7.16 Geometric Framework for the Quark Mass Spectrum

Abstract

This article establishes a geometric framework for the quark mass spectrum. The quark sector differs fundamentally from the lepton sector — confinement implies that quarks are not asymptotic states, color constraints render the hierarchy formula inapplicable, and there is no framework-endogenous anchor point analogous to the electron mass. The current framework is divided into four tiers: (I) **Structure Tier** — the constraint structure of three-generation coding weight configurations ({2,3,5} Interlock Property, Birkhoff Mixing Matrix Spectral Rigidity, Color Singlet), theorem-level; (II) **Scaling Tier** — the mass operator M̂ (3.1 §5) directly applicable to , theorem-level but with obtained by back-inference from external mass input; (III) **Anchoring Tier** — the geometric origin of first-generation quark , open; (IV) **Splitting Tier** — the differences between up-type and down-type quarks and the correction factor for heavy quarks, partially directional. Each tier's theorem propositions, external input status are stated. **Honest Statement:** The quark mass spectrum has not yet achieved theorem-level closure comparable to the lepton mass spectrum. The current framework provides the correct constraint structure (theorem-level), but numerical predictions still rely on external PDG mass input as anchor points. Once the Anchoring Tier is closed, the quark mass spectrum will become a pure prediction of the framework.