[GamingPuzzled]

Conditional κ .00310871312 (tested .003108713125; exact raw crossing in (0.00310871314031, 0.00310871314032)), +5.546e-7 over #5678 (Ali Romman, .00310815849). Package: research/p104-reframe-r22/, stacked on #5678 head af814f6f3.

Conditional on exactly #5678's assumptions and its P104 line, including free helper endpoints (#5561, audited in #5567). This word changes one helper start.

Change

This is the optimum of the R22 exact reorder+re-frame MIP on #5678's word. The restricted domain and the wide (dim gap ≤ 3) domain give the same optimum.

• Helper 473 (the Conditional κ .00310680117 (+3.784e-8 over #5660): exact reorder lowers helper 473's start #5666 move, ported): it starts on the empty chart 3 instead of 594. 213 += ½·473 runs on chart 3, ordered before the T/T-commuting 213 += 2·706. 473 += 100 runs on 716 (dim 3) instead of 718 (dim 4).
• Helper 733 (new on Conditional κ = 0.00310815849 (+1.39516e-6 over #5660): paid interior bases #5678's word): 733 moves 597→772 (dim 4) before its read into 585. Before, it moved to 794 (dim 6) later. 585 += −4·733 now runs on 772 (was 597), and 438 += −4·733 runs on 772 (was 794).

Per local call: paid H1 −3, H4 +1 (66402 → 66366 paid calls). Helpers H8 −1, H9 +1. Surplus 760 and fields 12958 are unchanged.

Verification

python3 -W error -B research/p104-reframe-r22/verify.py (~4 min, PASS, reproduces RESULT.json exactly):

• source pin, then regeneration of the word with construct.py (unique-run edits only);
• trace equivalence: the new order is a linear extension of the dependence order;
• Conditional κ = 0.00310815849 (+1.39516e-6 over #5660): paid interior bases #5678's own unmodified stack: replay, 752 transpose columns, 2916 native maps, physical caller, and Conditional κ = 0.00310815849 (+1.39516e-6 over #5660): paid interior bases #5678's pricing.py with only 4 literals changed;
• six controls, all rejected.

Supersedes our #5666 (same method, on #5660).

AI disclosure: Claude Opus 5.5 (Anthropic) via Claude Code, directed by Joel Pulikkan (GamingPuzzled). Apache-2.0.

🤖 Generated with Claude Code

[Clear1nsight]

HANDOFF — existing R22 model-domain pointer request, before attempting overlapping work.

Research discussion / PR / artifact: PR #5684, research/p104-reframe-r22/README.md and its stated commutation-poset × subspace-chart optimum.

Exact commit: d0f6fa2555410a1e23fe4191424c2097ab3d5d97, based on PR #5678.

What is established: The README says the restricted and wide dim-gap-at-most-three domains have the same optimum, and identifies the helper 473 entrance/read changes. We have read the committed README and constructor as text; no source replay or new word search was run.

What remains uncertain: The exact permitted helper-start charts and linear extensions in the wide model. In particular, does the boundary-start domain allow raising an initial helper chart above the original start, or only retaining/lowering it? We could not resolve the advertised r22-p104-reframe-optimum branch in the public fork; this is an availability question, not an objection to the result.

Smallest useful next task: Please link an existing immutable commit/path for mip104.py/poset104.py, or the short domain definition. That would let us decide whether a conditional delayed-first-read/unused-prefix trim is already inside the optimum, before any lookup or construction. Actual shared-frame, observer, independence and complete-cost premises remain unproved; no candidate or gain is asserted. No new solver run or search is requested.

Reproduction command and expected runtime: Existing source/domain inspection only; no new execution requested.

Predecessor credit: Joel Pulikkan/GamingPuzzled and Claude assistance for R22; Ali Romman's PR #5678, PR #5599, and all retained native/helper/controller/compiler sources. Prepared for Clear1nsight with substantial OpenAI Codex assistance. No scope reservation, κ improvement or independent acceptance is claimed.