Conditional κ = 0.001343518018117309: retimed pooled whole-owner complex supply

[eumemic]

κ = 0.001343518018117309

A frame-only retiming of #484's gauge/kernel complex word improves the frozen whole-owner result in #496 by 0.85885844%, while retaining #493's R489 bit supplier and #496's pooled whole-owner allocation. The complex side binds at the exact lower endpoint b = 1345325487149526878087/10^24; the strict outer assembly gives κ = 1343518018117309/10^18.

The 4,107 scalar payloads and their order stay fixed. A frozen map changes 411 A frames and 504 B frames while preserving all helper entrances, the first 531 A gates, target/centre boundaries and cleanup. The changed local rank distribution improves the complete paid moment without reducing its rank mass. All Gaussian phase recipes are rebuilt for the actual new transitions.

The complete complex profile is {1:172056, 2:19008, 3:42032, 4:6048, 5:22496, 6:6624, 7:1800, 8:4120}. Live stock is 7,680 and physical stock is 8,258, with no banks. All 40,320 helper roles remain whole on one physical family, every complete invocation has 800 distinct owners, and the 3,960 actual orthogonal 73-column charts are checked. The serial schedule restores borrowed work before the next invocation; the cross-replica-safe global prefix bound remains 142 bits within the retained 192-bit allowance.

Validation includes fresh reconstruction of both pinned suppliers; the actual new scalar word and both reflected 25,082-event ledgers; arbitrary dirty restoration on all 800 scalar columns; all 2,945 used transition operators and 122 helper chains on all 512 address columns; full physical programs on 806 basis plus eight dense dirty columns in both orientations; all actual owner maps; complete paid profiles and finite invoices; two rational moment engines; six bootstrap cutoffs; and all 47 strict outer inequalities. Guarded simulators bound integer expansion before execution and now explicitly assert and hash their identity-result JSONs, in addition to requiring successful subprocess exits. The independent frame review rejects 12 mutations, and the inherited source, Lemma G and pooled-controller mutation suites run freshly. Retiming removes a frame assumed by the original M8 mutation generator, so a derivative adapter nominates an available nonnested frame and recomputes both actual codimensions while preserving the total charge; the same source checker and physical test reject it, and all 14 necessity controls run.

Fresh source and literal committed-archive replays both pass with observed top-level exit 0 and identical complete EXACT-MATH.json results. The package is self-contained and verifies offline with Python 3.14, NumPy, SymPy, a C++17 compiler and genuine Boost headers. Its 309 manifest-listed files match their staged and archived Git bytes. Run:

python -B research/r489-pooled-retimed-complex/verify.py /absolute/new/output \
  --boost-include /path/to/boost/headers

This remains conditional on the inherited all-size compiler, mutable-basis/common-label, PR484 Lemma A realization, restored-row, precision/tape and analytic-transfer contracts. It is not an unconditional theorem or Lean proof. It makes a whole-owner comparison with #496; The higher #494/#499 draft numbers use a distinct disputed cross-family-split interface. Neither the bounded retiming search nor the allocation search establishes global optimality.

Provenance: #493 (c3a9a436b84fe44fdc223a5784d84736d1c2d3c7), #484 (035845ce95f31d0a2dcfb42b8c8e13411271fa5f), and frozen #496 (00cf70efd6a8637531deafef698157ca83e249ee). The original source notices, Apache-2.0 licenses and AI disclosures are preserved, including DreamingOfClouds' Claude Opus 5.5 assistance and all credited predecessors. The new search, independent audits, integration and documentation were prepared with substantial OpenAI Codex assistance. All previously published heads and claims remain frozen.

Release verification: commit 1dc056496fdbbc74073ed26d948a2dc235dbf356; manifest SHA256 a2295472662c4f845639c46305bd25cd713095fc23ca2478db8ee4eef3fd5e34. Source and literal-archive replays took 825.565 s and 827.254 s respectively, with all 18 root stages passing. Their common EXACT-MATH.json SHA256 is 940505b40dee096d0426ca545e15d98fa93b2e6af1a675e59d0760748a70a659. The reconstructed word matches the frozen nomination byte-for-byte after gzip decompression (SHA256 06d204be7a74dd41a88c6ba79133b6396fe66194c6e892715f8317ae86144e41); the gzip platform byte differs and is bound separately in the fresh receipts.