From Fractal Consistency to the Charged-Lepton Mass Hierarchy

This paper presents a theoretical and computational program for deriving the charged-lepton mass hierarchy from the Fractal Consistency Law (FCL) and its Principle of Minimal Inconsistency (PMI). The central thesis is that the charged leptons e, mu, and tau are not independent mass inputs but admissible eigenmodes of a graph-induced operator architecture in which geometry, dynamics, and grammar are jointly active. Geometry is encoded by a structural inconsistency functional IC|F, a textural correction ThetaL, and a textural Laplacian DeltaTheta; dynamics is encoded by a fractional transport operator UD with the balanced exponent alpha = 3/2; and grammar is encoded by PMI, which selects the least inconsistent family-compatible configurations. The paper reconstructs the sequence of FCL-PMI tests developed in this research session, from early graph-toy failures to a preregistered algebraic-operational validation, FCL-PMI-18b. The main result is that the full FCL-PMI module, using kvac = 4, Gammamax = log (1 + kvac²), deltachiTheta = 1/ (6 kvac²), and a PMI-derived modal-balance condition Qphase = 2/3, reproduces both charged-lepton mass ratios with sub-1% accuracy: mmu/me = 205. 9600667 against the CODATA value 206. 7682827, and mtau/mmu = 16. 8238358 against approximately 16. 8170. Ablations and null controls fail to reproduce both ratios simultaneously. The work does not claim a final empirical derivation of particle masses; rather, it provides the strongest operator-level and toy/medium computational closure obtained so far within the FCL program, and it defines the remaining path toward full microscopic graph-ensemble validation.