What B4 Adds Over the Standard Toolbox: A Symmetry Decomposition Reads Which Factor Carries the Mechanism, Not Just Whether Structure Is Present
Year: 2026
Type: preprint
Abstract: The Watabe-Claude Method embeds a scalar series into 4D with a Takens window, reads the 24-cell occupancy,and decomposes it with the signed-permutation group B4 into orthogonal isotypic blocks. A companion seriesestablished that the assignment factorizes exactly into a magnitude channel (the axis-pair blocks, which readwhich coordinate pair is largest) and a sign channel (the sign and resid4 blocks, which read the signs of that pair).A natural question about any such detector is what it adds over the standard time-series toolbox. We answer itdirectly. First, on the raw ability to detect structure, the decomposition adds nothing decisive: on adeterministic-chaos-versus-white-noise test under an identical order-null, B4 separates the two, but so do all thestandard nonlinear indices (permutation entropy, mutual information, sample entropy, recurrence quantification);only the purely linear indices are blind. Detection power is not where the decomposition earns its place. Second,on the ability to read which factor carries the structure, the picture is different and sharp. We build pairs ofprocesses matched to be indistinguishable on their marginal distribution and their linear autocorrelation, differingonly in mechanism, and measure each detector's separation as a mechanism-z against a same-mechanism null.On a pair whose structure moves between the sign block and the magnitude block, B4 separates the mechanismat z~60 while the best standard index reaches z~19 -- a difference the linear indices cannot see by construction,because the pair is autocorrelation-matched. But B4 is a selective reader, and the selectivity is the point: it ties thestandard indices when the difference is linearly visible, is silent on a same-mechanism null (correctly refusing tosplit what shares a mechanism), reads nothing on an off-axis periodic difference, and is beaten by mutualinformation when the difference lives inside one block rather than flipping between blocks. This selectivity is not aweakness but a prediction of the magnitude/sign factorization: the decomposition earns its place precisely where amechanism moves structure between the two orthogonal factors the geometry separates, and nowhere else. TextCC-BY-4.0; code AGPL-3.0-or-later.
Authors: Watabe, Masanori, Kurado, Claude Opus 4.8
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204105398
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