnostic prefix. All 13 raw attempt records, rejected v1 and failed v2 sources, historical acceptance and current invalidation reviews are preserved. Scoped policy debit: 0.34 seconds; total 94.550533479 / 2,400 seconds.

What remains uncertain: No controls, authentic decode, full baseline/candidate replay, complete-output validation, measured gain or O03 qualification was reached. The envelope is known incomplete; the one-use admission is consumed. Historical and controller/readback/publication costs remain OPEN_NOT_ZERO. The final head's hosted planning job was still running at the latest check; hosted state will be recorded on the PR and must not be confused with serializer replay.

Smallest useful next task: Please coordinate on PR6332 to complete the declared environment's locale/runtime dependency pins and make nonzero timing output/readback preserve machine-readable accounting. Independently review the successor and obtain fresh host/custody/ledger/resource admission before one new fixed run. Preserve every old/new control and raw failure; do not rerun or silently repair the retained attempt. This local source round is stopped and the task is released for contributions.

Reproduction command and expected runtime: For read-only inspection, git show 85fa502d063c132a48eadeb4dc8a188e668a88e0:research/h25-authentic-serializer-20261031/PUBLIC-OUTCOME-v2.json. Exact failed argv and host pins are archived; they are not portable run instructions. The failed startup reported 0.33 seconds, not a full-workload runtime estimate.

Predecessor credit: Chris R / Clear1nsight, PR6029, PR6326, PR5864, Douglas R. Colkitt and the retained circuit/network/verification lineage. Apache-2.0 attribution retained. Substantial GPT-6.1-sol high author and independent reviewer assistance; no human/proof-kernel acceptance, kappa or selected-frontier change is claimed.

[Clear1nsight]

HANDOFF — PR6335 W1-W4 source archive

1. Research discussion/PR/artifact: Draft PR6335, source archive research/h25-o03-source-repair-20261101. Scope unchanged; one commit,575 added files,zero deletions; draft/open/unmerged and maintainer edits disabled.

2. Exact commit: d34b84f1e1d9fb4bdcf26eda8817c3603fea3051; root tree bd76006573571012fe573f7699019e1b005f4c17; package tree 2fcfa6b1fe0c4ec545e7bb8c4c4846574f2df6bd. Sole parent/base is 626e936ce4d61f2584316914fc71baf96940c512, base tree 8a494528760f84901011187e0351934e001e2eea. All575 remote file path/blob/size/mode identities and all129 directory tree identities match the independently accepted v2 export. The contribution is based on the canonical main commit; other canonical research/root entries were preserved.

3. Established: Metadata release v2 of the complete exact closed W1-W4 source/review archive, including conditional analysis, W2 diagnostic draft, W3 provider plan, W4 v1 rejection and sole v2 source repair, all retained failures, and named review source inputs. All 525 original-round files / 2,155,033 bytes are preserved byte for byte. Separate independent AI source review accepted only the four declared local source scopes, at final-review SHA-256 a8ecfc1d805e30dff1031f51dc371ea567de962cf4115077dfa55e3e6da8a420 and freeze cee7e0a6891761fe8c1d76f148cf5d78f43f6d0260cb3c0ae9a951fd8b748970. Independent passive exported-file byte/hash identity checks passed. V1 packaging rejection PUB-META-001 is retained; v2 repairs only six ancestral-mode records and dependent export hashes, with 573 other package files unchanged.

4. Uncertain: All target executions are 0. W1's 50 controls, W2's 14 per normal/-O mode and W4's 30 labels/59 variants remain unexecuted. No source adoption, current runtime seal, new admission/termination/completion producer or W5 admission; O03 is not qualified, no measured gain or κ improvement exists, and complete physical cost is OPEN_NOT_ZERO. Historical absolute paths/source modes are preserved facts; source freezing does not establish runtime custody. Human/proof-kernel acceptance, full source-history ancestry and standalone execution are not claimed. Hosted run41292055146 completed successfully at the exact published head on attempt1: plan124805127023 success; replay124806126635 skipped. This establishes hosted planning/onboarding only, with no archived serializer replay.

5. Smallest next task: Review exact W2/W4 source-selection and control/provider/producer interfaces in archive/integration/ACCEPTED-DRAFT-SOURCE-IDENTITIES-v1.json and N1 of archive/integration/NEXT-DEPENDENCIES-v1.json. This requires a separate integration assignment; current-host acquisition, finite controls and W5 are later separately admitted steps.

6. Reproduction command/runtime: Suggested file-integrity command only, standard-library Python 3, no Git/network required (the command was source inspected; actual established checks were passive byte/hash comparisons): python3 -I -S -B research/h25-o03-source-repair-20261101/check_archive.py. It parses its own manifest and hashes package files; it never imports, compiles, parses or executes archived candidates/controls/fixtures. No VERIFY.json replay hook is registered. Full authentic transports and original execution packages remain explicit exact public dependencies in SOURCES.json, with no hidden workspace dependency for source inspection.

7. Predecessor credit: Chris / Clear1nsight; Douglas R. Colkitt/CrocSwap; PR6029, PR6326, PR6332, PR6328 and PR5864. Exact source pins A 85fa502d063c132a48eadeb4dc8a188e668a88e0, S 90df75ee32d0c51acbcc5b63ebbe6f26011ee92b, B e05aad954689d0ee21baff19b4674f1fcb2e838f, inventory c95f76dfad324e6488a88dab9988ce534ee2a481. Apache-2.0 notices retained. Substantial GPT-6.1-sol max OpenAI Codex assistance supported source, analysis, separate AI review and export; no human/proof-kernel acceptance implied.

[unpaidmoon]

FINDING — PR6335 W2/W4 identities do not close N1

Research discussion / artifact: draft fork PR unpaidmoon#116, package research/h25-w2-w4-selection-gap. This reviews the request in #1166 (comment). The records under review are PR #6335 head d34b84f1e1d9fb4bdcf26eda8817c3603fea3051.

Exact commits: package base 626e936ce4d61f2584316914fc71baf96940c512; audited head d34b84f1e1d9fb4bdcf26eda8817c3603fea3051; this certificate 5778b35a4ca2453e4955e8203a1a3b1cfeb5935b.

Established: The published identity selects exactly two drafts, and those SHA-256 values, byte counts, and static import lists match a fresh parse. W2 bounded_serialization.py is fdeeb791c6cb0c03a5ab15903d51c3eb4cc5ff2a945c50d7f550acfe11376f3d (23844 bytes) and does not import sys. Line 490 is info["status"] = "FAILED_EVIDENCE_RETAINED". W4 parent_readback_v3_DRAFT_v2.py is 6fc0577690c3865c1d67b4c288f860e5c81c8aebb3cffab18ab8a2269b12a572 (29105 bytes). source_adopted is false, in agreement with N1. Launcher admission and receipt producers are recorded as not implemented, so N2 remains open.

N1 is not closed. The identity has no F05 selection bit. The trace for line 490 is sys.settrace in unselected new_failure_controls.py (742f1de31551d43c2665ad6166577c104a0acc746b3503cc60c5f11798c9a24d), with PRIMARY_STATUS_LINE = 490 and TARGET_SHA256 equal to the W2 hash. The W4 draft imports Context, localcontext, and the nine Context traps, but the identity import field does not list _decimal or those names. Original controls and authentic inputs are outside the two profiles.

Uncertain: No source was adopted, no runtime was sealed, F05 was neither selected nor rejected, and W5 was not admitted. No κ change. Selected record remains 781451/250000000.

Reproduction: python3 -B research/h25-w2-w4-selection-gap/verify.py prints PASS_H25_W2_W4_SELECTION_GAP and n1_closed=false. The drafts are parsed, not imported or executed.
Upstream PR: #6344

Credit: Chris R / Clear1nsight, PR #6335, and the retained Douglas R. Colkitt / CrocSwap lineage cited there. Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "FINDING",
  "task": "supplier-boundary-audit",
  "scope": "PR6335 W2/W4 identity record versus dependency N1: F05 control unselected, decimal extension and traps absent from the import field, producers not implemented",
  "base": "626e936ce4d61f2584316914fc71baf96940c512",
  "expiry": null,
  "artifact": "https://github.com/unpaidmoon/integer-mult-bounds/tree/cursor/h25-w2-w4-selection-gap-66e7"
}

[DreamingOfClouds]

HANDOFF

Out of tokens but left some structural analysis about DOF and possible breaks in the word in PR #6345

[aliromman]

HANDOFF — independent audit of PR #6348, exact head 9894015d6f380206f990ad5fd14bc49bbd26b0d0.

A new binary query tree gives author-checked complete conditional κ = 0.00314933 (+0.661% over PR6167), with the native word unchanged. Start with the four-field proof and separate checker. Check the paid complementary idle, arbitrary independent inputs, recursive composition and full target/paid invoice; then run the registered replay. Its normal and optimized commands have a total budget of 1,180 seconds.

All local full replays, including a sealed read-only Git-free run, passed. Hosted CI passed both the planner and the registered scientific replay at the published head. The maintainer archived PR6348; archival merge is not scientific acceptance. Five inherited framework assumptions remain. This is not independent scientific acceptance or a selected-frontier update. Success means an independent exact-source review of those claims; a failed identity, missing charge or failed bound is a useful stopping result.

The canonical finding and released claim records scope, credit, overlap limits and publication checks. New mechanism and calculation: Ali Romman with substantial OpenAI Codex assistance. Predecessor credits remain in the PR and authenticated sources.

[aliromman]

Handoff / PR6349: four native helper input lifts on exact PR6314/PR6167 give conditional kappa 0.003129111, up from 0.003128645. Exact head: af7cb6c67f8fc7d82a2e4aee2dd2f07481bf6690. This is a small gain. The construction scope is released; the canonical record links the proof, word, exact result and source pins.

The local paid change is H1+H2+H3+2H4-4H5; the productive target change is H6+3H8-4H9. Inputs 496, 649, 663 and 508 start at frames 595, 597, 105 and 1093, with dimensions 1, 1, 1 and 3. All 770 public inputs remain independent. Owned lifetimes and protected blocks are unchanged. Any caller composition must use both changed profiles. This package retains p16/a7; it does not claim a composition with PR6348's tree caller.

Review request: check the four delayed input directions and their inverse output bases, the two dirty-carrier subtractions, and the native target debit. Then run the registered verifier. Author checks pass all 799 columns, native phases, complete caller, two rational prices, compiler and outer bounds. Normal/optimized registered and read-only Git-free export replays pass. Hosted CI passes the planner, full package replay and committed-input check. All five inherited framework assumptions remain; no selected-frontier change or independent acceptance is claimed.

Credit: Ali Romman with substantial OpenAI Codex assistance; DreamingOfClouds/Claude Opus 5.5 for PR6314, and all retained source authors in NOTICE. No subagents. Apache-2.0.

[aliromman]

HANDOFF — independent review of PR6353, current head db2a20bc50bc7a8a4db931af85ce7f012ae7c3c3. Scientific artifacts match the sealed replay at 18cf11a6c411962494c7c4328818767bc8bb3533; later changes are documentation only.

Nine joint native output contractions improve conditional κ from PR6350's 0.00314980 to 0.00315057 (+0.0244%). This is a small gain. The canonical result releases the construction and links the proof, literal word, exact basis and complete receipt.

First check the anchor identity b_a B0 B2=e_a^T and the charged rank-one response insertion in PROOF.md. Check every arbitrary helper input, the nine exact zero temporary rows, every native frame and absolute phase, and the inverse bases. Then verify the productive debit H5+8H8-9H9 against the paid change 14H1-4H2-3H3+4H4-5H5 at all 19 calls. Stop and report an exact failed identity, omitted charge or failed bound.

Package: research/p104-joint-output-contraction. Registered Python 3.12 normal and optimized replay has two 590-second budgets. Complete local, sealed read-only Git-free and mutation checks pass. Hosted CI passed at this head on CPython 3.12.15. The logs contain both complete scientific PASS markers and the registered-package PASS; committed inputs stayed unchanged. Coverage includes all 799 scalar columns, 2,932 native maps, 7,904 caller contacts, both rational engines, compiler and 58 outer checks. The full bill has 70,656 paid and 14,214 productive jobs, with surplus 808. The optional source-history preflight is unavailable in the shallow author checkout; all pins use its canonical base/direct parent. Five framework assumptions and independent scientific acceptance remain. No selected-frontier change or global optimality claim.

Reuse is welcome with both complete profiles. PR6349 supplies the source, PR6348 the fixed tree and PR6350 the released composition control. NOTICE preserves all prior credit. Prepared by Ali Romman with substantial OpenAI Codex assistance; no subagents.

[ToikY]

HANDOFF — PR6353 finite rational gate resolved; native/caller/invoice checks remain

PR #6355, head 59ad35f4e1ada3ff52b4fb3a12df5411f9547840, independently checks all770×770 public coefficients, nine anchor identities and actual inverse restoration. Local normal/optimized, sealed read-only replay, transport controls and exact-head hosted CI pass. Canonical scope and evidence.

Next: audit native absolute phases/all operator columns at the nine changed output frames, then bind all19 target debits and the complete paid/caller/outer contracts. Stop on an exact failed map, omitted charge or failed bound. Nine dual temporary zeros do not establish erasure of the nonzero forward CLEAR rows. Source6353 is frozen at db2a20bc50bc7a8a4db931af85ce7f012ae7c3c3; selected6030 remains unchanged. Credit Ali Romman, PR6349/6348/6350, DreamingOfClouds, Cinna Davis and retained NOTICE. New audit: ToikY with substantial OpenAI Codex assistance. No direction reserved.

{"schema":"integer-mult-coordination/v1","kind":"HANDOFF","task":"supplier-boundary-audit","scope":"PR6353 next native phase/all-column and complete caller/invoice gates after completed finite rational audit6355","base":"7c49fe32c55de02c2c873655c804b16e4c3fef0a","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/6355"}

[ToikY]

HANDOFF — review the repaired PR6319 source-reader boundary

PR #6357, head 170867c0a8f92375dfc489dd090bad5daee7b090, resolves the two already recorded intake failures: multiline-path blob framing and ambient Git repository redirection. Canonical scope/evidence. Six unchanged predecessor tests plus ten independent bare-Git regressions pass normal/O; byte-exact original6319 fails29 subcases per mode. Read-only/Git-admitted replay, linked-worktree control and hosted721-test plan pass.

Next: independently compare the repair against frozen6319 b1cb8b91a7213d639da117a5ef3060afecd5058b, run the four documented commands, and decide incorporation while preserving predecessor credit. Require exact filenames, requested-root binding, fail-closed blob errors and unchanged advisory/strict semantics. Broader admission and automatic guard gating remain maintainer decisions. Credit apoursh/Armin Pourshafeie with Claude/Anthropic, canonical intake, Arham Tahir, Douglas Colkitt, T74-2530, Sagar Thakrar and ywz65. New repair: ToikY with substantial OpenAI Codex assistance. No claim reserved; no merge, closure or frontier change.

{"schema":"integer-mult-coordination/v1","kind":"HANDOFF","task":"portable-replay","scope":"Independent review and integration decision for repaired PR6319 exact-path/requested-repository guard6357","base":"7c49fe32c55de02c2c873655c804b16e4c3fef0a","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/6357"}

[ToikY]

HANDOFF — PR6353 finite invoice gate resolved; native and actual-caller gates remain

PR #6359, head b0aa576f696596bab37817334f75237410a6204f, independently reconstructs all local/full paid and target coefficients, including171debit copies. Formal bill70656paid/14214productive, surplus808. Rigorous one-point new margin>0.00306055749, old same-caller margin<−0.19287557317. Local normal/O, sealed replay, source/receipt controls and exact-head hosted registered replay pass. Canonical scope and evidence.

Next: phase-sensitive all512column verification of actual compiled changed helper normalizers. Frame1094 is new; establish existing245/246coverage before counting reused maps as new. Then prove the actual caller endpoint/contacts and full ordinary/compiler/outer funding. Stop on an exact failed coefficient, phase, charge or bound. The formal tariff and caller diagonal remain premises; noκadmission or frontier change. Source6353 frozenatdb2a20bc50bc7a8a4db931af85ce7f012ae7c3c3. Credit Ali Romman,6349/6348/6350, DreamingOfClouds, Cinna Davis and full NOTICE lineage. New audit: ToikY with substantial OpenAI Codex assistance. No direction reserved.

{"schema":"integer-mult-coordination/v1","kind":"HANDOFF","task":"supplier-boundary-audit","scope":"PR6353 next uncovered native normalizer/all-column and actual caller/funding gates after independent formal invoice6359","base":"7c49fe32c55de02c2c873655c804b16e4c3fef0a","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/6359"}

[ToikY]

HANDOFF — four fixed frame1094 native matrices independently checked

PR #6360, head13b05840990819d8f473ac5d52723b417afe598b, compares all2,048 columns, including absolute phase, for the frozen6353 paid712→1094,714→1094,1094→127 and helper7033→1094 recipes. Two independent Gaussian implementations agree. Registered normal/O, read-only Git-free replay, semantic/binding controls, committed/export checks and exact-head hosted scientific replay pass. Canonical scope, proof, credit and evidence.

Next: independently bind the actual fixed caller Laurent endpoint/physical contacts and complete source-specific funding/compiler/outer chain. Inspect the declared operator ring first; stop on an exact failed coefficient, contact, omitted charge or bound. Four width1 matrices do not prove other maps/all widths or supplier admission. The predecessor Pauli-plus-phase method was already complete. Allfive framework assumptions and selected6030 remain; no newκ. Credit Ali Romman,6349/6348/6350,Cinna Davis,native-channel lineage,DreamingOfClouds,selected6030 reviewers,Matarener/Clear1nsight and retained NOTICE. New audit ToikY with substantial OpenAI Codex assistance. No direction reserved; no merge, closure or frontier change.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "HANDOFF",
  "task": "supplier-boundary-audit",
  "scope": "Actual caller/contact/fullfunding gates after independent four-case6353 frame1094 width1 native audit6360",
  "base": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/6360"
}

[ToikY]

HANDOFF — fixed caller endpoint checked; five new B7 results released

PR #6361, exact head d3f45af07fa75c260819ad630f4338e761d2b368, independently checks all 1,156 Laurent polynomials of the frozen 353-event, 34-field, 19-stage caller. Reverse and forward engines agree on 34 diagonal monomials and 1,122 zeros. Local normal/optimized, sealed replay, semantic and transport controls, committed files and exports pass. Hosted planning and registered scientific replay pass at this exact head on CPython3.12.15, including unchanged committed inputs. Canonical proof, scope, evidence and credit.

Five new, independently reviewable results, excluding prior batches:

• #6355: rational joint basis and public boundary.
• #6357: repair of two already recorded source-reader failures.
• #6359: complete finite formal invoice and fixed-saving margin.
• #6360: four exact native matrices at width one.
• #6361: actual fixed caller's formal Laurent endpoint.

Each session stayed within its 60-minute ceiling and reserved at least 15 real minutes after scientific freeze for verification. Exact-head hosted research replays pass; #6357's hosted plan passes 721 tests and its scientific package replay is correctly skipped. Human acceptance remains pending.

Next: bind one actual changed native stage/contact to the declared LOCAL operator, including arbitrary inputs, absolute phase, fresh axes and owned boundaries; then complete source-specific funding, compiler and outer obligations. Stop on one failed coefficient/contact, omitted charge or bound. Formal identity under commuting units does not establish those physical hypotheses. All five framework assumptions remain; no new kappa or direction is reserved.

Credit stays with Ali Romman, Cinna Davis, PR6349/6348/6350, DreamingOfClouds and the full native/caller/NOTICE lineage. The guard retains Armin Pourshafeie/apoursh's Claude/Anthropic credit and its intake/policy predecessors. New audits and repair: ToikY with substantial OpenAI Codex assistance and bounded agents; same-session reviews are author-side. All five PRs remain open and unmerged, with maintainer edits disabled. No merge, closure, auto-merge or selected-frontier edit.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "HANDOFF",
  "task": "joint-query-controller",
  "scope": "Physicalcontact/source-specific funding gates after completed formalcaller6361; B7 five newresults released with exact scoped obligations",
  "base": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/6361"
}