Overview
This article investigates how discrete generational structures can emerge from the spectral organisation of relational systems. In many physical theories the existence of particle generations and large mass hierarchies appears as an empirical fact rather than a structural necessity.
The analysis introduces the notion of spectral stratigraphy: a hierarchy of stabilisation depths associated with eigenmodes of a relational Laplacian. When spectral sectors become stabilisable at different stages of the relaxation cascade, the resulting profile naturally forms discrete stratified levels.
Within this framework, particle generations correspond to clusters of modes that stabilise at comparable cascade depths. The number of generations is therefore controlled by the structure of the underlying relational spectrum.
Core contributions
- Spectral stratigraphy: introduction of a stabilisation-depth profile describing when spectral modes become dynamically accessible.
- No-go result: scalar stabilisation thresholds cannot produce discrete generational structure.
- Representation-theoretic mechanism: discrete spectral levels arise naturally from the representation structure of relational graphs.
- Three-level spectra: several relational graphs exhibit exactly three non-zero spectral classes.
- Structural interpretation: particle generations correspond to spectral strata of stabilisable modes.
Interpretation
The analysis reveals a natural separation between the structural origin of particle generations and the physical mechanisms controlling mass scales.
- Group topology determines the number of spectral strata and therefore the number of particle generations.
- Projective dynamics determines the separation between stabilisation depths and therefore the hierarchy of masses.
- Admissibility constraints determine which spectral sectors stabilise first.
Within this perspective, the existence of three particle generations can be interpreted as a consequence of discrete spectral organisation rather than an arbitrary property of the Standard Model.
Relation to the Cosmochrony program
Spectral stratigraphy complements other components of the Cosmochrony research program. Spectral admissibility characterises which modes can exist under bounded relational flux, while spectral capacity measures the aggregate admissible content of a relational system.
Spectral stratigraphy adds a dynamical dimension by analysing when different sectors stabilise along the relaxation cascade. Together these elements form a coherent framework linking relational spectra to particle phenomenology.
References
Jérôme Beau. Spectral Stratigraphy and the Emergence of Particle Generations. Preprint, Zenodo.