Scoped negative result: asymmetric Hurwitz E8 copy cost is exactly 10

[Mister-Meeseeks]

Scoped negative result; no new kappa or physical supplier.

PR #620 leaves open the asymmetric copy cost for its ten quaternionic E8 lines. This contribution proves that the minimum is exactly 10 quaternionic rank units (40 rational rank units) for every fitting decoder matrix, with arbitrarily many scalar binary totals. The proof averages rank inequalities over the 32 choices of one line from each orthogonal pair. It does not assume symmetric decoding or full-rank totals and does not rely on the predecessor's unfinished SAT run.

Every one of the 1,024 fitting matrices, including 992 nonsymmetric matrices, has an attaining cost-ten row decomposition. Under the same rank-four Dfc accounting as #620/#595, even the optimistic copy budget gives D/T <= (s-1)*40 - s*40 = -40 for every positive stage count. This excludes this particular mechanism before adding helper, source-access, restoration or recursive costs. Other geometries, fitting patterns, vector-valued totals and stage formats remain outside scope.

Changes are confined to research/hurwitz-asymmetric-copy-floor/: the proof, portable verifier, deterministic receipt, source pins, local sprint claim, validation record and attribution. No existing file, upstream/, or selected-frontier pointer changes.

Reproduce from the repository root (Python 3.10+, standard library):

python3 -B research/hurwitz-asymmetric-copy-floor/verify.py

Expected: PASS_HURWITZ_ASYMMETRIC_COPY_FLOOR: cost 10; 1048576 support pairs; 1024 decoders; 8 negative controls.

Validation covers all 240 roots, 45 two-line spans, 3,025 Gram blocks using two independent exact rational elimination implementations, 1,048,576 support pairs, 32 transversals and 1,024 fitting matrices. All eight negative controls and both positive controls run by default. Python 3.14.6 and 3.12.8 pass, including isolated optimized execution. A relocated minimal-input replay passes; modified source bytes and a corrupted result receipt are rejected. Selected-record integrity, package links and staged whitespace pass. The unchanged expensive repository-wide and selected cold-replay suites were not repeated. No Linux CI pass or formal verification of the full multiplication theorem is claimed.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Assignment seed 49, structural decoder research. Main is unchanged after the final fetch; metadata was refreshed through #700 (520 open PRs). No pinned coordination issue exists, so the claim and one result update are local. New #697 concerns source scheduling for a different complex E8 supplier. The selected accepted conditional kappa remains 51110230636731/31250000000000000.

Predecessor: Joel Pulikkan / GamingPuzzled's #620, retained head 419c7374c3bf5f2eee28f08b1e50c1d57934081c; current open head e9cf03bbdf7094b5a83f6dbd1d74bfd77a05fb87. Its four relevant extension-ring files match the retained source bytes. The geometry, symmetric upper bound, exact asymmetric formulation and open question belong to that work. The new contribution is the weighted rank proof and independent portable replay. The package explicitly distinguishes the unfinished run recorded in its report from the stronger wording in its script docstring. DreamingOfClouds' #446/#595 accounting is credited and its use is conditional.

Prepared by Douglas R. Colkitt (@Mister-Meeseeks) with substantial OpenAI Codex assistance in proof development, implementation, verification and documentation. Apache-2.0. No independent human review is claimed.

[Mister-Meeseeks]

100-PR batch review at 358383e2f1b0f292d4d6eb897c06fd8558a4f5e6.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Hurwitz scalar-total copied-rank optimum 10 quaternionic / 40 rational, from weighted transversal inequalities; declared per-total pricing only.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.