Time as the Rate of Becoming: An Evoltropic Framework for Physical Time, Gravitational Evolution, and Finite Curvature

The nature of time remains one of the most fundamental unresolved questions in physics.Modern relativity successfully models time as a coordinate within spacetime, yet the physical meaning of temporal passage remains controversial. This work proposes an alternative operational definition: time is the measurable rate of becoming. Becoming is defined as the irreversible progression of physical systems between distinguishable states. An Evolution Rate Field E is introduced to quantify local rates of becoming. Atomic clocks are interpreted as instruments that measure local evolution rates rather than anindependent temporal dimension. Gravitational time dilation is reinterpreted as a reduction in the local rate of becoming. A central principle of the framework is the Non-Zero Evolution Principle, which states that physically realizable systems must possess a strictly positive evolution rate. This principle implies that complete cessation of becoming is impossible. Consequently, infinite curvature, infinite density, and physical singularities are excluded from nature. The framework develops a dynamical field theory of E from an action principle, derives the associated stress-energy tensor and modified Einstein equations, and explores implications for black-hole interiors, cosmology, and the interpretation of time. An exact analytic solution of the coupled Einstein–E system is derived under the saturation assumption: theinterior geometry is a regular static de Sitter metric with effective cosmological constant ΛE = κV (Emin), and all curvature invariants are explicitly verified finite. Free parameters are constrained to order of magnitude by neutron-star and gravitational-wave observations.The Finite Curvature Theorem is stated with an explicit asymptotic assumption; the Finite Density Theorem is qualified to standard collapse conditions; the saturated-core state is characterised as a traceless stress-energy configuration; dynamical stability of the GeneralRelativity limit is demonstrated analytically; and the Schwarzschild identification of E is clarified as a calibration condition rather than a derived result.