SlimeCodec: Commutator Norm-Based Continuous Non-Commutativity Quantification for Video Encoding Order Optimization
Authors/Creators
Description
This paper introduces the matrix commutator norm
d(A,B) = ||AB - BA||_F as a continuous, algebraically
grounded criterion for video encoding order optimization.
Four contributions are made:
(C1) Theorem 5 proves the inter-frame commutator identity
[F_{t-1}, F_t] = [F_{t-1}, Delta_t] and derives the
bound d(F_{t-1}, F_t) <= 2 ||F_{t-1}||_F ||Delta_t||_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 and
compression gain) is formally explained within rate-distortion
theory as I-frame quantization-error accumulation elimination.
Patent: JP 2026-046609 (filed 2026-03-20)
Inventor and patent owner: Hiroshi Sasaki
Implementation rights: Javatel Corporation
Abstract (English)
SlimeCodec introduces the matrix commutator norm d(A,B)
equal to the Frobenius norm of AB minus BA as a continuous
codec-orthogonal criterion for video encoding optimization.
This preprint converts scene-cut drift at extended GOP
lengths from an unbounded hazard into a mathematically
bounded one (Corollary 1, based on the Bottcher-Wenzel
inequality), enabling principled GOP extension in H.264,
VP9, and AV1 without modifying the encoding syntax.
Key experimental results:
GOP extension from 30 to 300 frames yields minus 14.2
percent VMAF-based BD-rate improvement on Xiph.org derf
sequences.
Multi-shot scene-cut safety achieves 100 percent detection
within plus or minus 2 frames at plus 0.92 percent BD-rate
cost versus fixed-300 baseline.
NormMAP QP redistribution achieves minus 52 to minus 65
percent file size at VMAF 83 to 88, with VMAF-based BD-rate
of minus 1.26 percent (RD-neutral redistribution).
4K AV1 real-time playback on 2-core CPU without GPU uses
a 54 KB WASM decoder, with 68.7 percent CPU reduction and
60 to 90 percent Canvas memory-bus reduction.
Near-commutativity of natural video is validated across
6 datasets, 4 operator representations, and 9.5 million
block pairs (84 to 87 percent convergence).
Status: Submitted to IEEE Transactions on Circuits and
Systems for Video Technology (TCSVT). Made available on
Zenodo as a preprint prior to peer review.
Supplementary material: Browser-based real-time demo and
reference binaries with H.264 NormMAP encoding pipeline
at https://1.docokame.biz/slimecodec/
Patent: JP 2026-046609 (filed 2026-03-20). Inventor and
patent owner: Hiroshi Sasaki. Implementation rights:
Javatel Corporation.
Files
SlimeCodec_TCSVT_v4_zenodo.pdf
Additional details
Additional titles
- Alternative title (English)
- SlimeCodec: Commutator Norm as a Continuous Criterion for GOP Safety and Perceptual Quality Redistribution in Video Encoding