Research: one-sided E8 mask rigidity on 1,373 punctured units (no new kappa)

[mightyOil]

Change and mathematical scope

Research note / scoped negative result; no new kappa or supplier. A decoder that is correct only on the even-inner-product mask already has the full all-pairs product if one factor lies in the live E8 root-coordinate column space. The other factor is unrestricted, and the term count is arbitrary. Diagonals and ordinary complex transpose are essential.

This covers P112, all 112 one-line P111 punctures, and all 1260 frame-pair P104 punctures. An elementary covariance/Bessel argument also covers deletions contained in at most eight orthogonal sets; that larger family is proved parametrically, not enumerated. Consequently mask relaxation alone offers no copied-information saving in this class. Unrestricted masked factors, better all-pairs decoders and physical supplier costs remain open.

Only research/complex-masked-rigidity-seed28/ is added. Start with its README.md and PROOF.md. The selected frontier, frozen inputs and upstream/ are unchanged.

Task and overlap

OS seed 28, complex-supplier track; exact base 1b59b624d21924f8e3537cdc1ac52d3be6eda2fe. CLAIM.md records the three candidates and bounded investigation; SOURCES.json pins predecessor heads and source hashes.

This addresses a restricted part of the masked-identity opening explicitly left by #968 and #1077. Concurrent #1180 instead extends the all-pairs cost floor with both factors root-linear and explicitly excludes masked identities. Its proof/README were inspected at the recorded head; its new theorem is not imported or certified here. The similar cancellation fixture is credited as a shared scope control. Final metadata inspection covered 798 open PRs and current discussion claims.

Validation

python3 -I -B research/complex-masked-rigidity-seed28/verify.py

Expected: PASS_ONE_SIDED_MASK_RIGIDITY_S28 sets=1373 local_spans=143584 controls=7.

Passed on macOS arm64 / CPython 3.14.7, also under -O:

• 7744 exact covariance entries and a 12544-entry nine-term positive example with a non-root-linear opposite factor.
• Independently implemented enumeration and exact minors covering all 143584 local spans across 1373 domains; 122 reused minors, nonzero integer determinants certified modulo 3.
• Seven main semantic controls, three oracle controls, and rejection of a corrupted saved witness. Separate AI review cross-checked every minor using integer Bareiss elimination and all coverage assignments.
• All five selected-record integrity tests and git diff --check.

One local replay took 0.43 seconds. No full selected-supplier cold replay, native admission, hosted Linux CI or formal multiplication theorem is claimed. VALIDATION.md records the boundary.

Credit

DreamingOfClouds (#717/#595), themilkman216 (#968), woklerx (#1077 and complementary #1180), Joel Pulikkan / GamingPuzzled (#620), icekylinx's P112 construction, and the selected supplier lineage retain attribution. Prepared for Philipp / @mightyOil with substantial OpenAI Codex assistance, including separate AI implementation and review; no independent human review claimed. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 640b43bb13d3d476a2d83b74ef0d33f14d1b5711.

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

Reviewed scope: One root-linear factor forces E8 masked exactness to full exactness via local covariance/span identities; arbitrary masked factors remain outside the theorem.

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.