{
  "$schema": "https://qft.org/data/schemas/qft-many-body-comparison-1.0.0.schema.json",
  "schema_version": "1.0.0",
  "artifact_id": "qft.artifact.many-body-quantum-matter.disorder-localization-glasses-claim-validity-ledger",
  "table_id": "disorder-localization-claim-test-matrix",
  "canonical_source": {
    "route": "/many-body-quantum-matter/disorder-localization-glasses/",
    "heading": "Disorder and glass claim test matrix",
    "anchor": "disorder-and-glass-claim-test-matrix"
  },
  "caption": "Ensembles, scaling tests, and limits of disorder and glass claims.",
  "common_scope": {
    "markdown": "",
    "math": [],
    "links": []
  },
  "qualifications": {
    "markdown": "",
    "math": [],
    "links": []
  },
  "columns": [
    {
      "key": "claim_or_regime",
      "label": "Claim or regime"
    },
    {
      "key": "ensemble_and_symmetry",
      "label": "Ensemble and symmetry"
    },
    {
      "key": "scaling_variable_or_interaction_effect",
      "label": "Scaling variable or interaction effect"
    },
    {
      "key": "rare_event_diagnostic_and_size_requirement",
      "label": "Rare-event diagnostic and size requirement"
    },
    {
      "key": "competing_explanation",
      "label": "Competing explanation"
    },
    {
      "key": "evidence_ceiling",
      "label": "Supported conclusion"
    }
  ],
  "rows": [
    {
      "key": "quenched-thermodynamics",
      "row_id": "disorder-localization-claim-test-matrix--quenched-thermodynamics",
      "cells": {
        "claim_or_regime": {
          "markdown": "Quenched thermodynamics",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Fixed $V$ during equilibration; declared $P[V]$",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "V"
            },
            {
              "kind": "inlineMath",
              "tex": "P[V]"
            }
          ],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "$\\overline{\\ln Z}$ and cumulants, not $\\ln\\overline Z$",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "\\overline{\\ln Z}"
            },
            {
              "kind": "inlineMath",
              "tex": "\\ln\\overline Z"
            }
          ],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Distribution over samples; increase sample count and volume separately",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Annealed disorder or nonstationary preparation",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Exact only for the stated ensemble and order of limits",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "replica-or-susy-representation",
      "row_id": "disorder-localization-claim-test-matrix--replica-or-susy-representation",
      "cells": {
        "claim_or_regime": {
          "markdown": "Replica or SUSY representation",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Replica number $n$ or balanced boson–fermion fields; convergence prescription stated",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "n"
            }
          ],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "$n\\to0$ continuation or exact normalization cancellation",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "n\\to0"
            }
          ],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Compare moments and tails before analytic continuation",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Wrong saddle, broken convergence contour, or nonunique continuation",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "A computational representation, not an independent physical phase",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "diffusive-nonlinear-sigma-model",
      "row_id": "disorder-localization-claim-test-matrix--diffusive-nonlinear-sigma-model",
      "cells": {
        "claim_or_regime": {
          "markdown": "Diffusive nonlinear sigma model",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Altland–Zirnbauer class fixed; $k_F\\ell\\gg1$",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "k_F\\ell\\gg1"
            }
          ],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "$q\\ell$, $\\lvert\\omega\\rvert\\tau\\ll1$; $Q^2=1$",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "q\\ell"
            },
            {
              "kind": "inlineMath",
              "tex": "\\lvert\\omega\\rvert\\tau\\ll1"
            },
            {
              "kind": "inlineMath",
              "tex": "Q^2=1"
            }
          ],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Sample dimensions must exceed $\\ell$ but remain within coherence window",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "\\ell"
            }
          ],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Ballistic modes, additional soft channels, or strong disorder",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Long-wavelength theory inside the declared class and cutoff",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "weak-localization-or-antilocalization",
      "row_id": "disorder-localization-claim-test-matrix--weak-localization-or-antilocalization",
      "cells": {
        "claim_or_regime": {
          "markdown": "Weak localization or antilocalization",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Orthogonal, unitary, or symplectic interference sector",
          "math": [],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "$L_\\phi/\\ell$ and magnetic or spin–orbit crossover",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "L_\\phi/\\ell"
            }
          ],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Magnetoconductance shape over several coherent scales",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Interaction correction, classical memory effect, or inhomogeneity",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Perturbative coherent correction, not a phase diagnosis",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "interaction-correction",
      "row_id": "disorder-localization-claim-test-matrix--interaction-correction",
      "cells": {
        "claim_or_regime": {
          "markdown": "Interaction correction",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Diffusive fermions with specified singlet/triplet channels",
          "math": [],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "Running resistance, $z$, and interaction amplitudes",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "z"
            }
          ],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Temperature and field scaling beyond one logarithmic window",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Heating, phonons, granularity, or band-structure anomaly",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Controlled only while conductance and retained couplings justify the expansion",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "anderson-transition",
      "row_id": "disorder-localization-claim-test-matrix--anderson-transition",
      "cells": {
        "claim_or_regime": {
          "markdown": "Anderson transition",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Noninteracting class and boundary conditions fixed",
          "math": [],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "$\\beta(g)=\\mathrm d\\ln g/\\mathrm d\\ln L$, $L/\\xi$",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "\\beta(g)=\\mathrm d\\ln g/\\mathrm d\\ln L"
            },
            {
              "kind": "inlineMath",
              "tex": "L/\\xi"
            }
          ],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Several sizes, disorder quantiles, and irrelevant-drift fit",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Crossover, mobility-edge averaging, or contact resistance",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Critical point only after stable scaling collapse and uncertainty analysis",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "topological-localization",
      "row_id": "disorder-localization-claim-test-matrix--topological-localization",
      "cells": {
        "claim_or_regime": {
          "markdown": "Topological localization",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Symmetry class plus bulk topological term or invariant",
          "math": [],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "Mass, conductance, localization length, and boundary response",
          "math": [],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Bulk and boundary scaling with symmetry-breaking controls",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Clean band transition or finite-size edge hybridization",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Class- and dimension-specific delocalization statement",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "bose-glass",
      "row_id": "disorder-localization-claim-test-matrix--bose-glass",
      "cells": {
        "claim_or_regime": {
          "markdown": "Bose glass",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Quenched potential with interacting bosons and $U(1)$ symmetry",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "U(1)"
            }
          ],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "Vanishing stiffness, nonzero compressibility, no spectral gap",
          "math": [],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Size and trap scaling of $\\rho_s$, $\\kappa$, and gap proxies",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "\\rho_s"
            },
            {
              "kind": "inlineMath",
              "tex": "\\kappa"
            }
          ],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Inhomogeneous superfluid puddles or Mott crossover",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Compressible insulating phase only in the homogeneous thermodynamic limit",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "griffiths-dynamics",
      "row_id": "disorder-localization-claim-test-matrix--griffiths-dynamics",
      "cells": {
        "claim_or_regime": {
          "markdown": "Griffiths dynamics",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Spatial rare regions in a declared disorder ensemble",
          "math": [],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "Tail exponent or dynamical exponent from full distributions",
          "math": [],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Rare-sample count grows with both volume and realization number",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Broad but ordinary relaxation-rate distribution",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Anomalous dynamics; does not alone imply localization or glass order",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "thermal-avalanche",
      "row_id": "disorder-localization-claim-test-matrix--thermal-avalanche",
      "cells": {
        "claim_or_regime": {
          "markdown": "Thermal avalanche",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Localized background plus an ergodic seed and local couplings",
          "math": [],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "Inclusion entropy versus distance-dependent matrix element",
          "math": [],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Seed size and growth followed beyond the crossing scale",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Long transient from a subcritical inclusion",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Instability criterion under the stated localization-length convention",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "many-body-localization",
      "row_id": "disorder-localization-claim-test-matrix--many-body-localization",
      "cells": {
        "claim_or_regime": {
          "markdown": "Many-body localization",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Isolated interacting system with conserved quantities fixed",
          "math": [],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "Level ratios, transport, entanglement, and local memory",
          "math": [],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Symmetry-resolved sizes, long times, bath-size drift, and rare seeds",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Prethermalization, fragmentation, Stark localization, or finite-size crossover",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "No thermodynamic phase claim from accessible finite-size crossing alone",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "mean-field-quantum-spin-glass",
      "row_id": "disorder-localization-claim-test-matrix--mean-field-quantum-spin-glass",
      "cells": {
        "claim_or_regime": {
          "markdown": "Mean-field quantum spin glass",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Infinite-range or large-connectivity quenched couplings",
          "math": [],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "Replicon stability and overlap distribution $P(q)$",
          "math": [
            {
              "kind": "inlineMath",
              "tex": "P(q)"
            }
          ],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Replica limit, imaginary-time discretization, and system-size convergence",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Replica-symmetric solution or competing ordered saddle",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Controlled mean-field RSB statement; finite-dimensional stability separate",
          "math": [],
          "links": []
        }
      }
    },
    {
      "key": "finite-dimensional-quantum-glass",
      "row_id": "disorder-localization-claim-test-matrix--finite-dimensional-quantum-glass",
      "cells": {
        "claim_or_regime": {
          "markdown": "Finite-dimensional quantum glass",
          "math": [],
          "links": []
        },
        "ensemble_and_symmetry": {
          "markdown": "Short-range model or material with declared preparation and bath",
          "math": [],
          "links": []
        },
        "scaling_variable_or_interaction_effect": {
          "markdown": "Aging, memory, nonlinear susceptibility, overlaps, and relaxation spectrum",
          "math": [],
          "links": []
        },
        "rare_event_diagnostic_and_size_requirement": {
          "markdown": "Joint size–time scaling and protocol variation",
          "math": [],
          "links": []
        },
        "competing_explanation": {
          "markdown": "Rare regions, domains, disorder pinning, MBL-like memory, or critical slowing",
          "math": [],
          "links": []
        },
        "evidence_ceiling": {
          "markdown": "Model- and window-specific evidence through 10 August 2026",
          "math": [],
          "links": []
        }
      }
    }
  ],
  "references": [
    {
      "id": "ref-e4993c1354bb5ec0",
      "markdown": "Abrahams, E., Anderson, P. W., Licciardello, D. C., and Ramakrishnan, T. V. (1979). “Scaling theory of localization: Absence of quantum diffusion in two dimensions.” *Physical Review Letters* **42**, 673–676. [doi:10.1103/PhysRevLett.42.673](https://doi.org/10.1103/PhysRevLett.42.673).",
      "urls": [
        "https://doi.org/10.1103/PhysRevLett.42.673"
      ]
    }
  ],
  "reference_scope": "The reference catalog reproduces the canonical chapter bibliography. Cell links are associated with references only when their resolved URL matches; uncited chapter references are not asserted as claim-specific support."
}