Sharp reverse entropy inequalities for uniform qubit ensembles

This computer-assisted preprint proves a sharp reverse relative entropy inequality L >= beta_m chi for uniform ensembles of individually normalized qubit states, for every m >= 2. Here chi is the Holevo quantity and L is the non-optimized quantum lautum information. The proof combines analytic Bloch-vector and Gram-matrix reductions with four interval certificates covering 855,780 boxes. For three matrices in arbitrary finite dimension, the paper also establishes local nonnegativity near faithful pairwise-commuting equality triples, allowing unequal traces and noncommuting perturbations. Further results include normalization bridges, an angular reduction for three qubits, and certified obstructions to proposed pinching and filtering descent arguments. The unrestricted unequal-trace ensemble inequality and the general equality of complete and ordinary modified logarithmic Sobolev constants are not proved. The accompanying archive contains sources, certificate inputs, verifiers, and reproduced results. Developed with AI assistance; not peer reviewed or formally verified. Companion paper: Christoph Hartmann, Reverse relative entropy and finite-time contraction for conditional expectations (2026).