Information as Structural Reduction of Future Possibility: A Formal Derivation from Restricted Transformability under Persistence Conditions

This paper derives information as a structural consequence of restricted transformability under persistence conditions. It does not define information as uncertainty over outcomes. Instead, it shows that for any system admitting determinable states, admissible transformations, and persistence constraints, the reachable state space contracts along the induced structural order. This contraction defines structural information as the reduction of future possibility: Σ(C) := −ln(|Reach(C)| / |S|) Three results are established. First, structural information is monotone increasing along the structural time order (Reachability Contraction Theorem). Second, structural information is coupled to persistence load near the boundary IR → 1: as the system approaches collapse, future possibility shrinks and structural information accumulates. Third, structural information is categorically distinct from Shannon entropy: it measures the contraction of the possibility space itself, not uncertainty over outcomes within a fixed space. The result establishes information as a derived property of the same underlying condition that generates time and directionality in Paper 111: restricted transformability under persistence.