DONE: joint selected k8 helper-end/frame ceiling (PR #1995)

[bitplane]

CLAIM — joint endpoint contractions and frame choices for the selected k8 word

Question: can any simultaneous nested contraction of all 78 restricted helper endpoints, jointly with all 5,413 A/B/early-cleanup gate frames, beat the selected word's packing ceiling by 5%?

Base main 15d2aca0385b61596155e8421140d08d27e543af. One random nonce 27a9e1612f686c5cfc60b3fb45d023cb, revision-3 complex-mechanisms / complex-new-helper-inventory, scope key 5868e5281a1e63d41a22; no reroll.

Exact domain: the R480 selected k8 scalar word (decompressed SHA256 c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8), unchanged scalar gates/order, entrances, centre cut, target levels and early/full cleanup membership/order. Each of the 78 originally restricted helper ends may be any subspace between its entrance and its original end, while every A/B/tail frame can change. The 402 helpers touched by full cleanup retain full ends. The low-end dirty-column/inverse-row cones must follow each chosen endpoint. Exposed local rank mass is charged as idle under the unchanged coverage law; it is not credited as eliminated work.

This changes the fixed-endpoint hypothesis of PR1671, and changes the fixed-gate-frame hypothesis of Arham Tahir's PR1583, head 04516881142961cdf97a828fbbc63d72e232a148. Alexander Schwartzman's PR1030 and Cinna Davis's PR1090 already construct specific rank-seven ends; they are positive controls/predecessors, not discoveries claimed here. Navinor's exact frame LP method, Douglas Colkitt's PR1240 ceiling and Sagar Thakrar's PR1012 coverage law retain credit.

The first optimistic budget waives the climbs of these 78 helpers, keeps all other local work, and recharges the released mass as ideal idle; it has headroom to justify the complete coupled feasibility screen. It is not a realizable endpoint assignment. Method: complete subspace intervals, variable endpoint nodes and exact zero-charge cone-containment edges, then an exact moment dual using variable-mass excess prices. Full native assignments and failure controls where applicable.

Expected artifact: one scoped proof/replay package or an exact obstruction/handoff; no new kappa or full selected cold replay is presumed. Excluded: changed entrances, scalar rewrites/reordering, nonnested endpoint rotations, new helpers, shared centre work or a changed coverage law. Stop after the complete nested-endpoint screen; claim expires 2026-10-14T08:16:38.069134+00:00.

Gareth Davidson / bitplane, with substantial OpenAI Codex assistance; no independent human review asserted.

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FINDING / DONE — published as PR1995.

All nested contractions of the 78 restricted helper ends, jointly with all 5,413 legal gate frames, have favorable primitive ceiling a < 0.001690198050303. This permits less than 0.00852% improvement over the fixed-end ceiling and excludes the declared 5% target. The proof fixes the exact scalar word/order, entrances, centre/target pins, cleanup membership and coverage/guard contract. It includes all 46 binary endpoint domains, 1,741 free gate domains and 106 low-end cone relations. No new kappa or full construction is claimed.

All 23,456 columns in 135 exact dual components are checked, and an integral assignment attains the relaxation objective. Contracting ends 574,575,580,581 gives profile {1:2400,2:446,3:416,4:142,5:82,8:8}, local mass 5,582 and idle mass 1,650. Released local mass is fully recharged as idle: retaining the obsolete 1,646 idle units would falsely pass the 5% target, which a control demonstrates.

The full registered CPython 3.12.3 replay and all 18 control groups passed. Both mathematical checkers also passed isolated, optimized, relocated read-only CPython 3.14.4 with unchanged files. The independent bitset/covector/integer-root checker imports no primary frame/LP/moment implementation. The retained scalar/frame auditor accepts the baseline, credited PR1090 two-end word and four-end optimum on all 704 input columns in both orientations. Emitted native programs, phase/wrapper admission, a new physical owner allocation, selected cold replay and global/outer invoices were not replayed.

Current main 01a65937ece11b56d515c81f039464ae3043c1c1 preserved all mathematical inputs and the selected record; its changed package runner also passed the full replay. Publication overlap covered 433 open PRs and 622 Discussions with complete pagination. PR1583, PR1090 and PR1671 heads were unchanged and are now merged. Ross Richardson's intervening uniform fixed-end frame audit is complementary; it does not cover variable ends. Metadata search is not a novelty certificate. Native-emission/helper450 and source-independent full-cleanup audits also have distinct scopes.

Credit remains with navinor's frame method, the full selected construction lineage, Alexander Schwartzman/PR1030 and Cinna Davis/PR1090 for earlier contracted ends, Arham Tahir/PR1583 for the fixed-frame endpoint audit, PR1671 for the fixed-end bound, and Douglas Colkitt/Sagar Thakrar for the complete ceiling/coverage model. NOTICE.md retains exact attribution.

Mathematical commit 73e323159d65c974debb180189694fd59144da5f; published head d47b4b656732f840c9b3252cad5a4efa20924b71. Canonical receipt 4b9847122d6cd93b61eaa391fa1a67191824e287fe2d828cb0f38ff6b5f1658f. Reproduce: /usr/bin/python3.12 -I -B scripts/research_package.py --package research/selected-k8-endpoint-contractions. Hosted CI status is separate from these local results.

Open next questions: nonnested ends/changed entrances, one changed scalar dependency or cleanup cut with a fully screened bill, and complete physical hosting of the four-end word. These require new interface and cost evidence; the available ceiling gain is tiny. Scope released; no continuing claim. Gareth Davidson / bitplane, with substantial OpenAI Codex assistance; no independent human review.