QQ16 first nonterminal C8: admitted recursion and complete one-generation bill

[JoyboyBrian]

DONE / FINDING — scoped certificate published in PR #4753, commit 44e2c79344e0090d4e829e0dde4f533d8d0273ec. The bounded investigation is complete; the full signed cost remains open.

At the retained p=2^8500 RootPlan, the first genuinely nonterminal C8 occurs at λ=45. Exactly 45≤λ≤72 gives one generation of selected-C children below every removed C8, with all those grandchildren and the added C1 calls terminal. This follows the actual global-height cutoff before remainder stripping; the source does not repeat that cutoff after stripping.

The complete 482-event source census gives 510,662 Γ selected child calls per C8, hence 8,170,592 Γ² internal park/restore pairs in the sixteen removed C8 calls per outer cover. The package binds both stock divisions and the packet volumes independently: each grandchild receives v/F, while its parent's bank retained during internal parking has volume v. The literal B* adapter changes the root wrapper only; recursive child bindings still invoke original C. The resulting internal parking lower term is included exactly once in the full symbolic comparison.

This is a scoped source-tree and cost-boundary result. It preserves #4177's terminal-band exclusion and does not establish a favorable full cost sign, production payload execution, supplier admission or a new κ. Unpriced native/monomial/nonchild work remains explicit. The next question is the complete matched signed bill on this admitted band.

Local validation passed: registered ordinary and optimized replays, committed-byte/source-history preflight, official export/check, Git-free ordinary and optimized replays, and source/typed-receipt corruption rejection. Independent AI-agent source/math review found no blocking issue. Hosted CI has not yet been verified. No historical full suite, Lean or Docker replay is claimed.

Submission checkpoint: canonical main and priority revision remained b58ad9ef4d4e861b0eaa5dba41742bdc072dca51 / 7. The refreshed snapshot covered 512 open PRs and 3,673 Discussion records; the scoped search found only this investigation, its hub pointer and the predecessor's open question/limits. Live heads #4166/#4167/#4172/#4177 matched the retained lineage. Closed arbitrary code and unpublished work are outside that coverage.

Original claim and attribution (historical)

CLAIM / 2026-10-22 18:53 UTC / priority revision 7. Evidence is LOCAL-ONLY; no result yet. Expiry: 2026-10-22 20:53 UTC.

I take the nonterminal follow-up left by PR #4177, head 4cdda81c2ad99ffe5add0ac5d894094c3cca101a. Its complete QQ16 exclusion applies to terminal C8 children. This investigation asks where the actual RootPlan first admits a nonterminal C8, and what its complete one-generation source tree charges. Width at least 73 alone does not establish recursion.

At the retained p=2^8500 descriptor family, I will check the exact global-height cutoff, independently reconstruct all source-event child multiplicities, and bind descendant stock, physical packet volumes and embedded parking. The target is an exact admitted interval and a complete symbolic cost boundary, or a specific failed implication. Unpriced native/monomial/control work stays explicit; this does not promise the full incremental sign, production payload execution or a new κ. Stop if the requested domain or source binding fails; no broad decoder search.

Fresh overlap covered all 506 open PR bodies, 3650 Discussion records and 5860 base local notes. The exact nonterminal search found the predecessor's open question and scoped audit limitations, with no competing result in that coverage. Closed PR histories/code and unpublished work are not exhaustive coverage.

Canonical main b58ad9ef4d4e861b0eaa5dba41742bdc072dca51. Credit Chris R/Clear1nsight's #4166/#4167/#4172/#4177, Jose Manuel's physical C/Ordinary/Compact source, ywz65, Sagar Thakrar, Tekalign, Ali Romman, Arham Tahir and the retained QQ16 lineage. Prepared by JoyboyBrian with substantial OpenAI Codex assistance.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "joint-query-controller",
  "scope": "QQ16 actual RootPlan first nonterminal rank-eight child: complete one-generation source tree, stock, volume and unmatched cost boundary",
  "base": "b58ad9ef4d4e861b0eaa5dba41742bdc072dca51",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/4753"
}

[JoyboyBrian]

DONE / FINDING — published as PR #4790, commit 38dd6b59d50d346bb34fea02a4ee1ac8d282ebbf.

The actual stale-cache failure reproduces after four producer child returns at the unchanged original inventory guard. The opt-in adapter composes #4167's existing protected-return exchange across both #4166 producer and service callers, refreshes the authoritative engine/external role tables, and preserves original guards and controlled disposal. Two nonconstant generations execute 24 actual source child calls with identical endpoints; whole-fixture record-Tape savings are (61488,24576,49200).

The complete inherited census includes every 510678Γ producer and 336Γ service invocation, including later root calls. Under the stated successful caller contracts, the exact matched tape-action difference is D − D* = 511014Γ(5v+2,2v,4v+2). The return transaction and its tariff remain credited to #4167. Finite compilation, validation and role-rebinding control has an explicitly separate, still unknown signed charge Δ_control: a step improvement requires Δ_control < 511014Γ(11v+4). No full D* versus B* win, production payload execution, supplier admission or κ change is claimed.

Local registered normal/optimized checks, committed-byte and source-history preflight, official 143-file export checks and Git-free cold replay pass. Stale engine/external inventory, output-alias and controlled service-stop tests retain their exact scoped rejection/cleanup observations; corrupt-source and typed-receipt controls reject. Hosted CI subsequently passed at this exact head. The published README gives the proof, source boundary, credit and open obligations.

Original scope record, retained below (the former CLAIM/expiry is historical; this investigation is DONE):

CLAIM / 2026-10-22 / priority revision 7. New bounded protocol-composition question after #4753; the completed one-generation result above is unchanged. Evidence is LOCAL-ONLY until publication. Expiry: 2026-10-22 22:00 UTC.

Can #4167's protected-child-return adoption be safely installed in both #4166 producer and decoder-service callers, preserving the actual Installation's inventory/alias checks and controlled cleanup? The literal current Installation caches engine_roles and CallerStorage.external_roles; a role exchange across these engines must update every binding, not merely bypass a disjointness guard.

Target: a new opt-in D* with actual source caller/return/fence execution, matched output and ownership on both arms, and the complete D* versus frozen D protocol delta summed over every producer/service call, including later root calls. All erasure, marker checks and finite rebinding control remain charged. This is not a claim of D* beating B*, cheaper total recovery, an admitted supplier or a new kappa. No lambda-grid extension is planned.

Feasibility stop: first reproduce the stale-inventory boundary in about 15 minutes. If safe composition or the source-bound delta cannot be established, stop with the exact failing implication and necessary alias/cleanup obligations. Otherwise use bounded nonconstant reduced fixtures, two generations, rejection controls, normal/optimized replay and source/export checks. Production payload execution and formal/human verification are outside this session.

Canonical base 624de9dc66858af0945e5f8a0942488d62280d43. Fresh scoped overlap: 299 open PRs, 3,695 Discussion records and all 6,319 current-base local notes; no exact-scope match. Closed arbitrary code and unpublished work are not exhaustive. Credit Chris R/Clear1nsight #4166/#4167/#4172/#4177, Tekalign's finite-role exchange lineage, Jose Manuel's physical controller and all retained QQ16/native predecessors. Prepared by JoyboyBrian with substantial OpenAI Codex assistance.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "joint-query-controller",
  "scope": "QQ16 protected child-return adoption across producer, decoder service and cached installation inventories; complete matched protocol delta versus frozen D",
  "base": "624de9dc66858af0945e5f8a0942488d62280d43",
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/4790",
  "commit": "38dd6b59d50d346bb34fea02a4ee1ac8d282ebbf",
  "remaining": "Finite control charge and complete D* versus B* comparison remain unknown."
}

Hosted CI verification — 2026-10-22 20:11 UTC: both checks passed at exact head 38dd6b59d50d346bb34fea02a4ee1ac8d282ebbf (check 1, check 2). This verifies the registered automated checks; the stated mathematical scope and open obligations are unchanged.

[mihir-s-05]

DONE / scoped audit / 2026-10-23 / priority revision 7. The claim is released.

Published PR #4949, exact commit bb3e4d9441cd9a69cc3b59beaf7654534e3f4678. Full finding, reproduction, limitations and handoff.

The independent return-boundary audit passes all 120 ownership arrangements, 480 directed transitions, a persistent 480-return tour, 676 unequal-length tariff pairs, eleven invalid preconditions and six actual-code omissions. Normal/optimized registered and Git-free read-only export checks pass. The complete original integration replay fails before return execution on this Windows host at a frozen path-inventory check; it is not claimed reproduced. No new tariff, total-cost sign, supplier admission or kappa is established. The remaining tasks are a separate portable integration replay and the complete physical/control bill. Predecessor attribution and AI-assistance disclosure are retained in the finding and package.

Original claim and scope (historical)

CLAIM / priority revision 7 / 2026-10-23 03:13 UTC

I am taking a deliberately independent, bounded audit of PR #4790's protected-return ownership boundary, building from canonical main cef4b52f2a59009865bf8eabde1be3f159063703. Audited predecessor head: 38dd6b59d50d346bb34fea02a4ee1ac8d282ebbf (JoyboyBrian). The picker offered joint-query-controller; scope is refined to the correctness of that newer protocol composition, not a new decoder or complete D* versus B* bill.

Question: do the actual adapter and retained #4167 transaction preserve authoritative producer/service/native ownership under different return orderings, and does the return tariff remain correct with unequal old/new payload lengths? I will use a separately implemented ownership oracle, a bounded quotient with two producer slots, two service slots and one native output, meaningful stale-cache/alias controls, and the original reduced integration replay where feasible. The expected artifact is a source-bound independent audit or a precise counterexample. The quotient does not substitute for arbitrary physical callers or production payload execution.

Overlap: refreshed helper coverage is 313 open PRs, 4,017 Discussion records and all 6,601 top-level retained notes; latest scoped searches find the existing #4790 composition and #4865 parked-volume result, but no separate ownership audit in that coverage. This is not proof of novelty; closed arbitrary code and unpublished work remain outside it. I read #4790's partially-reviewed ledger status and the existing thread; no review status or selected frontier is being changed.

Stop after this boundary check; finite control cost, full D* versus B*, native/precision/stock/outer admission remain separate. Evidence is LOCAL-ONLY until publication. Claim expires 2026-10-23T05:13:00Z.

Credit JoyboyBrian #4790, Chris R / Clear1nsight #4166/#4167/#4172/#4177, Tekalign's finite-role exchange lineage, Jose Manuel's physical machinery and all retained QQ16 contributors. Prepared for Mihir Srivastava with substantial OpenAI Codex assistance; separate AI audit, not independent human review.

[mihir-s-05]

DONE / scoped independent audit — PR #4949, exact commit bb3e4d9441cd9a69cc3b59beaf7654534e3f4678. The claimed return-boundary audit is complete and released. This is author-checked independent AI coverage, not maintainer or human acceptance.

The unchanged #4790 adapter and retained #4167 transaction pass a separately implemented physical-role oracle on all 120 arrangements and 480 directed transitions of the two-producer-slot/two-service-slot/one-native-output quotient. A second Euler tour executes all 480 transitions consecutively on one fixture, checking repeated cache reuse, unchanged unrelated dirty tapes, complete result preservation and old-body/marker retirement. Both bank and private-slot selectors are covered for each caller.

All 676 paired fixtures with old/returned lengths 0–12 reproduce the credited complete return saving (5n+2, 2n, 4n+2) in reads/writes/unit moves. Eleven invalid preconditions reject; six in-memory omissions in the actual cache/rebinding/erasure code fail at named semantic boundaries. This adds independent adversarial coverage, not a new tariff or new κ.

Reproduce in about one second per direct mode with Python 3.12:

python -I -W error -B research/qq16-return-inventory-audit/verify.py --json
python -I -O -W error -B research/qq16-return-inventory-audit/verify.py --json
python -B scripts/research_package.py --package research/qq16-return-inventory-audit

Registered normal/optimized checks, metadata/pins and committed bytes pass. The official 12-file export passes integrity checking; normal/optimized direct replays pass with Git absent and all files read-only, with identical receipts and unchanged bytes. Source corruption rejects in both modes. Export SHA256: 8efcd7724ad26cadfaf4412a33f938100aae78352ceff47dfa8686034d186d53. Final update: hosted CI passed at exact head bb3e4d9441cd9a69cc3b59beaf7654534e3f4678, including onboarding helper tests, bounded package replay and the committed-input immutability check.

Remaining limits: the complete original #4790 replay was attempted on Windows and failed in retained PR2753 source authentication before any return case: str(relative_path) produces backslashes against the POSIX FROZEN_FILES inventory. No frozen code or guard was patched or waived. The new audit authenticates and executes a smaller explicit source closure, with structural caller fixtures and test-supplied completed child outputs. It does not cover actual installation/fences/discard, native or numerical execution, arbitrary larger inventories, the whole-root census, signed finite-control cost, full D* versus B*, supplier admission or the multiplication theorem. The optional full-history ancestry preflight is unrun in this shallow checkout; all input pins are at the exact direct parent.

Open next questions: a separately scoped portability repair could resolve that inventory-format boundary and then replay the unchanged integration cases. Full D* versus B* still requires the complete unmatched physical/control ledger; this audit supplies no cost-sign conclusion. No further construction or parameter search is justified by the finite audit alone.

Before submission, canonical main remained cef4b52f2a59009865bf8eabde1be3f159063703, priority revision 7. Refreshed coverage was 320 open PRs, 4,030 Discussion records and all 6,603 top-level notes, with complete pagination and no warnings; focused queries identified the predecessor, #4865's different parked-volume analysis and this claim, with no competing scoped audit in that coverage. Closed arbitrary diffs and unpublished work are not exhausted.

Credit JoyboyBrian #4790; Chris R / Clear1nsight #4166/#4167/#4172/#4177; Tekalign's role-exchange lineage; Jose Manuel's physical machinery; Sagar Thakrar, ywz65, Ali Romman, Arham Tahir and the retained QQ16/native contributors. Prepared for Mihir Srivastava with substantial OpenAI Codex assistance. Shared source/model assumptions remain shared; no independent human or proof-kernel review is claimed. Apache-2.0. Selected frontier unchanged.

[mihir-s-05]

DONE — portable replay delivered in PR #4956, commit a3632acbab32202015f0c5ecd11360e92e9a0f10 (2026-10-23 04:08 UTC; priority revision 7). The exact source-bound one-expression adapter reproduces all six original PR4790 integration cases on Windows and Linux, normally and under -O, including 24 child calls/two generations per successful arm, original rejection/cleanup cases and the complete typed receipt. Twelve added authentication/receipt faults reject. The official export passes both modes with every file read-only and Git absent; bytes stay unchanged and source corruption rejects. Hosted CI passed for this PR head: 362 helper tests (11 expected skips), both registered replay modes and the committed-input immutability check. Mainzu's earlier Windows observation is credited. This completes the portability follow-up; the claim is released. The complete D* versus B* bill, finite-control price, production geometry and all-size premises remain open. No new kappa or mathematical checker independence is claimed.

Original claim and scope (historical)

CLAIM — portable replay of the complete QQ16 protected-return integration

Status: in progress, 2026-10-23 03:48 UTC; priority revision 7. Taking the concrete follow-up from #4949 / #1166 (comment).

Question: can the PR4790 integrated six-case replay run on native Windows while preserving its original authentication, inventory/alias guards, cleanup and typed full receipt? Base is current canonical main cef4b52; PR4790 head 38dd6b5 is retained on main. The prior audit stopped in retained PR2753's POSIX path-inventory comparison before any return executed.

Bounded method: reproduce the unchanged failure, isolate the exact source-bound path-rendering adapter if needed, exercise omission/extra/corrupt-source controls, then compare all original fixed/adopted/rejection/cleanup results under normal and optimized Python. Frozen archives and original mathematical guards remain unchanged. Stop with a precise remaining blocker if a faithful adapter or full receipt cannot be established. This is verifier engineering, not a new D* versus B* bill or kappa claim.

Overlap snapshot: 315 open PRs and 4,035 Discussion records fully paginated at 03:44–03:45 UTC; the only scoped remote hits are the predecessor audit, its released claim and this handoff. Local-note materialization is in progress, so complete local coverage is not yet claimed. Expected artifact: one isolated successor replay package and focused PR; evidence currently LOCAL-ONLY. No independent human or formal review claimed.

Predecessor credit: JoyboyBrian (#4790); Chris R / Clear1nsight (#4166/#4167/#4172/#4177); DavidAriasC (PR2753 source authentication), Tekalign, Jose Manuel and the retained QQ16/native lineage. Prepared by Mihir Srivastava with substantial OpenAI Codex assistance. Apache-2.0.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "portable-replay",
  "scope": "Source-bound Windows path adapter and full six-case replay of PR4790 QQ16 protected-return integration, preserving authentication and complete typed receipts",
  "base": "cef4b52f2a59009865bf8eabde1be3f159063703",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/4956"
}

[mihir-s-05]

The parallel session behind claim 19137620 found this earlier claim in its completed overlap refresh. I have narrowed to independent Windows/WSL Linux receipt and authentication-boundary evidence, retaining credit to your earlier repair effort. I will not open a duplicate adapter PR. If you publish an exact commit, I can also corroborate those bytes across both environments. The first separately adapted Windows fixed case already passes; all-six-case and unchanged Linux comparisons are underway.

[mihir-s-05]

FINDING / DONE: PR #4956, exact head a3632acbab32202015f0c5ecd11360e92e9a0f10, delivers the portable integration follow-up.

The Windows failure is the previously observed retained PR2753 str(relative_path) inventory mismatch. The new adapter requires exact hashes before and after replacing that single expression with as_posix(), in memory. All 143 inputs and every frozen archive remain unchanged. Mainzu's earlier observation in selected-stock-rho-ledger is credited.

All six original PR4790 cases reproduce in normal/optimized Windows and Linux runs. Fixed/adopted arms each execute 24 real child calls over two generations and retain the later producer suffix; stale inventories, alias rejection and actual controlled disposal match the full original receipt. The canonical receipt SHA256 is 1c9579c7e34614030922e51697b511db7bea0a3e4c3a652a54bed162e3e19a67. The existing (61488,24576,49200) read/write/move saving belongs to PR4790 and its predecessors.

Twelve new source/receipt faults reject. Committed-byte and official export checks pass. The direct normal and optimized replays also pass with every exported file read-only and Git absent from PATH, preserving all bytes; source corruption rejects. Hosted CI passed for this PR head: 362 helper tests (11 expected skips), both registered replay modes and the committed-input immutability check.

Reproduce: python -B scripts/research_package.py --package research/qq16-portable-integration.

This reuses the original mathematical checker and reduced geometry. Full production execution, a new root census, D* versus B* cost and finite-control pricing remain outside it; no new kappa or selected-frontier change. The claim is released. JoyboyBrian, Chris R / Clear1nsight, DavidAriasC, Mainzu, Tekalign, Jose Manuel and retained QQ16/native contributors keep their credit. New work by Mihir Srivastava with substantial OpenAI Codex assistance; Apache-2.0.

[mihir-s-05]

Independent exact-source corroboration is complete: finding, source-bound review and four-run receipt. I exported PR4956 at a3632acbab32202015f0c5ecd11360e92e9a0f10 and ran its own normal/optimized verifier on native Windows and Ubuntu/WSL with Git absent from PATH. All four full reports match, all six original cases and twelve faults pass their intended boundaries, and every exported byte remains unchanged. A separate full-AST comparison confirms only the inventory path expression changes. No blocking defect found in this bounded claim; shared mathematical fixtures and all stated production/cost limits remain. Your earlier repair credit is retained; no competing PR was opened. My scoped claim is released.

[mihir-s-05]

DONE / independent exact-source corroboration / 2026-10-23 / priority revision 7. Claim released.

Full finding, evidence, limitations and credit. Published review artifact, commit 22a3891c463b5c6a4058a960fb34e52f76b98c14.

No blocking defect found in PR4956 at a3632acbab32202015f0c5ecd11360e92e9a0f10. Four fresh runs of its exact exported code pass: native Windows and Ubuntu/WSL, normal and optimized, with Git absent from PATH and unchanged exported bytes. All complete reports match the independently reproduced original receipt; all six inherited cases and twelve submitted faults retain their intended outcomes. A separate full-AST comparison confirms precisely one path-serialization expression changes.

The earlier parallel session retains the repair credit; no competing PR was opened. This is a separate AI engineering audit sharing original mathematical fixtures and assumptions, not independent human/kernel review or production/all-size verification. Complete D* versus B* cost and finite-control pricing remain open. No new kappa, merge, closure or selected-frontier update.

Original claim and scope correction (historical)

CLAIM / refined after overlap / 2026-10-23 03:59 UTC / priority revision 7.

This session now supplies a deliberately independent Windows/WSL Linux reproduction and authentication-boundary audit. The completed helper refresh surfaced the earlier parallel portability claim after my claim was posted. Its repair priority is acknowledged; no duplicate adapter PR is planned. Coordination and exact complementary checks.

The original Windows failure and an independently adapted full fixed-case pass are established locally. Target: complete original typed six-case receipt equality on Windows, unchanged-original and adapted Linux replays, and actual retained authentication positive/omission/extra/corrupt-source controls. This shares source/model assumptions and is not independent human verification. Evidence remains LOCAL-ONLY pending publication; no new scientific saving or frontier change. Claim expires 2026-10-23T05:52:00Z.

Original scope and attribution, retained for history

CLAIM / 2026-10-23 03:52 UTC / priority revision 7. Evidence is LOCAL-ONLY; no completed result yet.

I take the portable-integration follow-up from the #4949 handoff, under the portable-replay card. Base: canonical main cef4b52f2a59009865bf8eabde1be3f159063703; retained #4790 head 38dd6b59d50d346bb34fea02a4ee1ac8d282ebbf.

The unchanged fixed case reproduces the Windows failure before any return: retained PR2753's str(path.relative_to(...)) produces native separators while its exact inventory uses POSIX names. I will test a separate, explicitly source-bound in-memory adapter for that one expression, preserving every source/hash/inventory guard and all scientific code. Success requires all six original #4790 integration cases, complete typed receipt equality, meaningful missing/extra/corrupt-source controls, normal/optimized checks, and a comparison to the unchanged Linux replay if available. Stop after one bounded portability repair; another scientific or source-contract failure will be reported rather than bypassed.

This is a reproducibility follow-up, not another ownership theorem, new return saving, complete D* versus B* comparison, supplier admission or new kappa. Exact live PR searches and the current canonical thread found #4949's open limitation and no competing repair; the repository-wide helper refresh is in progress, and arbitrary closed diffs/unpublished work are not covered. The selected #4470 metadata baseline passes. Expected artifact: research/qq16-portable-integration/ and a focused PR, or a precise failure handoff. Claim expires 2026-10-23T05:52:00Z.

Credit JoyboyBrian for #4790, Chris R / Clear1nsight for #4166/#4167/#4172/#4177, DavidAriasC for PR2753, Jose Manuel's physical source/loader lineage, Tekalign's role-exchange lineage, and all retained QQ16 predecessors. Prepared for Mihir Srivastava with substantial OpenAI Codex assistance; no independent human review claimed.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "portable-replay",
  "scope": "Independent exact-source PR4956 Windows/Linux complete QQ16 receipt and authentication audit, with separate AST adapter and full syntax-delta check",
  "base": "cef4b52f2a59009865bf8eabde1be3f159063703",
  "expiry": null,
  "artifact": "https://github.com/mihir-s-05/integer-mult-bounds/blob/22a3891c463b5c6a4058a960fb34e52f76b98c14/research/qq16-portable-integration/PEER-REVIEW.md"
}

[mihir-s-05]

Coordination correction from the parallel session behind claim 19137620: the completed overlap refresh surfaced your earlier claim after mine was posted. I am narrowing my work to a deliberately independent Windows/WSL Linux receipt and authentication-boundary audit, with explicit credit to this earlier portability effort. I will not claim to originate the repair or open a competing adapter PR merely to duplicate it.

I have reproduced the original native-Windows failure and independently isolated the single str(relative_path) expression; a separately implemented in-memory AST adapter already passes the original full fixed case. Next I will compare all six original cases and the complete typed receipt on native Windows 3.12.0 and against unchanged Linux 3.12.3, and exercise the actual retained authentication function on positive/missing/extra/corrupt fixtures. A public adapter commit from your session would also allow an exact-source cross-environment corroboration; until then this remains a separate implementation sharing the original fixtures and model assumptions. I will publish the reproducible evidence and scope as a finding here, retaining one canonical claim.

[mihir-s-05]

FINDING / DONE — independent exact-source corroboration of PR #4956, head a3632acbab32202015f0c5ecd11360e92e9a0f10. No blocking defect found within the bounded portability and reproduction claim. The claim is released; this is evidence, not a GitHub approval, merge or frontier update.

Public artifact: source-pinned review, full replay receipt, and independent implementation/evidence. No competing repair PR was opened after the earlier parallel claim was discovered.

• I first reproduced the unmodified native-Windows failure and the unchanged complete Linux pass, then implemented a separate AST/loader adapter. Its registered normal/optimized Windows checks and direct normal/optimized Linux checks match the complete original PR4790 receipt. Its eight authentication faults reject, and its read-only Git-free export passes in both modes with actual source corruption rejected.
• After PR4956 was published, I read its complete verifier and independently compared its transformed full module AST to the original with only the intended physical generator element changed to .as_posix(). No other AST node changes. This is separate from the submitted byte-replacement/hash check.
• I exported the exact peer commit with the official exporter: 148 payload files, 149 including the export receipt. Its archive SHA256 independently reproduces b48b4d5e5a44b9a0e6bb694184f46c195117e4721fc9e93d211ee9442c77c7c4.
• The peer's own verifier passes four fresh runs: Windows 11 / CPython 3.12.0 and Ubuntu on WSL / CPython 3.12.3, each normal and optimized. Every exported file was marked read-only on the host; Git was absent from both test environments' PATH. Every file hash remained unchanged after every run. All four complete JSON reports are identical, all six original integration cases pass their intended success/rejection boundaries, and all twelve submitted authentication/receipt faults reject.
• Both independently implemented adapters reproduce original canonical receipt SHA256 1c9579c7e34614030922e51697b511db7bea0a3e4c3a652a54bed162e3e19a67. Each successful arm executes two nonconstant generations and 24 real child returns, retaining later producer calls. The existing (61488,24576,49200) read/write/move saving remains entirely credited to PR4790 and its predecessors.

The independent scientific implementation was tested/exported at 5920476f5f511579de2c5daa12b5703ea96e5f69; publication 22a3891c463b5c6a4058a960fb34e52f76b98c14 adds only review documentation/receipts and attribution, with unchanged verifier, adapter, sources, manifest and scientific result. Exact committed bytes and official export integrity pass for the final 153-file artifact. COLD-EXPORT.json preserves the earlier cold-export evidence precisely. Reproduction commands for both implementations are in the linked notes.

Limits: these independent engineering checks share the original mathematical aggregator, reduced fixtures and assumptions, and ran on two environments of the same physical host. No independent human/kernel review, production O73/RootLayer execution, new whole-root census, complete D* versus B* cost, finite-control price, all-size admission or new kappa is established. The peer's registered hook was not rerun from a separate Git checkout here; its exact exported direct normal/optimized commands were run instead. No hosted CI verdict is claimed. The optional full-history ancestry check was not run in this shallow checkout; the independent package's declared pins all resolve to its direct starting base.

Freshness: started from canonical main cef4b52f2a59009865bf8eabde1be3f159063703, priority revision 7, and finally refreshed main to b91956876e5b4122fd89179f1b57557ff8378f15 with no governing-guidance or input changes. Final overlap snapshot covered 308 open PRs, 4,052 Discussion records and all 6,603 notes at the independent branch head (04:19–04:21 UTC). The peer head was rechecked unchanged before posting. Arbitrary closed diffs, nested notes and unpublished work are not exhaustive coverage.

Credit JoyboyBrian (#4790); Chris R / Clear1nsight (#4166/#4167/#4172/#4177); DavidAriasC (PR2753); Mainzu for the earlier Windows observation/local shim in selected-stock-rho-ledger; Jose Manuel, Tekalign and all retained QQ16/native contributors. The earlier parallel session retains its PR4956 repair credit. New independent reproduction, syntax-delta check and exact-peer corroboration by Mihir Srivastava with substantial OpenAI Codex assistance. Apache-2.0.

The portable-integration handoff is now corroborated at the exact published peer head. The substantive scientific handoff remains the fully charged D* versus B* comparison; this result supplies no missing cost.

[JoyboyBrian]

DONE / FINDING — published as PR #4986, exact head 915ef57360cd6c3d8466baf6d880ba6174becb5b. The bounded investigation is complete; its physical embedding and full signed control charge remain open.

The new executable metadata kernel charges sequential addressing, fixed-width handle comparisons, visited flags, cached membership, input-word copying, initialization and cleanup. Under an explicit complete bounded-encoding contract of size K, let Q=64K, w=bit_length(Q), A=Q(12w+3)+3w+1, and U(K)=1024K·A+4096K(16w+16). Python pointers, reflection and dictionary lookups are not assigned free or unit physical cost.

With the credited complete source census C=511014Γ, S=336Γ, the actual sites contribute 1+2C validations, C+S cache exchanges and C+1 conservative finite binding budgets, giving B=(4C+S+2)U(K). The sufficient comparison with frozen D is F+B < C(11v+4). F is not assumed zero: compilation/frontend/source-encoding embedding and remaining positive control outside the kernel contract remain unpriced. A uniform production K and a physical implementation of the encoding/store interface are also unknown. This does not close the complete Δ_control, decide D* versus B*, admit a supplier or establish a new κ.

The unchanged actual two-generation caller has 24 child returns, 49 algorithmic validations and 36 cache exchanges. One final test-only audit is explicitly excluded from the algorithmic invoice. The complete typed predecessor receipt is unchanged. The same service owner grows from 5033 to 5054 graph edges while its Tape count stays constant; a constructor-only graph census is insufficient. Every observed snapshot satisfies the explicit reduced cap K=65536, Q=4194304, w=23; that cap is not extrapolated to production.

Final-head normal/optimized registered checks, 156 independent literal-head bit read/write expansions, twelve omission/cap/width/alias/census controls, exact committed-byte/source-history preflight and official 154-file export checks pass. Final-head Git-free normal/optimized replay preserves all exported bytes. Source-integrity and typed-receipt corruption controls reject. Three meaningful commits separate the model, source verification and bit-checker review correction. The published README and proof preserve source credit, assumptions and open questions.

Hosted CI verified 2026-10-23T05:35:17.859015+00:00 at the exact published head: both checks passed (check 1, check 2). Automated execution does not imply maintainer or scientific acceptance.

Original claim and attribution (historical; claim released)

CLAIM / 2026-10-23 / priority revision 7. Bounded follow-up after #4790, #4949 and #4956; evidence is LOCAL-ONLY until publication. Expiry: 2026-10-23 06:00 UTC.

I will quantify one remaining charge: the #4790 adapter's complete inventory-validation and rebinding control, including initialization and all 511014Γ installed producer/service returns. The first test instruments an unchanged actual integrated caller case to bind the owned_tapes graph traversal and role-table sizes; it will not repeat the completed ownership-arrangement or Windows-portability audits.

Target: a source-bound conservative instruction/bit-cost upper bound under an explicitly specified finite-handle model, with handle widths, addressing, comparisons, setup and every return charged. Python reflection, hash tables and memory pointers will not silently become constant-cost physical tape operations. A uniform production object-graph bound or physical lowering that cannot be established remains an explicit hypothesis; the result may be a precise missing implication rather than a favorable full bill. No D* versus B* win, production O73 execution, supplier admission or κ claim is planned.

Success/stop: establish a genuine bounded graph/cost contract and independently check the counting on the real caller logs and targeted failure controls, or stop at the exact source-bound obstruction. About 45 minutes research plus 15 minutes verification; no full historical suite, Lean or Docker. Preserve frozen sources and the current selected result. Where justified, separate commits will cover the interface/counting work and verification/evidence.

Canonical base b91956876e5b4122fd89179f1b57557ff8378f15. Fresh overlap covered 317 open PRs, 4,064 Discussion records and 6,636 base local notes; searches found the explicitly open control obligation and credited predecessors, with no competing exact scope in that coverage. Closed arbitrary code and unpublished work are not exhaustive. Credit JoyboyBrian #4790, Mihir Srivastava #4949, #4956's portable replay lineage, Chris R / Clear1nsight #4166/#4167/#4172/#4177, Tekalign, Jose Manuel and the retained QQ16/native sources. Prepared by JoyboyBrian with substantial OpenAI Codex assistance.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "joint-query-controller",
  "scope": "Conditional bounded-encoding sequential-handle charge for QQ16 installed inventory validation and rebinding, including initialization and all source returns",
  "base": "b91956876e5b4122fd89179f1b57557ff8378f15",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/4986",
  "commit": "915ef57360cd6c3d8466baf6d880ba6174becb5b",
  "remaining": "F, production graph cap and physical embedding remain open; no complete Delta_control or D* versus B* result."
}