Hawking Radiation and Information Loss from Block-Alternating Infinite Products

We interpret the black hole event horizon within the framework of block-alternating infinite products A (K, d) and B (K, d). The horizon is identified with the null boundary K=1/2, at which the coherence parameter d undergoes a forced transition d=1 to d=1/2. Since A (1/2, d) =1 for all d, the parameter d loses physical meaning at the horizon, and all phase correlations are irreversibly destroyed. Hawking radiation, emitted from the horizon, is therefore already in the d=1/2 state: an incoherent sum of independent intensities with no phase memory. Building on the identification M=d and GM=d/4, we further show that the Hawking temperature satisfies TH=1/ (2pid) in natural units, and that black hole evaporation proceeds through the discrete sequence d=1, 1/2, 1/4,. . . with each step corresponding to a halving of the mass and a doubling of the temperature. This provides an algebraic derivation of the thermal nature of Hawking radiation and a structural account of black hole information loss, without invoking additional postulates.