
From C = T + M to C = T + R: Preparing an Event-First Causal Budget Framework This paper reframes the Causal Budget Framework (CBF) in preparation for an event-first formulation. It clarifies how relativistic, thermodynamic, and mass-energy relations emerge from discrete serial tick allocation rather than from geometric axioms. Key points include: Lorentz symmetry emerges dynamically. The Pythagorean form T² + M² = 1 used previously was an encoding, not a postulate. The Lorentz factor γ arises from frame-dependent allocation of discrete ticks between transport and resolution. Minkowski geometry appears as a large-scale statistical limit of this scheduling process. The budget is reformulated as C = T + R. Transport (T) denotes invariant per-tick causal propagation at rate c. Resolution (R) includes identity maintenance (M) and interaction capacity (I), so R = M + I. Mass is interpreted as the ongoing cost of self-continuity. Transport and resolution execute serially. Each tick is allocated either to propagation or to resolution. Apparent subluminal motion arises from resolution-limited displacement rather than from slowing transport. Discrete and continuous representations are observationally equivalent because only committed resolution events are measurable. Time and entropy arise from resolution. Proper time advances through resolution cycles, including identity maintenance. Photons accumulate no proper time. Entropy and irreversibility emerge from resolution congestion, while transport remains reversible in isolation. Mass is recyclable obligation. When renewal terminates, as in electron–positron annihilation, resolution capacity converts entirely to transport, recovering E=mc² as a unit conversion between renewal rate and propagation rate. Parts I–III remain valid but are conceptually reframed. This document prepares the groundwork for a forthcoming event-first treatment in which spacetime and relativistic effects emerge from discrete serial scheduling rather than geometric foundations. Keywords: Causal Budget Framework, event-first physics, cellular automata, Lorentz invariance, emergent spacetime, computational physics, resolution dynamics
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