Geometric Control of Quantum Time Delay in Non-Smooth Regimes: Operational Descriptors, Spectral Mechanism, Scaling Laws, and Falsifiability

Scope (minimal thesis): The record contains (i) the main preprint (PDF), (ii) LaTeX source (fully reproducible), and (iii) an extended “explainer” PDF (intuition-first, minimal prerequisites, with figures and tables). Key idea: effective degradation of geometric regularity—defined without smooth curvature—can act as a temporal bottleneck, increasing measurable quantum time delays. Operational proxies: (1) volume-growth/ball-measure deficit proxy , and (2) spectral/heat-kernel descriptors including spectral dimension . Mechanism anchor: geometry-induced spectral modifications can shift scattering phase through spectral shift theory (Kreĭn / Birman–Yafaev viewpoint), hence modifying EWS delays. Test program: controlled families where a geometric scale is varied at fixed probe conditions; fit versus and apply falsifiability Types I–III. Non-claims: no new gravity, no QM violation, no “free energy”, no universal constant assumed a priori. Reproducibility: theoretical/conceptual; no proprietary data required.