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Generalized notions of global symmetry extending ordinary 0-form symmetry: higher-form (p-form) symmetries, higher-category/generalized symmetry structures, their operators, backgrounds, and realizations in quantum field theory and many-body systems. Claims about how these symmetries are defined, realized, or used to characterize or distinguish phases of matter belong here; ordinary 0-form symmetr

Distinct realizations of generalized global symmetries correspond to distinct phases of matter

SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Phase transitions Topological orderimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

Topological order corresponds to spontaneous breaking of higher-form global symmetries

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Topological orderimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

Gauge theories with matter in the fundamental representation lack an exact one-form center symmetry

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Confinement in gauge theoriesimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

Confinement and deconfinement in pure Yang-Mills theory correspond to distinct realizations of the center one-form symmetry

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Confinement in gauge theories Phase transitionsimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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