ZENODO DEPOSIT TEXT — PAPER IX, DRAFT 0.6

TITLE
OMEGA NAUGHT -- Paper IX: Exact Recovery on the 600-Cell

SUBTITLE
Quantization, Residue Witnesses, and Finite Histories

CREATOR
Newman, Matthew Alan
ORCID: https://orcid.org/0009-0007-5468-3125

RESOURCE TYPE
Publication / Preprint

VERSION
0.6

LANGUAGE
English

MANUSCRIPT DATE
5 November 2026. Enter the applicable publication date in the deposit form.

KEYWORDS
Reversible quantization; Exact recovery; 600-cell; Integer separation; Side information; Lattice fibers; Finite histories

DESCRIPTION / ABSTRACT — COPY THIS PARAGRAPH
We study exact recovery for a quantized linear network on the 120 vertices of the regular 600-cell. Let A be its specified adjacency matrix, M = 13I + A, and T(d) = floor(339949771344778 Md / (25 × 10^15)) for d in Z^120. Although T is not injective, we prove that the reduced output together with the 120 predecessor residues modulo eight determines every integer input uniquely. The witness occupies exactly 360 bits, or 45 packed bytes. The proof combines an exact positive-definiteness certificate for M − 9I with integer separation and the strict difference bound for equal quantization cells. An exact inverse bounds each coordinate to an interval of width less than twelve; fixing its residue leaves at most two candidates, giving a complete finite decoder. Backward induction extends recovery to every finite trajectory when its terminal state and ordered witnesses are retained. We specify coordinate order, byte packing, portable integer interchange, and history framing, and provide reproducible exact checks. The 360-bit minimum for independently representing the complete residue vector is distinguished from the minimum of an arbitrary recovery witness conditioned on the output. A separate lattice-coset and geometric argument gives 307 ≤ ell* ≤ 352 for that latter problem. Its exact optimum, efficient general decoding, and application advantages remain open.

PREPARATION DISCLOSURE
The OMEGA research direction is Matthew Alan Newman's. Mathematical exposition, software preparation, consolidation, source comparison, and document production were AI-assisted. The author is responsible for the submitted claims. Additional AI-assisted reviews are not represented as independent human peer review or complete proof-assistant certification.

SUPPLEMENTARY MATERIAL DESCRIPTION
The source archive contains the editable LaTeX manuscript, exact integer
verification programs, finite decoder and record-format implementation,
coefficient and permanent checks, actual execution reports, reproduction
commands, audit response, and file manifests. The exact output-conditioned
minimum remains between 307 and 352 bits. No efficient general compressed
ranker, new endpoint, or complete Lean formalization is claimed.

DOI
Author-supplied identifier: 10.5281/zenodo.23688676.
Its reservation and deposit association remain unverified in this preparation.
Confirm it inside the actual deposit before using it as the final citation DOI.
The citation files omit a final DOI until that confirmation.

LICENSE
Choose the intended license as author in the deposit form. No license has
been selected on the author's behalf. Retain the bundled font license.

FILES TO UPLOAD TO THE SAME RECORD
1. OMEGA_NAUGHT_Paper_IX_Draft_0_6_2026-11-05.pdf
2. Paper_IX_Draft_0_6_Source_and_Certificates.zip

No deposit, public release, or peer review is claimed by these preparation files.

ILLUSTRATIONS
Two original images created by ChatGPT from the verified graph fixture
and a documented exact 2D packing analogue. No mathematical endpoint changes.
