Continuity Admissibility in Time-Extended Systems (CSS-Ω): An Irrecoverable Invariant and a Binary Boundary for Action

This paper introduces continuity admissibility as a distinct evaluative object for time-extended systems operating under irrecoverable loss. Across engineered, institutional, and socio-technical domains, systems often collapse after long periods of apparent success—passing performance, robustness, and outcome-based validation until recovery is no longer possible. The paper argues that this pattern is structural, arising from the absence of a formal representation of irreversibility in existing evaluation frameworks. Within Continuity Systems Science (CSS-Ω), the paper defines a scalar invariant κ∈[0,1]\kappa \in [0,1]κ∈[0,1] representing accumulated, irrecoverable continuity loss along a system trajectory. An absorbing threshold κ∗\kappa^*κ∗ establishes a binary admissibility boundary: once crossed, no subsequent performance, repair, or favorable outcome can restore admissibility. Admissibility is therefore history-dependent, outcome-orthogonal, and non-reducible to success metrics, robustness margins, or constraint satisfaction. The paper proves a non-reducibility theorem showing that admissibility cannot be inferred from observable outcomes alone, and introduces minimal diagnostic patterns explaining why late-stage collapse remains systematically invisible under outcome-based validation. A Universal Test Interface (UTI) specifies structural requirements for admissibility tests without prescribing implementation, while executable estimators are treated as fallible witnesses rather than definitions. Auditability is addressed through traceable, replayable admissibility claims rather than system-level certification. CSS-Ω is intentionally narrow and non-prescriptive. It does not optimize, govern, or recommend actions. Its contribution is formal: identifying irrecoverable continuity loss as a primitive constraint on action and providing a minimal, falsifiable framework for determining when action ceases to be admissible—prior to collapse—independent of outcomes or performance.