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14 claims

Claims about what distinguishes thermodynamic or quantum phases of matter and about the criteria or diagnostics marking phase boundaries — e.g., order parameters, nonanalyticities in observables or correlation functions, symmetry-breaking and topological distinctions. Specific named systems (QCD phase diagram, CFL phase) have their own tags.

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 →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 →

Phases of matter with the same symmetry-breaking pattern can always be connected without a phase transition

ContradictedAvailable evidence weighs against the claim.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →importance · 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 →

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 →Generalized global symmetries 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 →

Physical distinctions between phases must be detectable by measurements on finite-energy physical states

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 →importance · 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 →

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 Topological orderimportance · 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 →

Nonanalytic behavior of gauge-invariant correlation functions marks a physical distinction between phases

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 →Gauge-invariant correlation functions Physical Detectability of Phase Distinctionsimportance · 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 Topological order Dense Quark Matterimportance · 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 →

Higgs and confining regimes of gauge theories with fundamental matter are continuously connected without 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 →Higgs-Confinement Distinction Particle physicsimportance · 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 theory phases are standardly diagnosed by the asymptotic behavior of gauge-invariant extended operators

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 →Gauge-invariant correlation functionsimportance · minorImportance 0.25, 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 →

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 →Generalized global symmetries Confinement in gauge theoriesimportance · 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 →

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 Topological orderimportance · 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 →Topological orderimportance · 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 →

Genuine thermodynamic phase transitions produce nonanalytic behavior in measurable bulk observables

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 →Physical Detectability of Phase Distinctionsimportance · 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 Topological orderimportance · 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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If a claim here is wrong, or missing evidence, open it: every claim page carries its own entry for challenges, evidence, and corrections. If the graph is missing a claim entirely, propose it below. A proposal is reviewed on its merits; accepted claims are matched against the graph and enter it with their reasoning on record.