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Research: sharp 27-deletion boundary for one-sided E8 masked rigidity - #1609
Mister-Meeseeks merged 1 commit into
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Scoped boundary theorem and independently replayed exact witness; no new kappa. Prepared with substantial OpenAI Codex assistance.
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Batch review at Merged to Reviewed scope: Complete E7 root-flat closure census and a certified minor bound prove the sharp 26/27 deletion threshold for one-sided root-linear masked rigidity. The explicit first failure preserves the old COPY72 bill; unrestricted factors and supplier savings are not claimed. 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. |
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Change and mathematical scope
One-sided E8 masked exactness has a sharp arbitrary-deletion boundary: with one root-linear factor, it forces all-pairs exactness through 26 deleted root lines, while an exact eight-term 27-deletion counterexample exists. The package also proves the necessary/sufficient neighborhood-span criterion for full-rank live roots. The implication covers all finite term counts and Q/R/C coefficients with ordinary transpose.
Only
research/masked-e8-puncture-threshold/is added. Two separate implementations reconstruct all 8,821 E7 rank-six flats and agree on every support set. The primary closed-flat lattice supplies finite completeness; the independent rational Weyl/Bareiss method retains the standard parabolic-conjugacy premise. Both check all 8,649 witness entries (4,521 masked): zero masked errors, 56 unmasked errors, COPY72 equal to its coordinate comparator. All 27 one-line restorations reject this witness at 26 deletions.No new kappa, copied-rank saving, physical supplier or selected-frontier change is claimed. Gathering, helper endpoints, arbitrary-dirty restoration, frames, hosting, precision/tape, all-size/compiler realization, bit H1-H5 and analytic transfer remain obligations for supplier use.
Task and overlap
complex-masked-decoder, catalogue revision 2; scope explicitly changed to a boundary audit/side result. Baseebedc0895eb4c06725af020bc1af165722b0a3ce, nonce7f2fe6d500e852352c16e435370ff87d. Claim and handoff #1597.The precise delta over #1191 is the sharp deletion-cardinality boundary and first explicit one-sided mask-only example; its local spanning mechanism and orthogonal-set extension are credited as predecessor results. #1212/#1399/#1469/#1474/#1568 permit both factors outside the root space on particular punctures and have different hypotheses. #595/#897 supply the prior E7 census, independently reconstructed here.
Fresh overlap checked 733 unique open PR bodies including drafts at 03:53 UTC plus live relevant board/search results. Complete Discussion reply pagination was unavailable. Exact compared heads and coverage limits are in TASK/SOURCES; arbitrary code diffs were not searched and no universal novelty guarantee is claimed.
Validation
python3.12 -B scripts/research_package.py --package research/masked-e8-puncture-thresholdpasses on CPython 3.12.14, macOS arm64, in 25.976 seconds. Both optimized exact engines, 28 primary semantic controls, independent diagonal/affine controls, and six on-disk package test groups pass, including source/receipt corruption, no-overwrite, output preservation and minimal relocated replay. Metadata/pins and whitespace checks pass. VALIDATION.json and VALIDATION.txt retain the command, source hashes, receipts and output.The two frozen local implementation hashes and both exact receipt hashes are pinned in SOURCES.json. Selected record bytes remain unchanged. Selected cold replay, native/physical supplier admission, proof-assistant formalization and independent human review were not run. Hosted CI remains to be checked.
Credit
Philipp/@mightyOil (#1191) for one-sided rigidity and the local spanning argument; DreamingOfClouds (#595/#717) for the E7 census and masked decoder model; DaysSky (#897) for flat classification; @themilkman216 (#968) and @woklerx (#1077) for the scoped all-pairs floors; retained E8 lineage including icekylinx, Joel Pulikkan/GamingPuzzled and Douglas Colkitt. No predecessor executable is imported or frozen input modified.
Prepared for @ToikY with substantial OpenAI Codex assistance in mathematics, two implementations, review, tests and writing. Separate AI checks are not independent human review. Apache-2.0.
Open next questions
Vary the deficient-column perturbation and count all eight support pairing ranks against the coordinate comparator before attempting a physical word. This matters because the first-failure identity retains COPY72; a favorable complete physical invoice remains the blocker. The bounded next question is structured in TASK.json and explained in README.md.
Workflow feedback
Body-level overlap found the existing one-sided mechanism in #1191 and redirected the session to its sharp first-failure boundary. Task allocation alone did not establish novelty.