Conditional kappa = 0.001673260706543984: adaptive joint kernel demotion on PR1117

[Dugongue]

Result

Conditional kappa = 0.001673260706543984, compared with the frozen PR1117 claim 0.001672846995880185 at 342b67f23dfa8f41a520a0d58978b2875e9eb0dd.

The absolute gain is 0.000000413710663799, approximately 0.02473093 percent relative. This is a concrete combined kernel-and-owner improvement under the inherited conditional interfaces. It is not an unconditional multiplication theorem or a claim that the full open-proposal queue has been accepted.

Only research/adaptive-kernel-demotion/ is added. The selected certificate, upstream sources and existing submissions are unchanged.

Mechanism: choose the kernel prefix to fit the actual pending stock

PR1117 supplies the rank-seven end word and its T16 owner schedule. PR1111 supplies a four-helper entrance-demotion recipe. Applying one fixed provider everywhere ignores the actual pending capacities. This package constructs and checks five joint local prefixes and chooses the prefix separately at every literal call:

1. Groups are ordered 635, 603, 611, 619, 627. Their helper indices are respectively (411,413,414,415), (379,381,382,383), (387,389,390,391), (395,397,398,399), and (403,405,406,407).
2. Prefix k changes exactly 4k helper widths from four to five. The complete local profile change is k * (-8H1 + 8H2 + 4H3 - 4H4), verified by recounting each actual joint word, rather than assuming recipe gains add.
3. Within a call, selected helper occurrences eligible to use their own slack remain in place. The remaining selected occurrences exchange owners bijectively with distinct width-four donor occurrences. Every extra width consumes an actual unused axis; all shared owner remainders are updated before the next insertion.
4. Every insertion uses a gap pattern [1,1,1,r], with r equal to one, two or three. The resulting complete local-plus-remainder differences are respectively -12H1+8H2+4H3-4H4, -10H1+7H2+4H3-4H4, and -11H1+9H2+3H3-4H4. The written proof establishes strict moment improvement for every 0 < b < 1.
5. Before these insertions, one legal three-owner cycle replaces two rank-six remainders by rank one and rank eleven: +H1 - 2H6 + H11. This preserves all literal helper occurrences and has a strict concavity saving for every 0 < b < 1.

The realized assignment contains 359 group demotions across 103 of 144 calls: 356 four-unit patterns, one [1,1,1,2] pattern and two [1,1,1,3] patterns. Prefixes zero through five occur 41, 24, 8, 15, 6 and 50 times. These counts come from the final table and dispatch; no advertised kappa gains are added together.

Complete paid profile and exact pricing

{1:344363, 2:65097, 3:62855, 4:19012, 5:11808,
 7:8, 8:1152, 11:2, 48:4873}

Live stock remains 14,336, paid rank mass 1,041,408, and deficit 5,120. The final map has 6,034 paid idle remainders, 1,433 fewer than PR1117, and 9,898 actual 73-column chart types, compared with 10,057. The complete literal difference contains 4,594 owner records; unchanged rows are retained exactly.

Both retained exact rational moment engines certify the native and conservative endpoints. The complete outer assembly checks all 47 strict inequalities. The bit supplier remains the pinned inherited supplier; the complex side binds. Finite work, adapters, restoration and the six-provider dispatch are retained in the invoice instead of being treated as free.

Reproduction and checked scope

Python 3.10+ and its standard library, from the repository root, using a fresh output directory outside this package:

python -I -B research/adaptive-kernel-demotion/verify.py --out ../adaptive-result

The delivered verifier binds the complete source inventory and checks:

• Every actual joint prefix on all 704 arbitrary input columns, including dirty helpers, in forward and inverse-transpose orientations; native emitted words and 25 corruption controls per provider.
• The changed phase edges and wrappers for each prefix. These are fresh checks of the changed local constructions, not a cold reconstruction of every unchanged ancestral phase.
• Every one of the 69,120 literal roles, all 144 calls, their actual provider widths, independent source-derived inactivity windows, physical family uniqueness, chronological coordinate blocks and actual orthogonal 73-column charts.
• A complete remainder/profile recount, all nine finite invoice guards, exact native/conservative and inherited-bit moment brackets, and all 47 strict outer inequalities. Negative controls and source/manifest binding remain explicit.

The changed local constructions, adaptive dispatch and new owner map are concretely checked. The all-size/compiler, common-label and mutable-source realization, whole-call hosting interface, precision/tape and exact-recovery, analytic-transfer and inherited bit-contract assumptions remain conditional. No complete ancestral cold replay, new Lean certificate, hosted CI pass, independent human review or global packing optimum is claimed.

Mathematical sources and future reuse

The package notes and source ledger in research/adaptive-kernel-demotion/README.md record two distinct OpenAI-proof mechanisms investigated by each of the four workers, including their exact source statements and their actual contribution or limitation. In the owner construction, alternating matching-layer switches provide the cycle replacement, and a disjoint first-hit projector partition supplies the canonical self-donor/external-donor separation. The other worker ledgers explain the local transfer, inventory, dispatch and arithmetic adaptations.

These are explicitly sourced adaptations. They are not eight independently additive exponent improvements or new priority claims for the underlying mathematics. The reusable contribution is the checked sufficient coupling: actual joint provider prefixes plus literal donor assignments and a uniform saving proof. The notes retain the one-group fallback, bounded allocation comparisons and routes that were not assigned numerical gains.

Credit and disclosure

Direct construction inputs: PR1117 (rank-seven ends and frozen T16 owners), PR1111 (entrance demotion), and PR1030 (the demotion/lowering context). Local and schedule ancestry: PR1018/987 (seven slots), PR1005/1004 (mutable-leaver cells), PR1022/858 (T16 and whole-family owner scheduling), together with PR869, PR799, PR741, PR685 and PR645. PR635 and its retained notices record the ported cold-end, frame, native compiler and source lineage; PR589 supplies the inherited bit endpoint.

PR1063/1094 provide neutral recolouring and owner-exchange context, and PR1072 supplies the related promotion-to-gap construction. Their numerical gains are not copied or added to this result. Original author attribution, AI disclosures and the Apache-2.0 license are preserved in the vendored notices.

The new adaptive construction, proofs, independent checks and packaging were prepared with substantial OpenAI Codex assistance. No name or email of the submitting user is added by this package, and the assistant did not publish or push anything.

The final self-contained replay passed from the delivered source inventory. It additionally rejects optimized Python and mutated source bytes before running the mathematical checks. The manual browser-upload batch contains 73 files (approximately 7.7 MB), with SHA-256 identity to that inventory.

[Mister-Meeseeks]

100-PR batch review at 390de2866a03758e7f4ddbb2846e5b2ee4e72154.

This remains open after scoped triage. Next review step: Whole-head supplier review remains open for research/adaptive-kernel-demotion. Bind its exact native providers, physical owner allocation and admission evidence, then reconcile changed predecessor blobs before merge. Path overlap with a replayed descendant does not establish complete coverage; see SUPPLIER-FAMILIES.json.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.