Causal Update Cosmology VI:Why Causal Update Dynamics Generically Produce Exactly Three Regimes

Abstract

Title:Causal Update Cosmology VI: Why Causal Update Dynamics Generically Produce Exactly Three Regimes Description: This paper presents the sixth installment of Causal Update Cosmology (CUC), a research program that explores how large-scale temporal and causal structure can emerge from repeated local causal updates without presupposing motion, metric geometry, or physical time. Earlier works (CUC I–V) established that causal update dynamics robustly exhibit a characteristic three-regime organization—initial, central, and terminal—across a wide range of parameters and strong rule-preserving perturbations. It was further shown that this structure collapses only when the causal update rule itself is violated. CUC VI addresses a foundational structural question left open by previous studies:Why do causal update dynamics generically produce exactly three regimes, rather than two, four, or an arbitrary number? Rather than introducing new numerical experiments, this paper provides a structural explanation. Under minimal and model-independent assumptions—locality, irreversible accumulation of update history, finite-path competition, and rule preservation—it is argued that the effective degrees of freedom governing causal propagation admit at most two qualitative transitions in their growth behavior. As a direct consequence, the update process necessarily decomposes into exactly three regimes. The argument is deliberately non-metric and non-thermodynamic. No global state function, numerical invariant, entropy measure, or dynamical equation is assumed. The three-regime structure is thus elevated from an empirically observed regularity to a necessary organizational feature of causal update dynamics. This work is intended as an explanatory bridge between the empirical robustness results of CUC IV–V and future interpretative developments (e.g., entropic or thermodynamic interpretations), which are deferred to subsequent studies. Note on AI Use This work also explores the broader question of whether new physical theories can emerge through collaboration with AI systems. ChatGPT (OpenAI) was used extensively in the generation and structuring of theoretical ideas and manuscript text, beyond simple editing or polishing. All numerical experiments and scientific validation were performed by the human author.

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