ÆTHER COSMOLOGY XIV ADDENDUM A: TSTU-to-SI Calibration: Robust Plateau, Conditional Coefficient, and Open Variables for Paper XV

Abstract:

Paper XIV introduced the central thesis of the TSTU programme: physical time emerges as the dissipative integral $t_{phys}=(1/\Lambda^{2})\int\dot{\phi}^{2}d\tau$ following discrete topological ruptures of a scalar field. Internal consistency was numerically demonstrated through the cosmological/terrestrial temporal-rarefaction ratio of $1.343 \pm 1.3\%$ (Section 6.7). However, this result was internal to the formalism and did not connect to standard physical observables in SI units. The present addendum addresses this gap by extracting a TSTU-to-SI calibration coefficient $\kappa_{SI}$ from the well-measured Lyman-$\alpha$ transition of atomic hydrogen.

We report two complementary results, both transparent in scope. (i) Positive plateau result: the calibration coefficient exhibits a robust plateau over ~3 orders of magnitude in $\lambda_{eff}$ (effective potential stiffness), with relative variation below $\pm5\%$ across the saturated regime. (ii) Honest identification of limits: the calibration is highly dependent on the intrinsic substrate viscosity ($\gamma$) and the integration window (event noise cut-off). This reframes these numerical artifacts as physical variables, defining the operational scope of Paper XIV and setting the theoretical agenda for Paper XV.