Robustness of Three-Regime Structure in Causal Update Cosmology under Large Perturbations (V5)

Title:Robustness of Three-Regime Structure in Causal Update Cosmology under Rule-Preserving and Rule-Breaking Perturbations (CUC v5) Description: This repository contains the final PDF of CUC v5, which investigates the robustness of the three-regime structure previously identified in Causal Update Cosmology (CUC v4). The central question addressed in this work is whether the observed three-regime structure is merely a consequence of network connectivity, or whether it is fundamentally protected by the causal update rule itself. To answer this, we systematically examine two qualitatively different classes of perturbations: Rule-preserving perturbations(noise injection, dropout, and pure link percolation)These perturbations reduce connectivity but leave the causal update rule intact. Rule-breaking perturbationsExplicit violations of the causal update rule. The results demonstrate a clear and robust distinction: Under rule-preserving perturbations, the three-regime structure is maintained even under large noise levels and severe connectivity loss.While local stalls and increased fluctuations may appear, global collapse does not occur. Under rule-breaking perturbations, the system exhibits immediate global failure, characterized by dominant stalled dynamics and explosive band-breaking behavior. These findings establish the core claim of CUC v5: Connectivity loss is not equivalent to causal rule failure.Collapse in CUC occurs only when the causal update rule itself is violated. This work provides strong empirical evidence that the stability of CUC is governed by causal consistency rather than simple network connectivity, significantly strengthening the theoretical foundations introduced in earlier versions. Methods:All simulations were conducted using deterministic update rules with controlled perturbations. Analysis focuses on reached fraction, band-break metrics, and FAIL criteria across multiple regimes and perturbation types. 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. Author:TI Keywords:Causal Update Cosmology, causal dynamics, robustness, percolation, noise, dropout, complex systems Supplementary JSON files containing simulation outputs for Case09, Case10, and Case11 are provided to ensure full reproducibility of the reported results.