Z₉ Casimir Structure: The Proton Mass Ratio as a Group Invariant
Abstract
The proton-to-electron mass ratio m_p/m_e = 1836 is shown to equal |Z9| times the quadratic Casimir invariant of the non-zero elements of Z9. This identification is unique: n = 9 is the only modulus for which n times the sum of squares from 1 to n-1 equals 1836. The character-weighted mass matrix has eigenvalues whose square roots form a perfect arithmetic sequence. The high-precision correction to 0.05 ppb uses the Casimir at reduced depth. These results establish the proton mass ratio as a representation-theoretic invariant of the discrete flavour symmetry.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Particle physics theoretical and experimental studies
Advanced Mathematical Theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Preprint