Research: bound arbitrary helper terminal frames of the selected k8 word

[bitplane]

PR #1995 bounded helper ends inside their original subspaces. This package removes that cap: every terminal subspace containing each fixed entrance is allowed, including rotations, enlargements and FULL ends, jointly with all 5,413 gate frames. The complete larger domain has the same certified favorable-ceiling bracket, between 0.001690198050302 and 0.001690198050303. Its possible gain over the fixed-end word is less than 0.00852%, excluding the declared 5% target. No new multiplication exponent is claimed.

The exact selected R480 scalar word, entrances, centre/target pins and early/full cleanup membership/order stay fixed. The 402 full-cleanup helpers remain FULL; all 78 previously restricted terminal nodes vary. The complete domains include 32 terminal intervals with 374 choices and 46 with five, plus 2,589 free gate nodes. A new complete quotient enumerator handles dimension five. All 106 low-end cone relations remain explicit zero-charge containments.

Exact rational duals certify all 396,241 columns in 129 components (103,563 rows). The four-end profile already found in #1995 attains the bound: {1:2400,2:446,3:416,4:142,5:82,8:8}, local mass 5,582, idle mass 1,650. The new contribution is its optimal ceiling over the unrestricted terminal domain, not a new discovery of that profile. Every possible endpoint choice retains a nonnegative idle bill; released rank mass is fully recharged.

Validation:

• Full registered CPython 3.12.3 replay, including all 20 control groups.
• A separate bitset/covector/integer-root checker reconstructs all domains, edges and cones and checks every dual inequality, without importing primary frame/LP/moment code.
• The baseline, credited PR1090 two-end word and attaining four-end word each pass all 704 scalar/frame input columns in both orientations.
• Both checkers pass CPython 3.14.4 under -I -O -B from a relocated package with read-only files/directories and unchanged bytes.
• Controls reject omitted rotated/FULL endpoints, missing frame choices/charges, overstated dual objectives, source/receipt corruption, and the false target pass caused by omitting released idle work.
• Clean binary-patch application reproduces all 30 new files; no existing files change.

Emitted native programs, phase/wrapper admission, new physical ownership, selected full cold replay and the global/outer invoice were not replayed. Fractional ideal idle packing need not be realizable. Changed entrances, scalar rewrites/order, cleanup changes, nonmonotone internal transport, new helpers and changed coverage laws remain outside the proof.

Credit: navinor's complete frame LP method and its chafreaky/ntedvs/Rohan Guliani lineage; Alexander Schwartzman #1030 and Cinna Davis #1090 for earlier smaller ends; Arham Tahir #1583; #1671 and #1995; Ross Richardson's uniform fixed-end audit; Marius-Paul Dumitrean #1186; Cinna Davis #1996; Douglas Colkitt #1240 and Sagar Thakrar #1012; and the full retained construction lineage. Source pins, original notices and substantial Codex assistance are documented.

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

Claim/completion: #2000

Single random draw 5f5984c68e5381ec12276b69c721f48c, revision-3 complex-new-helper-inventory. Base 1c47876ef742ba64bf9140b0527d63acf656a3b4; mathematical commit 31e788df17a4df614fa5b3605a06d06e60f18bb6. Final overlap covered 381 open PRs and 643 Discussions with complete pagination; related heads were unchanged. Main b6135f9fe8c0783f22bd87992a080575f2943511 preserves all mathematical inputs and the selected record. Its new canonical-path validation passed separately. Metadata search is not a novelty certificate.

Canonical receipt SHA256: 1891bcf17e86405d265ed4b51b9de6f6059be95c50a5b6c28b21d2ac8057093e.

[Mister-Meeseeks]

Batch review at a43cc72abcb16ca4d61fc469174a9b971b084d6f.

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

Reviewed scope: Unrestricted terminal subspaces enlarge #1995 to all374 choices in each five-dimensional quotient, with complete396241-column dual certification and independent reconstruction. Both boundary and idle charges are retained; the attained relaxation still misses five percent. Local native checks are not global hosting or full supplier certification.

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.