Source-assisted common-frame compression for conditional kappa = 6.566436e-4

[icekylinx]

This extends the reviewed integration of my PR #144, merged through #149, from main at d1d6c070f5a8c684727ee7ec35d930f9ebfa9758, with one new commit. The selected construction uses eumemic's substantial PR #168 reference at fd25adb7fbaa12ee761d02c733c54d1d2a7687ee. Its later module refresh is not mixed into this fixed experiment.

Under the retained analytic, uniform-recursion, precision, routing, restored-row and fixed-tape interfaces,

$$ T(n)=O!\left(n(\log n)^{1-\kappa}\right),\qquad \kappa=\frac{6566436}{10000000000}=6.566436\times10^{-4}. $$

Construction

At an identical actual frame and chronological phase, let n incoming physical auxiliary coordinates have fresh rank d, and let t outgoing requests have fresh rank r, after quotienting by original-source controls available at that frame. Assuming the requested forms lie in the incoming span plus those controls, the minimum additional arbitrary dirty stock is max(0,t+d-r-n). Explicit invertible lifts retain every physical complement. Only exact zero-fresh complements are reused through paid, compatible later transitions.

The complex branch refactors the local channels into sum/difference blocks at their actual frames. Original-source controls erase 1,410 background responses at already paid parity frames, exposing 706 reusable zero-fresh coordinates. The exact local maps and all-column endpoint certificate supply the complete new ledger. The bit branch uses source-pair controls and invertible XOR templates to remove 440 unpaired rank-two retirees while preserving the entire high boundary and compensated-reuse interface.

Selected supplier	Complex	Bit
Dimension m	66	72
Physical auxiliary rows	11,056	17,852
Persistent roles per vertex	13,696	21,372
Complete child rank	902,616	1,536,848
Rank deficit	1,320	1,936
Strict coarse saving	0.0006570752	0.0006656467

The bit supplier keeps all 3,960 gauges, 1,760 compensated pairs and 2,200 width-sixty exterior children. The selected ledger is combined_fixed_boundary_profile; the file's top-level comparison is not used for the bound. The stopped bit saving exceeds the complex saving, so the complex branch binds the assembly. Both exact moments, the conservative finite bridge, all 47 strict constraints and seven margins pass.

Cleanup reverses the complete new controlled transcript: for z_final = M z_initial + L x, it restores M^-1(z_final-Lx). Its dirty response is recomputed from the new program. Old terminal-sink deductions, canceled scalar supports, or an inherited dirty-response replay are not used to certify the new flow.

Contribution sources and prior PRs

My preceding contributions are retained through the reviewed main integration:

PR	Conditional kappa	Contribution
#10	1.2299998e-7	Batched recursive boundaries.
#18	1.884586e-6	Partial-swap frames and unequal tensor factors.
#24	5.98615e-6	Endpoint and gauge integration.
#32	1.2523415e-5	Improved compatible constructions and certificates.
#36, merged	3.84569e-5	Structured semantic/bulk assembly.
#104	7.79476e-5	Stopped product-ring integration.
#115	9.26336e-5	Selected partial gauges.
#130	3.146011e-4	General frames and three-stage covers.
#144, integrated by #149	4.609169e-4	Paired cubes, original-source chronology, shared completed cores and exact integration.

The current construction also retains these attributed dependencies:

Source	Contributor	Retained contribution
#168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee	eumemic	Substantial public reference: frozen query modules, operation frames, physical words, compensated reuse, bit gauges and assembly. Original Anthropic Claude disclosure retained.
#117	eumemic	Earlier local producer/module lineage.
#162	DaysSky	Closure and scheduling lineage.
#124, #166	jamesyc	Compatible birth/reuse and terminal-target lineage; the new complex ledger does not import the old terminal deduction.
#163	chafreaky / Chafik	Same-singleton fusion lineage.
#158, #153	geckods	Atom-edge stopping and phase-stop lineage.
#20, #34	RaD / hipotures, jamesyc and Chafik Boukhalfa	Balanced positional prefix and retained assembly composition.
PR #23, #97	Zhihao Chen / jacklightChen	Semantic assembly and physical bit-word/frame conventions.
#128	an664	Completed-core sharing principle, retaining reported Codex assistance.
Underlying bit witnesses and pair modules	Swapnil Jain	Frozen bit/module lineage and original assistance disclosure.
Original repository and manuscript	Douglas Colkitt and the upstream OpenAI authors	Analytic framework and original machine model.

Most of the improvement over reviewed main is inherited from the public reference. This round adds source-assisted common-frame lifts, controlled affine cleanup, compatible fresh-zero routing, exact local and boundary certificates, prefix-optimal kernel allocation and the new integration. It claims no exclusive priority for broad register reuse, paired cubes or ordinary elimination. Full original credits and source-specific licenses remain in research/source-assisted/CREDITS.md and the byte-preserved dependency closure.

Proof and attribution

• notes/source-assisted-note.tex: dirty-lift theorem, actual control availability, cleanup, complete selected ledgers and conditional assembly; LaTeX source only.
• research/source-assisted/: selected complex flow/lifts, bit boundary/templates, finite bridge and immutable PR168 dependency closure. The flow and immutable 101-file reference are stored compressed; the verifier materializes them outside tracked sources.
• scripts/source_assisted_verify.py: source-bound focused regeneration and deterministic published certificate.
• scripts/source_assisted/complex_allocated_replay.py: independently allocated new complex scalar transcript, newly evaluated dirty response, endpoint/restoration probes and mutation controls.
• certificates/source-assisted-network.json and certificates/source-assisted-validation.json: exact arithmetic and the explicit validation receipt.

The new research is contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance; repository integration and the independent scalar replay use Codex assistance. Imported authorship, copyright, licenses and historical assistance disclosures are preserved.

The result remains conditional on the retained framework. The new complex transcript is a scalar quotient replay, not a materialized Clifford/router implementation or exhaustive dirty-column proof. The new globally renumbered bit transcript and its dirty replay are not exported; the bit construction is supported by exact local lifts, unchanged boundary/resource checks and the retained suffix proof. These limits are stated separately from the arithmetic result. The reviewed main selection is preserved pending maintainer review.

Validation

• Checked the supplied selected source hashes and all 76 certificate-bound parent inputs.
• Regenerated the complex graph, frozen physical matching and kernel flow; matched the selected witness, all complete histograms and exact scalar-program digest.
• Checked 18,369 exact local maps, 60,900 inverse elementary operations, every fresh endpoint column and the actual source-control/target chronology.
• Reconstructed 2,640 bit lift instances and compared all 37,436 high-boundary/suffix forms and 2,832 rank-three resources, retaining the gauge tails and compensated aliases.
• Checked all 20 matching-prefix certificates, both exact moments, rare-class charges, atom stopping, the finite bridge and all 47 strict assembly constraints and seven margins.
• Emitted 68,393 operations on 11,056 globally allocated complex auxiliary slots. Four nonzero dirty probes over two primes passed endpoint and restoration; omitting a source erasure or reversing an original V injection was rejected.
• Refreshed the joint-dual source manifest and dependent certificate/receipt hashes; confirmed unchanged joint mathematical fields and prior replay payload.
• Checked deterministic certificate bindings and staged whitespace. No PDF compilation or unchanged historical full-suite rerun.

Reproduce this increment with make source-assisted-verify after installing research/source-assisted/requirements-round13.txt. make source-assisted-arithmetic checks recorded profiles and exact arithmetic only.

[icekylinx]

Closing this PR because newer work has superseded its result. The source-assisted construction, proofs, and validation records remain available in this branch for reference.