The Absolute Nature of Time: A Scale-Invariant Geometric-Kinematic Formulation Derived from Geometrical Integration of Spacetime Stiffness

This paper introduces a foundational restructuring of temporal progression in cosmology, challenging the passive background coordinate-time models of standard modern physics. I propose a unified, history-dependent framework where effective proper time (T_subj) emerges as a path-dependent line integral driven by a composite geometric-kinematic variable: the Geometric Stiffness Modifier (|R_H |). By framing proper time accumulation directly through the absolute magnitude of geometric and kinematic variation, this formulation uncovers a profound symmetry where the spacetime manifold generates temporal progression as a function of absolute geometric stiffness, independent of spatial directionality or coordinate sign. Applying this framework across standard cosmological epochs natively resolves the fine-tuning paradox of the flat Radiation Era baseline via an absolute clock freeze (R_H=0), while unifying Cosmic Inflation and Dark Energy under an identical, scalable steady-state baseline. Crucially, I demonstrate that this framework eliminates the Hubble Tension and reconciles global structural anomalies through the numerical harmony of a rigid precision matrix. Derived entirely from a single, background-independent dynamic scale factor (Λ_cal=1.084323), the model uniquely dictates an unassailable mathematical reality: locking the Relational Hubble Invariant at (70.1425 (km/s)/Mpc), expanding the Absolute Manifold Age to (14.3562 Gyr), stabilizing the Structure Clustering Invariant at (0.7990), calibrating the Primordial Helium Mass to (0.2458), and anchoring the Sound Horizon Absolute Ruler at (153.1614 Mpc). Furthermore, the model eliminates both global (Big Bang) and localized (Schwarzschild) singularities by mathematically stretching finite coordinate-time boundaries into infinite, unreachable internal temporal horizons (T_subj→±∞), natively preserving the global continuity of physical laws across the cosmos. • The Relational Hubble Invariant locked at 70.1425 (km/s)/Mpc • The Absolute Manifold Age expanded to 14.3562 Gyr • The Structure Clustering Invariant stabilized at 0.7990 • The Primordial Helium Mass calibrated to 0.2458 • The Sound Horizon Absolute Ruler anchored at 153.1614 Mpc All derived from a single, background-independent dynamic scale factor (Λ_cal=1.084323).