Statistical Persistence and Emergent Inference in Mechanistic Adaptive Systems

Inferential methods have illuminated the research in cognitive functions across biological systems from complex cognition to cellular processes, however the physical and mechanistic origins of such dynamics remain underexplored. This work investigates how inferential update can emerge directly from the physical and probabilistic characteristics of a system interactively embedded into informationally-regular environment. Through a substrate-neutral framework, we demonstrate that inferential posteriors arise naturally from low-level adaptive processes governed by persistence selection i.e., retaining states with higher informational alignment with the interactive environment. Formally, we prove that the embedding conditions of statistical regularity and empirical accountability cause adaptive update’s convergence to inference-compliant structure without postulating or presupposing explicit inferential rules. The results provide a principled, physically grounded pathway for understanding the emergence of inferential dynamics in mechanistic adaptive systems, from chemical networks to artificial mechanical systems bridging multiple domains where adaptivity emerges and evolves.