Momentum as Spectral Flow: Dynamical Derivation from M3(C) Geometry

Momentum has traditionally been treated as a fundamental dynamical quantity, largely due to the historical development of analytical mechanics and the canonical quantization framework of the 20th century. This perspective elevated momentum to primitive status and obscured the deeper structural role of mass. In this work, momentum is reinterpreted as a derived expression of spectral flow: the spatial projection of the invariant mass-generating gap Δλ. By restoring Δλ as the sole primitive of dynamics, Cognitional Mechanics resolves the long‑standing inversion between “dynamic shadows” and their underlying invariant source. This paper develops the dynamical consequences of this correction. Momentum is defined through operational proper time, revealing its dependence on background clock modulation rather than independent degrees of freedom. The relativistic energy–momentum relation is reformulated as an allocation of a single invariant resource, and the equation of motion emerges from an optimization of operational latency rather than force balance. This framework unifies inertial and gravitational behavior, eliminates the fictitious sovereignty of phase space, and clarifies the structural origin of several empirical phenomena, including gravitational redshift, galactic rotation anomalies, and gravitational wave propagation. This work completes a three‑part series: mass as spectral gap, the equivalence principle as spectral identity, and momentum as spectral flow. Together, they establish a coherent dynamical picture in which mass is primitive and momentum is derivative.