[JoyboyBrian]

Answers Nick Petalas's PR #4828 Open next question2 for Dugongue's actual #4743 full-input ports: the sharp Euclidean endpoint constant does not determine how initial quantization and each ordered paid-call defect reach the outputs. This package preserves the literal monomial phases and all two/three forward/reverse calls, including the third forward defect's post-call monomial.

For every positive tensor width f, let L=2^(f/2). Under explicit independent complex-coordinate defects of size rho on each completed call's actual input and exact free grid arithmetic, the sharp complete error factors are:

Schedule	Sharp factor
Forward2	3L²+4L+1
Forward3	2L³+4L²+2L+1
Reverse2	L+4
Reverse3	L²+L+4

The all-width proof uses exact flat base-row norms and coherent row-zero overlaps preserved under individual tensor products. Independent defect phases attain the sums. Sufficient fractional accuracy requests become P+f+3, P+ceil(3f/2)+3, P+ceil(f/2)+2 and P+f+2 respectively. These are external completed-call accuracy contracts, not measured word/time savings from a new Gaussian implementation, and their abstract sharp defects need not be actual errors generated by one quantizer.

Validation: registered warning-strict CPython3.12 normal/optimized replay;12width1/2/3 cases,54exact perturbed dirty schedules and144independent impulse columns; six phase/order/cap controls;13-file source-history/committed-byte preflight; official export and Git-free cold replays; source/bool-int receipt corruption rejection. Hosted CI is unverified when opening this PR.

Gaussian internal-prefix/error guarantees and costs, physical address/workspace execution, recursive substitution and complete supplier/outer admission remain prerequisites. Paid counts, selected frontier andκ are unchanged. The package gives a scoped proof with finite source-bound corroboration and a concrete implementation next question.

Canonical record: #1166 (comment). Base bee95ce88f9f19802f0613f92838895cd0e14a1f, priority7. Initial overlap covered310openPRs,4096Discussion records and6690base notes with reported complete pagination/inventory; arbitrary diffs and unpublished work remain outside coverage. Submission refresh is recorded separately.

Credit Nick Petalas #4828, Dugongue #4743, Yiyang/Lyy-iiis #4710, lee-phys #4688, Jacob Alan Sussman #4628, eumemic, Swapnil Jain and all retained notices. Prepared by JoyboyBrian with substantial OpenAI Codex assistance, Apache-2.0; no independent human or formal-kernel acceptance claimed.

Submission refresh (2026-10-23 06:22–06:24 UTC): canonical main f259dabc7d70e0db8d6d36bfda888f008bbfecc1 was fetched; guidance, selected record and scientific input bytes remain unchanged. Pinned scientific base bee95ce88f9f19802f0613f92838895cd0e14a1f is retained; new package paths are disjoint from upstream changes. Complete remote coverage: 304 open PRs,4,114 Discussion records; local coverage: all6,690 notes at the scientific base. Coverage is advisory, not novelty proof.