[jmbarrancoml]

In PR3477, I chose the physical T74 root's internal width from precision p, even when its caller selected fewer bits. I now use the actual selected width g and prove the resulting source-relative bound

O(V g^.99827101 log p) time, O(V)+F_q space,
1 <= g <= floor(p^.997).

I preserve the normalized H0 endpoint, pointwise spectators, borrowed input, full-depth row stock and one final truncation. The theorem requires actual complete coefficient records with 2^(b(log2 p)^2) <= r and log2 r <= Bp, for fixed b,B>0, plus the retained O(p) descriptor, source-native, hosting and physical-refinement premises. The constants may depend on b,B,q and the finite source.

I bind PR3562's ordinary profile c=1/577 to the same physical cohort, change the stopping power from 1000 to 10^6, and retain the complete 2,394,506-child T74 invoice. The proof pays the deeper stop, reserved leaves and small-g fallback. I compare the copied transitions against their frozen predecessors and authenticate all 23 ordinary-backend files.

I also prove a single-bit exposure identity for a complete global tensor, with final permutation support at most 2g. Its global cost remains conditional on the richer paid support-router contract and retains polylog p. I supply finite algebra and a 16-record physical-root/reference-permutation composition. I do not supply an executable fast arbitrary-support router or a multiplication-exponent improvement.

I started from canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. I add one isolated package and leave the selected frontier unchanged. In the final overlap check at 07:18:53 UTC on 2026-10-18, I covered 314 open PRs and 2,436 Discussion records with complete pagination. I found no additional duplicate or objection beyond the credited work below. Canonical investigation.

Validation at 72df81b8cee17ffd990fc18b2d54024f65971556:

• I passed metadata/pin and committed-byte/source-history checks. I exported and checked the 24 committed package/input files, replayed all six declared commands outside Git with CPython 3.12.13 and -I -O -Werror -B, and verified that the 25 regular files including the receipt remained byte-identical. Export SHA256: 7eae80a477788a72899e0a7d1992f20cf82d58db1387e1b209911f32e77c090c.
• Six declared groups cover exact rational margins and negative rate controls; source/function binding; literal Count plans; 40 observed retuned native-selector calls; stopping/root/ownership endpoints; and source corruption controls. The native group also checks the whole production constructor with reduced binding/native substitutes and rejects a stale binding alias.
• Runtime fixtures use reduced guards and geometry. I do not execute the full production T74/O73 payload, GL64 construction or production binding initialization. I preserve the predecessor admission evidence and its qualifications.

In the first CI run, I passed science and source contracts, then hit the plan suite's 240-second timeout on Ubuntu. I retained its four full-field cases, reused the p=5,g=2 result for the old/new comparison, and allowed 300 seconds within the 1200-second total budget. I measured 75 seconds locally and 185.615 seconds on the hosted runner for the revised plan check. I passed CI run39108314551 on the current head with CPython 3.12.15, including all six registered groups and the unchanged-committed-input check.

Reproduce with Python 3.12 and the standard library:

python3.12 -B scripts/research_package.py --package research/t74-retuned-physical-layer
python3.12 -B scripts/check_research_commit.py --package research/t74-retuned-physical-layer --check-source-history

I retain Jose Manuel's PR3385/3477/3562, David Arias's PR2753 caller, Nick Petalas's PR2808/3493 wrappers, Adam Gall's PR2087 lifting, Marius-Paul Dumitrean/Dugongue and Jeremy Kothe's T74 word/profile, and Vlado Vojdanovski's PR1673 router/tensor arguments. The source exports preserve the remaining notices.

Hiroki Kumazaki's concurrent PR3576, head 1630afea0fc1083717b5b2799b8de7a819a6ea02, retunes the older root and stop. I credit that shared factory/rate step and adapt his binding-module namespace and constructor checks. Nick Petalas's PR3581, head 282915e57cf71d7a6f0087fbb6ae03345a0b33d4, proves a Theta(Vg) barrier for a restricted materialized B1-only exposure adapter. I preserve that boundary and require the richer conditional router.

I leave fast support-router implementation, missing-record placement, larger-group/outer error and packing integration, and independent scientific review open. Jose Manuel (jmbarrancoml), with substantial OpenAI Codex assistance in proof, implementation, verification and source analysis. Apache-2.0.