TMDD: The Dynamic Landscape of Galaxies

This work presents a detailed examination of the correspondence between the Tensor Model of Discrete Dynamics (TMDD) and the complete set of observational data on galactic dynamics from the SPARC catalog. Based on an independent statistical analysis of rotation curves presented in [8, 9], a rigorous set of empirical requirements is formulated, constituting a `phenomenological landscape': 1) the existence of three statistically significant asymptotic regimes (rising, at, falling) with proportions of 16%, 71%, and 13% respectively; 2) universal oscillations in velocity and acceleration proles, observed in 88% of galaxies, with resonant wavelength ratios of 1:2, 2:3, 1:3; 3) manifestation of the universal Feigenbaum constant δF ≈ 4.669 in acceleration proles with a significance of Z = 13.25σ; 4) a dynamic classification of galaxies into four classes based on effective Reynolds number (Reeff). It is shown that all these phenomena emerge naturally from a single hydrodynamic equation, derived from the calibrated TMDD action with ontologically fixed parameters (ξ = 1.803×10−66 m3 ·s−2, ρ = 3.21×10−123 m2 ·s−2, γ = 5.34×10−28 m3 ·s−2). It is found that the asymptotic regimes are determined by the gradient of the external coherence parameter dRij/dr, oscillations are generated by the eigenmodes of the θ-network, and the scatter in the Radial Acceleration Relation (RAR) is a direct consequence of the oscillatory structure. Thus, TMDD successfully passes through a stringent empirical filter, offering an ontologically coherent explanation for both the averaged regularities and the fine structure of galactic dynamics within a unified framework that links microscopic spacetime discreteness with macroscopic observations.