Scoped negative result: classify the E8 rank-five boundary at 36 punctures

[mightyOil]

Scoped negative result; no new κ or supplier. PR631 leaves 36 E8 root-line punctures as the first boundary where its coarse reader-rank floor no longer excludes a better star copy ratio. This closes that exact boundary and extends its at-most-35 exclusion to at most 36 punctures.

There are exactly 7,560 36-puncture sets admitting a rank-five reader, all in one Weyl orbit. The complete standard-flat equality census has two representatives. Each has reader-rank histogram {5:1,7:42,8:468}; its cheap readers span only eight binary dimensions, forcing the exact optimum basis weights 5,7,7,7,7,7,7,7,8 and cost 62 on 84 live ports. Every other 36-puncture set costs at least 54. Both ratios exceed the inherited 63/111 benchmark. The overall minimum cost among all 36-puncture sets is not claimed.

Only research/e8-rank5-boundary/ is added: proof, explicit certificates, source pins, unmodified predecessor sources, independent checker, mutation tests, attribution and the local sprint claim. Existing generators, upstream/ and the selected frontier are unchanged.

python3 -B research/e8-rank5-boundary/verify.py

Expected: PASS_E8_RANK5_BOUNDARY: 28616 rank-five pairs; 2 representatives; 7560 conjugate punctures; cost 62; 72 restorations; 5 negative controls; no new kappa.

Validation passed on macOS/CPython 3.14.7 and 3.11.15, including isolated optimized execution. A separate Fraction-RREF/span-membership implementation matches both complete 511-reader rank tables and the equality census. The primary verifier checks the full 7,560-mask orbit. All 72 single-port restorations, the tempting cost-61 nonspanning decoder, geometry/decoder/flat controls, receipt/source mutation tests, relocated byte-identical regeneration, the retained PR631 controls and make selected-record-check pass. The full repository suite, selected cold replay, hosted CI and proof-assistant verification are not claimed.

Base: f567884aeb8851b6e794af1184119a3bfbe1e631. Assignment seed 46, structural decoder research. Final overlap inventory: 667 open PRs through #874; main and the pinned PR631 head were unchanged. No pinned coordination issue existed, so the claim/result is local. New #868 concerns Gaussian all-clique bounds; this note concerns root-only E8 rank-five equality punctures.

Credit Chi Zhao's PR631, pinned at fb893b5ee1317c2da3b297e6fe78eca0857d1a76, for the all-flat reduction, sharp single-reader thresholds and earlier theorem; Joel Pulikkan / GamingPuzzled's PR620 for the star model and basis formulation; and DreamingOfClouds' PR595/PR602, eumemic's PR543 and their predecessors for context. This adds the equality classification, exact orbit/invoice and the 36-puncture exclusion.

Scope remains additive star copy-rank accounting. General pairing-rank decoders, non-root ports, 37+ punctures, helper savings and changed geometry are outside the new theorem. All-size/compiler, hosting, precision/tape and analytic obligations remain inherited. Prepared by Philipp (@mightyOil) with substantial OpenAI Codex assistance, including independent AI-assisted computation and proof review. Apache-2.0; no independent human review claimed.