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Conditional κ = 0.001661956299899884: PR858's sixteen-replica owner controller on the U8 word - #870
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…roller on the U8 word
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…low owner map of the seven-slot k8 word New package research/gauge44-slots-t16-arcflow: research/gauge44-slots-t16's T16 controller (Hao Yan's CrocSwap#858 via CrocSwap#870) on research/gauge44-slots-arcflow's T8 admission, with a new 16-replica owner map from the same exactly liftable pattern/time MILP and Konig lift. Idle remainder {1:2430, 2:1, 16:1, 48:4887} over 69,120 roles (time-free optimum {1:2431, 17:1}). Strict T16 replay, admission, bit-supplier, controller-mutation and independent T16 controls pass. Prepared by G. V. Chudnovsky with Anthropic Claude assistance. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01KBSZTxNtzYkGa6MNbKajRo
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…low owner map of the seven-slot k8 word New package research/gauge44-slots-t16-arcflow: research/gauge44-slots-t16's T16 controller (Hao Yan's CrocSwap#858 via CrocSwap#870) on research/gauge44-slots-arcflow's T8 admission, with a new 16-replica owner map from the same exactly liftable pattern/time MILP and Konig lift. Idle remainder {1:2430, 2:1, 16:1, 48:4887} over 69,120 roles (time-free optimum {1:2431, 17:1}). Strict T16 replay, admission, bit-supplier, controller-mutation and independent T16 controls pass. Prepared by G. V. Chudnovsky with Anthropic Claude assistance. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01KBSZTxNtzYkGa6MNbKajRo
This was referenced Oct 14, 2026
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Summary
Conditional κ = 0.001661956299899884 (conservative 0.001661956297017522). This is +7.60×10⁻⁹ over the U8 package (research/gauge44-barch, 0.001661948695165034).
Change: FanPUYen's PR858 sixteen-replica owner controller, applied to the U8 word. PR858 (closed, unmerged) introduced a controller with 16 data replicas in two 8-replica parent bank groups (144 invocations), plus 11 whole-helper owner edits that turn idle remainders (44,3,3) into (48,2,0). U8's owner map is the same file as PR799's, so PR858's edits apply verbatim to the U8 word. Prefix 401 ≤ 512 bits; row coefficient 16,469 ≤ 20,161; deficit 5,120.
Code: U8's reviewed code plus PR858's edits applied verbatim, plus one glue edit (72→144 in freeze_spec).
t16/build_owners.py,build_parent.pyandsource_adapters.pyare byte-identical to PR858, andt16/MOVES.jsonis exactly PR858's 11 edits. The newverify_t16.pyruns every check of the 8-replicaverify_global.py(69 admission, 12 bit-supplier and 6 independent controls) plus PR858's owner audit, its 11 omitted-move controls, the changed-role count, bank-group accounting, literal windows, the prefix and coefficient limits, and all of PR858's final-binding asserts.Independent review: SOUND. The reviewer rebuilt every changed code file from U8 plus PR858's edits (all matched), reproduced the strict run, and confirmed that a wrong owner move, a wrong offset, an omitted move, a bank-group overlap, a window-violating move and a 513-bit prefix overflow are each rejected end-to-end.
Verification
From a fresh clone of commit b734850 (Windows, CPython 3.11.11), using U8 locals rebuilt from scratch by the U8 chain (the clean replay of research/gauge44-barch above):
verify_manifest.py: PASS, 152 filesverify_t16.py: PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY 0.001661956299899884Credits
Conditional on PR645's premises and PR589's bit-supplier assumptions. No optimality is claimed for sixteen replicas.
Prepared with Claude Code (Anthropic).