Reduced Identifiability of Marked Rotor Memory

This note shows that marked‑rotor identifiability on the admissible biaxial wall is a toric reduced‑map problem: the two intrinsic observables form a monomial map with a primitive one‑parameter fiber, the invariant ring has Hilbert basis {qN, r, M} with the single syzygy M² = qN r, and the image is the positive quadric cone. A non‑invariant probe lifts the exponent matrix to unimodular form and identifies the full positive sector, while the dark locus appears as the toric boundary stratification.