A Minimal Moduli-Space Realisation of the Finkelstein–Rubinstein Spinoriality Criterion on a (2,1)-Torus Curve

We present a minimal geometric configuration that realises the Finkelstein–Rubinstein spinoriality cri-terion in a reduced moduli space: a Z3-symmetric three-marker arrangement on a (2, 1)-torus curve whosecollective-coordinate moduli space is SO(3) × S1. Under a 2π spatial rotation about the symmetry axis,the collective internal phase advances by ∆s0 = 1/2, a shift lying outside the Z3 orbit. Consequently the2π-rotation path represents the nontrivial spinorial class in the reduced moduli description. Subject to thestandard lifting assumption, the construction yields spin- 12 behaviour under spatial rotations. The modelis fully visualisable and serves as a pedagogical illustration of the Finkelstein–Rubinstein mechanism.