# Publication Status and Claim Boundaries

Version 1.0, 18 October 2026. This is an illustrated mathematical research report and a reproducibility collection prepared for the Mathematics of Sound section of the Bass Plus website.

## What the package establishes

The mathematical appendix supplies full proofs for the results promoted in the current report, including the normalization, phase-mass estimate, fixed-size attainment, moment hierarchy specialization, explicit Chebyshev sufficient degree, spectral identities, finite-box error, grid counterexample, grid discretization bounds, weighted-amplitude obstruction, and several limitations of proposed detector functionals. Exact certificates and finite enumeration records support the stated examples on their declared domains.

## What remains open

The package neither proves nor disproves the existence of an absolute positive constant in Chowla's square-root lower bound. It does not identify the best universal constant. Values from finite searches, including 7/20 for a specific Riesz-product quotient on subsets of {1,...,18}, are not promoted to universal theorems.

## Attribution and priority

The polynomial quotient hierarchy is a specialization of Lasserre's established pushforward measure hierarchy. Chebyshev and needle-polynomial concentration methods are established prior art, including work by Slot and Laurent. The appendix proves explicit constants for a specialization uniform in the largest frequency, but priority for that specialization has not been established. No result is marketed as a newly proved famous conjecture or as an independently verified OpenAI discovery.

## Review status

The materials were checked through derivations, exact arithmetic, selected repeated computations, and review within the same ChatGPT-assisted workflow. They have not received external peer review and were not formally verified in Lean, Coq, or another proof assistant. Code checks certify their specified computations, not every mathematical sentence in the research history.

## Historical completeness

All currently available research source files are included. The original bytes of approaches 41–50 were not available; explicit reconstructions are supplied. In particular, the earlier set of 1,980 certificates associated with approach 42 is missing. Historical notes are preserved for traceability and can contain superseded statements. The curated English report, catalogue, and corrections take precedence over those older statements.

## Authorship and publication

Prepared as CliDeck Research Notes, initiated by the Bass Plus project owner with ChatGPT assistance for research, writing, calculations, and code. No unprovided personal name, institutional affiliation, or third-party endorsement is assigned. This package is a publication handoff: preparing it has not changed the live Bass Plus website. The accompanying Codex instructions specify the website publication task.