Cubic blindness and quartic recovery in scalar Rains invariants of four-qubit rank-two code projectors

Scalar Rains invariants of degree k are k-copy observables for quantum-code projectors, yet the copy order required for local differential separation is poorly understood. We construct an explicit eight-dimensional family of rank-two four-qubit code projectors whose complete degree-at-most-three transcript has rank seven on a smooth five-dimensional critical germ. On a skew-Hermitian sheet, every quadratic and cubic coordinate reduces to three pair purities. The unique blind tangent is non-local-unitary and changes only the determinant of a Bell-diagonal marginal. A connected crossed quartic realignment moment supplies the missing cotangent direction and restores rank eight, establishing an exact four-copy local threshold.

This is a preprint and has not yet undergone journal peer review.