A Symmetry-Based Orthogonal Decomposition of Polytope Occupancy Vectors for Multi-Component Detection of Temporal Structure in Earthquake Magnitude Sequences

We introduce a detector that separates the temporal structure of an earthquake catalog's magnitude sequence intoa small number of interpretable, mutually orthogonal physical dimensions. The prior framework (WCM-PL)embeds a sequence in a 4-dimensional Takens delay space, assigns each point to a vertex of the 24-cell (theregular 4-polytope with 24 vertices), and collapses the resulting occupancy vector to a single scalar - the cosinedistance from the uniform distribution. We show, on both synthetic and real data, that this single-scalar collapseconflates several qualitatively distinct temporal structures (correlation sign, time scale, hyperuniformity, andtemporal asymmetry) into one number, making physically unrelated earthquakes look alike and same-typeearthquakes look different. To undo the conflation we decompose the 24-dimensional occupancy space into theirreducible representations of the signed-permutation group B4 (order 384), which acts transitively on the 24vertices. The space splits cleanly into six orthogonal blocks - uniform(1), sign(6), axispair_a(3), axispair_b(2),resid8(8), resid4(4) - and standardizing each block's energy against a value-multiset-fixed (full-permutation) nullyields a signed multi-component fingerprint. Applied to over one hundred real earthquakes (a global candidatepool, major Japanese JMA events, and USGS global M7.8+ events), the five informative blocks behave nearlyorthogonally (max inter-component correlation 0.51 raw, 0.36 robust), and earthquake affinities that a singlescalar cannot express appear differently in different components. In particular the time-scale component providesan identification axis statistically independent of the conventional index, placing a strongly-structured and anegatively-structured earthquake at the same coordinate. A hypothesis-driven split of one residual block, backedby an explicit null test, adds a seventh "arrow-of-time" component. Our claim is that the new detector separatesseismic temporal structure into orthogonal physical dimensions; we do not claim an exhaustive classification of allearthquakes, nor precursory prediction. --- Data ---Two earthquake catalogs are used and are NOT redistributed in this record:- Global catalog (USGS-derived), 1986-2026, public domain (earthquake.usgs.gov).- JMA unified hypocenter catalog, 1998-2023, obtained per JMA terms of use.Extraction query (identical for every event): all catalog events within 180 daysafter and 100 km (haversine) of the epicenter, sorted by time; the magnitudecolumn of that window is the analyzed sequence. --- Licenses ---Code (code/ in the repro package): AGPL-3.0-or-later.Paper, figures, README, derived data: CC BY 4.0.The WCM-PL core module is published separately atgithub.com/watabe-masanori/cds-polytope (AGPL-3.0-or-later).