Paper II
Ordered Euclidean Remainders for Exact Orbit Reconstruction and Parameter Intervals in Rational Floor Maps
Newman, Matthew Alan (2026-08-09). ORCID 0009-0007-5468-3125.
Quotient and remainder data, forward and reverse reconstruction, finite-domain agreement and first-disagreement boundaries.
DOI: 10.5281/zenodo.21843485 · Zenodo record
Publication: Zenodo preprint. Peer review: not peer reviewed. Published 2026-08-09. Zenodo deposit version 1.
Zenodo deposit v1. The PDF filename contains a working-draft revision label v2; that is not a separate deposit version.
Open PDF: https://zenodo.org/records/21843485/files/V2Newman_Paper_II_Phase_Winding_2026-08-09_v2.pdf?download=1. Unique Zenodo PDF for this work.
Bundled local copy of Papers I–V: Global_Mathematical_Object_Papers_I-V_v1.0.pdf. Historical provenance bundle; bytes preserved; served noindex, noarchive. The canonical deposit remains the unique Zenodo record, not this bundle. The filename preserves historical “Global Mathematical Object” packaging and does not define current mathematical dependence.
Research branch: dynamics · All source works
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Cite this work
@misc{newman2026omega-ii,
author = {Newman, Matthew Alan},
title = {Ordered Euclidean Remainders for Exact Orbit Reconstruction and Parameter Intervals in Rational Floor Maps},
year = {2026},
date = {2026-08-09},
doi = {10.5281/zenodo.21843485},
url = {https://zenodo.org/records/21843485},
note = {Zenodo deposit v1. The PDF filename contains a working-draft revision label v2; that is not a separate deposit version.}
}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
- First floor-map disagreement at 42189065 — certificate-backed finite exact fact
- Exact 15-bit admissible interval and constrained optima — certificate-backed finite exact facts
- No accepted successor contract — status statement
- Omega-Alpha finite integer kernel and codebooks — exhaustively verified finite facts in the locally hosted synthesis
- Omega-Alpha is not a source paper — status statement
- 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
- 399 rational-floor reference kernel — Explanatory supplement for the map already published on /dynamics and used by the reconstruction tool. Not a new theorem and not an additional source paper. A valid suffix is another seed.
- General integer floor transition — Standard Euclidean division, written as an application record. Not a new theorem and not an amendment of Papers I–III.