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…inder donors on PR3148's T740 fill Idle remainders of partially used bins donate axes, under PR1252's commuting rule, to unhosted idle children of the same replica and port (cap 51), followed by PR3184's stars. 391,964 axis moves; complex root 0.00173477055711151316 exceeds the PR589 bit saving, so kappa is bit-capped: +3.238e-6 over PR3184. Independent verifier with eight rejected controls; native admission and outer release with the overlay not rerun. Done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…RIFY schema, open questions, read-only verifier Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…h PR3190's idle-remainder donors PR3190 pushed the complex root (0.0017347705571115131604951) past the PR589 bit saving. The R438 bit supplier natively replayed on main (0.001734846264120199151475) is above it, so the complex side binds again: +1.3435e-6 over PR3190. Independent re-derivation of both endpoints and the composed kappa; 3 controls rejected. Done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…e on PR3198 (R438 bit) Adds a third phase of single-axis PR1252-rule moves between unhosted idle children to PR3190's remainder donors and PR3184's stars: 430,164 moves, complex root 0.0017348070217261275520343, still below the R438 bit endpoint. +3.646e-8 over PR3198. Independent verifier re-derives the moves, the complex bracket and the R438 endpoint; 8 controls rejected. Done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…34815770385098563484 Idea credit: OpenCode (Space bunny free) - exact search within each replica/port group instead of PR3200's greedy phase 1, scored by the final group cost after phases 2/3. +8.7487e-9 over PR3200; complex binds. PR3200's independent verifier passes (8/8 controls), deterministic build. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01F5n4jqR72j3QDY71gGBVb1
Fixes the registered-package replay check (README.md needs an "## Open next questions" section). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01F5n4jqR72j3QDY71gGBVb1
…pen questions actual_scope/evidence were inherited from PR3200 (greedy phase, 430,164 moves); now describe the exact search and 435,604 moves. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01F5n4jqR72j3QDY71gGBVb1
…mainders as receivers on PR3251 After PR3251's exact idle-donor search, idle-remainder axes may also move into the remainder of another partially hosted bin of the same (replica, port) when they commute with its full recipe frame and the PR1252 translations. 437,978 moves; complex root 0.0017348651784727109982331 passes the R438 bit endpoint, so kappa reaches R438 (+0.00176% over PR3251). Independent verifier with nine rejected controls; native admission and outer release not rerun. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…38 slack across bit replicas on PR3934 An explicit cross-replica owner map (35 moves) realizes the pooled32 slot-model optimum for R438's width-8 slack: bit endpoint 0.001734900431583947157341, above PR3934's complex root, so the complex side binds again. All 126,144 roles audited against R438's slot rules; baseline equals the R438 certificate; 6 controls rejected. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…ame selection on PR3939 A bin hosting used helper cells may map them to any used-subset of its recipe frame, so the idle remainder is chosen per bin. PR3934's move classes then lift the complex root to 0.0017411726 (+0.36%); kappa reaches the pooled R438 bit endpoint. Independent verifier: 9/9 controls rejected; registered replay passes. Done with help from OpenCode (Space bunny free) in the stacked predecessors. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…plex side with PR3647's R437 bit PR3955 lifted the complex root to 0.0017411726, above PR3647's R437 bit endpoint (ai-nanachi; helper464 GL + PR1043 helper470 + PR3700 OQ4). Both endpoints are re-derived with an independent exact engine; bit binds. 6/6 controls rejected; registered replay passes. Complex-side lineage done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
This was referenced Oct 19, 2026
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Retracted, closing. This draft belongs to the #3934 → #3959 chain, which is built on #3251's idle-axis moves. Those were retracted on 2026-10-18 because #3190's donations change the exact eight-stream operator (see #3296/#3311/#3187). Native admission, the controller audit and the outer release never ran. #3995 and #4046 show the pooled move is rejected. The κ claimed here is not valid. Prepared by Rohan Arun with Anthropic Claude assistance. |
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Author-checked conditional candidate. Composition of two open lines: the complex side of #3955 (hosted frame selection, stacked on #3939 → #3934 → … → #3148 → #3133) and the R437 bit supplier of #3647 by @ai-nanachi. #3647 composes the helper464 GL deletion with Ali Romman's #1043 helper470 deletion and adds Sagar Thakrar's #3700 OQ4 slot coalescing. Draft. The full verification run is still going.
+0.1006% over #3955. #3955 lifted the complex root about 6.3e-6 above the pooled R438 bit endpoint. #3647's R437 endpoint lies inside that window, so κ rises to it. About 4.5e-6 of complex headroom remains.
Verification
python3 -B research/rank7-frame-select-r437-bit/verify.pyis self-contained, standard library only, and runs in about 2 s.RESULT.jsonis bound to Conditional κ = 0.001734900431583947157341 (+0.00203%): hosted frame selection on #3939 #3955's committedAUDIT.json; Conditional κ = 0.001734900431583947157341 (+0.00203%): hosted frame selection on #3939 #3955's own verifier audits all 521,798 moves.EXPECTED.jsonis vendored (heada24f9ff9, blobbc2585e1; the LF-normalized bytes are SHA-256 bound). Its paid profile is re-priced independently at m = 64, W = 28416, with the inherited 10⁻¹⁶·32m²·N fallback envelope: accepted at c, rejected at c + 10⁻²⁴.PASS_REGISTERED_RESEARCH_PACKAGE.Scope
This inherits every premise of both endpoints:
This package re-prices #3647's declared profile; it does not replay #3647's word or hosting. #3700 independently audited the original R437 word.
Next: pool R437's own slack across the 32 bit replicas, as #3939 did for R438.
Credit @ai-nanachi (#3647), Ali Romman (#1043), Sagar Thakrar (#3700/#2423) and the full #3955 stack. Complex-side ideas in the stacked predecessors were done with help from OpenCode (Space bunny free). Prepared by Rohan Arun with Anthropic Claude assistance.
🤖 Generated with Claude Code
https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy