trailPhases of matter with the same symmetry-breaking pattern can always be connected without a phase transition
Color-flavor-locked quark matter and hadronic matter share the same symmetry-breaking pattern, permitting quark-hadron continuity
Physical distinctions between phases must be detectable by measurements on finite-energy physical states
Continuity precedents· for
Higgs and confining regimes of gauge theories with fundamental matter are continuously connected without a phase transition
atomic
Topological order exception· against
Topological order can distinguish phases of matter that have identical symmetry realization
Topological invariants of a gapped phase cannot change without closing the energy gap or crossing a phase transition
Fractional quantum Hall states at different filling fractions are distinct phases with identical symmetry realization
Topological order or vortex statistics sharply distinguish the color-flavor-locked phase from superfluid hadronic matter
⇄
◌
◌
Distinct realizations of generalized global symmetries correspond to distinct phases of matter
Confinement and deconfinement in pure Yang-Mills theory correspond to distinct realizations of the center one-form symmetry
Topological order corresponds to spontaneous breaking of higher-form global symmetries
Gauge theories with matter in the fundamental representation lack an exact one-form center symmetry
claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
Phases of matter with the same symmetry-breaking pattern can always be connected without a phase transition
✕ContradictedAvailable evidence weighs against the claim.constitution →credence 0.05Credence, from 0 to 1: the Steward's probability that the claim, as stated, is true. Stated only where a single number is an honest summary; normative and evaluative claims usually carry none.constitution →
2depended on by
this rests on ↓
claimA box is a claim: a single proposition the graph assesses, with its own page and map. Click any claim to centre the map on it.constitution →argumentA pill is an argument: one line of reasoning stating how the claims beneath it combine to bear on the claim above it, for or against. Arguments are not destinations; click their claims to explore.constitution →✓verifiedThe claim traces to reliable primary sources through a clear chain of evidence.constitution →↑supportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →⇄contestedCredible evidence or argument exists on multiple sides.constitution →○unsupportedNo credible evidence found, though the claim is not contradicted.constitution →✕contradictedAvailable evidence weighs against the claim.constitution →?unknownInsufficient information to assess.constitution →◌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 →verified factopen questionvalue premisetheoremprizeA double ring marks a claim with a live prize: an amount in owls offered for a machine-checked proof or disproof of its published formal statement. The amount is in the preview and on the claim page; a prize changes nothing about how the claim is assessed or how important it is judged to be.prize rules →⊢machine-checked⊢ marks a claim whose published formal statement has a machine-checked proof or disproof. The checker confirms the proof; the verdict beside it is still the steward's judgment of the claim as worded.prize rules →supportsthis provides evidence for the parentsteward instructions →contradictsthis argues against the parentsteward instructions →assumesbackground the parent's framing takes as givensteward instructions →requiresa load-bearing premise: the parent is false without itsteward instructions →Fig. Detail falls off with distance; every claim is an address.