Continuity Admissibility in Time-Extended Systems (CSS-Ω)

This paper introduces a foundational evaluative framework—Continuity Systems Science (CSS-Ω)—that defines admissibility as a binary, history-dependent property in time-extended systems subject to irrecoverable continuity loss. At its core is a scalar invariant κ∈[0,1]\kappa \in [0,1]κ∈[0,1], representing accumulated, irreversible system degradation. A critical threshold κ∗\kappa^*κ∗ is established, beyond which no action remains admissible, irrespective of performance, robustness, or outcome success. The work proves that admissibility is non-reducible to traditional validation metrics and introduces a universal test interface and audit ledger to ensure claims are falsifiable and domain-transferrable without theory leakage. CSS-Ω addresses late-stage collapses that occur despite apparent system success, offering a minimal, outcome-orthogonal core that anticipates system invalidity before collapse becomes observable. The framework applies to engineered, socio-technical, and institutional systems where path-dependent degradation constrains future action, and it remains agnostic to policy, optimization, or governance.