Frontier Field-Dynamics in Action: Structural Impossibility Results under Fixed Observational Granularity

This paper investigates what happens when Frontier Field-Dynamics (FFD) is applied to concrete mathematical settings in theoretical computer science and adjacent areas.FFD, introduced in a companion foundational work, is a structural framework for analyzing reasoning and search processes under fixed observational granularity, identifying regions—frontiers—where internal evolution yields no observable informational progress. We show that applying FFD does not produce isolated phenomena, but systematically forces structural impossibility results.In particular, we analyze two distinct frontier mechanisms. First, we prove a finite-grain non-factorization theorem for the counting problem #SAT: for any finite observational scheme, the counting function fails to stabilize even pointwise. This result is model-independent and reveals an intrinsic oscillation phenomenon that prevents localization of global counts from finite information. Second, we establish a general no-go theorem for canonical selection under natural coherence constraints, showing that no non-trivial selection rule can be simultaneously intrinsic, compatible with loss of information, and stable under extension. This obstruction is purely structural and yields, as immediate corollaries, familiar non-canonicity phenomena in general topology (absence of canonical minimal bases), Ramsey-type settings (impossibility of equivariant witness selection), and concurrent systems such as Petri nets. These results are not presented as independent discoveries, but as inevitable manifestations of FFD when applied in action.Together, they show that frontiers arise not only as search stagnation, but also as collapse of guidance and canonicity. The contribution of this paper is therefore twofold: it provides new structural impossibility theorems, and it demonstrates that FFD functions as a generative tool for identifying classes of necessary failure modes under fixed observation.Implications for rational search control and abstraction change are discussed, preparing the ground for subsequent work.