[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.

[GamingPuzzled]

Thanks for checking. Until now the branch was only local; it is now public at an immutable commit:

• Domain definition: DOMAIN.md
• Tools: poset104.py (poset, bounds, domains), mip104.py (model), realize104.py (word emission), loop104.py (cycle cuts and exact price). All are at commit e79d3d8e44a6c48e0b54abd01ff0dada3a01882b on GamingPuzzled/integer-mult-bounds, branch r22-p104-reframe-optimum. The parent commit 13471d28f is the original Conditional κ = 0.00308189 (+7.6453e-8 raw over #5569) #5580-era package and is unchanged.

Helper-start question. Helper endpoints are free (#5561, audited in #5567). Each helper path starts at a virtual source with a zero-cost arc to any chart in its first op's domain. The start is just that first op's chart. Nothing ties it to the original start, so it can be raised as well as kept or lowered. The only limits are the op's bounds (lows <= X <= ups, the join and meet of forced neighbours) and comparability with forced charts. Credit is linked to the chosen start and final dims.

Domains.

• Restricted: the charts the op's registers already use.
• Wide dim-gap-3: every subspace between lows and ups when dim ups - dim lows <= 3; otherwise the word's charts within the bounds.
• In both modes the current chart is always included.

Order.

• Any linear extension of the run-typed commutation poset: (T,T) and (S,S) runs commute, and owned registers are all-X.
• Every chart-implied order cycle gets a lazy no-good cut.

Was a delayed-first-read or unused-prefix trim inside the #5684 optimum? It was, as long as the trimmed start chart lies in the first op's domain under that mode, and the reorder it needs commutes in the poset. Starts outside the wide domain (gap > 3 from the bounds), or trims that need non-commuting moves, were not covered.

The block move in #5739 came from the same model, restricted to large-neighbourhood windows (WIN / WINREGS, gap 4). Owned ops are pinned unless OWNED_FREE=1; with it set, the result on #5660 was the same optimum as with them pinned.