Research: bridge high-cube calls to fitted B1

[1337isnot1337]

Change and mathematical scope

This is a refined contribution to uniform-transfer-audit (priority revision 6; base 6f100d4bb5083f8c35d96fd95a539811c62f245c). It answers the fitted-B1 next question recorded by merged PR3301, binding its actual high-cube caller to the conditional ordinary interchange theorem in PR2899.

For each fixed prime (q>2^{80}), integer (u\ge311311), dimension (N=d^2\ge4), fibre (F\ge1), and valid distinct axes (0\le i<j<N), the pinned PR2915 adapter passes width (u) and positive complete spectators
[
P=Q^i,\qquad G=Q^{j-i-1},\qquad S=FQ^{N-j-1},\qquad Q=q^u.
]
The algebraic identity (PQGQS=FQ^N=V) holds for every such input. The source-bound radix loop supplies exactly (u) yields, and the actual native call uses PR2899's (payload, original, prefixes, gap, suffix) interface.

Conditional on PR2899's retained C0 endpoint, chronology, source-refinement and uniform-charge hypotheses, and on successful execution with sufficient capacity, its endpoint and fitted-branch tariff transfer to each reached call:
[
A_j\le C_q V u^{99830289/100000000},
]
with fixed-q constant (C_q). The optional complete adapter corollary also assumes merged PR3301's separately proved outside-call charge (100000V), yielding (A_j+100000V) per call. PR3301's charge is author-checked and still awaiting independent review; the caller/callee bridge itself does not depend on it.

No selected result, supplier admission, or (\kappa) changes. The exact source pins, proof, assumptions and remaining questions are in research/high-cube-b1-fit-bridge/.

Task and overlap

The task card is pinned in TASK.json; its broad catalogue question is refined to this one source-bound call boundary. The active claim/handoff is #2319. The refreshed overlap check at 2026-10-17 22:14 UTC covered 249 open PRs and 2,172 Discussion records with complete pagination and no warnings. It found the PR3301 handoff and adjacent merged PR3330, which changes an opt-in schedule but leaves the fitted-native contract unchanged; no separate caller/callee bridge claim appeared in those fetched records. The overlap scan is not a novelty certificate.

Validation

On CPython 3.12.15, the registered command python3.12 scripts/research_package.py --package research/high-cube-b1-fit-bridge passes in normal and optimized modes. It checks source pins and the literal route/adapter/wrapper binding, 972 finite symbolic axis/parameter instances, one Mersenne-127 prime-domain witness and seven rejection controls. The universal exponent and volume identity are proved algebraically in PROOF.md; finite instances are corroboration, not the proof. No fitted payload was executed.

The metadata check passes. scripts/check_research_commit.py --package research/high-cube-b1-fit-bridge reports PASS_RESEARCH_COMMIT_BYTES for 19 package/input files, and git diff origin/main...HEAD --check passes.

Credit

Preserves the source credit for Jose Manuel (jmbarrancoml; PR2915, PR2899, PR2234) and Krzysztof Wójt (PR3301). Prepared by OpenAI Codex (GPT-6) under user direction, with substantial AI assistance. This is author-checked work, not independent human or proof-assistant review.

Open next questions

The package lists the exact range, capacity, GL64 execution/formalization, and PR3330 schedule limits with a smallest follow-up and blocker for each. In particular, it does not establish the C0 premises, cover (q\le2^{80}) or composite bases, prove enclosing numeric backing/capacity, recover from interrupted calls, execute the fitted GL64 payload, audit PR3330's optimizer or prove a new multiplication bound.