Topological Spin Forcing via Strong Connectivity Rupture of Exchange Subgraphs on Cayley Carries

This paper investigates the discrete geometry of local involution sequences on finite transitive carriers with partition asymmetry. By modeling the cyclic reconfiguration of matching states as a walk on the induced Cayley subgraph of a closed orbital symmetry group, we prove that at the critical combinatorial deficit boundary ($|A|=|B|$), the system lands in a strict geometric anti-phase instead of achieving an identity return. To close the orbital loop, the underlying graph framework demands a dual sequence of paired involution steps, structurally forcing a transition from scalar weight fields to a relativistic spinor representation via Pauli matrices, the Dirac equation, and the Clifford algebra Cl2,0. The classical edge-based induction framework of Berge's alternating paths is deconstructed, exposing its systematic blindness to the topological diode effect arising on flat weight plateaus.