Global 3D hydrodynamical simulations of near-Chandrasekhar-mass carbon-oxygen white dwarfs now incorporate a laboratory-validated turbulence-driven deflagration-to-detonation transition (tDDT) for the first time, replacing decades of ad-hoc detonation triggers. Across ignition densities spanning a factor of six and qualitatively different flame topologies, every model converges on nearly identical peak-luminosity spectra matching the overluminous SN 1999aa. The turbulence-driven Chapman-Jouguet criterion enforces a common detonation configuration irrespective of initial conditions, supplying the missing physical basis for the empirical standardizability that underpins cosmic-distance ladders. This arXiv preprint (2605.21575, May 2026) is not yet peer-reviewed and relies on a modest ensemble of simulations rather than exhaustive parameter surveys. Prior DDT prescriptions could be tuned to produce either normal or subluminous events; the new mechanism is highly efficient, initiating detonation promptly and thereby limiting the window for pre-expansion that might otherwise yield SNe Iax. Connections to cosmology are direct: refined explosion physics tightens the intrinsic scatter in the Phillips relation, potentially reducing systematic uncertainty in dark-energy constraints from surveys such as DES and LSST. Earlier work (e.g., Seitenzahl et al. 2013 on gravitationally confined detonations) lacked this ab-initio turbulence closure and therefore could not demonstrate convergence from diverse progenitors. The present results suggest that observed homogeneity of normal SNe Ia may be a dynamical attractor rather than a fine-tuned outcome, though the study notes that further modeling is required to recover delayed detonations and the full range of SN Ia subtypes.