We examine black hole information unitarity within the Mathematical Foundations of Reflexive Reality (MFRR) framework SpivackNEMSMFRRBridge. The MFRR Transputation operator PT^-1 provides a physical mechanism for unitary information recovery consistent with the Perfect Self-Containment condition. Since every CPTP map admits a Stinespring dilation (a mathematical theorem independent of gravitational modelling), Hawking evaporation is unitarily equivalent to a reversible evolution on a system-plus-environment space. We construct the evaporation channel _ t = e^ tL as a GKSL master equation for a JT-like system of n=3 bosonic modes (d_H = 8) at T_H 0.004. Stinespring dilation achieves fidelity F 1 - 10^-8; detailed balance holds to 0.00\%; the entropy curve reaches 97.2\% of the ideal thermal value. In two complementary closed unitary models - a pure initial BH state and a purified thermal initial state with reference system R - the full Page curve with turnover is reproduced and PT^-1 recovery achieves F = 1.000000. Open fronts are stated explicitly: extension to 3+1 quantum gravity, the firewall tension, and a first-principles derivation of PT^-1.