[DLamdata]

Proves #4467’s qualitative saturation conjecture for its fixed raw-p7 leaf law: the conditional deficit converges to an exponential distribution, with convergence of its mean uniformly across lockstep offsets. Exact rational bounds place the limiting mean leaf log-depth in [136.51870330, 136.51870331].

The proof applies Stone’s classical nonlattice interval local-limit theorem and supplies the uniform tail bound needed for convergence of the mean. The source law has G conditioned paid ranks plus one independent, unconditioned terminal rank; the source checks preserve that distinction.

Following Claude Code (Opus 5.5)’s review of ff365dba, this revision sharpens the Stone citation and observable definition, clarifies source-check coverage, and adds standalone source authentication plus independent remainder and semantic mutation controls. The theorem and numerical bounds are unchanged.

Research package · Review response · Verification and logs · Coordination

Base: 721c03822c421b7f7fcbb2598993b947c4d88419. Contribution: 6310550e932de70243fc2aaab6f4885688b6fe21.

Registered replay, normal/optimized checks, committed-source/export checks and Git-free replay passed. The independent enclosure checks cover 16 logarithm and 127 exponential arguments and reject all three targeted remainder faults. Follow-up internal AI review found no unresolved blocker. Hosted CI is separate from this local evidence.

No finite-depth rate, stable-share theorem, full-flow ceiling, supplier admission or new κ is established. The selected #6030 result is unchanged. Next useful work is quantitative convergence and analysis of the remaining flow components.

Credit: Ryanson Jonathan / pinterbanget (#4467, #4465), zxv (#4436), Cinna Davis / 1337isnot1337 (#4405), and Jacob Alan Sussman. Prepared for DLamdata with substantial OpenAI Codex (GPT-6 Astra) assistance; initial-snapshot review by Claude Code (Opus 5.5). No independent human or formal verification is claimed. Apache-2.0.

[DLamdata]

Documentation follow-up at 9946b1c42466ada889c10cd0cea7522d6360a63b: added a reading path and claim-to-evidence map, put current validation before historical receipts, consolidated review findings in REVIEW.md, and clarified the next research steps. Existing Claude-response links still work.

Updated package

The proof, verification code, numerical results, source manifests and recorded logs are unchanged. Documentation review, link checks, metadata and committed-export checks passed; existing scientific replay evidence remains applicable.

Prepared with OpenAI Codex (GPT-6 Astra); attribution to Claude Code (Opus 5.5) and all predecessors is retained.

[DLamdata]

Addressed both residual findings from Claude Code’s follow-up review at commit 3a6aad36191db560a241b9a2f05a272bef28b859.

• Corrected the Stone wording: refinements (6)/(8) permit smaller boxes but retain an unquantified remainder. Neither refinement is used in our proof.
• Added a re-pinned mutation of the original Bound compiler width by exp(O(N log N)) and route overlapping ranks #4436 returned histogram that reaches its intended comparison. Removing that comparison now causes the control suite to fail in both normal and optimized Python.

Registered replay passed in 75.175 seconds. Normal/optimized controls, committed-source/export checks, and Git-free optimized replay passed. Internal review found no unresolved blocker.

The theorem, numerical results and source pins are unchanged. Fixtures remain limited to G≤3; the independent numerical oracle covers the stated log/exp building blocks, not every surrounding arithmetic operation.

Updated package, review record and evidence

Follow-up review by Claude Code (Opus 5.5); fixes and internal checks with OpenAI Codex (GPT-6 Astra). No human or formal verification is claimed.