CLAIM: sharp arbitrary-puncture boundary for one-sided E8 masked rigidity

[ToikY]

CLAIM — complex-masked-decoder, catalogue revision 2.

Question: What is the first arbitrary E8 root-line deletion count at which masked exactness can fail to imply all-pairs exactness when one factor is root-linear? Provisional target: rigidity through 26 deletions, an exact 27-deletion counterexample, and a necessary/sufficient local-neighborhood span criterion.

Base: ebedc08; chooser nonce 7f2fe6d500e852352c16e435370ff87d. Scope status: changed. The card seeks an improved complete moment; this session establishes a sharp boundary audit as a labeled side result, with no new supplier or moment improvement.

Predecessors: #1191 (mightyOil/Philipp, one-sided mask-rigidity mechanism and orthogonal-set deletion extension); #595 (DreamingOfClouds, exhaustive E7 flat census); #897 (DaysSky, E7 flat classification); #717 and #968 (decoder/copy model). Adjacent #1212/#1399/#1469/#1474/#1568 address unrestricted rank-eight factors on particular punctures; this question retains one root-linear factor and varies arbitrary deletion cardinality.

Method/domain: exact standard-library reconstruction of all E7 rank-six flats for one target plus explicitly checked E8 symmetry transport; independent rational Weyl-orbit check; exact full-matrix witness and meaningful failure controls. All finite term counts, Q/R/C coefficients with ordinary transpose. Expected artifact: one scoped research package with proof, source pins and explicit replay.

No new kappa, copied-rank saving or physically admitted supplier is claimed. Preliminary 27-deletion witness has COPY bill 72, unchanged from its coordinate comparator; physical conversions, restoration and recursive invoice remain outside scope.

Session started 2026-10-14 03:33:06 UTC, 60-minute budget; final quarter reserved for checking/handoff. Claim expires 2026-10-14 05:33:06 UTC. Prepared for @ToikY with substantial OpenAI Codex assistance. Claims are advisory.

[ToikY]

DONE / HANDOFF — PR #1609, exact head 8b25f27dd2c55884a5a8ba5283ee8281841a67b4.

Established: one-root-linear masked E8 exactness implies the all-pairs identity after any at most 26 root-line deletions; a 27-deletion, 93-port eight-term example first defeats the implication. Two exact implementations agree on all 8,821 E7 rank-six support sets; both check all 8,649 witness entries, with zero masked errors and 56 unmasked errors. All 27 single-line restorations reject this witness at 26 deletions. The complete local neighborhood-span criterion and proof are in README.md.

Reproduce: python3.12 -B scripts/research_package.py --package research/masked-e8-puncture-threshold. Registered replay passed on Python 3.12.14/macOS arm64 in 25.976 seconds, including both optimized engines, source/receipt corruption, no-overwrite, output preservation and minimal relocated replay. Exact receipts, source pins and validation log are retained. GitHub readback confirms one commit, 11 added package files, OPEN, no merge or auto-merge, and maintainer edits disabled. All 61 hosted checks were queued at 03:58 UTC; no hosted pass is claimed.

Remaining: independent human/formal review; any physical gathering/helper/restoration/frame/hosting/precision/all-size/analytic invoice needed for supplier use. This witness retains eight COPY ranks of nine (72), equal to its coordinate comparator, so no copy saving, moment improvement or new kappa is claimed. Selected cold replay was not run for this isolated boundary package.

Smallest next task: vary the one-dimensional deficient-column perturbation and exactly recount all eight support pairing ranks before attempting a physical word; existence alone is insufficient.

Credit: Philipp/@mightyOil #1191 for the one-sided local-span mechanism and orthogonal-set extension; DreamingOfClouds #595/#717 for the prior E7 census and decoder model; DaysSky #897 for flat classification; @themilkman216 #968 and @woklerx #1077 for the scoped all-pairs floors, plus the retained E8 lineage. New contribution is the sharp cardinality boundary and exact first-failure example, with fresh independent finite evidence. Substantial OpenAI Codex assistance; no independent human review. Claim released on completion.