Conditional T16 κ gain through neutral whole-helper hosting paths

[pai-scaffolde]

This candidate removes the seven rank-7 idle remainders in selected PR1094's T16 owner map through 24 legal whole-helper moves in eleven neutral-then-concentrating paths. The complete paid profile changes by {1:+1, 7:-7, 16:+3}, increasing the conditional finite value from 836330098538459/500000000000000000 = 0.001672660197076918 to 836340409246491/500000000000000000 = 0.001672680818492982. The exact gain is 161104813/7812500000000000 = 0.000000020621416064.

All changes are confined to research/astra-ultra-hosting-20261013/; the selected result and existing sources are unchanged. The 69,120 helpers across 144 calls retain their full width and complete invocation identity. Local words, phases, bridge schedule and deadlines remain fixed. Assigned helper residuals and the remaining suffix partition the same pending axes inside each original strict no-touch interval before the same deadline. PROOF.md states the all-input argument for arbitrary correlated helper dirt under the inherited local supplier contract. This is a scoped finite conditional construction, not a new hosting principle, optimality claim, unconditional multiplication theorem or adoption proposal.

Validation and reproduction:

• The retained author receipts report all eleven unchanged native T16 stages passing, both exact rational moment engines, all 47 outer inequalities, 102 inherited rejection controls and five new owner mutation controls. The complete bit endpoint and surcharge are retained. Live/physical stock remains 14336/14826; prefix 397 is charged at 512; the maximum child remains 48. The inherited independent check's conservative reserve of 14850 gives the same 2642-bit stock bound and row coefficient 16469.
• Publication checks reproduced OWNER-CHECK.json byte for byte from a temporary package copy and confirmed all candidate/source pins. Every code file, mathematical input and native receipt is byte-identical to the frozen research version; only publication wording and internal metadata were adjusted.
• A fresh-context cross-vendor AI review of exact public head d8640f5b7ae99b43f5d56146cb94ca62b8b3835d independently exported that head, reproduced the owner receipt and ran the unchanged native driver: all eleven stages passed at the candidate κ, with the reused supplier unchanged. This is source-bound reuse, not a cold ancestry rebuild.
• From the repository root: bun research/astra-ultra-hosting-20261013/verify.ts and bun research/astra-ultra-hosting-20261013/verify-native.ts /path/to/checked-selected-native-local /path/to/fresh-output. Use a temporary package copy for the first command if preserving the committed receipt. Unset an expired RESEARCH_DEADLINE_UTC. The native replay validates the immutable PR1087 archive and overlays only the three candidate data files before running its unchanged driver.

The native supplier is reused through explicit source-bound checks, as in selected PR1094; there is no fresh full cold ancestry rebuild. Inherited all-size/compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer and bit H1-H5 assumptions remain. There is no full Lean multiplication theorem. The package is not registered in the optional Python-only package format, so repository CI does not certify its native candidate replay.

Review and draft gate: independent cross-vendor mathematical AI review of the frozen witness and fresh-context AI review of exact public head d8640f5b7ae99b43f5d56146cb94ca62b8b3835d have both completed with ACCEPT_SCOPED and no blocking findings. The mathematical review includes a finite exact identity-cover chronology probe; the local dirty-helper/stage-label and non-identity-cover conjugation contracts remain inherited. All review observations and their dispositions are recorded in the PR comments. All six hosted workflows currently report action_required before any jobs execute. GitHub states: "This workflow is awaiting approval from a maintainer in #1407" (artifact verification, registered packages). CI has not run. The PR remains draft until applicable CI is green and no mathematical blocker is unresolved; maintainer review owns integration.

Credit: Rohan Arun's PR1094 and earlier neutral-exchange/repacking work; Jeremy Kothe's PR1087 and owner ancestry; Hao Yan / FanPUYen's PR858 controller; PR1018/987/1005 local suppliers; the PR589 bit supplier; Douglas Colkitt's selected composition; and Arham-Tahir64's PR1343 obstruction, which explicitly leaves neutral paths open. No priority is claimed for neutral moves or compound owner optimization. Original sources and notices are preserved. Substantial AI assistance: OpenAI gpt-6-astra ULTRA for the research, OpenAI gpt-6.1-sol for publication preparation. Claude Opus 5.5 performed both cross-vendor AI reviews; this is not independent human or proof-assistant certification. New material is Apache-2.0.

[pai-scaffolde]

Cross-vendor mathematical AI review has completed with ACCEPT_SCOPED, with no blocking findings. This is my summary and disposition of Claude Opus 5.5's review; it is not a human review or formal certification. The exact publication-head review remains pending. Scientific inputs, code and retained receipts in public head d8640f5b7ae99b43f5d56146cb94ca62b8b3835d are unchanged from the reviewed witness.

The reviewer independently reproduced all eleven native stages and the selected-map positive control; reconstructed all 288 windows and checked all 69,120 roles; reproduced the five owner rejection controls; and confirmed κ, the delta and all 47 outer slacks through independent arithmetic. An exact eight-stream chronology probe on the identity cover, with each hosted factor applied at its actual call, had zero failures across 224,000 cases per map for the unhosted control, selected map and candidate. Four mutations (late, early, omitted and duplicated factors) were detected. These finite probes support the source-bound hosting argument; they do not rederive the local dirty-helper contract or prove all non-identity cover classes.

All seven nonblocking findings are dispositioned here:

• F1 — move count: 24 edit actions relocate 23 distinct helpers; role 44384 moves twice. The 47 changed serialized rows comprise 23 relocated roles and 24 changes to offsets alone. The package's “24 moves” counts actions; no claim of 24 distinct relocated helpers is intended.
• F2 — inherited translations: every idle sweep applies its rank-zero translation_after, including fully hosted bins with no remaining suffix. The inherited template's adapter policy requires the exact translations in DATA-PHASES.json, and the invoice charges all parent idle children. The candidate fully hosts four more translation-carrying bins. Applying translations only when a remainder exists fails for both the selected map and this candidate in 52,029 of 224,000 probe cases each. This contribution retains the inherited translation-at-every-sweep contract.
• F3 — verifier scope: native PASS establishes chart, binding, invoice and arithmetic acceptance. Operator identity also requires the argument in PROOF.md; the independent chronology probe covers the identity cover. The local dirty-helper/stage-label contracts and conjugation for non-identity cover classes remain inherited assumptions.
• F4 — charts: 16 chart instances are added and ten removed, with no new (child, width) type. The new instances passed native chart audits and were exercised by the chronology probe.
• F5 — reserve: historical reserve 14850 versus emitted stock 14826 is already disclosed. Both yield 2642 stock bits and row coefficient 16469; no stock saving is claimed.
• F6 — supplier reuse: the checked supplier is reused through the unchanged source/semantic identity contract, including exclusion of the receipt's timing-only field. Reproduction requires that checked supplier directory. No fresh cold ancestry rebuild is claimed.
• F7 — phase wording: single-axis conjugation is exact, P_G C_e P_G^-1 = C_(Ge), with no additional phase. Full-basis translation corrections belong to the inherited bank/cover adapters. The package's broad adapter wording does not authorize an extra single-axis correction.

No scientific payload or verifier was changed to settle these findings. The PR remains draft: the fresh exact-head AI review is pending, and all six hosted workflows await maintainer approval before running. Artifact verification explicitly reports that approval gate. There has been no cold supplier/bit ancestry rebuild, local primitive replay, non-identity-cover operator replay, full Lean multiplication theorem, selected-frontier change or integration.

[pai-scaffolde]

Fresh-context cross-vendor AI review of exact public head d8640f5b7ae99b43f5d56146cb94ca62b8b3835d has completed with ACCEPT_SCOPED and no blocking findings. This is my author summary of Claude Opus 5.5's review, not an independent human approval or formal theorem certification.

The reviewer confirmed the public head and clean ancestry, all 36 package additions, unchanged scientific fields, all three candidate SHA256 pins and all ten source pins. Of the 36 package files, 32 are byte-identical to the frozen research version; four contain only publication wording or metadata changes. A fresh export of this exact public head reproduced OWNER-CHECK.json byte for byte. The reviewer also ran the unchanged native driver on an exact-head export: all eleven stages passed at the candidate κ, and the checked supplier's hashes remained unchanged. This uses the existing source-bound supplier; it is not a cold ancestry rebuild. The completed mathematical review's operator/arithmetic probe evidence applies to the unchanged scientific payload with its stated limitations.

Publication observations are dispositioned as follows:

• F8 — review status: the PR body is updated to record both completed ACCEPT_SCOPED reviews, including the exact public head and their limitations. Earlier pending statements describe the status when first posted.
• F11 — README title: it refers to an improved owner map for the selected T16 construction used as the baseline. Its opening explicitly says the selected record is unchanged and no adoption is claimed; this PR's title and body describe a conditional candidate. It does not claim to be the selected frontier.
• F9 — packaging metadata: package.ts is the preserved author-sprint packaging utility with a fixed historical output location. Its historical review/publication metadata differs intentionally from the edited public RESULT.json: only scope was changed and parent_independent_review removed. It is not a documented acceptance command. Reproduction uses verify.ts and verify-native.ts; scientific result fields and candidate pins are unchanged. Publication/review status belongs to this PR. The original code and receipts were retained without modification.
• F10 — receipt paths: portable path substitution in VALIDATION.md applies to the displayed command transcript. Untouched native receipts retain anonymous temporary input and output paths, including the checked-supplier path. Those paths contain no personal checkout or session identifiers; preserving them keeps the receipts byte-identical.
• The “no public posts, pushes, PRs” statements in the sprint validation record describe the author sprint. This PR documents the subsequent publication separately.
• F12 — contributor identity: commit attribution uses the existing Git contributor identity for this authorized public contribution. An anonymous or agent-only author identity was not requested; contributor metadata was not copied from private harness identity or memory files.
• F1–F7 — mathematical observations: these remain dispositioned in the previous comment: 24 actions on 23 relocated helpers, translations at every idle sweep, precise native/operator scope, audited chart changes, inherited reserve and source-bound supplier reuse, and exact single-axis conjugation.

F13 — readiness: CI remains unrun, not green: all six hosted workflows report action_required and await maintainer approval. The PR remains draft for that gate; no readiness exception or CI weakening is proposed. The selected record remains unchanged; there is no merge, frontier adoption, full cold ancestry rebuild or unconditional multiplication theorem claim.

[philippeVV]

Independent review of head d8640f5b (prepared with Claude Code for philippeVV). This covers the owner-semantics and native-admission obligations that the merged #1457 arithmetic audit explicitly left open.

• Registered native verifier. bun was not available, so I ported verify-native.ts to Python. The port does the same things: pinned PR1087 archive extraction, manifest and file pins, overlay of the three data files, then the unchanged verify_t16.py under CPython 3.12. All 11 stages pass, ending in PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY 0.001672680818492982. Controls: admission 69, bit 12, indep-t16 6, mutations 15. The conservative value is 0.001672680815641053.
• Owner map. Josie Elliston's seed67 owner auditor (R1–R7, X1 rebuilt from the event stream, X2) accepts the map, and all 11 mutation controls reject.
  • 47 rows change: 23 relocations and 24 offset-only.
  • Every role sits strictly inside its window, and each call hosts each helper exactly once.
  • Idle profile is {1:2277,3:377,16:3,48:4866}; mass 1,041,408 and deficit 5,120 are unchanged.
  • The replay profile equals the audited profile.
• Pricing. The Independent verification: code-disjoint pricing of all 16 pending kappa claims; every one has deficit W - 64N (no new kappa) #1069 sweep passes (complex binding). Repricing with the pinned engines gives exactly 0.001672680818492982, and the selected map reprices to the record.
• Hosting paths. These add no mechanism beyond the final T16 owner map, which is what the checks above admit.

Note for maintainers: #2077's four moves cannot be added on top of this map, because the bins they target are already full here. A follow-up on top of #1407, using two-stage ejection cycles, reaches κ = 0.001672684510394236; it also passes the strict replay and the auditor. I'll open it as a separate PR that depends on this one.