METRIC TOPOLOGICAL RELAXATION (MTR): A Unified Framework for Spacetime Elasticity, Hubble Tension, and Quantum Uncertainty₃rd edition

The MTR (Metric Topological Relaxation) model offers a fundamental unification of quantum mechanics and cosmology based on the classical theory of continuum elasticity. Establishing a physical identification of Heisenberg's quantum constraints with the mechanical yield strength of space (𝜖𝑚𝑎𝑥 ≈ 10¹13 J/m³) allows for the elimination of singularities in black holes and replaces the concept of "dark" substances with the dynamic process of metric relaxation. Within the proposed paradigm: - Dark Energy is interpreted as the result of the phase decay of ultra-dense topological structures (matter) into free metric volume. The process of space generation within singularities (injection of 0. 25 m³ per proton) is the physical driver of the Universe's expansion. - Dark Matter is described as the inertial response (tension) of the vacuum substrate around active conversion zones. The derivation of the Milgrom constant from the background pressure ρΛ confirms the elastic nature of galactic halos. The transition from descriptive geometry to metric engineering allows for a quantitative justification of the observed Hubble, Pioneer, and JWST anomalies, confirming the unity of matter and space as distinct phase states of a single dynamic continuum with an elastic modulus of 𝜖 ≈ 10¹11 J/m³. The model provides a physically deterministic view of the Universe's structure, unifying continuum mechanics with the geometry of GR and quantum effects. Resolving the 122-orders- of-magnitude paradox and deriving the Milgrom constant from the vacuum's elastic modulus indicate that the metric continuum is the primary physical object, while matter is merely a form of its local topological relaxation.