Toward a Structural Law of Non-Exponential Quantum Coherence

This paper develops a publication-grade and explicitly falsifiable program for testing whether non-exponential quantum coherence admits a structural description compatible with the Fractal Consistency Law (FCL). The manuscript does not claim that every trajectory with a fitted exponent below unity is uniquely diagnostic of FCL. Instead, it proposes a hierarchy of evidence and a statistical workflow designed to separate compact structural description from genuine incremental specificity. The core inferential architecture compares three candidate laws for the normalized coherence function: an exponential model, a stretched-exponential model, and a Mittag–Leffler model representing stronger effective memory. A structural descriptor, G = Lf / rnn, is then tested against the fitted exponent beta through bootstrap inference, penalized predictive comparison, and nonlinear cross-validation. The evidence is organized as an evidence ladder. First, a published high-harmonic-generation (HHG) route is used as a negative control and shows that the methodology can return an unfavorable answer when the data prefer simple exponential decay. Second, a real quantum-dissipative benchmark based on QD3SET-1 spin-boson coherence trajectories shows that non-exponential behavior is physically meaningful and occupies a nontrivial region of parameter space. Third, synthetic banks validate the pipeline technically: they show that the workflow can recover beta–G laws when such laws are present and can discriminate G from collinear rivals when the structural signal is deliberately encoded. Fourth, a broad benchmark family demonstrates strong non-exponential prevalence, a persistent negative beta–G relation, and moderate support for G as a compact structural descriptor. The current evidence therefore supports an FCL-inspired structural program at a moderate level, but not yet at the level of strong empirical validation. The paper’s principal contribution is thus scientific and programmatic at once. It provides a coherent mathematical framework, a transparent hierarchy of evidential strength, benchmark-level quantitative results, and a detailed experimental NV-center program capable—in principle—of delivering strong validation. The manuscript is intentionally referee-hardened: it states explicit failure modes, preserves the distinction between benchmark and experimental evidence, and specifies what would be required for publication-grade strong validation in future real-data campaigns.