Corrected Theory of 8196D→32D Block Folding: A Unified Compression-Theory Account — Spectral Calculus, Distortion, Experiments, and Discussion

Version 3.0.0 rewrites the 8196→32 folding manuscript in the shared HTML format of the folding-program papers, with a unified Compression Theory (CT) dictionary aligned to doi:10.5281/zenodo.18679011 and doi:10.5281/zenodo.20406073. Maintained compression theory: shape ratio κ=n/m=256.125; shape efficiency ηshape=m/n; isotropic second-moment preservation ρ2=‖P‖F2/n; spectral efficiency ηspec=σmin+/σmax. For the corrected map P⋆ (weights B−1/2, remainder discarded), P⋆P⋆⊤=I32, so ηspec=1 and ρ2=ηshape. Scoped Frobenius optimality among contractive linear maps; isometric retention on the row space; multi-level hierarchies. Withdrawn from v1: 96.23% folding efficiency; 95.92% information preservation for arbitrary measures; OT/JL/topology overclaims. Prior draft φ has exact singular values √(257/256) (×4) and 1/16 (×28). Manuscript: 20 pages — CT dictionary, axioms, distortion calculus (mean-norm vs RMS), AWGN mutual-information proposition, experiments, hierarchies/stability, discussion, consolidated errata, Appendices A–F, reproducibility JSON.