C05.2 · Interpretation

The strongest fully derived statements here are conditional implications of explicitly stated operator identities: the quadratic relation supplies a polynomial square root, and symmetric Clifford matrices supply an isotropic Frobenius Gram. These are not extra physical inputs disguised as numerical fits, but neither do they establish the provenance of the identities they consume.

The negative result is equally substantive. A nonscalar central involution on a carrier with both active and inactive sectors cannot disappear by a single projectivization. The additional metric countercontrol prevents an abstract Clifford isomorphism from being mistaken for a Frobenius-isometric one.

The registered tick, cylinder and scale results remain source reports. Their positive conclusions and their fences travel together. The source's statement that a parity pattern is not a spin structure is part of the result, not a provisional caveat to be dropped.