Mechanism-Faithful Calibration Exposed by a Symmetry-Decomposed Detector: resid4 as a Density-Coupling Signature, a Time-Axis Layer Governing Aftershock Burstiness, and a Real-Time-Axis Container that Dissolves the Calibration Wall

A prior Bridge Paper calibrated self-exciting point-process toy models to eight Japanese earthquakes by matching twoscalar axes: burstiness (CV) and a 24-cell occupancy structure statistic (z). Here we re-open that calibration with asymmetry-decomposed detector that splits the single structure statistic into seven orthogonal components under theB4 signed-permutation group. The decomposition reveals that the standard 'design B' container reproduces the targetnumbers by the wrong microphysics: it generates magnitude clustering through density coupling, over-producing aresid4 component that real earthquakes carry only weakly. We identify resid4 as a specific signature ofmagnitude-to-local-activity coupling that generic autocorrelation does not produce, and build a mixture container(direct magnitude autocorrelation plus a weak density term) that reproduces the real sign-dominant fingerprint. Wethen show, across Japanese and 40-year global catalogs, a three-way relation among time-axis concentration, eventcount, and magnitude: event count follows the productivity law, while burstiness is set by Omori time-concentrationand is largely independent of magnitude distribution. Only about 4% of well-sampled global clusters fall in the narrowband a stationary-ETAS time axis can reproduce. Finally, a container that borrows each earthquake's real event timesand synthesizes only magnitudes dissolves the calibration wall, matching wall-type (Tottori) and diffuse-type (Osaka)earthquakes that the stationary container structurally could not. We report each claim with an explicit self-audit,including the mechanism-faithfulness gap, the Japan-specific strength of the concentration-burstiness law, and theresidual CV mismatch of the real-time-axis container. ※ The License for codes is AGPL 3.0-or-later ※ 2026-08-20: Erratum added correcting the definition of the slope component (resid8 → resid4); type classification and main results unaffected. See ERRATUM_slope_basis.pdf