[DLamdata]

Answers the scoped audit question in #6110 by specializing the retained support-local transfer proofs to the selected construction in #6030. No new κ or selected-record change.

Result

• Correct recurrence: use the compiled uniform supplier, rather than the raw mixed P104 histogram.
• Exact moment bounds:
  $$
  \mu_{1-b}<2^{-47005},
  \qquad
  \mu_{1-a}<2^{-94010}.
  $$
• Current BIT stock: use atom $1/250$, replacing the historical $0.003$ in this specialization. An explicit symbolic stock threshold has logarithmic degree $250/83$.
• Complete conditional cost argument: weighted-tree and separately derived induction proofs cover integer floors, remainders, stopped leaves, deferred phases and per-phase padding deletion.

The generic deferral method is already present in #1673 and the selected finite-template/outer-transfer sources. This audit credits those proofs and supplies the current parameter substitution; it does not claim a new deferral method.

Research package · Proof · Canonical Discussion

Verification

python -B scripts/research_package.py --package research/p104-6030-deferred-layer

All four normal/optimized checks pass on CPython 3.12.14:

Check	Coverage
Primary verifier	48 threshold fixtures, 528 padding fixtures, 12 rejection controls
Independent verifier	4,152 recursion widths, 255 deferred schedules, 3 parameter rejection controls
Publication checks	Committed bytes, source history, 26-file export and integrity
Portable replay	Both verifiers pass normally and optimized in a read-only Git-free export with empty PATH; all bytes remain unchanged

Two separate Codex agents independently derived or reviewed the result. No unresolved blocking issue remained. See validation and logs and internal review. These are local results; hosted CI is separate.

Scope and next step

The compiler bill, physical node costs, complete-field interface, BIT stock law and exact return/padding deletion remain premises. The stock threshold depends on unmaterialized fixed constants. All five framework assumptions remain; no full selected replay, materialized rounded multiplier, human review or proof-kernel certification is claimed.

The next useful task is to audit an actual emitted child/row boundary against those physical contracts. A future maintainer review can also cite the already-selected transfer sources explicitly.

Source pins and credit

• Base / latest checked upstream: 721c03822c421b7f7fcbb2598993b947c4d88419
• Contribution: 643891684cf7890e22f4256ae22ae441040d10cd
• Motivating Bind PR6030's remaining 30 strict and 4 functional outer checks to written sources; stopped-recursion theorem's 1−c term has no row (no new κ) #6110 head: 7f82486e987e556a221085092d8f7aff271ecb35

CI note: the shared planning job fails two existing selected-result navigation checks, matching the issue addressed by #6050. Consequently, this package's hosted replay was skipped.

All documented local normal/optimized, committed-byte, source-history and portable-export checks passed. Hosted scientific replay remains outstanding.

Run: https://github.com/CrocSwap/integer-mult-bounds/actions/runs/40676258936

Prepared for DLamdata with substantial OpenAI Codex assistance. Retain DreamingOfClouds, Ali Romman, Vlado Vojdanovski, philippeVV, zxv, Jacob Alan Sussman, Cao Yifan, Douglas Colkitt, JoyboyBrian, JosieElliston and the source-specific predecessor credits detailed in the package. Apache-2.0.