Frontier Field-Dynamics: Structural Limits of Reasoning under Finite Observational Granularity

This paper introduces Frontier Field-Dynamics (FFD), a minimal structural framework for analyzing reasoning processes under finite observational granularity. FFD models reasoning as a dynamical evolution over internal states, coupled with an explicit observational projection capturing which distinctions are operationally accessible at a given level of abstraction.Within this setting, the paper identifies frontiers: regions of the state space where extensive internal evolution yields no observable informational progress. Core result The paper proves a general no-go theorem:under a fixed observational granularity, confinement within a frontier implies that no property expressible at that granularity can be decided; escape from the region is impossible without an explicit change in observable information. This result is structural, not algorithmic: it does not depend on complexity assumptions, heuristics, or the specific reasoning domain. Why this matters Reasoning systems often spend large computational resources exploring regions that are internally active but epistemically stagnant.FFD provides a principled way to distinguish activity from progress, and to explain why persistence under fixed observation may be structurally unjustified, rather than merely inefficient. Scope The framework is domain-independent and applies to proof search, planning, model construction, and related reasoning tasks. The paper includes an instantiation in propositional resolution proof search, explaining resolution plateaus at fixed width without appeal to heuristic failure. FFD does not propose new algorithms, heuristics, or performance improvements. What this paper is (and is not) ✔ A structural analysis of limits of reasoning under partial observation ✔ A foundation for rational search control decisions Not a new solver, heuristic, or optimization technique Not a complexity-theoretic separation result FFD should be read as a diagnostic and control framework: it clarifies when continued search is rational, when termination is justified, and when a change of representation or observation is necessary in principle.