Irreversible Accessibility in Oriented State Spaces

Foundational approaches in mathematics and systems theory often rely on local regularity, continuity, or admissibility to infer global properties of a system. In this article, we introduce a minimal structural framework in which such local coherence coexists with an irreversible contraction of accessible futures. Without invoking metrics, probabilities, or dynamical equations, we formalize accessibility in oriented state spaces and define the notion of an irreversible accessibility boundary: a locally indistinguishable threshold beyond which the set of reachable future states contracts irreversibly. This phenomenon does not correspond to instability, bifurcation, or phase transition, and remains invisible to state-based analyses. Rather than proposing a new topology or theorem, this work identifies a structural class of irreversibility that precedes observable rupture. A brief conceptual articulation with Poincaré’s logic of global determination situates the contribution within a foundational perspective.