This paper presents a computational bridge audit between the Fractal Consistency Law (FCL) research program and the modern theory of quasiperiodic quantum localization. The external physical anchor is the spinful quasiperiodic Raman Hamiltonian introduced by Zhou et al. (2026), where a single framework is proposed for organizing the fundamental Anderson localization phases: extended, critical, localized, and their coexistence grammars. The present work does not claim a direct validation of FCL cosmology, dark matter, dark energy, black-hole physics, or spacetime fractality. It tests a narrower methodological hypothesis: whether a structured quasiperiodic quantum substrate can generate a statistically separable corridor of multifractal critical coexistence when compared with random-potential nulls. The audit chain FCL-QP-8 to FCL-QP-13 uses multi-size participation-ratio scaling, phase averaging, generalized multifractal dimensions Dq, bootstrap confidence intervals, Mann-Whitney tests, Cliff’s dominance effect size, and a composite critical score. The final hardening audit, FCL-QP-13, finds that phase grammar alone is insufficient: the random-potential null can also yield the mixed grammar E + C + L. However, the quasiperiodic Hamiltonian exhibits a much stronger critical fraction, higher mean D2, higher scaling quality R², larger Dq-spread, and a critical score more than sixty times larger than the null. Bootstrap intervals for the core deltas remain strictly positive, and Mann-Whitney p-values are of order 10−13, with Cliff’s δ = 1 for all central metrics. These results support the FCL interpretation of multifractal criticality as an admissible intermediate regime between propagation and localization in a structured quasiperiodic quantum substrate. The result should be read as a laboratory-level methodological bridge for the FCL program, not as direct cosmological confirmation.
César Daniel Reyna Ugarriza (Mon,) studied this question.