Conditional κ = 0.001332077359286333: pooled whole-owner complex supply

[eumemic]

κ = 0.001332077359286333

Conditional whole-owner improvement: κ = 1332077359286333/10^18, using PR493's R489 bit word and a new placement of PR484's gauge/kernel complex word. Pooling the eight physical data replicas removes all 66 complex bank families. This improves the PR493 + PR484 whole-owner pairing (0.001325031497415498) by about 0.532%.

Every helper residual remains on one physical family. Each of the 72 complete local invocations has 800 distinct owners, including its active data wires. The larger draft PR494 number depends on PR448's disputed cross-family split; this PR retains the whole-owner interface and does not claim to exceed submissions under that different assumption.

Construction

The local bit and complex words, Gaussian phase recipes, entrance wrappers and cleanup are unchanged from the pinned suppliers. The new frozen allocation places each whole complex residual in an idle child. A bipartite edge coloring assigns its invocation replica: each actual helper occurs exactly once per invocation, and no physical family is reused within that invocation. A host may belong to another physical replica.

The serialized controller keeps complete invocations sequential. Entry wrapper, scalar word and exit wrapper finish before another invocation borrows the family. The explicit leftover idle children name their actual physical family and replica and execute once. There are no split residuals and no bank padding.

• Complex: m=73, live stock 7680, physical stock 8258, 40320 whole helper routes, 3960 actual orthogonal 73-column maps.
• Paid profile: {1:148440, 2:66816, 3:7472, 4:19728, 5:25664, 6:144, 7:1800, 8:4120}; rank mass 558144, deficit 2496.
• Exact complex saving: b = 133385415620840915601/10^23 = 0.001333854156208409156010.
• Fresh PR493 bit saving: c = 391360506745414227149/250000000000000000000000 = 0.001565442026981656908596; complex binds.
• A global norm argument valid across replicas gives 142 prefix bits < 192. It uses per-call bijections of the actual orthogonal cover and unitary completed helper endpoints, with no replica-independence or cover-cardinality shortcut.

Verification

python3 -B research/r489-pooled-whole-complex/verify.py /absolute/fresh/output --boost-include /path/to/boost/headers

The package runs both complete pinned supplier verifiers from source, then the changed allocation and independent physical/invoice/assembly checks. It uses real Boost, records the header trace and a 257-bit integer probe, and guards expanding int64 operations before executing the exact Gaussian tests.

Checks include arbitrary dirty restoration, both reflected local ledgers, actual whole-family maps and spectators, complete idle remainders, 18 controller mutations, a separate serial-pooling operator regression with five controls, both exact moment engines, six bootstrap cutoffs and all 47 strict outer inequalities. The next grid point and zero-eta/zero-beta/unit-beta controls are rejected. Verification uses the frozen map and does not run an optimizer.

Both complete release runs finished with observed exit 0 on Python 3.14.7 and real Boost 1.88: immutable source (441.064 s), and a fresh literal archive of commit 00cf70efd6a8637531deafef698157ca83e249ee (440.999 s). All 14 root stages passed in each run and their complete mathematical results are identical. Package manifest SHA-256: b7a3bdb801f4a9ae8c389edaee545a8d0cb16fd6211f38b54b71b5c50eb5a80c; exact mathematical receipt SHA-256: bede0887eaf7ccc5b1c9607ca15572c5e595c2574f0eb174f2b4982d11f32369. The dedicated CI workflow is included; no CI success is claimed before it runs.

Scope, provenance and AI disclosure

This is a conditional finite construction. It retains the suppliers' all-size compiler, mutable-basis/common-label, PR484 Lemma A realization, restored-row, precision/tape and analytic-transfer contracts. PR484's Lemma G local identities are freshly checked; finite checks do not establish the inherited all-size assumptions. No unconditional theorem or Lean proof is claimed.

The package pins PR493 at c3a9a436b84fe44fdc223a5784d84736d1c2d3c7 and PR484 at 035845ce95f31d0a2dcfb42b8c8e13411271fa5f, including 266 original supplier/dependency files. The original packages and every previously published PR head and claim remain unchanged. SOURCE.json, MANIFEST.json, PROOF.md and NOTICE.md record the exact sources, argument, attribution and limitations.

Credits include eumemic (PR493), DreamingOfClouds (PR484, with Claude Opus 5.5 assistance), DaysSky, icekylinx, chafreaky, Zhihao Chen, Rohan Arun, Dylan Crow, Jacob Sussman and the source-pinned authors credited by the suppliers. The new allocation, coloring, independent audits and integration were prepared with substantial OpenAI Codex assistance. Original licenses and AI disclosures are preserved.