Harvestability

This paper studies fin_harvestability as a horizon object for horizon-dependent allocation within a CRRA investor facing Ornstein-Uhlenbeck eigenmodes. The main object is the fin_harvestability function \(h(T, \tau) = 1 - e^{-T/\tau}\), which measures how much of a risky mode's premium is reliably capturable at horizon \(T\) when the mode has characteristic time scale \(\tau\). The paper's primary role is proof-first: it isolates this object, derives it from an OU/HJB/Riccati spine, and makes the proof boundary explicit. Its central allocation claim is benchmark-centered: fin_harvestability organizes the horizon-dependent correction around the myopic Merton benchmark rather than replacing that benchmark with a pure multiplicative rescaling. The theory then records a downstream lifecycle-filter form, in which horizon, bequest, mortality, Bayesian caution, and safety constraints enter multiplicatively; this should be read as a structured extension layer rather than as an exhaustive lifecycle model. Within this hierarchy, the Samuelson Error \(\varepsilon(T,\tau) = e^{-T/\tau}\) and the failure of horizon independence are treated as derived consequences rather than as the paper's foundational identity. The paper does not claim to settle the broader long-horizon allocation literature or to solve the full lifecycle problem in one calibrated economic model. In the surrounding paper family, the manuscript plays the role of a proof-oriented foundation note that downstream benchmark and calibration notes can import from without re-establishing the derivation. Its Lean contribution should be read as checking the structural backbone of the argument; some surrounding analytic estimates remain classical.