Conditional κ = 0.0017137844912361143: repacked owner fill on #2530's source-partner words

[rohanarun]

Result

Conditional κ = 0.0017137844912361143131449999999999999999999998999999999999999999999999. The exact rational is in research/source-partner-repack/CLAIM.json.

• Over Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting #2530 (zxv, 0.0017137379215475043…): +4.6569688609966393E-8 (exact 46569688609966393/1000000000000000000000000).
• Certified complex endpoint: 342756898247222862629/200000000000000000000000. The 1e-24 endpoint grid and the outer settings are the same as Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting #2530's.

What changed

Only the owner fill changes. The eight source-partner aliases, the 422-helper words, the diagonal call order and windows, and every native/global/outer stage are #2530's. research/source-partner-repack/build.py runs #2530's own unchanged build.py, swaps in evidence/repack-fill.json.gz, and re-runs the package's reconstruct.py and lift_parent.py.

#2530's fill leaves idle {1:21976, 3:6662, 5:440, 8:114, 16:172, 32:3, 48:26488}. Most of the expensive idle sits at the start of the diagonal order, where the first windows can draw only on the first few calls:

• rank-16 window (replica 0, child 0) is empty;
• (1, 2) is half empty;
• one rank-8 window is empty.

The repack places single 9s into some of those bins (remainder 16 → 7). It pays for them by emptying (9,9,9)+5 rank-32 bins and re-concentrating idle elsewhere, so the moment drops. New idle: {1:21987, 3:6659, 5:423, 7:81, 8:102, 14:2, 16:90, 32:25, 48:26492}.

Unchanged: the local profile {1:2369, 2:632, 3:320, 4:118, 5:26, 7:8}, the inventory {4:33, 5:9, 7:62, 8:78, 9:240}, rank mass 4,816,512, live 66304 and deficit 23680.

Method. This was an offline search; only the result is shipped, and reconstruct.py verifies it literally. I used large-neighbourhood search with an exact CP-SAT subproblem (OR-tools 9.15):

• Each step frees every role in about 80 bins: the holes plus donor bins from time-overlapping windows.
• It re-solves their placement under the package's rules: the window of every role, bin capacity, prefix packing, and one role per call and physical family.
• It minimises the idle moment weight at fixed a, and a step is kept only on strict improvement.
• The search starts from Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting #2530's fill.

This attacks #2530's first open question. The window-free pattern LP (#2387/#2442) still caps these words at b < 0.0017142284.

Validation

• Full replay. python3 -B research/source-partner-repack/full_replay.py --work <fresh dir> gave PASS_SOURCE_PARTNER_REPACK_COMPLETE_FINITE_ADMISSION_AND_OUTER. It runs the same stages as Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting #2530's full_replay.py: retained parent, natives, rebind, discovery, strict global admission (PASS_STRICT_MIXED_T74_EXACT_FILL), geometry controls, exact outer ledger (63 strict inequalities, 17 rejecting controls), independent balance and the outer evidence replays. Stages: retained-parent reused, native-base reused, native-extra reused, rebind 1.2s, discover 152.9s, strict 156.8s, geometry-controls 0.6s, outer-check_ledger.py 0.1s, outer-independent_check.py 0.0s, outer-evidence 44.7s.
• Reuse. The retained parent and the two native directories were reused through the script's status- and hash-checked --parent-from, --native-base and --native-extra options. All three were fresh runs of the same unchanged scripts in this session; the defaults are fully fresh.
• Bounded check. python3 -B research/source-partner-repack/verify.py gave PASS_SOURCE_PARTNER_REPACK_LITERAL_OWNERS: literal owners for all 281,052 roles, three rejecting physical controls (missing role, out-of-window role, duplicated family) and the exact claim/profile/endpoint bindings.
• Metadata. python3 scripts/research_package.py --package research/source-partner-repack --check-only gave PASS_PACKAGE_METADATA_AND_PINS.
• Environment. Linux, CPython 3.13, NumPy 2.5, SymPy 1.14, SciPy 1.18.

Scope

This is a conditional finite construction, as in #2530. These obligations remain: all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, the PR559 recurrence correction and PR589 bit H1–H5. No independent human review, complete multiplication theorem or global packing optimality is claimed. The selected frontier is unchanged.

Credit

• Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting #2530 (zxv, with OpenAI Codex): source-partner lifetimes, the diagonal order and the whole pipeline this builds on.
• Conditional κ = 0.001703552312979594: optimal owner fill for #2436's aliases on the entrance-raised T74 words #2462 / Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447 / Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435 and the T74 line (Jeremy Kothe).
• Conditional bound: four aliases + 24 entrance raises give κ = 0.001699160892139825 #2436 (tekuuu).
• Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322 (Vlado Vojdanovski).
• Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226 (Cinna Davis).
• Negative result (no κ): legal 400-helper owner fill of #2339's 80-alias T74 words reaches b = 0.00168654, 99.994% of a certified width-aware cap b < 0.0016867 — below #2269 #2387 / Audit (no κ): exact owner-fill optima on the T74 handoff line — #2374's fill is optimal over all fills; #2435's fill leaves +5.8e-10 (pattern optimum certified) #2442 / Independent verification (no κ): #2447's owner fill is exactly the certified optimum for #2435's words; the same optimum in 4 role moves (fewer charts) #2466 (thakrarsagar): the pattern-LP ceiling and owner-optimality method.
• Everyone credited in the source packages.

New here, by Rohan Arun with AI assistance (Claude, Anthropic): the repacked fill and its wrapper package. Apache-2.0.

🤖 Generated with Claude Code

https://claude.ai/code/session_016kRUbVkAPKY4Bbinm9zWvZ