Inertial-Induced Time Dilation Near Criticality: A Double Scaling Exponent Beyond Critical Slowing Down

Classical critical slowing down (CSD) predicts τ _ relax ~ ε^{-β} near a bifurcation. We derive from two canon-published IDT theorems that physical-time relaxation yields τ _relax^phys ~ ε^{-2β}: a double scaling exponent arising from the Generalised Structural Inertia M(ω) and the reparametrisation dt = M(ω)dτ. Numerical simulation confirms slopes −1.000 (CSD) and −2.000 (IDT) to machine precision. The 2017 Taniguchi et al. experiment on STNO is fully consistent: they measured in the ε ∈ [0.1, 1.0] regime where both theories agree. A November 2025 experiment by Devolder et al. (arXiv:2511.10450) observes a divergent incubation delay at the magnon scattering threshold but does not measure the scaling exponent. We show the IDT-distinctive signal requires ε < 0.05, and provide a complete experimental protocol for immediate testing via µ-BLS on vortex STNO. Builds on: IDT P3 (10.5281/zenodo.18948975) · P7 v2.1 (10.5281/zenodo.18995629) · GAP3 (10.5281/zenodo.19014454)