Structural Propagation Bounds under Local Updates: Reachability, Schedule, History, Capacity, and State-Continuation

Abstract

This preprint presents a structural propagation-bound framework for local-update systems, distinguishing structural reachability from schedule-, history-, capacity-, and continuation-dependent constraints. It also gives a limited formal comparison with finite-rate and cone-like representations without identifying update stages with physical time or deriving relativistic spacetime. AI assistance Developed with assistance from OpenAI ChatGPT, including GPT-5.5 Thinking and GPT-5.6 Sol, for conceptual discussion, formalization, review, and manuscript revision. Minimal version note v1.1 clarifies the separation between ordinary executable reachability and continuation-preserving reachability. The executable admissibility predicate no longer includes the continuation criterion Γ; Γ is applied separately only in the continuation-preserving layer. The finite-stage propagation bound, structural metric baseline, toy-model results, effective-rate discussion, and scope are unchanged.