This paper introduces the matrix commutator normd (A, B) = ||AB - BA||F as a continuous, algebraicallygrounded criterion for video encoding order optimization. Four contributions are made: (C1) Theorem 5 proves the inter-frame commutator identity Fₓ-₁, Fₜ = Fₓ-₁, Deltaₜ and derives the bound d (Fₓ-₁, Fₜ) <= 2 ||Fₓ-₁||F ||Deltaₜ||F. (C2) Corollary 4 (Bottcher-Wenzel) proves that permuting near-commutative operators introduces output error at most epsilon. (C3) Proposition 7 establishes statistical consistency of the adaptive threshold epsilon* via the Glivenko-Cantelli theorem. (C4) Hypothesis 1, validated across five datasets and four operator representations, demonstrates that natural video signals reside in a near-commutative operator subspace (84-87 percent convergence). Experiments across H. 264, H. 265, VP9, AV1, XDCAM HD422, and XAVC-L demonstrate: - BD-rate -15 to -27 percent, BD-PSNR +1. 4 to +2. 8 dB- XDCAM: I-frame count 27 to 2 (13. 5x reduction) - Optimization score 100/100- Real-time feasibility at under 1 percent encoding overhead The PSNR paradox (simultaneous quality improvement andcompression gain) is formally explained within rate-distortiontheory as I-frame quantization-error accumulation elimination. Patent: JP 2026-046609 (filed 2026-03-20) Inventor and patent owner: Hiroshi SasakiImplementation rights: Javatel Corporation
HIROSHI SASAKI (Sun,) studied this question.