Abstract

This paper develops a geometric account of time based on persistence and coherence. Time is defined as the length accumulated along a system’s trajectory through spacetime or state space. Interior time arises when coherence persists across that trajectory. Consciousness is framed as sustained interior time rather than as an instantaneous state. The paper situates this definition within established physics. In relativity, elapsed time corresponds to proper time measured along a worldline. In quantum mechanics and quantum gravity, time emerges relationally from correlated change across degrees of freedom. These approaches are unified by treating time as accumulated distance along a path through a structured space. A coherence condition is introduced to distinguish trajectories that generate interior duration from those that do not. Within the Aleph Harmonic Qualia framework, this condition is expressed as a coherence ratio R with a critical threshold R★ above which persistence supports interior time. Recurring invariants, termed patrons, stabilize coherence across variation and support continuity across scales. The paper also examines how analogue correspondence shifts with scale. At classical scales, analogue mappings operate locally through shared equations. At quantum and nanoscale regimes, structure is carried by phase and interference, producing distributed encoding with holographic form. By defining time as the length of a coherent trajectory, this framework provides a unified account of time, persistence, and interiority that applies across physical, biological, cognitive, and symbolic systems.