DONE: critical-root adaptive gates and p7/p16 leaf bounds (#4532)

[dillona]

DONE: PR #4532, head 644607ba59ebe401ac7ecd627ae7f331f924d1b0, supplies a sufficient profile theorem for #4483’s adaptive compiler.

A moment crossing plus strict pointwise mirror slack implies integer height geometry and rational tail parameters. The tilted-mean gap follows from an integral identity, so it is not an extra hypothesis. The funded majorant works at the exact crossing exponent. At a fixed exponent with T/P >= 1, the proof also gives an exact one-scalar criterion for the two tail gates and ratio ordering, with a counterexample to weaker fixed-exponent tests.

The separate exact checker certifies the retained p7 and p16 roots and full critical-root bounds L(n) <= A n^theta (c+log n)^p, using p=1/10 and p=2/5 respectively, the predecessor’s height/base choices, and explicit revised covers. This is a conditional normalized leaf-count result; no new native word, paid invoice, κ or selected-frontier update.

Evidence: written proof with separate author-side AI reviews; registered Python 3.12 replay; 21 semantic rejections, exact arithmetic and symbolic integral controls; committed-byte/source-history checks; checked export and replay without Git under a network-denied policy. Source-corruption and underfunding mutants reject. Canonical main was refreshed at submission and remains f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc; final overlap covered 316 open PR bodies and 3,411 Discussion records with complete reported pagination. Scope limits are recorded in TASK.json.

The #4532 hosted run failed the same four pre-existing navigation tests (331 tests, 11 skipped), and package replay was skipped. An upstream navigation repair and hosted rerun remain necessary; local replay does not imply hosted CI success. Native all-column semantics, owned restoration, chronological widths/adapters, movement, precision, stock, tape costs, analytic transfer and recovery remain inherited obligations. Next useful work is a weaker boundary condition or actual physical-word constants; more root digits are not the missing result.

Credit zxv (#4436/#4483 and p7 source), Jacob Alan Sussman, Ryanson Jonathan, @1337isnot1337’s p7 lineage, Cinna Davis (#4470), Dugongue (#4479), and the retained native/outer contributors. Prepared by Dillon with substantial OpenAI Codex assistance; no formal or independent human verification.

{"schema":"integer-mult-coordination/v1","kind":"DONE","task":"uniform-transfer-audit","scope":"Critical-root adaptive gate criterion and funded p7/p16 leaf-count majorants","base":"f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/4532"}