τ-Heavy Quark Families (charm, strange, top, bottom)
The τ-heavy quark families (charm, strange, top, bottom) are the second- and third-generation quark modes on the T² fiber: rungs 3–6 of the Epstein-zeta quark spectrum, sharing the up/down winding-fraction template but at higher generation labels, with the top quark distinguished as the unique confinement-free quark by mass-scale theorem.
τ-Definition
The τ-heavy quark families (charm, strange, top, bottom) are the second- and third-generation quark modes on the T² fiber: rungs 3–6 of the Epstein-zeta quark spectrum, sharing the up/down winding-fraction template but at higher generation labels, with the top quark distinguished as the unique confinement-free quark by mass-scale theorem.
Categorical invariant. Rungs 3–6 of the Epstein-zeta quark spectrum: second-generation (c, s) and third-generation (t, b) winding modes on T².
Primary registry anchor:
IV.D549
Supporting items:
IV.D187,
IV.D374,
IV.D377,
IV.D382,
IV.D189,
IV.P218,
IV.T183,
IV.P113,
IV.T275
τ-Derivation Chain
-
IV.D12— Particle Kind: a particle is a stable defect bundle on the T² fiber -
IV.D187— Quark mode: the fractional-winding family on T² fiber -
IV.D549— Six Quark Flavours organized in three generations -
IV.D189— Quark generations from Lemniscate caps the family count at three -
IV.D374— Epstein-Zeta Quark Mode Spectrum sets the mass ladder -
IV.D382— Updated Six-Quark Table (Wave 45) — current ledger of mass values -
IV.P113— Quark electric charges = ±1/3, ±2/3 from winding fractions (generation-independent) -
IV.T183— Top Quark Mass from Fiber Amplitude at +7200 ppm -
IV.P218— Confinement-Free Top Quark — mass-scale exceeds confinement scale
Lean modules referenced:
TauLib.BookIV.Strong.QuarksGluons,
TauLib.BookIV.Particles.ThreeGenerations
SI Translation
Numerical value: see-table-below ± see-table-below kg
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- ι_τ ≈ 0.341304
- Epstein-zeta quark mode spectrum (IV.D374)
- Wave-45 six-quark table (IV.D382)
Manuscript reference: manuscript-sources/book-04/part05/ch36-koide-mass-hierarchies.tex
Lean Coverage
Status: Formalized
Module: TauLib.BookIV.Strong.QuarksGluons
Lean kind: theorem
Lean symbol: QuarksGluons