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Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges - #1094
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Exact frame solver, exact pricing harness for B-phase delivery rewrites, fusion and repair searches, slot-recipe splitting and composition, interface transplant onto newer words, an exact kappa pricer for any replica count, and drivers that reuse unchanged package engines for the native local chain, PLAN/SPEC rebinding, discovery/unpin/freeze and negative controls. selftest.py reproduces #1094's and #942's kappa, the seven-slot k8 frame optimum, the per-slot and per-site cost deltas and the composed word's kappa on #1094's owners, using only files on main. Pure Python with NumPy; no C++, Boost or solver.
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… aliases on the seven-slot k8 word at T = 8 research/gauge44-slots-borrow47 applies PR2226's anticipatory dirty borrowing (Cinna Davis) to the selected PR1042/1094 word, keeping the 47 full aliases (R 480 -> 433, 73 private zero buffers), lowers it with research/gmx-t74-borrow43-handoff's native borrow chain, hosts it at T = 8 on research/gauge44-slots-arcflow's schedule with a new whole-owner map, and admits it with the borrow-aware global code (strict replay, 19 mutation, 69 admission and 12 bit controls). +0.6956% over CrocSwap#1175 (0.001675867534384272), +0.8887% over the selected CrocSwap#1094. verify_borrow47.py rebuilds everything from pinned main sources in about 5 minutes. Prepared by G. V. Chudnovsky with Anthropic Claude assistance. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01KBSZTxNtzYkGa6MNbKajRo
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… word Restates the incumbent packing ceiling of the CrocSwap#1094 complex local word as a function of the largest paid local child rank, over every cap s = 1..51 the outer halving guard allows, and inverts the table at the a = 1/99 target. The retained lever table stops at rank 16 and uses fractional child counts. This adds, for each cap s, an ideal fractional upper bound and an exact integer-child-count lower bound, so a_int(s) <= cap_s <= a_frac(s) holds with no search over histograms. Arithmetic is the sibling package's unchanged exact rational intervals at that package's own 1e-15 grid. Measured (RESULT.json): - base ceiling re-derived from the pinned assembly inputs and matched exactly against the pinned sibling RESULT.json: 0.001690054109089 - the a = 1/99 crossing is at cap 44 for both bounds; a_43 = 0.0099889993, a_44 = 0.0103695754 (kappa <= 0.0102631508) - at the guard cap 51 the integer histogram {51: 109, 27: 1} gives a = 0.0135848308, kappa <= 0.0134027566, 8.04x the incumbent, with the centre charge and the coverage law untouched - integer child counts cost at most 0.6605% of the ceiling anywhere - greedy equals the exact-enclosure DP optimum at 11 caps x 3 screening savings with 0 ambiguous comparisons - bimodal inversion: at cap 44 the target is unreachable unless 42 residual units ride at rank 42 rather than rank 1; at cap 51, 96.78% of the local paid mass must be rank-51 children Scoped obstruction and planning table. No new kappa, no construction, no supplier, and the selected record is unchanged. The card's acceptance gate requires a constructed profile with copies, frames and restoration counted; this is the certified relaxation the gate calls insufficient, and TASK.json records the scope as refined. Replay: python3 -I -B research/local-word-rank-shape-ceiling/verify.py
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… word Restates the incumbent packing ceiling of the CrocSwap#1094 complex local word as a function of the largest paid local child rank, over every cap s = 1..51 the outer halving guard allows, and inverts the table at the a = 1/99 target. The retained lever table stops at rank 16 and uses fractional child counts. This adds, for each cap s, an ideal fractional upper bound and an exact integer-child-count lower bound, so a_int(s) <= cap_s <= a_frac(s) holds with no search over histograms. Arithmetic is the sibling package's unchanged exact rational intervals at that package's own 1e-15 grid. Measured (RESULT.json): - base ceiling re-derived from the pinned assembly inputs and matched exactly against the pinned sibling RESULT.json: 0.001690054109089 - the a = 1/99 crossing is at cap 44 for both bounds; a_43 = 0.0099889993, a_44 = 0.0103695754 (kappa <= 0.0102631508) - at the guard cap 51 the integer histogram {51: 109, 27: 1} gives a = 0.0135848308, kappa <= 0.0134027566, 8.04x the incumbent, with the centre charge and the coverage law untouched - integer child counts cost at most 0.6605% of the ceiling anywhere - greedy equals the exact-enclosure DP optimum at 11 caps x 3 screening savings with 0 ambiguous comparisons - bimodal inversion: at cap 44 the target is unreachable unless 42 residual units ride at rank 42 rather than rank 1; at cap 51, 96.78% of the local paid mass must be rank-51 children Scoped obstruction and planning table. No new kappa, no construction, no supplier, and the selected record is unchanged. The card's acceptance gate requires a constructed profile with copies, frames and restoration counted; this is the certified relaxation the gate calls insufficient, and TASK.json records the scope as refined. Replay: python3 -I -B research/local-word-rank-shape-ceiling/verify.py
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… word Restates the incumbent packing ceiling of the CrocSwap#1094 complex local word as a function of the largest paid local child rank, over every cap s = 1..51 the outer halving guard allows, and inverts the table at the a = 1/99 target. The retained lever table stops at rank 16 and uses fractional child counts. This adds, for each cap s, an ideal fractional upper bound and an exact integer-child-count lower bound, so a_int(s) <= cap_s <= a_frac(s) holds with no search over histograms. Arithmetic is the sibling package's unchanged exact rational intervals at that package's own 1e-15 grid. Measured (RESULT.json): - base ceiling re-derived from the pinned assembly inputs and matched exactly against the pinned sibling RESULT.json: 0.001690054109089 - the a = 1/99 crossing is at cap 44 for both bounds; a_43 = 0.0099889993, a_44 = 0.0103695754 (kappa <= 0.0102631508) - at the guard cap 51 the integer histogram {51: 109, 27: 1} gives a = 0.0135848308, kappa <= 0.0134027566, 8.04x the incumbent, with the centre charge and the coverage law untouched - integer child counts cost at most 0.6605% of the ceiling anywhere - greedy equals the exact-enclosure DP optimum at 11 caps x 3 screening savings with 0 ambiguous comparisons - bimodal inversion: at cap 44 the target is unreachable unless 42 residual units ride at rank 42 rather than rank 1; at cap 51, 96.78% of the local paid mass must be rank-51 children Scoped obstruction and planning table. No new kappa, no construction, no supplier, and the selected record is unchanged. The card's acceptance gate requires a constructed profile with copies, frames and restoration counted; this is the certified relaxation the gate calls insufficient, and TASK.json records the scope as refined. Replay: python3 -I -B research/local-word-rank-shape-ceiling/verify.py
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This was referenced Oct 19, 2026
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Conditional candidate kappa 0.001672660197076918, +0.000338096% over PR1087 (0.001672654541898561). Repeated sixteen-bin whole-helper repacking, seeded through rare full-bin patterns, improves the idle-rank profile. The scalar word, role widths and source-event times are unchanged.
Published and revised as a draft before full verification, then passed the complete publication-package replay through the unchanged PR1087 strict verifier. All 69 admission controls, 12 bit controls, 15 controller mutations, six independent owner controls, two exact moment engines and 47 outer inequalities pass. The finite witness changes 193 role placements. VALIDATION.json records local evidence. Hosted CI remains separate; this reuses the checked PR1018 native baseline and PR1005 chain rather than rebuilding the full ancestry.
All-size/compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer and PR589 bit H1-H5 assumptions remain. No unconditional theorem, global optimum or Lean claim.
Credit PR1087 and preceding owner-packing work by jeremykothe2 with Claude assistance; FanPUYen PR858; PR1018 including rohanarun PR987; PR1005; NewBArch PR869 and the retained PR799/741/685/645/589 lineage. Prepared by Rohan Arun with substantial OpenAI Codex assistance; new material Apache-2.0.