Causal Priority Theory part-7: On Event Partition Dependence, Coarse-Graining, and the Stable Order of Derived Time

This paper formulates "Event Partition Dependence" in Causal Priority Theory (CPT)—the principle that the flow of derived time depends on how an observer partitions events. • Partition Dependence: Formalizes time as a quantity dependent on the resolution of observation. • Stability of Order: Identifies the physical conditions under which the time order remains stable despite information loss (coarse-graining). • Conclusion: Proves that the "arrow of time" is robustly preserved under specific uniformity conditions, regardless of the partition. This work extends the unified framework (Episodes 0–6) to address the hierarchical nature of physical observation.