Multispectral object detection requires detectors to exploit material-dependent spectral responses while maintaining consistent localization under geometric variations. Existing MOD detectors learn discriminative spectral representations, yet lack a unified mechanism that preserves spectral order, adapts spectral-context fusion across pyramid levels, and regulates geometric responses under rotation. To address these limitations, we propose S$^3$E-Det, a strict spatial-spectral equivariant detector that couples ordered spectral modeling with transformation-consistent prediction. Spectral Order-aware Sampling Calibration (SOSC) imposes local order constraints on input-derived spectral features through first-order variation, while Common-Differential Equivariant Fusion (CDEF) adapts spectral-context aggregation across pyramid levels. A compact Geometric Alignment Head (GAH) reconciles invariant and equivariant output properties within a unified prediction stage. Across MODA, HOD3K, and DroneVehicle, S$^3$E-Det combines high detection accuracy with a compact parameter footprint and reduced rotation-induced variation. Code is available at https://github.com/Riiluo/S3E-Det.

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