Mass Hierarchy

Why is the muon 206.8× heavier than the electron, and the tau 3477× heavier still? The mass hierarchy of leptons and quarks from the torus knot spectrum is an open investigation.

Unlike the Standard Model, where masses are free parameters, the CPT framework views the three generations of leptons as excited states of the same topological class. The electron , muon , and tau share identical quantum numbers but possess radically different rest masses.

Excited State Hypothesis

Another remarkable mystery is the Koide formula, an empirical relation completely unexplained by the Standard Model. CPT models aim to derive this relationship directly from the energy quantisation rules of the torus knot.

Koide Formula

A similar problem is the quark mass hierarchy: why is GeV but MeV? Currently, the mass hierarchy is ordered by the self-linking number, indicating that different generations represent higher resonances of a fundamental topological class. Identifying the exact eigenvalue spectrum for higher winding levels is an ongoing research direction.

Integrity Status: Open [O]

While the qualitative mechanism of resonance states is clear, the exact numerical derivation of the mass hierarchy, including the Koide formula and quark mass extremes, remains an active open investigation.

Source Documents

The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.

Genuine Spectrum Programme

Documents open in the CPT Research Library — a formatted viewer for all source research files.