Research: bound joint helper-end and frame contractions of the selected k8 word

[bitplane]

Shrinking the selected k8 word's helper ends changes both the legal frame domains and the amount of idle work. This package certifies the complete joint nested-end/frame optimization: the favorable primitive ceiling lies between 0.001690198050302 and 0.001690198050303, less than 0.00852% above the fixed-end ceiling. It excludes the declared 5% target for this class; it does not improve the selected multiplication bound.

The scope includes every nested contraction of the 78 originally restricted helper ends, jointly with all 5,413 A/B/early-cleanup gate frames. Entrances, scalar operations/order, centre cut, target levels, cleanup membership and the coverage/guard contract remain fixed. All 46 nontrivial endpoint domains, 1,741 free gate domains and 106 low-end cone relations are covered. Exact rational duals check all 23,456 columns in 135 components, and an integral assignment attains the objective. Contracting ends 574, 575, 580 and 581 gives profile {1:2400,2:446,3:416,4:142,5:82,8:8}, local mass 5,582 and idle mass 1,650.

The variable-mass objective charges the four released rank units as idle work. A control demonstrates that retaining the obsolete idle mass 1,646 would falsely pass the 5% target. A separate bitset/covector checker reconstructs the graph, complete subspace domains and cone relations, and checks all dual inequalities and full-moment bounds with integer-root arithmetic.

Predecessors: navinor's retained frame/LP method; Alexander Schwartzman's #1030 and Cinna Davis's #1090 particular smaller-end constructions; Arham Tahir's #1583 fixed-frame endpoint audit; and #1671's fixed-end frame bound. The new result is the joint quantified bound with correctly recharged variable mass, not the first contracted-end construction or a new LP method. Full contributor/source pins and substantial Codex assistance are disclosed in NOTICE.md and SOURCES.json.

Validation:

• Full registered replay on CPython 3.12.3, including all 18 control groups.
• Unchanged local scalar/frame auditor checks the baseline, credited two-end word and four-end optimum, each on all 704 input columns in both orientations.
• Both exact checkers pass CPython 3.14.4 with -I -O -B from a relocated, read-only package, without changing any files.
• Clean binary-patch application reproduces all 30 new package files. No existing repository files change.

Emitted native programs, phase/wrapper admission, a new physical owner allocation, selected full cold replay and the global/outer invoice were not replayed. Fractional ideal idle packing is a planning relaxation. Nonnested ends, changed entrances, scalar rewrites, cleanup changes and new coverage laws are outside scope.

Run: /usr/bin/python3.12 -I -B scripts/research_package.py --package research/selected-k8-endpoint-contractions.

Claim and completion: #1674

Single random draw: 27a9e1612f686c5cfc60b3fb45d023cb, revision-3 complex-new-helper-inventory. Base main: 15d2aca0385b61596155e8421140d08d27e543af. Mathematical commit: 73e323159d65c974debb180189694fd59144da5f. The resumed publication refresh covered 433 open PRs and 622 discussions, with complete pagination; related heads were unchanged and PR1583/1671 are now merged. Main 01a65937ece11b56d515c81f039464ae3043c1c1 preserves all 12 mathematical inputs and the selected record. Its changed package runner passed a fresh full CPython 3.12 replay. Ross Richardson's intervening uniform fixed-end frame audit is complementary and does not cover variable ends. Metadata search is not a novelty certificate.

Canonical receipt SHA256: 4b9847122d6cd93b61eaa391fa1a67191824e287fe2d828cb0f38ff6b5f1658f.

[Mister-Meeseeks]

Batch review at d47b4b656732f840c9b3252cad5a4efa20924b71.

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

Reviewed scope: Complete nested-end contraction domains and coupled cone constraints yield an attained LP lower bound, with exact dual reduced-cost checks, independent reconstruction and native scalar/frame audits. All saved local mass is charged back to idle work. The resulting fixed-word relaxation stays below the five-percent target; no supplier admission.

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.