[mason-hale]

Result

Proposes conditional κ = 0.001715599770234969498857, about 0.05829% above PR2673's outer κ and 2.5671% above the selected PR1094 point. The selected record is unchanged.

The new construction assigns all eight recovered source-partner lenders jointly to later helper roles. Their target corrections avoid four centre readouts, replacing four charged 7+1 paths with rank 8. Savings in A are exactly repaid in B; the complete local delta is 4(H8−H7−H1) per call, with every correction, restoration and cleanup cost included. Both providers retain 422 helpers, 78 private zero buffers and rank mass 5,251.

This composes with Jeremy Kothe's PR2673 order/fill through an explicit width-preserving helper permutation. The source order, physical ownership and occupied intervals are preserved. Across 666 calls, the complete delta against PR2673 is exactly 2664(H8−H7−H1). Subadditivity proves it favorable for every 0<p<1; no packing improvement beyond PR2673 is claimed.

The directed complex-root bracket is

0.001715599770234969498858 < root < 0.001715599770234969498859.

The published rational lies below the separately checked outer witness. Complete profile: {1:1595736,2:420912,3:218382,4:79920,5:17870,7:2664,8:2664,32:1,48:26558}. Physical stock is 66,814; full rank mass is 4,816,512. The fixed-profile packing relaxation has upper endpoint .001744165345454; this is not an attainable-optimum claim.

PROOF.md supplies exact source-recovery identities, two correction matrices, the twelve target levels, full section costs, inverse-buffer cleanup and the actual helper-slot bijection. These are arbitrary-input symbolic statements, not tests through a finite bit length. The inherited all-size compiler, common-label/mutable-source realization, physical hosting, precision/tape, exact recovery, analytic transfer, recurrence and bit H1–H5 premises remain conditional. This is an incremental conditional improvement, not an unconditional multiplication theorem or practical speed measurement.

Validation

The complete fresh public full_replay.py passed: source authentication; reproduction of PR2530 and PR2588 words; regeneration and complete-payload binding of both candidates; a fresh PR2588 release; both changed native/phase pipelines; word rebuild and local controls; rebind/Lemma G; strict whole-owner/global invoice; geometry controls; 63 exact outer inequalities, independent balance derivation and 19 inherited outer replays.

A separate standard-library checker verifies all 646 independent input columns in both orientations for both providers, every frame and the 4,529-event cleanup, every owner role against reconstructed strict windows/families/prefixes, and a rational moment bracket. Six mathematical mutation controls and ten evidence-integrity controls reject. Source/word/hosting corruption, optimized-Python rejection, output preservation and Git-free read-only replay were also checked. VALIDATION.md records commands, environments and retained receipts.

python3.12 -B scripts/research_package.py --package research/t74-concentrated-source-partners

This bounded command checks mathematics and retained full-replay bindings. README gives the separate complete fresh command; that command accepts no baseline/native cache. admit.py is an internal stage.

Two inherited negative-test adaptations retain their original failures: the old target swap became an identity between equal additions, so its replacement uses distinct sources and has an explicitly nonzero residual; a target-frame mutant correctly rejected but needed its expected error string updated. No mathematical acceptance check was weakened. Maintainer-selected cold replay and formal proof of the full multiplication theorem are not claimed; the applicable pending PR2588-to-candidate chain was replayed.

Provenance and scope

Explicit donor assignment to improve κ after reviewing recent results; refined complex-new-helper-inventory scope. Scientific base 0fdd7d82, branch base 1884c509, priority revision 5. Canonical investigation. Exact main dependencies: PR2462 ef34071f, PR2530 b4012098, PR2588 8cd9dc88, PR2673 45aadf0f. PR2673's outer claim is the numerical comparison; its smaller historical supplier-only CLAIM.json is not.

All 292 recent PR bodies through 2689 were read across the research and submission snapshots. The final refresh found PR2679’s distinct 415-helper claim, κ≈0.0017148565406944334; the present point is also about 0.04334% above that claim. PR2679 itself was not independently replayed. Main advanced to 06164c03 without changing the selected record, pinned inputs or applicable T74 guidance. Relevant exact dependencies were inspected and replayed. RECENT-RESULTS.md, TASK.json and retained review records describe coverage and limits. No unpublished-work or exhaustive novelty claim is made.

Prepared by Mason Hale with substantial OpenAI Codex assistance in derivation, implementation, checking and writing, including separate agent reviews; no independent human review. Credit zxv/2530 for source-partner recovery, tekuuu/2436 for lifted targets, Jeremy Kothe/2462/2588/2673 for words, replay and hosting, themilkman216/2621 for the priority-order idea, Philippe Van Velzen/2559 for evacuation, Rohan Arun's owner work, and the retained native/bit/outer lineage. Raw source bytes and notices are preserved; new work is Apache-2.0.

Open next questions

Can a different exact assignment remove the four remaining centre splits? Derive a full compensated candidate or a target-support obstruction first. Can another strict whole-role exchange improve the final fill? Check its complete windows, families and prefixes before expanding a search. Scoped follow-ups and blockers are in TASK.json; no search completeness is claimed.

Only research/t74-concentrated-source-partners/ is added.