Scoped negative result: sharp global-star punctures and 67 attaining patterns

[thakrarsagar]

Result

Scoped negative result with exact attaining decoders; no new kappa. For every power-of-two k >= 2 with p = k+1 signed coordinate pairs, arbitrary off-target proper stars require exactly three deleted ports to decode one retained target. This extends PR #669's target-local puncture theorem into a class it explicitly leaves open.

For k=4,p=5, an algebraic dimension argument characterizes the full 65-dimensional decoder space. A fixed target has exactly 67 minimum puncture patterns: 35 affine planes inside its sign cube and 32 pairs of edges across two cubes. Only four admit target-local decoders. The package gives every literal decoder plus a three-star off-target example that can be checked by hand.

Only research/global-star-puncture/ is added. The proof, standard-library checker, deterministic certificates, source pins, local claim and attribution are included. No existing supplier, generator, assembly, selected-frontier pointer or upstream/ file changes.

Reproduce

Python 3.10+ from the repository root:

python3 -I -B research/global-star-puncture/verify.py

Expected:

PASS_GLOBAL_STAR_PUNCTURE threshold=3 supports=82240 witnesses=67 local=4 dual_rank=15 controls=7 no_new_kappa

The replay enumerates all 82,240 exact supports through size four containing the recorded target, checks primal and dual membership independently, and evaluates all 67 decoder identities at every surviving source. Seven controls cover corrupted duals, forbidden singletons, invalid decoders and punctures, and the non-power-of-two hypothesis boundary. It compares the complete regenerated receipt with the committed JSON.

Validation passed on Python 3.14.8, 3.12.15 and 3.11.15, including isolated optimized execution. A separate Codex agent checked the proof, source pins and coverage and replayed the certificates. make selected-record-check and staged whitespace validation pass. The expensive repository-wide suite, selected supplier cold replay, Lean and remote CI were not run; no existing construction changes. Finite replay is not a formal verification of the multiplication theorem.

Scope and provenance

• Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60; OS seed 40, structural decoder track. Sources have SHA-256 and Git-blob pins.
• Predecessor Research: exact star-decoder hierarchies, target budgets, and COPY bounds #669: 308f1e6ec3bb0b6ec0584cf7bfe219addc219b1e, Sam Sung / @the-missionary-company. Credit Joel Pulikkan / GamingPuzzled's The paired-cube decoder does not extend to 4-dimensional ports: a Lucas-parity obstruction (no new κ) #231 symmetric parity result and the earlier paired-cube work of icekylinx and eumemic. No predecessor implementation is imported.
• Final metadata scan covered 541 open PRs through Research: share JP8 cleanup coefficient work, saving 19,688 primitives (no new kappa) #722. Research: exact star-decoder hierarchies, target budgets, and COPY bounds #669 is the precise predecessor; Prove E8 star-decoder puncture thresholds through 35 deleted lines #631/Scoped negative result: minimal E8 mixed-port extension is saturated #715 concern E8 geometry, Scoped negative result: asymmetric Hurwitz E8 copy cost is exactly 10 #703 quaternionic geometry, and Format limits part 2 (no κ claim): erratum to #595, exact invoice prices, frontier-word censuses, decoder floors, spec requirements, centre and fragmentation walls #717 complex decoder floors. None supplies this global puncture result. Main and Research: exact star-decoder hierarchies, target budgets, and COPY bounds #669 were unchanged. No pinned coordination issue exists, so the claim and result update are local.
• The result is for one retained target in the stated linear decoder model. It does not provide an all-target supplier, frames, dirty restoration, a paid recurrence, or a sharp global threshold for p>k+1.
• The selected conditional kappa remains 51110230636731/31250000000000000. Its inherited all-size, realization, hosting, precision/tape and analytic obligations remain.
• Prepared by Sagar Thakrar / @thakrarsagar, with substantial OpenAI Codex assistance in research, proof development, implementation, verification and documentation. Apache-2.0. No independent human review is claimed.

[Mister-Meeseeks]

100-PR batch review at 6eadc4eb4ebc355b13fa36a3138d97a583ea7f37.

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

Reviewed scope: Power-of-two k, p=k+1: three global-star punctures are necessary and sufficient; all 67 minimum patterns at k=4 checked.

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.