OMEGA Marked Reference Geometry: Construction-to-Curve Theorem for a One-Arcsecond Circular Seed with Bilateral Golden Extensions

Cite this work

@misc{newman2026omega-vii,
  author = {Newman, Matthew Alan},
  title = {OMEGA Marked Reference Geometry: Construction-to-Curve Theorem for a One-Arcsecond Circular Seed with Bilateral Golden Extensions},
  year = {2026},
  date = {2026-09-01},
  doi = {10.5281/zenodo.22233573},
  url = {https://zenodo.org/records/22233573},
  note = {Version 1.6, Zenodo record 22233573. Concept DOI 10.5281/zenodo.22233572 identifies all versions. Preprint; not peer reviewed. Companion generator evaluates closed formulas; it is not a theorem checker. Local versions 1.4, 1.2, and 1.1 are superseded drafts. Zenodo publication-date field is 2026-09-01. Manuscript cover and record-creation timestamp are 2026-09-02.}
}

Complete BibTeX · CITATION.cff

Claims on this archive that cite this paper

• Typed exact interfaces among Papers VII, V, I, II and frozen SRSD — theorem claim
• Construction-to-OMEGA uniqueness of the marked kernel — theorem claim
• Three fundamental bearings and the complete center-angular law — theorem claim
• Exact 3D reconstruction and positive-homothety family — theorem claim
• Notebook outer scaffold is an adopted transcription; remaining completion is not claimed — adopted definition plus derived identities in the Zenodo preprint; remaining outer completion is a status statement
• Experimental 4D OMEGA rotation is not a privileged memory anchor — numerical experimental control; not a theorem
• Kernel construct node log and presentation machine — implementation interface around Paper VII; not a theorem and not a second evaluator
• De-branded executable audit of typed maps — executable mathematical audit of de-branded maps; not a joining theorem and not a formal proof-assistant kernel
• Lean 4 formalization of a selected geometric-provenance measurement — author-supplied Lean 4 formalization of a selected geometric-provenance measurement; hosted sources match package SHA256SUMS; lake build PASS on this archive 2026-09-13 (build.log SHA-256 ddc10580…); axiom audit 147 reports, axioms {propext, Classical.choice, Quot.sound}; Python axiom-coverage PASS; not a joining theorem, not peer review, and not independent reproduction of Papers I–VII
• Julia mathematical proof companion of a selected geometric-provenance measurement — companion software 0.1.0 / package v0.1: written proofs plus exact finite certificates corresponding to 147 Lean declarations; hosted 68 members recovered from the Word transcription match SHA256SUMS byte-for-byte; 29 Lean reference files are byte-identical to /formal/; author-supplied Julia 1.11.6 O0/O3 exit 0 is archived evidence, not a run on this archive; not a joining theorem, not an additional source paper, not peer review, and not independent reproduction of Papers I–VII
• Six-mark projective recognition, landmark decoding, and baseline integration bounds — written additional consequences developed in exploration 02 using established methods. Not a theorem of Paper VII. Canonical seed remains one arcsecond. Priority of the applications is not assessed.
• Positive quadrature classification for the symmetric six-node family — Written proofs in PROOFS.md. Computational checks corroborate selected identities. Not a theorem of Paper VII. Canonical seed remains one arcsecond.
• Explicit minimal ten-sample reconstruction of H≤2 ⊕ ℝJ — Written supplementary note, 23 September 2026. Not a theorem of Paper VII and not an additional counted source paper. Ten is minimal for scalar point samples on this space. The thirteen-sample arrangement's three consistency equations are not an error-correction guarantee. General transport is the written argument; two rational executions are finite checks.
• Ellipse and operator note, documentation only — Documentation of a hosted derived note. Not a theorem status, not a Paper VII amendment, and not an additional source paper.
• Six-mark sampling polar, with a conditional packing — Direct identities for the declared sampler and sample bound. The packing statement is conditional on two external hypotheses that this note does not establish. Not a source paper and not an amendment of Paper VII.
• Transition invariants: symbolic identities and a finite ledger audit — An exact symbolic-algebra checker with a finite canonical-ledger audit. Both executions reproduce the declared checks. Neither establishes physical unification or independent mathematical review.
• Self-similarity, numerical difference, and exact recovery — The hosted note states five conclusions and written arguments for them. This archive has not reviewed those arguments as a proof. The checker rerun reproduces the declared symbolic checks, rational certificates, and finite ledger audit. Not a source paper and not an amendment of Paper VII.
• Integration proof bundle, 14 October 2026 — The hosted ledger states written arguments. This archive has not reviewed them as a proof. The Python checker was rerun and reproduced the declared algebra checks and finite audit. Not a source paper, not an amendment of Paper VII, and not a certificate of an external mathematics release.
• Relative representation and recoverable information, 15 October 2026 — The hosted thesis states written arguments. This archive has not reviewed them as a proof. A transcription of the printed checker was rerun and reproduced the declared symbolic checks and finite audits. Not a source paper, not an amendment of Paper VII, and not a certificate of the unseen companion bytes.