The Ramanujan-Yett Hamiltonian: Quantum Sovereignty and the Spectral Gap of the Sovereign Action (v1.1 — audit-corrected)

Dual-audit elementary-error fix on the v1.0 edition (PR #169, independent Claude-workbench and Chyren-via-Manus audits). Two real errors corrected: R2 — the Ramanujan tau function τ(n) was equated to the operator eigenvalue sequence {λ_n}, but τ(n) is sign-changing (τ(2)=−24) and unbounded (|τ(n)|~n^11/2), contradicting Theorem 1's proved bounded-below, gapped spectrum. Reframed τ(n) as a tonal-frequency labelling motif, explicitly decoupled from the literal H_RY spectrum. R6 — "boundedness below is immediate from V_s≥0" was false (V_s=−log(χ/θ)<0 throughout the sovereign band χ>θ); corrected to the valid argument that V_s has a finite floor logθ and T_r≥0. Conclusions of both theorems survive; the arguments supporting them are now correct. The Yang–Mills mass-gap identification remains an explicitly declared axiom [conj], not a discharged theorem.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-23
DOI
https://doi.org/10.5281/zenodo.21233985
Primary Topic
Quantum and electron transport phenomena
Type
article
Field-Weighted Citation Impact
0.00
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article

The Ramanujan-Yett Hamiltonian: Quantum Sovereignty and the Spectral Gap of the Sovereign Action (v1.1 — audit-corrected)

Ryan W. Yett
Zenodo (CERN European Organization for Nuclear Research)
Quantum and electron transport phenomena
article

The Ramanujan-Yett Hamiltonian: Quantum Sovereignty and the Spectral Gap of the Sovereign Action (v1.1 — audit-corrected)

Ryan W. Yett
article en

Abstract

Dual-audit elementary-error fix on the v1.0 edition (PR #169, independent Claude-workbench and Chyren-via-Manus audits). Two real errors corrected: R2 — the Ramanujan tau function τ(n) was equated to the operator eigenvalue sequence {λ_n}, but τ(n) is sign-changing (τ(2)=−24) and unbounded (|τ(n)|~n^11/2), contradicting Theorem 1's proved bounded-below, gapped spectrum. Reframed τ(n) as a tonal-frequency labelling motif, explicitly decoupled from the literal H_RY spectrum. R6 — "boundedness below is immediate from V_s≥0" was false (V_s=−log(χ/θ)<0 throughout the sovereign band χ>θ); corrected to the valid argument that V_s has a finite floor logθ and T_r≥0. Conclusions of both theorems survive; the arguments supporting them are now correct. The Yang–Mills mass-gap identification remains an explicitly declared axiom [conj], not a discharged theorem.

Zenodo (CERN European Organization for Nuclear Research)
Oldham Council (GB), Analysis Group (United States) (US)
Affordable and clean energy
Openalex Percentile: Top 18%
Quantum and electron transport phenomena
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