Binary Tetrahedral Defects and a Central Spinorial Disclination from Tetrahedral Cellular Geometry

We show that a medium built from tetrahedral cells, with an orientational order parameter taking values in the coset space SO(3)/A4, has fundamental group equal to the binary tetrahedral group 2T (order 24). The central element -I of 2T, which is the spinorial "rotation by 2π equals -1" sign, is realised explicitly and exactly by the smallest closed loop of the diamond lattice (the chair hexagon), under the natural C3 bond assignment of a 120-degree rotation about each bond axis. We prove that this realisation is universal: under that assignment, every chair hexagon, in every orientation, carries holonomy exactly -I. This gives a non-circular geometric realisation of a spinorial Z2 structure, in the sense that it does not assume an SU(2) bond variable in order to recover one. The -I object is topologically protected, is naturally a line defect (a disclination) rather than a point particle, and carries logarithmically divergent line energy. We also separate three distinct Z2 structures that are routinely conflated: the orientability class w1 (killed by the bipartiteness of the lattice), the central element -I (which survives, since 2T abelianises to Z3 and admits no Z2 parity obstruction), and the fermion/statistics sign (which remains open). The work is deliberately narrow in scope. It does not derive fermions, spin-statistics, or the Standard Model, and it does not claim to. What remains conditional and open is stated plainly: the choice of SO(3)/A4 as configuration space (the largest input), the choice of bond angle (120 degrees), which after the universality theorem is the only remaining freedom within the present construction, and the selection (as opposed to mere classification) of the spinorial sector. Localised fermion candidates, if any, live in the third homotopy group (π3), not in this π1 line. Epistemic classification: conditional overall, resting on one stated assumption (SO(3)/A4 as the orientation space); given that assumption, the topological and computational results are solid, while the selection of the fermionic sector is open. This is a preprint in the Granular Entropic Physics (GEP) series; a revised version is planned once the surrounding structure is closed.