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8 claims

Characterization of quantum phases by topology rather than symmetry breaking: ground-state structure, topological invariants, and statistics of defects or excitations (e.g., vortices). Claims about whether a phase carries topological order, or that use topological or vortex-based diagnostics to distinguish phases, belong here; ordinary symmetry-breaking phase-transition claims do not.

Topological order can distinguish phases of matter that have identical symmetry realization

VerifiedThe claim traces to reliable primary sources through a clear chain of evidence.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Phase transitionsimportance · 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 →

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

SupportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Phase transitions Generalized global symmetriesimportance · 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 →

The phase of a vortex-line operator linking an electric Wilson line distinguishes Higgs from confining regimes

ContestedCredible evidence or argument exists on multiple sides.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Higgs-Confinement Distinction Phase transitionsimportance · minorImportance 0.40, 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 or vortex statistics sharply distinguish the color-flavor-locked phase from superfluid hadronic matter

ContestedCredible evidence or argument exists on multiple sides.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Color-flavor-locked phase Dense Quark Matter Phase transitionsimportance · notableImportance 0.45, from 0 to 1 · notable: a contested point in a live debate (also the default before judging). 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 →Generalized global symmetriesimportance · 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 →

Fractional quantum Hall states at different filling fractions are distinct phases with identical symmetry realization

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 →Fractional Quantum Hall Effect Condensed Matter Physics 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 →

Topological invariants of a gapped phase cannot change without closing the energy gap or crossing a phase transition

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 →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 →

Symmetry breaking on vortex worldsheets can distinguish Higgs and confining regimes without a bulk phase transition

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 →Higgs-Confinement Distinction Phase transitionsimportance · settledImportance 0.22, 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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