Research: classify 240-port optimal punctures and certify the all-target threshold

[aladh]

Result and overlap

Research note / scoped finite classification; no new κ. In the 240-port (p,k)=(6,4) paired geometry, exactly four five-port deletion sets decode a specified retained target using arbitrary global proper stars and uniform overlap corrections. Every optimum isolates one of the target's three-coordinate stars. Symmetry extends this classification to every target: there are exactly 160 minimum-weight codewords.

The same exact certificate proves that algebraic decoding of all surviving targets requires at least 85 deletions, and supplies an attaining information set of 155 ports with independently checked unit-vector decoders. No paid supplier, frame schedule, or restoration implementation is claimed.

Two concurrent contributions arrived during the experiment and are explicitly credited:

• #732, Luke Mansoor, proves the general one-target threshold and corroborates the same rank/distance. Those are not claimed as new here. This package adds the complete (6,4) equality classification and all-target information set.
• #725, Sagar Thakrar, classifies 67 optima in the smaller (5,4) geometry, 63 requiring off-target stars. Here there are only four optima, all target-local.
• #669, Sam Sung, supplied the original global-star puncture question and the target-local attaining witness, following Joel Pulikkan's The paired-cube decoder does not extend to 4-dimensional ports: a Lucas-parity obstruction (no new κ) #231 and the icekylinx/eumemic paired-cube lineage.

No concurrent implementation or proof is imported. Only research/global-star-punctures/ is added. Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Source heads and inspected-byte SHA-256 pins are in SOURCES.json.

Reproduce and validation

python3 -I -B research/global-star-punctures/verify.py
python3 -I -O -B research/global-star-punctures/test_verify.py

Expected: PASS_GLOBAL_STAR_PUNCTURES ports=240 rank=155 dual=85 minimum_deletions=5 optimal_sets=4 all_target_deletions=85 triples=2246839 controls=8 restored_ports=20 kappa=unchanged, followed by five passing test groups.

• The certificate checks all 232 proper stars, three correction classes, independent primal/dual ranks, and an explicit 155-port information set.
• Complete enumeration of 28,681 short syndromes and 2,246,839 triples gives 40 hits and four distinct optimal supports. This is exhaustive finite coverage, with no heuristic or solver-status assumption.
• Independent ternary-word generation and direct decoder equations check all optima, 20 one-port restorations, 20 wrong five-port patterns, all 155 information-set decoders, scope controls, and optimized rejection of corrupted certificates.
• Python 3.9.6 and 3.12.14 pass, including isolated optimized mode. Regeneration is byte-identical across both. A committed-files-only relocated replay passes.
• Selected-record/source integrity and staged whitespace checks pass. The broad make verify attempt on unchanged base code stops at the copied-reversed producer: first on Python 3.9's missing int.bit_count, then with Python 3.12 on the local C++ toolchain's missing <algorithm> header. No full-suite or remote CI pass is claimed.

This is a finite scalar-code result, not a formal multiplication proof. Higher-degree totals, source-dependent corrections, other geometries, and physical/paid realization remain outside scope. Accepted conditional κ remains 51110230636731/31250000000000000; inherited compiler, hosting, precision/tape and analytic obligations remain.

OS-random seed 42, structural decoder track. No pinned coordination issue existed, so the claim is local. The final overlap refinement is recorded in CLAIM.json. Prepared by Alishan Ladhani (@aladh) with substantial OpenAI Codex assistance, under Apache-2.0. No independent human review is claimed.

Publication refresh: 562 open PRs through #743; #725 and #732 remain at the credited heads, and main remains the exact base. The later arrivals add no matching (6,4) equality classification or all-target information set.

[Mister-Meeseeks]

100-PR batch review at aeaf0899179a14644b412e838ede14db967c765e.

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

Reviewed scope: Finite (6,4) global-star puncture classification: minimum five deletions and exact attaining decoders, no uniform all-parameter claim.

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.