Cosets and Holonomy in Gauge-Stoquastic Rotor Hamiltonians

This record contains a manuscript on stoquasticity, sign problems, subgroup-coset rigidity, and cycle holonomy in q-ary rotor Hamiltonians over Zq. The paper studies difference-set edges over Zq and their local-Fourier-conjugated rotor Hamiltonians. Within the rotor basis, and allowing only local diagonal gauges, it proves that a single edge is stoquastic up to gauge if and only if the allowed-difference set is empty or a coset of a subgroup of Zq. For networks of individually sign-free edges, it further gives a complete cycle-flux criterion: global diagonal-gauge stoquasticity is equivalent to the vanishing of the relevant mixed-modulus cycle holonomies. The manuscript also provides explicit arithmetic tests and constructive algorithms for detecting local coset structure and global flatness, clarifying when sign obstructions in this rotor family are local and when they are genuinely global.