From C = T + M to C = T + R: Preparing an Event-First Causal Budget Framework

From C = T + M to C = T + R: Preparing an Event-First Causal Budget Framework

This document is a transition piece in the Causal Budget Framework (CBF) series. It clarifies several interpretive points that prepare for a shift in emphasis toward an event-first formulation.

1. Lorentz symmetry emerges dynamically, not geometrically. The Pythagorean form T² + M² = 1 used in Part III was a useful encoding, but CBF does not require geometric assumptions to produce relativistic effects. Lorentz invariance emerges from discrete tick scheduling between transport and resolution across frames; observed commit rates encode the resulting time dilation. Minkowski geometry is the thermodynamic limit of the CA, not its foundation.

2. Renames and clarifies the budget terms. Translation (T) becomes Transport; Maintenance (M) becomes Resolution (R). Resolution contains two components: M (identity maintenance) and I (interaction capacity). So R = M + I. Mass is the cost of self-continuity.

3. Transport always hops at c; apparent velocity is hop frequency. When transport executes, it always advances one cell at maximum speed. Slower motion arises because R blocks T on occupied ticks, not because T itself slows down. Whether transport "hops" or "slides" is observationally indistinguishable since all observations are commits.

4. Time accumulates only through resolution. Proper time advances only when events commit. A photon experiences no time. Entropy and irreversibility live in R (congestion, backlog, history), not in T, which is reversible and lossless.

5. Mass is recyclable obligation that can be destroyed. Identity maintenance (M) is continuous self-commitment. When renewal terminates completely, as in electron-positron annihilation, the resolution capacity converts entirely to transport (gamma radiation).

Relation to prior work:

Parts I–III explored CBF through cellular automata, wave propagation, and budget partitioning. Those results remain valid. This document reframes their conceptual foundation and signals a forthcoming event-first treatment where spacetime and relativistic effects emerge from discrete resolution scheduling rather than geometric axioms.

Keywords: Causal Budget Framework, event-first physics, cellular automata, Lorentz invariance, resolution, transport, computational physics, emergent spacetime