Scoped negative result: E8 star-copy ratio cannot improve through 55 punctures (no new kappa)

[RossRichardson]

Scoped structural negative result; no new kappa or supplier. In the fixed binary star-reader model on the 120 real E8 root lines, no deletion of at most 55 lines improves the copy-cost/live-port ratio 63/111. This extends Chi Zhao's PR631 exclusion through 35 punctures and Philipp's PR875 equality analysis at 36.

The new mechanism is a shared-deletion constraint. Two distinct nonzero readers have support union at least 84, while a surviving rank-d reader occupies at most M_d root lines. Thus their ranks a,b satisfy M_a + M_b >= 84-p after the same p deletions. Exact integer relaxation gives universal star-cost bounds 53 for p=36–43, 45 for p=44–51, and 44 for p=52–55, all too expensive to improve 63/111. These relaxed costs are not claimed attainable. At 56 deletions the live label rank can decrease, so the theorem stops there.

Only research/e8-joint-reader-bound/ is added: written proof, complete exact certificate, two implementations, meaningful negative controls, retained source pins, attribution and local claim. PR875's exact orbit and stronger equality-class invoice remain distinct contributions. Neither existing generators nor upstream/ nor the selected frontier is changed.

Reproduce offline with Python 3.10+ and the standard library:

python3 -I -B research/e8-joint-reader-bound/verify.py

Expected: PASS_E8_JOINT_READER: 256 flats; 511 readers; 130305 pairs; punctures 0..55; 6 rejection controls; no new kappa.

Validation passed on CPython 3.14.6 and 3.12.12. An implementation importing neither the primary checker nor predecessor code independently reconstructs the root capacities with Fraction RREF and checks 486,200 sorted-rank profiles. All five package tests pass, including evidence/source corruption rejection, isolated optimized relocation, byte-identical regeneration and the pinned PR631 replay/controls. A staged Git-tree export passes both new checkers under -I -O -B; selected-record integrity and whitespace checks pass. Full repository/supplier cold replays and hosted CI are not claimed for this isolated package.

Exact base: 91a2094. OS assignment seed 46, structural decoder track. PR631 is pinned to fb893b5ee1317c2da3b297e6fe78eca0857d1a76; PR875 context to 7f334e4c749fd83d03feb6c1de4e4cda9534c9dc, with verified Git-blob/SHA256 pins. The final full overlap inventory covered 706 open PRs through #934, followed by a recent-PR refresh through #937. No pinned coordination issue existed, so the claim/result are local. Upstream advanced during verification to 47481c89fd30a43f8f882eb4b391e89c29273fd0, selecting PR890 at conditional kappa 0.001661957774647029; this structural theorem is independent of that update.

Scope remains fixed root-only labels, independent input bits and additive star copy-rank accounting. General pairing-rank/nonlinear decoders, non-root ports, 56+ punctures, helper savings and changed geometry remain open. The written parabolic coverage proof is essential; finite enumeration is not a formal multiplication theorem. All-size/compiler, hosting, precision/tape and analytic obligations remain inherited.

Credit Chi Zhao/PR631, Philipp (@mightyOil)/PR875, Joel Pulikkan/GamingPuzzled/PR620, DreamingOfClouds/PR595/PR602, eumemic/PR543 and the earlier E8 lineage. Prepared by Ross Richardson (@RossRichardson) with substantial OpenAI Codex assistance, including separate AI-assisted checking and proof review. Apache-2.0; no independent human review claimed.