Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting

[zxv]

Change and mathematical scope

Eight additional dirty aliases on the pinned PR2462 words, followed by a new whole-call owner schedule, give conditional κ ≈ 0.0017137379215475043, about 0.59058% above the pinned PR2474 comparison claim. The exact rational is in research/source-partner-lifetimes/CLAIM.json.

Restore jointly recoverable source partners before handoffs destroy required reads, transport exact target residuals through the target precondition, and derive inverse cleanup from the changed word. Helpers fall from 430 to 422 per call. Both orientations are checked on all 646 independent inputs; all 78 cold endpoints and private cleanup buffers remain charged. The diagonal call order and literal fill admit all 281,052 whole-helper roles.

The full global paid profile is {1:1599730, 2:420912, 3:219782, 4:78588, 5:17756, 7:5328, 8:114, 16:172, 32:3, 48:26488}. There are 74 replicas, 666 calls, dimension 73, live stock 66304, physical stock 66814, deficit 23680, and charged prefix reserve 2048 bits. The exact hosted rank mass is 4,816,512. The supplier endpoint is 0.001713737921547504346752; exact outer refinement establishes the final claim.

This is a conditional finite construction with exact outer arithmetic. Inherited all-size/compiler, common-label/mutable-source, realization, precision/exact-recovery, analytic, and other multiplication-theorem obligations remain. No independent human review or complete multiplication theorem is claimed. The selected frontier is unchanged.

Task and overlap

Explicit user assignment; task complex-new-helper-inventory, scope refined to recoverable source-partner lifetimes and physical rehosting. This changes the local inventory before optimizing the fully hosted recursive moment. Main base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; the source-partner package starts from preceding local package commit 930a1d0ab9b1562ce925118b3654d94b24e6e9ab.

Pinned supplier: #2462 at ef34071fee6dfb0286e9850a5cec4e36d9eb126d, reconstructed byte-for-byte from #2435 at 324d7d3590dc21003940a44cb0cbdc32b3620f25 plus a hash-bound 40-file overlay. #2474 at 5298f86c5193db65f869121eab3cac16d557196c is a claim comparison, not a supplier; its current claim was rechecked before submission. Relative to #2462, this adds eight source aliases and changes the physical schedule. #2474 independently reuses source 31 for helper 637; this word uses source 31 for helper 633 and includes seven other aliases. The explicit centre-only cut guard responds to #2478.

The branch includes research/source-partner-lifetimes and preceding scoped research/t74-owner-consolidation, which supplies the immutable PR2435 archive. The latter realizes the four-owner exchange also audited independently in #2442 and #2466 and numerically superseded by the source-partner construction. Frozen predecessors remain unchanged. Full source bindings and predecessor attribution are in the package READMEs and manifests.

Validation

• Registered bounded replay: exact forward/dual words on all independent inputs, literal physical ownership, and eleven rejecting controls covering source restoration, prelude coefficients, missing roles, windows, and duplicated families.
• Fresh complete cold replay: retained parent; native base/extra providers; discovery and strict global admission; geometry controls; exact outer ledger and independent balance; all nineteen outer evidence replays, 63 strict inequalities, and seventeen outer rejecting controls.
• Exact claim/profile/rank-mass and comparison-source bindings; proof-input hashes; package metadata and clean diff. Hosted Linux CI has not been run locally.

Bounded checks (Python 3.12, standard library):

python3.12 scripts/research_package.py --package research/t74-owner-consolidation
python3.12 scripts/research_package.py --package research/source-partner-lifetimes

Complete cold replay (Python 3.11.11, NumPy 1.26.4, SymPy 1.14.0, SciPy 1.15.3; see package requirements):

python3 -B research/source-partner-lifetimes/full_replay.py --work /fresh/absolute/replay

Evidence: research/source-partner-lifetimes/VALIDATION.json, receipts/, and evidence/. Archived ephemeral paths are explicitly normalized. The bounded hook is not a substitute for complete native/global/outer admission.

Credit

Jeremy Kothe/#2462 and #2435; Tekalign/#2436; Vlado Vojdanovski/#2322; Cinna Davis/#2226; Dugongue/#2309; Sagar Thakrar/#2315 and #2442; Marius-Paul Dumitrean/#2478; Rohan Arun and the #1297/#1319 supplier lineage; and retained native/global/outer authors. The READMEs and source archives preserve detailed attribution and notices.

Prepared with substantial OpenAI Codex assistance at the user's direction. No subagents or independent human review. Apache-2.0, with predecessor notices retained.

Open next questions

See research/source-partner-lifetimes/README.md: improve the changed-word fill through diagonal-order variants and residual concentration; test lender reassignment with displaced helpers explicitly reintroduced; or derive low-frame inverse rows for larger jointly recoverable source subspaces. The first needs a sharper exact feasible fill; the latter two need a complete changed word and native/global admission. The remaining fixed-word packing gap is small, so substantial further gains require a new local inventory.

[thakrarsagar]

An independent, source-bound verification of this PR's research/source-partner-lifetimes at head b4012098 is in #2804. No defect was found.

It checks:

• both words end to end, forward and dual;
• physical stock 66,814;
• the endpoint enclosure at C, and the κ grid conditions;
• the overrides;
• the owner fill, R-a..R-g.

Two small, non-blocking documentation notes:

1. The 24-digit outer endpoint. It is set in SPEC.json and build.py and stated in the sibling t74-owner-consolidation README (line 21), but not in this package's README, CLAIM.json or the PR body. It forgoes about 7e-25 of κ.
2. prefix_l1 denominators. They grow from 2 to 16 and are not charged by prefix_bits. This is inherited and well inside the 606-bit headroom.

Details and remaining author-checked items: #2804 and Discussion #2606.