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 two interpretive points that prepare for a shift in emphasis toward an event-first formulation.

1. Clarifies the role of the Lorentz factor. The original CBF work presented the budget constraint C = T + M in a way that could suggest the Lorentz factor emerges from budget arithmetic. This document corrects the conceptual ordering: the Lorentz factor arises from frame synchronization and constrains how the budget partitions, not the other way around.

2. Renames the budget terms. Translation (T) becomes Transport — capacity to carry unresolved causal structure forward. Maintenance (M) becomes Resolution (R) — capacity to commit events into the ledger. These renames reflect a shift in emphasis from particle persistence to event commitment, without changing the underlying dynamics.

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 particle interaction timing under frame synchronization.