A Generic Full-Spectrum Converse for Free Parafermions at Every Order N >= 3

This candidate proves an all-order converse for independently coupled universal Weyl graph algebras whose commutation phases are 1, q and q inverse. Canonical full-spectrum freeness is equivalent to the oriented graph being an oriented indifference graph. Outside this class the free-coupling locus is a proper complex algebraic set. The package also provides a cubic-time switching recogniser, an injective-label physical-realisation criterion and an exact census through six Hamiltonian terms. Arbitrary phases, dependent labels and sector-specific mode lists are outside the theorem.

Unrefereed candidate. All local finite replay and supplied reviewer checks passed. The universal proof is not formally verified; supplied AI-assisted review and separate implementations are not unaffiliated reproduction or external human peer review. No exhaustive priority clearance or applied validation is claimed.

Original prose/data CC0-1.0; original code MIT. Preserved third-party records retain their own rights. See LICENSES.md. Version 1.0.1 clarifies the real-to-complex sufficiency extension, even-order central phase, explicit N=4 fork invariant, physical applicability and Ruh–Elman comparison. Main classification unchanged.