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Whether some generalized symmetry or order parameter still separates them is unknown.","posed_since":"1979","precise":"With dynamical matter in the fundamental representation, the $Z_N$ one-form center symmetry is explicitly broken and the Wilson-loop area law is no longer an order parameter; Fradkin and Shenker (1979) showed the phases can be connected. Determine whether, in theories with additional global symmetries (for example a $U(1)$ broken in both regimes, as in dense QCD), a vortex-holonomy or other non-local order parameter sharply separates Higgs and confining phases, and whether this holds generally.","problem_ref":null,"references":"","settled_by":"A proof that the proposed order parameter is quantized and differs between the phases, confirmed by lattice simulation of a model with a phase transition along every path.","status_note":"Cherman, Jacobson, Sen and Yaffe (2020-2024) proposed a vortex-holonomy order parameter; its validity is disputed, and lattice studies (2023-2025) report gauge-independent transitions in SU(2) gauge-scalar models.","title":"Sharp distinction between Higgs and confining phases with fundamental 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