Observability and Identifiability of Viability: Reconstruction of V from Available Measurements and Distinguishability of Alternative Viability States

This article formalizes the problem of observability and identifiability of viability as a necessary condition for further empirical testing of Vitology. The internal state of a system X(t), observable measurements Y(t), the viability profile Π_V(t), and, where appropriate, an integral coordinate V(t) are distinguished. The following general measurement framework is introduced: dX/dt = f(X,U,E,θ,t) Y(t) = h(X,θ,t) + ε(t) V(t;τ) = g(X,E,L,F*,τ,θ_V). Observability of V is defined as the possibility of distinguishing values or profiles of viability from the available observation history under a prespecified observation frame. If two admissible internal configurations produce identical observations but different V, viability is considered unobservable or only partially observable relative to that measurement regime. The identifiability of the V metrology itself is considered separately. Even when the internal state of the system is measured sufficiently well, several different aggregation rules, weights, or functions g may generate different V. Therefore, state reconstructability and uniqueness of the definition of V are distinct problems. The concepts of structural observability of V, practical observability of V, partial observability, metrological identifiability of V, observational equivalence of alternative V, and predictive distinguishability are introduced. A principle of scientific restraint is formulated: if several alternative V are equally compatible with observations and produce indistinguishable independent predictions, Vitology should report a class of equivalent solutions rather than arbitrarily selecting one. Eight I1 hypotheses define a future testing program for observability and identifiability of V using synthetic, technical, biological, and other external data. I1 does not claim that V has already been demonstrated to be an observable or identifiable cross-domain coordinate. The article establishes the criteria after which such a claim could, in principle, obtain empirical support. Keywords Vitology, viability, observability, identifiability, structural identifiability, practical identifiability, latent state, viability profile, measurement, state reconstruction, uncertainty, model equivalence, distinguishability, Model A, Model B, dynamic system, cross-domain metrology, Field of Life.