Punctured Hamming ports for conditional κ = 0.001457945761723368

[icekylinx]

This removes eight isolated coordinate ports from the pinned #514 complex construction and supplies a new complete physical owner allocation, in one commit based on main at 12a4934d15006e8c10f9b2264f13f8f341be802b.

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

$$ T(n)=O!\left(n(\log n)^{1-\kappa}\right),\qquad \kappa=\frac{182243220215421}{125000000000000000} =0.001457945761723368. $$

The saving is 4.77335% above #514 and 4.61251% above #518. The complex supplier binds the assembly. These percentages compare exponent savings, not practical runtime.

Construction

The eight coordinate source/target pairs occur only as eight independent unit shears in the complete scalar word. Removing these direct summands leaves 112 code ports and all 560 helpers, with the same frames, gauges, kernel relations and arbitrary-dirt restoration. Each removed pair saves two rank-eight children and one rank-one center descent.

The global controller restricts at complete invocation boundaries. A new literal assignment hosts all 40,320 helper uses on whole idle data families, with 784 distinct active owners per invocation. Actual charts, idle windows, spectator restoration and every remaining child are checked against the emitted program.

Quantity	Pinned #514	This construction
Local data ports	120	112
Helpers	560	560
Sum of center ranks	72	64
Live families	7,680	7,168
Physical families	8,258	7,738
Global rank deficit	2,496	2,560
Certified complex saving	0.001393462495344162153490	0.001460074471110324279467

Two rational 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 operator remains a cited dependency.

Contribution sources and prior PRs

Source	Contributor	Retained contribution
#514, 246bfacd4cb4072836ae3147099f548bb728229f	Dugongue	Combined 92-pivot word, coordinated gauges, asynchronous whole-owner construction and offline verifier.
#507	eumemic	Partial-own factory and retiming map.
#484, #496	DreamingOfClouds; eumemic	Gauge/kernel construction, normalized residual wrappers and whole-owner invoice.
#493, c3a9a436b84fe44fdc223a5784d84736d1c2d3c7	eumemic	Unchanged R489 bit supplier.
#425, #370, #361, #315 and retained framework	Credited upstream contributors	Geometry, scalar/phase compilation, exact moments and outer arithmetic. Original notices are preserved.

My #433 supplied split centers and source-basis reuse. Dugongue’s #505 supplied complete-invocation asynchronous scheduling. Earlier work includes #10, #18, #24, #32, #36, #104, #115, #130 and #144, covering batched boundaries, partial swaps, gauges, certified assembly and frame/cover constructions. These are provenance, not separately additive gains.

The new port restriction, owner allocation and independent audit are contributed by icekylinx, with GPT-6 Astra assistance. Local review and submission packaging used OpenAI Codex. NOTICE.md, SOURCES.json, ADAPTATIONS.json and the retained vendor notices record detailed ancestry, including #458, #473, #495, #501, #502 and #506. #518 and #520 are comparisons only; their new code is not incorporated.

Proof and validation

The selected package is research/punctured112-global/:

• PROOF.md and proof/: direct-sum restriction, global controller and physical-owner argument.
• evidence/EXACT-ASSEMBLY.json: both moments, finite invoice, bootstrap and all 47 strict margins.
• EXPECTED.json, SOURCES.json, MANIFEST.json: exact result, immutable source pins and file bindings.
• verify.py: offline standard-library reconstruction, with dedicated Python 3.11/3.14 CI.

python -B research/punctured112-global/verify.py --work /tmp/punctured112-check

Local clean reconstruction passed on Python 3.14.8 in 487.47 seconds: all 14 top-level stages and 13 nested predecessor stages passed. Packaged executable Python ASTs and mathematical inputs match that validated source; only documentation, attribution and manifests were adjusted. The final package manifest SHA256 is e353b0e9d76cf6253d502f7410d17c228180e98bb6e56072eb869a1d923c3c17. See LOCAL-VALIDATION.json. Remote CI is pending. The package checks both orientations on all 784 arbitrary scalar columns, exact local phases and wrappers, the 112-port global restriction, all 40,320 whole-owner roles, complete paid histograms, coefficient/routing allowances, rational moments and strict assembly. The selected template content SHA256 is 2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99.

This also repairs the previously identified historical joint-dual CI source freeze: only the stale top-level Makefile and README.md pins and their two derived hash bindings change. The historical mathematical certificate is unchanged. Optional search files remain outside the submission; no PDF is generated.

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