Direct delivery with 504 helpers for conditional κ = 0.001517760977820331

[icekylinx]

This builds on my #523, retaining its 112-port data controller and replacing its complex supplier with a 504-helper construction. The branch contains the #523 commit followed by one new commit for this increment.

Under the retained all-size compiler, common-label/mutable-basis realization, normalized Lemma A, restored-row, precision/tape and analytic-transfer interfaces,

$$ T(n)=O!\left(n(\log n)^{1-\kappa}\right),\qquad \kappa=\frac{1517760977820331}{10^{18}} =0.001517760977820331. $$

The saving is 4.10271% above #523 and 3.27687% above #529. The complex supplier still binds. These percentages compare exponent savings, not practical runtime.

Construction

Use the same coordinate partition in both target tetrahedra. Eight retired rows form an invertible source basis, allowing the coordinate centers to finish before the own-block terms are loaded directly into the target basis. Selected cross-block sums are delivered in two reads from existing face copies; 56 assembled packet sums are omitted.

The resulting word uses 504 helpers, with 72 compatible line gauges and 80 exact shared-donor pivots. A further 248 legal frame promotions combine delivery climbs without changing scalar coefficients, chronology or endpoints. Arbitrary helper dirt is handled by newly computed response compensation and explicit cleanup.

A new allocation assigns all 36,288 helper roles to whole idle physical families. Each complete invocation has 728 distinct active owners. Actual windows, orthogonal charts, spectators and all 7,968 remaining children are checked from the emitted program.

Quantity	#523	This increment
Local data ports	112	112
Helpers	560	504
Local rank mass	6,706	6,240
Live families	7,168	7,168
Physical families	7,738	7,682
Global rank deficit	2,560	2,560
Certified complex saving	0.001460074471110324279467	0.001520068077832496458155

Two exact moment engines, six bootstrap levels and all 47 strict outer inequalities give the displayed κ. The unchanged #493 bit supplier is repriced at 0.001565442026981656908596; its physical operator remains a cited dependency.

Contribution sources and prior PRs

Source	Contributor	Retained contribution
#523, a900f98be8ff2c09d3292b5112d4731dbd0c8438	icekylinx	112-port restriction, data controller, phase cache and prior verified baseline.
#514, #507	Dugongue; eumemic	Hamming packet/scalar constructor ancestry and partial-own factory.
#484 and wrapper/hosting lineage	DreamingOfClouds and credited contributors	Shared-donor kernels, entrance gauges and normalized paid wrappers; original assistance notices retained.
#493, c3a9a436b84fe44fdc223a5784d84736d1c2d3c7	eumemic	Unchanged bit supplier.
#522, #520	Dugongue; higherbeing	Related rank-sector and delivery-geometry ideas. Their implementations are not imported.
#425, #370, #361, #315 and retained framework	Credited upstream contributors	Geometry, phase compilation, rational moments and analytic/outer interfaces.

My earlier #433 supplied split centers and source-basis reuse. Earlier contributions in #10, #18, #24, #32, #36, #104, #115, #130 and #144 concern batched boundaries, partial swaps, gauges, certified assembly and frame/cover constructions. These identify provenance rather than additive numerical gains. Dugongue's #505 remains credited for asynchronous scheduling.

The new direct-delivery architecture, compatible entrance selection, frame coalescing and physical allocation are contributed by icekylinx, with GPT-6 Astra assistance. Local review and submission packaging used OpenAI Codex. NOTICE.md, SOURCES.json and the retained ancestry preserve source-specific credits. #527 and #529 are numerical comparisons only.

Proof and validation

The new package is research/direct-delivery504-global/:

• proof/: source-frontier identity, direct delivery, frame coalescing and whole-owner argument.
• evidence/audit/EXACT-ASSEMBLY.json: exact moments, bootstrap and strict margins.
• EXPECTED.json, SOURCES.json, MANIFEST.json: exact result and source/file bindings.
• LOCAL-VALIDATION.json: local incremental validation and verified dependency reuse.

python -B research/direct-delivery504-global/verify_fast.py --work /tmp/direct504-check

Local validation additionally used --rebuild-local --delta-phases on Python 3.14.8 with NumPy 2.3.5. It passed in 23.89 seconds: the selected factory and rational entrance relations were rebuilt, all 1,680 changed phase edges were checked, and the physical owner audit, fresh invoice and strict assembly passed. The 1,242 unchanged phase edges and 224 endpoint adapters reuse a cache checked against #523 byte-for-byte. Retained controller inputs also match the previous local validation.

Separate fresh checks passed for both emitted local orientations on all 728 columns, all seven residual wrappers, the fourteen exact source-frontier bases, and 112 delivery incidences. Thirteen local and five wrapper mutation controls were rejected. No predecessor cold replay or unchanged bit-operator reconstruction was repeated. The final prefix is 225 bits within the retained 512-bit allowance.

Final package manifest SHA256: c1997405c5c0ccd9bdb0a30b0eb9a5a2dc7dc7ce7b59c6a83a2152b80f6410d1.

Global template content SHA256: ed47b5454779f7ad6b32ae492a13f8b5172b11c94c3877cbc5cc5d7a4c357738.

Dedicated Python 3.11/3.14 CI performs supplier reconstruction and changed-edge verification. Remote CI is pending. Optional discovery files are excluded, and no PDF is generated. The historical joint-dual hash correction is inherited from #523.

This remains a finite conditional witness. The inherited all-size and analytic interfaces remain assumptions; no new Lean proof, unrestricted optimality or unconditional multiplication theorem is claimed.