Exact Recovery on the 600-Cell: Quantization, Residue Witnesses, and Finite Histories

Zenodo preprint, version 0.6. Publication-date field 2026-11-05. Exact recovery of an integer state on the 120 vertices of the 600-cell from the specified reduced output and 120 predecessor residues modulo 8. The residue witness is 360 bits, 45 bytes. A separate output-conditioned capacity argument gives 307 ≤ ℓ* ≤ 352. The exact optimum, efficient general decoding, and application advantages remain open.

Site label Paper IX matches the manuscript heading. Zenodo record 23688676 is published. Resource type: preprint. Version field: 0.6. Version DOI 10.5281/zenodo.23688676. Concept DOI 10.5281/zenodo.23688675. The Zenodo title field is “OMEGA NAUGHT. Paper IX: Exact Recovery on the 600-Cell”, with two spaces after the period. Publication-date field 2026-11-05. Record created 2026-11-05T22:13:34.402171+00:00. Not journal acceptance and not peer review.

The stated theorem is that the reduced output together with the 120 predecessor residues modulo 8 determines the integer input. That witness is exactly 360 bits, packed as 45 bytes. Those 360 bits are the complete residue vector. They are not claimed to be the minimum width of every recovery witness that may use the output. A separate lattice-coset argument gives 307 ≤ ℓ* ≤ 352 for that output-conditioned question. The exact optimum, a fast general decoder, and any application advantage remain open.

The 27 October pages keep the assessment statement 306 ≤ ℓ* ≤ 360. This preprint does not rewrite those pages. The hosted graph fixture matches that assessment: SHA-256 40bc6a1d52efab3d75cf343e65ac06b314f9c9c375fc02bf6d45bf6bb21f9529.

The Zenodo PDF key is “The Paper 9 .pdf”, 549,706 bytes, SHA-256 edb90f35abe01f474ef14c0a77071d30a474bdbd420993ec82ca5b286649f7a3. That digest matches the package’s RELEASE_METADATA field for the file it names OMEGA_NAUGHT_Paper_IX.pdf. The Zenodo ZIP key is “The PAPER 9 zip .zip”, 3,193,848 bytes, SHA-256 139a299cc03ddfed868533c48508e1f90af2ae1842812952021acbbb07cd8d02. Those two files are not the earlier hosted draft PDF (460,107 bytes, SHA-256 61692f43daec78371e6e3690e5ef2b436ecea5047f0d66c5d6e964e142118c2f) or the earlier hosted ZIP (3,199,041 bytes, SHA-256 b9799759c4cfcea0b29259bdf460fc4ae89225f10f09250502a3d4e210065ea2). The manuscript source inside the Zenodo ZIP is SHA-256 cf4218348c63d3540a4152ccec892cad0c25e87b76450e0fc661dc117e32b8e5, not the earlier hosted source c7136b24c646bb87c089b0ff1f427f243f50737a69c04f58cc717d3c297f5fb5. Flags inside the ZIP that say publication was not performed are preparation text. They are not the retrieved API state.

The checker inside the Zenodo ZIP is byte-identical to the hosted core_certificate_check.py, SHA-256 79e67b233c345cd57aa3a3789923ae06336fc07045907c6eb4ee2ea7da452ad4. This archive ran that script on Python 3.10.21, normal and optimized, before the deposit retrieval. Both exited 0, stderr was empty, and both JSON reports matched the supplied files (SHA-256 1cda37c790071935774be9e98e95feee42465c7a654a3534cf6e5f71dce096f1). The report status is PASS. Its global_cover_checked_by_this_script flag is false. That run was not repeated for this retrieval. The reference-bounds suite was not rerun. Formalization was not completed. A matching digest checks byte integrity. It does not itself verify that the recorded execution occurred or that the checker is mathematically correct.

Deposit mirror: PDF · source ZIP · retrieval note · Zenodo API snapshot. Earlier hosted draft, not the deposit bytes: draft PDF · draft ZIP · core certificate checker · checker execution note. The readiness file’s status string remains the package’s own earlier record. It is not this publication status.

Publication: Zenodo preprint. Peer review: not peer reviewed. Zenodo publication-date field 2026-11-05. Record created 2026-11-05T22:13:34.402171+00:00. Document version 0.6. Zenodo deposit version 0.6.

Zenodo preprint version 0.6, record 23688676. Version DOI 10.5281/zenodo.23688676. Concept DOI 10.5281/zenodo.23688675. Zenodo metadata title is “OMEGA NAUGHT. Paper IX: Exact Recovery on the 600-Cell” (two spaces after the period). Publication-date field 2026-11-05. Record created 2026-11-05T22:13:34.402171+00:00. Not peer reviewed. The Zenodo file keys are not the package’s intended filenames, and those bytes are not the earlier hosted draft PDF or ZIP. The 27 October interval 306 ≤ ℓ* ≤ 360 is a separate record and is not rewritten.

Open PDF: /papers/ix/zenodo-OMEGA_NAUGHT_Paper_IX.pdf. Local mirror on this archive.

Zenodo file download: https://zenodo.org/records/23688676/files/The%20Paper%209%20.pdf?download=1

Research branch: dynamics · All source works

The archive makes no blanket claim of novelty, priority, peer review, or independent validation. Some displayed identities are standard or definitional and are included to make the computational specification self-contained. Any claim of originality must concern a specifically stated formulation or derived result and must be evaluated separately against the relevant prior literature.