τ-Down Quark
The τ-down quark is the heavier member of the first-generation quark mode pair on the T² fiber: a fractional-charge (−1/3) winding mode that, paired with the up mode, supplies the neutron's (udd) and proton's (uud) winding signatures and is the d→u differentiation handle for β-decay.
τ-Definition
The τ-down quark is the heavier member of the first-generation quark mode pair on the T² fiber: a fractional-charge (−1/3) winding mode that, paired with the up mode, supplies the neutron's (udd) and proton's (uud) winding signatures and is the d→u differentiation handle for β-decay.
Categorical invariant. Heavier first-generation quark mode on T²; fractional charge −1/3; differentiation partner of the up mode under β-decay.
Primary registry anchor:
IV.D187
Supporting items:
IV.D549,
IV.D374,
IV.D377,
IV.D382,
IV.P113,
IV.T275,
IV.P330
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.D374— Epstein-zeta quark mode spectrum sets the mass ladder -
IV.P113— Quark electric charges = ±1/3, ±2/3 from winding fractions -
IV.T275— Fractional Quark Charges theorem — winding sums project to thirds -
IV.P330— Down mode appears twice in (udd) neutron, once in (uud) proton
Lean modules referenced:
TauLib.BookIV.Strong.QuarksGluons,
TauLib.BookIV.Particles.BetaDecay
SI Translation
Numerical value: 8.46e-30 ± 0.5e-30 kg
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- ι_τ ≈ 0.341304
- Epstein-zeta spectrum (IV.D374)
- Six-Quark Wave-45 table (IV.D382)
Manuscript reference: manuscript-sources/book-04/part04/ch32-strong-coupling-quarks.tex
Lean Coverage
Status: Formalized
Module: TauLib.BookIV.Strong.QuarksGluons
Lean kind: theorem
Lean symbol: QuarksGluons