{
  "schema_version": "1.0.0",
  "artifact_id": "qft.artifact.many-body-quantum-matter.superfluidity-superconductivity-validity-and-failure-map",
  "title": "Paired-matter validity and failure map",
  "classification": "original schematic independent-gate map",
  "reader_question": "Which claim-specific test is required before a gauge, retardation, crossover, symmetry, mechanism, topology, or Majorana-platform inference is licensed, and what narrower statement survives when that test fails?",
  "dominant_point": "The seven gates are independent tests selected for the claim being made; passing one licenses only that layer, while failure preserves a narrower observation rather than invalidating every other branch.",
  "status": {
    "schematic": true,
    "not_to_scale": true,
    "contains_experimental_data": false,
    "contains_simulation_data": false,
    "platform_evidence_cutoff": "2026-08-23"
  },
  "arrow_semantics": {
    "shared_spine": "A candidate paired-matter claim selects the gate appropriate to its own layer; vertical position does not define a temporal or logical sequence.",
    "solid_arrow": "Apply the listed controls before licensing that claim layer.",
    "dashed_arrow": "If the gate fails, stop at the stated narrower inference."
  },
  "gates": [
    {
      "id": "gauge_and_winding",
      "claim_layer": "gauge, fluxoid, or periodicity response",
      "required_controls": ["pair charge", "response limit", "dissipation", "parity relaxation"],
      "licensed_if_passed": "A gauge-and-winding conclusion in the declared geometry and circuit model.",
      "ceiling_if_failed": "Response feature only; no anomalous fluxoid or periodicity conclusion."
    },
    {
      "id": "migdal_eliashberg_retardation",
      "claim_layer": "controlled Migdal-Eliashberg approximation",
      "required_controls": ["vertex ratio", "momentum transfer", "bandwidth or electronic recoil scale", "coupling", "Coulomb sector"],
      "licensed_if_passed": "A noncrossing retarded calculation controlled in the stated kinematic regime.",
      "ceiling_if_failed": "Use a vertex-complete or nonadiabatic theory; no controlled Migdal-Eliashberg claim."
    },
    {
      "id": "bcs_bec_crossover",
      "claim_layer": "BCS-BEC crossover interpretation",
      "required_controls": ["matched scattering data", "number equation", "range and density control", "stiffness or fluctuation treatment"],
      "licensed_if_passed": "A crossover-regime conclusion with pair formation separated from condensation.",
      "ceiling_if_failed": "Pair formation or a spectral gap only; condensation and crossover regime not established."
    },
    {
      "id": "unconventional_symmetry",
      "claim_layer": "pairing symmetry",
      "required_controls": ["fermionic antisymmetry", "crystal representation", "nodes", "relative phase sign", "spin-orbital structure", "domains"],
      "licensed_if_passed": "A pairing-symmetry conclusion in the declared basis and domain model.",
      "ceiling_if_failed": "Gap phenomenology only; symmetry alternatives remain."
    },
    {
      "id": "microscopic_mechanism",
      "claim_layer": "dominant or causal pairing mechanism",
      "required_controls": ["momentum structure", "frequency structure", "controlled perturbations", "held-out predictions", "explicit alternative kernels"],
      "licensed_if_passed": "A mechanism claim bounded by the compared alternatives and calibrated forward models.",
      "ceiling_if_failed": "Compatible kernel only; no dominant or causal mechanism."
    },
    {
      "id": "topological_bdg",
      "claim_layer": "topological BdG bulk-boundary conclusion",
      "required_controls": ["local ultraviolet-complete gapped BdG model", "protecting symmetry", "bulk invariant", "interface or defect across which the invariant changes", "finite-size convergence"],
      "licensed_if_passed": "The corresponding protected boundary or defect spectral-flow statement for the specified model and interface.",
      "ceiling_if_failed": "Subgap state only; no protected bulk-boundary conclusion."
    },
    {
      "id": "majorana_platform",
      "claim_layer": "protected Majorana platform or non-Abelian operation",
      "required_controls": ["device calibration", "nonlocality", "parity dynamics", "device replication", "length or protection scaling", "fusion or braiding comparator"],
      "licensed_if_passed": "Only the evidence rung whose lower controls and operation-level alternatives have passed.",
      "ceiling_if_failed": "Platform advance at its measured rung; no unique non-Abelian demonstration.",
      "evidence_cutoff": "2026-08-23"
    }
  ],
  "reading_order": [
    "identify the exact claim being made",
    "select only the gate governing that claim layer",
    "check every declared control on the solid branch",
    "if a control fails, follow the dashed exit to the narrower surviving statement",
    "do not infer that passing one branch passes any other branch"
  ],
  "nonclaims": [
    "The vertical layout is not a chronology, derivation, prerequisite graph, evidence ladder, or renormalization-group flow.",
    "A failed gate does not erase a correctly measured lower-level feature; it limits the interpretation of that feature.",
    "A symmetry claim does not identify a mechanism, and mechanism identification is not a prerequisite for classifying a specified model topologically.",
    "A model-level topological result does not establish a material or device realization.",
    "The Majorana branch states a dated evidence standard and does not claim that the record is current after 23 August 2026."
  ],
  "scientific_checks": [
    "Each gate has one solid control branch and one dashed stopping rule.",
    "The crossover failure text does not treat BCS-BEC crossover as a phase transition or universal endpoint.",
    "The topology gate includes locality, ultraviolet completion, protecting symmetry, an invariant-changing interface or defect, and finite-size convergence.",
    "The Majorana gate keeps local zero-bias, parity readout, length protection, and non-Abelian operations on separate evidentiary rungs.",
    "No gate is encoded as a prerequisite for a different independent claim layer."
  ],
  "sources": [
    { "citation": "Byers and Yang, Physical Review Letters 7 (1961) 46-49", "doi": "10.1103/PhysRevLett.7.46", "use": "gauge periodicity and winding" },
    { "citation": "Migdal, Soviet Physics JETP 7 (1958) 996-1001", "url": "https://www.jetp.ras.ru/cgi-bin/dn/e_007_06_0996.pdf", "use": "adiabatic vertex control" },
    { "citation": "Eliashberg, Soviet Physics JETP 11 (1960) 696-702", "url": "http://www.jetp.ras.ru/cgi-bin/e/index/e/11/3/p696?a=list", "use": "retarded self-consistent pairing equations" },
    { "citation": "Sigrist and Ueda, Reviews of Modern Physics 63 (1991) 239-311", "doi": "10.1103/RevModPhys.63.239", "use": "pairing representation and symmetry diagnostics" },
    { "citation": "Kitaev, Physics-Uspekhi 44 (2001) 131-136", "doi": "10.1070/1063-7869/44/10S/S29", "use": "topological BdG invariant and boundary consequence" },
    { "citation": "Prada et al., Nature Reviews Physics 2 (2020) 575-594", "doi": "10.1038/s42254-020-0228-y", "use": "Majorana-platform alternatives and nonlocal evidence" }
  ],
  "alt_text": "Paired-matter claims branch into independent gauge-and-winding, Migdal-Eliashberg, BCS-BEC, symmetry, mechanism, topology, and platform tests; each failed control stops its own inference at a narrower claim.",
  "caption": "Validity and failure map for paired matter. Gauge and winding, controlled Migdal-Eliashberg theory, BCS-BEC interpretation, symmetry, microscopic mechanism, a topological BdG phase, and a protected Majorana platform are independent claim-specific tests rather than a temporal sequence. Original schematic, not to scale; platform evidence is bounded through 23 August 2026.",
  "rights": {
    "basis": "Original QFT.org schematic derived from independently checked validity relations; no third-party figure, geometry, data, or artwork was copied or restyled.",
    "creator": "OpenAI Codex, for QFT.org",
    "date": "2026-08-31"
  }
}