[ToikY]

External written review of alephnan PR #6713 at cd666f05c4e9006025b634687cc493911c8371c8: PROOF sections 2–8 and LOCAL_LIMIT sections 8–9, with the exact canonical #6329 mirror/conservation predecessor. No analytic propagation gap was found under the named finite identities, numerical margin premises and uniform interval estimate. The source already proves this theorem; this adds external review, not a new exponent or onset.

The reviewed conclusion for the exact default-height raw-p7 scalar recurrence is:

s=99739/100000; G0=2*2^(10^12)+2; N0=121*5^G0,
L(n)<=N0^(1-s)*n^s for every integer n>=1.

The review derives the J/A=1-q normalization and full leaf coefficient; half-open Stieltjes bounds; the first 3001 mixed layers; complete middle layers and missing infinite geometric weight; zero-paid-letter end layers without LLT; both the atomic leaf tail and Lebesgue tail; every floor offset; and conservation-to-linear-to-power strong induction. Total loss is below 1564.2010002<1600, so the inherited D_full>40000 gives D_N/F_G>38400>0. Three component derivations and an assembled adversarial review display the arguments and limits. Agreement between review roles is not substituted for proof.

A short hand certificate supplies the tail comparisons: exp(3)>89641/4480>20 and exp(3/2)>5/2 imply exp(36)>10^15 and exp(37.5)>10^16. Written controls expose omitted normalization/geometric weight, a second terminal cap, lost endpoint/Stieltjes terms, and invalid global monotonicity or shift-uniform flattening. For example, the inherited rule at N=121 retains 448 terminal-rank-48 exits despite a base cap of one. These are unexecuted hand arguments, not numerical tests or counterexamples to the stated theorem.

Inherited premises remain explicit: actual Flow/mirror/conservation/census/rank realization; finite q/J/tau/c_sigma and complete margin certification; the earlier uniform local-limit estimate and classical approximation. PRs #6723 and #6728 cover their own H/tilt implications and do not admit every other premise. No scientific source program/checker was read, imported or run; no new scientific program, test, numerical experiment, convolution or proof kernel was executed. No enormous onset or flow was materialized. There is no scientific VERIFY manifest; hosted scientific replay must be reported as SKIPPED.

Integrity checks passed: five exact inert Git/SHA source pins; 16 frozen committed files, all mode 100644; the exact parent, scoped diff and unchanged selected record; individual resident-Git byte comparison and a separate peer audit. The first Git archive attempt failed on an unavailable promisor object and remains recorded. A manual scoped tar built from individually verified committed bytes passed all 16 file/mode/hash readbacks and a separate archive audit. This is not an official/Git-archive export pass. Frozen mathematical and source bytes remain unchanged. Original hosted run41945650520, attempt 1, passed 711 repository helper tests with 24 platform skips. Scientific replay was SKIPPED: zero registered scientific commands. Synthetic checkout 8d036374 has exactly the published 4921aa69 tree and canonical/public parents. Completed logs are retained once; no rerun. A control-only pass is not mathematical or proof-kernel acceptance.

Task uniform-transfer-audit is explicitly changed to this historical scalar caller; its selected-assumption gate remains unmet. Seed 960520eda05a1c8521932977d8238257, scope key cdee6027333168fe48af. The proposition differs from #6723's local-limit and #6728's root audit. Fresh main 7c49fe32, all eight guidance bindings, revision 8, selected #6030, source head and empty source feedback are unchanged. The refresh covered 679 distinct open bodies non-atomically, complete targeted indexed all-state sets, sparse overlap and live Hub/start. Middle Discussions, closed-corpus, arbitrary-diff and hidden-work coverage remain incomplete. Advance claim. Review frozen at 00:55:40 UTC November 5; minimum finish 01:10:40 after 15 minutes of verification; session cap 01:40:59.

Remaining work: independently admit the finite census/source-to-recurrence identities, bind all numerical premises to an intended caller, and supply the physical/native/owned-erasure/compiler/precision/stock/tape/recovery/full-invoice/outer obligations. All five selected assumptions remain. The smallest next task checks one exact finite identity or binds its actual physical caller; neither follows from this conditional all-size review. No paid profile, kappa, frontier, adoption or merge changes.

Credit: alephnan #6713; CubeJerry #6329; zxv #4436/#4483; Ryanson Jonathan/pinterbanget #4459/#4467 and mirror lineage; DLamdata #6118; Nick Petalas #6125/#6128; Cinna Davis/1337isnot1337; Jacob Alan Sussman and retained contributors; the scoped #6723/#6728 audits. Beurling, Selberg, Vaaler and Shou retain classical analytic credit; Stieltjes integration, tails and induction are classical. ToikY with substantial OpenAI Codex assistance and separate source-aware AI derivation/review roles, Apache-2.0. Prior review exposure is disclosed; no human or proof-kernel acceptance. Maintainer edits and auto-merge are disabled. No merge or frontier change.