F.L.A.V.O.R.: Fractional Lattice Anchors Via Orthogonal Reduction

Within the Standard Model, the mass hierarchy of the quark family is governed by arbitrary Yukawa couplings, offering no fundamental mechanical explanation for the vast disparity between the ultra-light up quark and the phenomenally massive top quark. Building upon the discrete 6D (3s+3t) spacetime lattice, this letter demonstrates that the entire quark mass spectrum is not dictated by arbitrary field couplings, but by strict topological limits of a confined temporal tether. By applying the geometric operators established in the P. R. I. S. M. framework, I geometrically derive the masses of all six quark flavors without the use of free parameters. The top quark (mₜ = v / 2) represents the un-reduced isometric projection of the Higgs rigidity. Crucially, this geometric reduction reveals a hidden scale-invariant cascade, where the quark generations are separated by exact powers of the fine-structure constant (mc = mₜ ₀, and ₔₔ₃ = mₜ ₀²). The bottom quark represents the 3D spherical saturation limit, and the light quarks (strange, down, up) emerge through dimensional subdivision of the internal hadronic floor. This provides a complete, parameter-free geometric origin for fractional charges, hadronic color confinement, and the analytical 1\% proton mass fraction.