Study formalizes broken-phase thresholds in quantum field theories, suggesting new insights into coherence.
GCFT-0439 formalizes the broken-phase threshold as a constraint-topology gate rather than a temperature switch. It defines an admissible constraint manifold M_c = {Xi | C[Xi] > C_c}, freezes rules for the symbolic coherence functional, and specifies when previously vanishing operator sectors may acquire nonzero matrix elements. The endpoint remains sealed: the full coherence functional, BRST operator basis, and finite broken-phase matching are still open.
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Nicky Joseph Hubertus Catharina Hacquier (2026) studied this question.
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