Causal Priority Theory: Partition Dependence, Breakdown Structure, and No-Go Results for Derived Time Second Integrated Volume: Parts 7–13

This document is the Second Integrated Volume of the Causal Priority Theory (CPT) series, synthesizing the results and theoretical developments from Parts 7 through 13 without altering their original content. While the first integrated volume (Parts 0–6) established the foundational framework, this volume serves as a comprehensive archive and a structural roadmap for the latter half of the series. It brings together the various discussions on the boundaries of derived-time assignment, with detailed derivations and proofs deferred to the individual parts. Key Roles of this Integrated Volume: 1. Systematization of the Breakdown Taxonomy (Parts 7–12) It consolidates the various failure modes of time assignment into a unified four-layered taxonomy (Types D, R, A, and C). This allows for a systematic overview of the boundaries where the conventional notion of time ceases to function within the CPT framework. 2. Consolidation of No-Go Results (Part 13) It formally integrates the critical findings regarding the non-existence of a process-only canonical time selector, establishing them as the formal constraints that define the reach of the theory. 3. A Structural Roadmap for Reference By preserving the integrity of the original individual papers, this volume provides a high-level synthesis necessary to understand how time structurally emerges (or fails to emerge) from discrete causal updates. This volume marks a significant milestone in the CPT series, offering a definitive reference for the inherent limits and formal constraints of time as a derived quantity.