{ "schema_version": "1.0.0", "artifact_id": "qft.artifact.many-body-quantum-matter.superfluidity-superconductivity-claim-validity-ledger", "title": "Paired-matter claim test matrix", "classification": "semantic claim-validity table", "purpose": "Compare paired-matter claim layers by defining input, licensed observable or invariant, necessary control, and decisive negative test or evidence ceiling.", "canonical_source": { "path": "src/content/docs/many-body-quantum-matter/superfluidity-superconductivity/index.md", "section": "Paired-matter claim test matrix" }, "columns": [ "claim_or_regime", "defining_input", "observable_or_invariant", "necessary_control", "decisive_negative_test_or_ceiling" ], "reading_rule": "Read left to right: declare the input, identify the calculated or measured consequence, verify the controls, and stop at the narrower claim if the negative test succeeds or a required control fails.", "rows": [ { "claim_or_regime": "Cooper instability", "defining_input": "Attractive eigenvalue of the antisymmetrized Fermi-surface kernel", "observable_or_invariant": "Diverging normal-state pair susceptibility and instability scale E_*, or mean-field T_c within a saddle approximation", "necessary_control": "Density-of-states, cutoff, and channel normalization fixed", "decisive_negative_test_or_ceiling": "Pair breaking or competing flow cuts off the logarithm before the claimed scale" }, { "claim_or_regime": "BCS paired saddle", "defining_input": "Gap function, dispersion, interaction, and ensemble", "observable_or_invariant": "E_k, coherence factors, gap equation, and number equation", "necessary_control": "Saddle stability and ultraviolet matching", "decisive_negative_test_or_ceiling": "Negative fluctuation mode, violated number constraint, or cutoff-dependent observable" }, { "claim_or_regime": "Nambu or BdG spectrum", "defining_input": "Pairing matrix, Nambu convention, and boundary conditions", "observable_or_invariant": "Poles, local density of states, and particle-hole-related eigenpairs", "necessary_control": "No double counting; complete basis and converged geometry", "decisive_negative_test_or_ceiling": "The complete numerical BdG eigenspectrum lacks its C-related plus/minus E partner, finite-size splitting is unresolved, or a claimed observable is gauge dependent" }, { "claim_or_regime": "Collective mode", "defining_input": "Zero of the analytically continued fluctuation kernel", "observable_or_invariant": "Phase, amplitude, or relative-phase pole and residue", "necessary_control": "Conserving vertices, continuum threshold, and damping included", "decisive_negative_test_or_ceiling": "Response maximum moves with the background model or lies inside an unresolved continuum" }, { "claim_or_regime": "Superfluid stiffness", "defining_input": "Free-energy curvature under a twist", "observable_or_invariant": "Pair-phase helicity modulus or static transverse phase response", "necessary_control": "Thermodynamic and static limits declared", "decisive_negative_test_or_ceiling": "Curvature vanishes after size extrapolation although a pairing gap remains" }, { "claim_or_regime": "Meissner response", "defining_input": "Gauge-invariant current kernel", "observable_or_invariant": "Static transverse screening kernel and penetration depth; optical delta or missing-area weight only after translating the limit order", "necessary_control": "Set omega = 0 before q -> 0; retain contact and paramagnetic terms; enforce Ward and sum rules; separate ballistic weights", "decisive_negative_test_or_ceiling": "A normal-state kernel survives spuriously, spectral weight is unaccounted for, or the result changes under a gauge-consistent reformulation" }, { "claim_or_regime": "Vortex, fluxoid, or Josephson response", "defining_input": "Compact phase, pair charge, geometry, and weak-link model", "observable_or_invariant": "Winding, fluxoid sectors, current-phase relation, and voltage-frequency relation", "necessary_control": "Core scale, screening, capacitance, dissipation, and parity relaxation stated", "decisive_negative_test_or_ceiling": "Phase slips, trapped flux, ordinary harmonics, or poisoning explain the signal" }, { "claim_or_regime": "Migdal-Eliashberg regime", "defining_input": "Retarded interaction spectrum and electronic structure", "observable_or_invariant": "Frequency-dependent Z, phi, gap, and thermodynamics", "necessary_control": "Vertex ratio, momentum structure, bandwidth, coupling, and Coulomb treatment controlled", "decisive_negative_test_or_ceiling": "Vertex or nonadiabatic corrections are not small, or inversion is nonunique" }, { "claim_or_regime": "BCS-BEC crossover", "defining_input": "Matched scattering data, density, and number equation", "observable_or_invariant": "Chemical potential, pair size, and excitation spectrum; the condensation transition only after a fluctuation or stiffness calculation", "necessary_control": "Range and density parameters; pairing distinguished from condensation", "decisive_negative_test_or_ceiling": "Pseudogap or molecular population is promoted to phase coherence without stiffness" }, { "claim_or_regime": "Unconventional symmetry", "defining_input": "Antisymmetry, crystal irrep, and spin-orbital structure", "observable_or_invariant": "Nodes, relative phase sign, spin response, and symmetry-resolved perturbations", "necessary_control": "Domains, matrix elements, disorder, and surface reconstruction modelled", "decisive_negative_test_or_ceiling": "A different irrep or accidental-node state fits the same joint data" }, { "claim_or_regime": "Microscopic mechanism", "defining_input": "Irreducible pairing kernel and competing channels", "observable_or_invariant": "Momentum- and frequency-resolved predictions under controlled perturbations", "necessary_control": "Common likelihood, calibrated nuisance terms, and held-out observables", "decisive_negative_test_or_ceiling": "Only T_c or gap symmetry is fitted, or mixed mechanisms remain viable" }, { "claim_or_regime": "Topological BdG phase", "defining_input": "Local ultraviolet-complete gapped BdG Hamiltonian, protecting symmetry, and an interface or defect to a phase with a different invariant", "observable_or_invariant": "Bulk invariant and boundary or defect spectral flow", "necessary_control": "Gap, locality, interface, symmetry, and finite-size convergence", "decisive_negative_test_or_ceiling": "The relevant gap closes, the protecting symmetry is absent, or the state is removable by a local symmetry-preserving perturbation" }, { "claim_or_regime": "Majorana platform", "defining_input": "Calibrated device forward model and parity sector", "observable_or_invariant": "Nonlocal end correlation, parity dynamics, fusion, or braiding operation", "necessary_control": "Parent gap, disorder, temperature, transfer function, device replication, and trivial comparators", "decisive_negative_test_or_ceiling": "Local zero-bias, tune-up, or minimal-chain parity signal remains reproducible by Andreev, Kondo, disorder, or ordinary dynamics", "evidence_cutoff": "2026-08-23" } ], "nonclaims": [ "The rows are claim layers and validity tests, not a chronological sequence or a catalogue of thermodynamic phases.", "Passing one row does not pass any other row.", "A gap, response maximum, fitted kernel, zero-bias peak, or parity signal is not promoted beyond the controls in its own row.", "The platform row is date-bounded through 23 August 2026 and is not asserted to be current after that cutoff." ], "accessibility": { "color_dependency": "none", "visual_equivalent": "The canonical Markdown table on the owner page presents the same thirteen rows and five columns.", "horizontal_overflow": "The rendered table is locally scrollable on narrow screens without page-wide overflow." }, "rights": { "basis": "Original QFT.org semantic table synthesized from the governed chapter contracts and independently checked source chain; no third-party table or artwork was copied or restyled.", "creator": "OpenAI Codex, for QFT.org", "date": "2026-08-31" } }