Scoped negative result: certify one K-triangle relocation neighborhood

[cbethin]

This closes one finite complex-supplier search neighborhood: moving one read in the negative (6,7) K-triangle of PR622's raw 492-helper word cannot improve its paid profile under minimal join frames. Of 841 distinct relocations, 708 violate a target hyperplane and 133 preserve every terminal frame and the profile {1:48, 2:6}. This is a scoped negative result / research note, with no new κ.

Only research/k-triangle-relocation/ is added. It contains the complete per-order certificate, rejection witnesses, pinned inputs, reproduction code, local sprint claim, and validation record. The six source registers contribute 24 of the window's 60 rank units; the complete raw profile, including terminal restoration and centre scatters, remains at rank mass 6284.

python3 research/k-triangle-relocation/verify.py

Expected: PASS: 841 distinct relocations; 708 illegal; 133 unchanged profiles; two exact engines; six controls. Python 3.11+, standard library, offline. The command freshly rebuilds the pinned raw word and compares every certificate field.

Validation passes locally on Python 3.13 and 3.14. Binary elimination and explicit vector-set arithmetic agree on every case; they share traversal code. Exact rational maps cover arbitrary values in all 12 touched registers. The other 704 registers remain unchanged in the window, so equality extends through the fixed prefix and suffix. Six mathematical controls cover coefficients, missing/duplicate reads, cap enforcement, and omitted source climbs. test_package.py also reproduces from a minimal checkout in a path with spaces, rejects source/evidence corruption and -O, and preserves existing output. The selected-result source inventory and whitespace checks pass.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Reviewed PR622 head: f69477f4f6d3c7eb1f740b166881bffed4ffa9f6. OS seed 27 assigns the complex-supplier track and selects triangle 27 % 4 = 3. The exhaustive domain has 870 move pairs minus 29 duplicate adjacent swaps. No timeout or sampled optimum is reported.

The overlap refresh reaches #686. #646 changes signed triangle count; Sreekanth Nair's #651 studies target/face sharing; Alluri's #681 resynthesizes a coordinate-total circuit; Douglas Colkitt's #683 studies mixed K/M bypass carriers. This fixed-window census uses none of their pending results. There is no pinned coordination issue, so the claim is local.

The result does not cover arbitrary permutations, deliberate frame promotions, other triangles, or the final optimized CK/JP8 providers. The existing frame_regroup improvement lies outside the minimal-join domain. No selected cold replay, full make verify, global admission, Linux CI completion, or Lean proof is claimed. All inherited compiler, realization, hosting, precision/tape, recovery, analytic and bit-supplier assumptions remain. upstream/ and the selected frontier are unchanged.

Credit: Jeremy Kothe/AtomScout's #622 schedule; icekylinx's #531 architecture; Dugongue's #514 scalar helpers; Chafik Boukhalfa's #626 source package; DreamingOfClouds and the retained predecessor notices. Prepared by Charles Bethin with substantial OpenAI Codex assistance in research, code, verification, and writing, under Apache-2.0.

[Mister-Meeseeks]

Integrated at ee055dc44815497927ef618fc985b93c2dcbda2a in the 20-PR pilot, retaining your original commit, source notices and contributor credit.

Fixed K-triangle relocation domain: 841 distinct relocations, 708 illegal, 133 same-profile. Both exact engines and six controls pass; other orders/promotions/providers remain outside scope.

The scoped package check passed at 82bbb9c3ac34540f196410d137ebc59d9c2c43a9. This is research integration; the selected κ and inherited theorem assumptions are unchanged. Review, evidence and attribution. Thank you for the contribution.