Logic Realism Theory: Black Hole Information Return — Operator Formalism and FC-2 Prediction

This working paper develops the formal operator treatment of black hole information return within Logic Realism Theory (LRT), derived from the single foundational equation A_Ω = L₃(I∞). Black holes are formalized as sites where L₃ selection becomes maximally constrained: the singularity operator D_sing is defined as the partial inverse of L₃, mapping configurations from A_Ω back toward I∞ at maximum logical strain (ε = ε_max). Two output channels are identified: configurations retaining L₃-admissibility remain in A_Ω as structured Hawking radiation; configurations losing L₃-admissibility return to I∞ \ A_Ω. Information conservation is trivial at the I∞ level; within A_Ω the constraint is S_in = S_rad + S_ret. The paper derives falsifiability criterion FC-2b (strict inequality: total integrated Hawking radiation energy is less than absorbed mass-energy) and a modified Page curve that asymptotes below zero at S_ret rather than recovering to full unitarity. The Hilbert space objection is dissolved: no second Hilbert space is required. One space — I∞ — with A_Ω as subset. Seven open problems are identified including the derivation of the branching ratio R_desel and Lorentz invariance of the formalism.