Paper 39: Discrete Time, Action, and the Geometry of the Holosphere Metric

This paper presents a coherence-based reformulation of energy, momentum, time, action, and geometry using the discrete angular structure of the Holosphere lattice. Instead of assuming a smooth spacetime manifold, the framework treats admissible phase transitions and their associated strain costs as the primary physical data. Holospheres are modeled as hadronic-scale coherence units whose relative angular alignment determines whether propagation and reconfiguration are allowed. Energy is defined as stored angular strain on admissible links, momentum as the directed transport of strain-bearing configurations, inertia as resistance to reconfiguration that increases with coherence depth, and time as an ordered count of discrete reconfiguration events (“coherence ticks”). Action is introduced as a discrete cumulative cost over admissible update steps, rather than as a continuum time integral. The paper introduces a coherence-based metric in which distance and duration arise from shortest-path structure in an admissibility graph, while gravitationally relevant effects correspond to strain-cost gradients that bias propagation paths and local tick rates. Causality is enforced structurally through coherence cones defined by admissibility and propagation budgets, rather than by a universal speed limit. This work establishes the geometric and energetic foundations for the discrete Holosphere Lagrangian developed in Paper 25 and provides falsifiable, protocol-ready predictions involving directional inertia, strain-dependent clock rates, propagation delays, and redshift-like behavior arising from cumulative coherence transport rather than spacetime expansion.