Charged Lepton Masses from the Recognition Composition Law: A Derivation with Zero Continuously Adjustable Dimensionless Parameters

We derive the charged lepton mass chain from the Recognition Composition Law (RCL) together with normalization, curvature normalization, and standard regularity. Through the theorem chain Tr1–Tr8, these postulates fix the golden ratio: φ = (1 + \ (5\) ) /2, the minimal period Tmin = 8, the selected dimension D = 3 and the cube integers entering the master mass law. The charged lepton formula is then assembled from the coherence scale, the lepton-sector baseline, the charge correction, and the derived generation steps. All parameters are discrete structural inputs, integers from cube geometry, named symmetry factors, and one external mathematical constant, rather than continuously adjustable dials. The construction is a structural constraint on the effective charged-lepton flavor pattern, not a replacement for the electroweak Higgs mechanism or for the full Standard Model quantum field theory. At the conversion stage to the International System of Units (SI), the electron fixes the single calibration anchor τ0, while the fine-structure constant α enters only as a fixed external dimensionless constant in the refinement layer. The phrase “zero continuously adjustable parameters” refers to the dimensionless content of the framework: the anchor τ0 is a unit-scale calibration fixed by the measured electron mass and cancels identically from every charged-lepton mass ratio. With that one anchor set, the remaining charged leptons become forward predictions: mμ∈ (105. 5, 105. 9) MeV and mτ∈ (1774, 1779) MeV, with relative errors below 0. 3% and 0. 2%, respectively. Floating-point evaluation gives mμ ≈ 105. 658 MeV and mτ ≈ 1776. 71 MeV.