[ToikY]

The retuned ordinary wrapper has a source-bound scalar decision gap behind its conservative fit estimate. This package classifies its complete fits/fallback decision, under the explicit Count scalar abstraction, for every integer original width e>=1 and every prime q>2^80.

With R=269241600, P(q)=product(i=1..64,1-q^-i) and m(q)=ceil(log_q(R^19 P(q)^19)), the decision is exactly e>=311297+2m(q), where m=1..7. All seven cutoff values311299,311301,…,311311 are attained by primes with exact half-power/order certificates. The proof covers every lower-width rejection, the second body guard, and the infinite tail across later width/depth jumps.

Predecessor boundary: Aakash (@aakashthakkar)/Codex already proved the older17/10000 profile's uniform311311 borrowing bound and supplied its proof method and selected-prime witness. Those are credited, not claimed as new. The new coverage is the complete retuned selector classification and seven prime classes. The fixed production prime is class7; there is no selected-exponent/frontier change.

Validation:12 exact current-main inputs; all36 backend archive members authenticated and encoded/ordinary bytes matched; complete source declaration/AST contracts with16 version-binding controls; seven exact prime/stock certificates and21 behavioral selector controls; a separate bottom-up census of 7,340,032 decisions; full typed regenerated binding/primary/oracle payload comparison; normal/optimized isolated warning-strict Python3.12 replay and Git-free committed exports. No predecessor executable, active loader, native factory or GL64 catalogue runs. The written proof supplies the universal quantifiers; the finite census is separate evidence.

Count/Counter arithmetic and lifetime semantics, all-q native denominator/chart hypotheses, SOURCE/history/restoration, physical stock/cleanup/time/space, complete tau/beta invoices and the multiplication join remain inherited or UNKNOWN. No native supplier, human or proof-kernel acceptance is claimed.

Credit: Aakash/Codex's bit2234-stock-threshold theorem; Jose Manuel/#2234/#2899/#3562/#3599 and retained source lineage; Nick Petalas/#2808; Ryanson Jonathan (pinterbanget)/#4332/#4340; Ross Richardson/#4338. New work by ToikY with substantial OpenAI Codex assistance and separate implementation/proof/review contexts.

Canonical claim: #4352 . Takes one narrow source-fit premise from handoff1166#19094382; uniform-transfer-audit is explicitly refined from #4100. Current-main priority7 and live overlap checked. Maintainer edits disabled; no merge requested.