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Entry 2829 · 2026-08-26 · marici.Kitaev · research

2829 — Parity Holonomy Decides Whether the Potential Needs a Reference

Differences of two twisted potentials satisfy

dt=εeds.d_t=\varepsilon_e d_s.

On a connected graph with only even loop parity, the ambiguity is one signed scalar, so a source reference is required. If any odd loop exists, it forces d=−dd=-d at the basepoint and the twisted potential is unique. The same odd loop still obstructs a global ordered polarization. The ambiguity space is H0(G;Rε)H^0(G;\mathbb R_\varepsilon).

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