[rohanarun]

Summary

This replaces #3200's greedy phase-1 idle-donor selection with an exact memoised search inside each (replica, port) group.

• Search space. Every hosted-remainder axis either stays put or moves to any legal unhosted receiver. Legality is PR1252's commuting rule, with receivers capped at rank ≤ 51.
• Scoring. Each choice is scored by the group's final Σ Hf(rank) after phase 2 (stars, optional) and Conditional κ = 0.001734807021726127552033: greedy idle-axis phase on #3198 with the R438 bit supplier (+0.0021%) #3200's unchanged phase 3.
• Unchanged. PR3133's words and PR3148's fill, order and dispatch.

	κ headline (− 10⁻⁴⁶ − 10⁻⁷⁰)	binds
#3200	0.001734807021726127552033	complex
this	0.001734815770385098563484	complex

The gain is +8.7487e-9, exactly 174973179420229/2·10²². About 3.05e-8 of headroom to the R438 bit endpoint remains.

An exact phase 1 that scores only its own cost reproduces #3200's moves exactly. The gain comes from scoring phase 1 jointly with phases 2 and 3, and from letting a group skip stars when that is cheaper. The result is 435,604 axis moves. Rank mass 65088·740 is conserved, the maximum child rank is 51, and the halving check gives [5329, 5202].

Verification

python3 -B research/coupled-carrier-cap740/materialize.py --output /tmp/t740   # PR3148
python3 -B research/rank7-idle-donors-exact-r438/build.py  --t740 /tmp/t740
python3 -B research/rank7-idle-donors-exact-r438/verify.py --t740 /tmp/t740

• Verifier. The package runs Conditional κ = 0.001734807021726127552033: greedy idle-axis phase on #3198 with the R438 bit supplier (+0.0021%) #3200's independent verifier, which does not import build.py. Only the status string is renamed and a Conditional κ = 0.001734807021726127552033: greedy idle-axis phase on #3198 with the R438 bit supplier (+0.0021%) #3200 gate is added. It outputs PASS_IDLE_DONOR_EXACT_R438_AUDIT moves=435604 controls=8 kappa=0.0017348157703850986 binding=complex, with all 8 mutation controls rejected.
• Cross-check. Conditional κ = 0.001734807021726127552033: greedy idle-axis phase on #3198 with the R438 bit supplier (+0.0021%) #3200's unmodified verify.py also passes on these BINS/MOVES/RESULT files.
• Determinism. build.py is byte-deterministic over two runs.

Scope

This is an author-checked conditional candidate, not maintainer-reviewed. It inherits #3200's scope:

• the hosted-remainder donor hypothesis and multi-donor receivers rely on PR1252's per-axis rule;
• native admission, the overlay-aware controller audit and the outer release were not rerun;
• it is conditional on R438, whose source PR1043 is open.

Credits

• Idea: OpenCode (Space bunny free): exact per-group search in place of the greedy selection.
• Base: Conditional κ = 0.001734807021726127552033: greedy idle-axis phase on #3198 with the R438 bit supplier (+0.0021%) #3200, Conditional κ = 0.001734770557111513160495: R438 bit supplier with #3190's idle-remainder donors (complex binds again, +0.0775%) #3198 and Conditional κ = 0.001733427039589844234749 (bit-bound): idle-remainder donors on #3148's T740 fill (+0.187% over #3184) #3190 (rohanarun); PR1252 Gonzalo-Mier; star class Gueorgui Maissouradze; PR3148 Jeremy Diviney; PR3133 dcharb78; PR1043 Ali Romman; PR2423 Sagar Thakrar.
• Prepared by Rohan Arun with Anthropic Claude assistance.

🤖 Generated with Claude Code

https://claude.ai/code/session_01F5n4jqR72j3QDY71gGBVb1

[rohanarun]

Retracted. The κ claimed here is not supported, so I'm closing this PR.

Why. This PR's MOVES file begins with #3190's idle-remainder donations. Merged audit #3296, independently confirmed by merged #3311, shows those donations change the exact eight-stream physical operator under the unchanged local-invocation contract: at owner replica 0, port 0, character 2^72, the scalar baseline i·I₈ changes in 10 entries. Merged #3187 shows the same for #3184-type star exchanges.

The per-axis rule from PR1252 that these moves were checked against is necessary but not sufficient. The exact operator replay is the real test, and our verifier did not run it.

Can any part be saved? Before retracting I checked this with #3187's replay and #3296's code, unchanged except for the owner index.

• Every single-axis remainder transfer at every owner replica. The T740 fill is 10 lifted copies of the T74 base plus 145 journal edits. So 74 base owners × 112 ports, plus the 27 groups the edits touch, cover all 740 owners exactly.
  • 266,732 transfers pass Conditional κ = 0.001733427039589844234749 (bit-bound): idle-remainder donors on #3148's T740 fill (+0.187% over #3184) #3190's declared rule, across 2,328 distinct hosting configurations.
  • All 266,732 change the operator at their own axis character. None survives.
• Multi-copy moves of the same axis. Each axis has six copies, so phases could in principle cancel. I searched these exactly by meet-in-the-middle.
  • So far about 93,000 axes and 50 million configurations, over 2,800 (owner, port) groups, find no operator-preserving set.
  • Controls: the search re-finds the baseline placement on every searched axis. An independent brute force over all one- and two-copy moves on 180 axes agrees: 0 of 38,688 preserve the operator.
  • The sweep is still running, and I'll update here only if it finds anything.

Distinct axes are orthogonal, so at an axis character the operator depends only on where that axis's copies sit. Any donation set that moves a copy of axis k must therefore pass the axis-k check.

Result. The idle-donor mechanism gives no legal gain on PR3148's fill, and this chain falls back to #3148 / #3361. I'm closing #3184, #3190, #3198, #3200 and this PR.

Thanks to the authors of #3187, #3296, #3311 and #3432 for the exact replays.