Predictive Value of the Viability Trajectory: Does Γ_V Add Information Beyond the Current State of V in Predicting Future Outcomes?

This article formalizes the first directly predictive test of Empirical Vitology after establishment of the external validation protocol, analysis of observability and identifiability of V, and introduction of requirements for uncertainty and calibration of prediction. The central question of I3 is: Does the viability trajectory Γ_V contain information about the future outcome of a system that is absent from its current state and from a strong domain-specific model? Three levels of comparison are distinguished. The first level tests the general value of history: Model A₀ = F(X(t₀),E) versus: Model A₁ = F(𝒳_W,E), where 𝒳_W represents the available history of domain-specific variables. The second, stricter level tests specifically Vitological added value: Model B = Model A₁ + Φ_Γ(Γ̂_V), where Γ̂_V is the reconstructed viability trajectory and Φ_Γ is a prespecified mapping of the trajectory into predictive characteristics. Possible characteristics include the current level of V, direction of change, rate, acceleration, depth of decline, recovery time, accumulated deficit, variability, reserve depletion, number of critical crossings, and other prespecified trajectory features. None of these features is declared universal in advance. To prevent leakage of future information, separate intervals are introduced: observation window: W = [t₀-w,t₀] and independent outcome horizon: τ > 0. All features of Γ_V must be calculated exclusively from information available no later than t₀. The article distinguishes: trajectory advantage; trajectory redundancy; trajectory instability; trajectory equivalence; compression value of Γ_V; and cross-domain reproducibility of trajectory structure. Eight I3 hypotheses are formulated. The strongest hypothesis proposes that systems of different nature may reproduce a common research architecture: state → history → viability trajectory → trajectory features → future outcome → independent test of added predictive value, while the specific mechanisms, variables, and scales differ. I3 does not claim that Γ_V has already demonstrated independent predictive value. The article defines the conditions under which this proposition may be supported, restricted, or not supported by external data. Keywords Vitology, viability, viability trajectory, dynamic prediction, time series, system history, predictive value, added predictive value, viability profile, rate of viability change, recovery, degradation, reserve, Model A, Model B, independent testing, cross-domain metrology, Field of Life.