OMEGA NAUGHT Julia mathematical proof companion

The 68 original members were recovered from OMEGA_NAUGHT_Julia_Proof_v0.1_Complete_Verbatim.docx and match SHA256SUMS byte-for-byte (74,508 source lines). Author-supplied Julia 1.11.6 O0/O3 run records are archived evidence and are not a run performed by this site. The reproduction driver updates run metadata, so archived evidence should be retained separately from any later execution. The original ZIP container was not recovered from the Word file; those same bytes are now hosted as /extension/sources/Julia_OMEGA_NAUGHT_Julia_Proof_v0.1(1).zip (1,681,923 bytes, SHA-256 ef8f1eb7…). The reconstructed transport ZIP under /julia-proofs/downloads/ is a later packaging of the recovered members and is not that original container. Cubature 10–21 and f=23,24 exact packages are hosted separately under /cubature/; they are not supplied by this Julia companion. lake build of the Lean package was run on this archive on 2026-09-13; see /formal.

Package README: README.md · 6289 bytes · SHA-256 71de22038e8c4ebe9bb391d7e4b995adf4061b1494e4d075f629c73bd0746c78Copy. Inventory: SHA256SUMS · 6301 bytes · SHA-256 716a6659ff5893f722854e13a6a97e7d30235e7f5268ad3a4e02c21cd25096f9Copy. Theorem guide: THEOREM_GUIDE.md. Machine inventory: THEOREMS.toml. Lean sources of the corresponding selected-measurement formalization: /formal.

The companion is written mathematics plus exact finite certificates for maps already typed among the marked kernel, the selected golden and circular readouts, the contraction parameter, the 15-bit floor agreement, quantized trajectories, and ledger reconstruction. Frozen SRSD v1.0 remains an external encoder. Cubature remains independent.

The eight source works stay eight. Registering this package as companion software does not add an additional source paper.

The companion preserves all 147 theorem declarations of Lake package omega_provenance v0.1 and all 29 Lean reference files under reference/Lean/. Those 29 files are byte-identical to the overlapping hosted files at /formal. The Lean page keeps archived Lean evidence and the Julia execution records separately identified. A Python axiom-coverage PASS on the axiom log is not a Julia run. lake build of the Lean package PASS on this archive 2026-09-13; that is not a Julia execution.

Main Lean result: Omega.central_provenance_theorem in /formal/Omega/Main.lean. Selected measurement, not uniqueness among all measurements of an unmarked outline.

Under the specified measurement rules of the marked construction, the selected golden readout is the average of the two outer segment lengths, and the selected circular readout is the opposite-semicircle length:

Then $\lambda=\varphi/(\varphi+\pi)$ is the declared contraction parameter of Newman’s Omega map, obtained as the ratio of those two selected lengths. Those are measurements of named components of the specified construction. The total outline length is a different quantity.

From the hosted TRANSLATION.md (9240 bytes · SHA-256 9b6c232e062806665a3223f90edad4e838988f188b36bfb95a147d39245eadb7Copy):

• The finite-gap inequality includes equality at $d=0$.
• The general arc integral is oriented.
• The signed-ledger and validated-API domains must be stated accurately.
• Frozen SRSD remains the external interface.

Author-supplied Julia 1.11.6 records, hosted as archived transcripts and not executed on this archive:

Typed-network maps that the companion evidences: geometric readout, weighted mean, finite-domain floor agreement, quantized trajectories, and ledger reconstruction. Proof chapters: PROOFS.md. See typed network.

Tested environment named by the package: Julia 1.11.6, standard library only. Run from the package root (the hosted tree at /julia-proofs/). The reproduction driver updates run metadata, so archived evidence should be retained separately from any later execution.

Expected, from the author record, not generated here: inventory match against SHA256SUMS; O0/O3 exit 0; six identical certificate files; 147 indexed declarations. Julia is not installed on this archive.

Author-stated original ZIP Julia_OMEGA_NAUGHT_Julia_Proof_v0.1.zip SHA-256 ef8f1eb75b83f1e5763d280374eb8b73d9ab00b8dcb76b1824aee771869cd27aCopy. Those bytes were not recovered from the Word file. The same original container is now hosted at /extension/sources/Julia_OMEGA_NAUGHT_Julia_Proof_v0.1(1).zip (1,681,923 bytes, SHA-256 ef8f1eb7…). The reconstructed transport ZIP below is a later packaging of the 68 recovered members and is not that original container. The Word document preserved the 68 members, recovered here via styles FileMetadata, SourceBoundary, SourceText, and SourceData.

68 files, 74,508 source lines, 3,847,030 uncompressed bytes. Prefix OMEGA_NAUGHT_Julia_Proof_v0.1/ stripped, as with /formal/. Extra files under /julia-proofs/downloads/ are not members of SHA256SUMS.

• Not an additional source paper.
• Not a joining theorem of the eight source works.
• Not peer review.
• Not independent third-party reproduction.
• Not the cubature packages. Frequencies 10–21 and 23–24 are hosted separately under /cubature.
• Not a replacement for lake build of the Lean package (that kernel-check was run on this archive on 2026-09-13; see /formal).
• Not a Julia execution performed on this archive.
• Not the existing geometry plotting script omega_kernel_oriented_r3.jl, which remains a numerical visualization tool.

Related: Lean formalization · Geometry · Typed network · Dynamics · Ω₀ · Reproduce · Status