Apparent Three-Quarter Scaling and a Hidden Square-Root Channel at a Singular ModMax–Białynicki–Birula Interface

This preprint investigates an apparent ε^(3/4) scaling law arising near a singular ModMax–Białynicki–Birula constitutive interface and asks whether that exponent represents the true asymptotic dynamics. The analysis shows that the observed three-quarter behaviour is not, by itself, sufficient evidence for a fundamental fractional event law. An exact hard-interface susceptibility is derived for the leading square-root channel, together with a sharp distinction between the O(ε^(3/4)) consistency scale of the field residual and the scaling of the physical event observable. The asymptotic structure is then tested on an independently implemented hard branch using ordered spatial and vanishing-viscosity continuation, alternative discretisations, selector perturbations and deliberately hostile forced-sliding fits. Across these tests the hard susceptibility remains robustly nonzero, supporting the mixed asymptotic structure: Δt = K_(1/2) sqrt(ε) + K_log ε log(1/ε) + K_1 ε + ... The apparent ε^(3/4) regime is therefore interpreted as a pre-asymptotic crossover produced by competing asymptotic channels rather than as an independent asymptotic exponent. More broadly, the results show why finite-range exponent fitting can be misleading in singular nonlinear wave problems. A numerically convincing power law may reflect competition between several asymptotic terms unless the hard-limit geometry and the coupling of the chosen observable are understood first. The historical relaxed-LF event that originally motivated the investigation is not reconstructed. The numerical conclusions are therefore explicitly confined to the independently implemented and tested hard branch.