Scoped negative result: minimal E8 mixed-port extension is saturated

[thakrarsagar]

Result

Scoped negative result; no new kappa. Every compatible non-root port added after at most 14 E8 root-line deletions, with the inherited nine-dimensional labels, forces the same D7 equality case up to Weyl symmetry. Exactly one non-root port type fits. Adding it makes every nonzero reader span all eight physical dimensions, so no further nonzero port can be added within this model.

The exact star copy cost rises from 64 on 106 root ports to 72 on 107 mixed ports. This rules out improving the copied-information ratio by the minimum-puncture mixed-port mechanism before implementing helper or restoration work.

This extends Chi Zhao's #631 sharp threshold with equality classification and saturation. GamingPuzzled's #620 already computed the coordinate-axis example's approximate ratio; that example is credited, not claimed as new. #669's paired-hypercube result and #703's quaternionic result have different scopes.

Changes are confined to four files in research/e8-minimal-mixed-port/: proof, independent standard-library checker, exact receipt, and source pins. The checker uses a Gram-row basis instead of the predecessor's orthonormal factorization. The written Weyl-chamber reduction separates exhaustive coverage from finite replay.

Reproduce

python3 -B research/e8-minimal-mixed-port/verify.py

Expected: PASS for 8 maximal flats, all 511 nonzero readers before and after augmentation, one non-root candidate, and 5 negative-control categories; star costs 64 and 72. Every run compares the complete regenerated receipt with the checked-in JSON.

Validation passed on Python 3.14.8 and Python 3.11.15 with optimized mode. Controls reject duplicate non-root ports, even labels, each of the 14 forbidden root restorations, a full-rank normal request, and a malformed simple system. A separate AI-assisted implementation generated the signed roots in a different order, chose another binary basis, and checked ranks over GF(3), with exact annihilators for deficient spans. It independently confirmed costs 64 and 72. Selected-record integrity, source hashes, and staged whitespace checks pass.

The expensive repository-wide and selected supplier cold replays were not repeated. No existing supplier, generator, assembly, upstream/ file, or selected-frontier pointer changes.

Scope, pins and credit

• Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60; OS-random seed 40, structural decoder research. Source pins and claim details are in SOURCES.json.
• Prove E8 star-decoder puncture thresholds through 35 deleted lines #631 head: fb893b5ee1317c2da3b297e6fe78eca0857d1a76. Research notes (no κ claim): E8 decoder floors are tight; extension-ring, triple and Lorentzian units lose after helpers; cold-end, dispatch and fusion-search negatives #620 head: e9cf03bbdf7094b5a83f6dbd1d74bfd77a05fb87. The relevant imported source bytes have explicit hashes.
• The theorem keeps the original labels, nine binary dimensions, nonzero rational physical vectors, and the Euclidean ambient form. More than 14 punctures, relabelling, extra label dimensions, and other decoder families are outside scope. Helper-saving tradeoffs and complete paid suppliers remain unpriced.
• The accepted conditional kappa remains 51110230636731/31250000000000000. All inherited all-size, realization, restoration, precision and analytic obligations remain. This is not formal verification of the multiplication theorem.
• No pinned coordination issue existed, so the claim was local. The final overlap scan covered 528 open PRs through Tooling: cache exact R420 geometry for 6.47x faster mutation replay #709 and found no competing equality-classification result.
• Prepared by Sagar Thakrar / @thakrarsagar, with substantial OpenAI Codex assistance in research, implementation, proof review and documentation. Apache-2.0. Predecessor credit includes GamingPuzzled, Chi Zhao, DreamingOfClouds, artuskg, eumemic, OpenAI Weighted dual-suffix carriers: conditional κ = 7.9961717358e-5 #109 and the cumulative community work.

[Mister-Meeseeks]

100-PR batch review at d8ed5c6cf2781d6efa0062a2636e1a2644f96c85.

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

Reviewed scope: Fixed E8 labels: minimum 14 punctures for a non-root port and D7 equality classification; added port worsens the stated star-copy objective.

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.