Structural Notes on Viability and Constraint Geometry

We present a structural analysis of admissible viability regions for open systems under perturbation.
Let $S$ denote a system state space and let $V_0 \subset S$ denote its physically admissible viable region.
Under standard assumptions drawn from viability theory and stochastic perturbation theory, we observe
that admissible viability regions can be characterized purely through exclusionary (negative) invariants.
We further distinguish between positive invariants that are reducible to collapse-state exclusion and
those that impose additional persistent constraints on admissible states.

Under sufficiently mixing perturbations, non-reducible positive invariants strictly contract the
admissible viable region and induce monotone upper bounds on first-exit probabilities and expected
survival times. A compatibility remark is given showing that, for finite systems with bounded free
energy, protocols enforcing non-vanishing asymptotic work extraction correspond to such non-reducible
constraints. The analysis introduces no new dynamics and is intended as an organizational perspective
on viability, first-passage, and admissibility frameworks.