Partial Stabilization and Self-Representability in Finite Resolution Physics

Translator This paper develops a closure-first analysis of stabilization within the framework of Finite Resolution Physics (FRP). It addresses a question that arises naturally once FRP is formulated operationally: given that physical description is probe-conditioned and resolution-limited, under what conditions does closure stabilize, and what does stabilization enable? The paper does not introduce a new foundational framework. Instead, it is explicitly situated within the FRP program and its associated closure-theoretic formulations. Stabilization is treated as a contingent structural property of probe-induced closure, not as an assumed feature of physical systems. Representability—including the representability of a system to itself—is shown to depend on stabilization rather than being primitive. Within this context, the paper introduces a minimal operational notion of “self” as a stabilized reflexive subsystem. Minimal selfhood is characterized by:(i) a stabilized identity criterion,(ii) a stabilized space of admissible self-actions,and (iii) stabilization of at least one reflexive invariant linking actions to outcomes.This structure is shown to require only local and partial stabilization, and to be compatible with failure of stabilization elsewhere. The analysis explains why partial stabilization is the generic outcome in closure-first formulations of FRP, while global stabilization and global self-representability are structurally exceptional. No external observer, ontic global state, or universal dynamical law is assumed. The results are intended to clarify the conceptual architecture of FRP and to situate stabilization as a necessary intermediate layer between operational probing and representational regimes (quantum, statistical, geometric). This work should be read as a conceptual companion to formal FRP and closure-theoretic papers. Its purpose is to articulate why stabilization matters, when it can be expected, and why its failure is informative rather than pathological, all within the FRP program.