ABSTRACTThis paper integrates cyclic symmetry tools with exoplanet environmental inference. We define a radix-12 phase encoding of orbital observables and prove that equivariant encoding combined with symmetry averaging extracts a persistent invariant component from underdetermined datasets. Dihedral extension introduces empirically testable mirror constraints. Multi-clock accumulation explains the emergence of stable discrete signatures from continuous variability. The framework emphasizes coherence across datasets rather than single-feature claims.