{ "$schema": "https://qft.org/data/conformal-bootstrap/numerical-claim-taxonomy.schema.json", "schema_version": 1, "artifact_id": "qft.artifact.conformal-bootstrap.numerical.claim-taxonomy", "taxonomy_version": "1.0.0", "review_cutoff": "2026-09-01", "title": "Numerical-bootstrap outputs, supported interpretations, and stop rules", "scope": "Method-level claims for finite represented conformal-bootstrap problems. Benchmark reproduction is governed separately by the numerical claim-evidence ladder.", "freshness_contract": { "evidence_cutoff_required": true, "reproduction_timestamp_required": true, "software_or_analytic_environment_required": true, "frozen_inputs_outputs_required": true, "independent_check_required": true, "minimum_independent_refinement_axes": 2 }, "owner_page_ids": [ "qft.topic.numerical-bootstrap.single-correlator-bounds", "qft.topic.numerical-bootstrap.symmetry-spinning-systems", "qft.topic.numerical-bootstrap.extremal-navigator-reconstruction" ], "canonical_source": { "page_id": "qft.topic.numerical-bootstrap.symmetry-spinning-systems", "path": "src/content/docs/conformal-bootstrap/numerical-bootstrap/symmetry-spinning-systems.md", "heading": "Numerical claim taxonomy", "fragment": "numerical-claim-taxonomy", "public_data_path": "public/data/conformal-bootstrap/numerical-claim-taxonomy.json" }, "columns": [ { "key": "label", "label": "Claim class", "definition": "The computed or reconstructed object being reported." }, { "key": "verified_output", "label": "Verified output", "definition": "Exactly what the retained certificate or numerical record establishes in the finite represented problem." }, { "key": "supported_interpretation", "label": "Supported interpretation", "definition": "The strongest defensible reader-facing interpretation." }, { "key": "required_assumptions", "label": "Required assumptions", "definition": "The correlators, sectors, gaps, normalizations, positivity hypotheses, approximations, and search domain on which the interpretation depends." }, { "key": "convergence_study", "label": "Convergence study", "definition": "The exact checks and independently varied approximation axes required before acceptance." }, { "key": "failure_or_downgrade_trigger", "label": "Failure or downgrade trigger", "definition": "An observation that invalidates, weakens, or downgrades the stated claim." }, { "key": "evidence_record", "label": "Evidence and freshness record", "definition": "The serialized inputs, outputs, residuals, certificates, environments, dates, evidence cutoffs, and independent checks that must be retained." }, { "key": "unsupported_inference", "label": "Unsupported inference", "definition": "A stronger conclusion that the row does not establish." } ], "specializations": [ { "id": "symmetry_spinning", "label": "Global-symmetry and spinning-system precondition", "applies_to_row_ids": [ "certified_exclusion", "conditional_bound", "stable_feature", "scan_delimited_component", "navigator_evaluation", "navigator_search", "extremal_support", "primal_spectrum_estimate", "model_compatibility" ], "preconditions": [ { "id": "group_recoupling", "statement": "group projectors or matrix units are complete and satisfy exact multiplication and recoupling identities" }, { "id": "tensor_basis", "statement": "the physical-dimension tensor basis has verified rank and permutation closure" }, { "id": "conservation_ward", "statement": "conservation rank, Ward normalization, shortening branches, and contact-term scope are correct" }, { "id": "statistics_parity_reality", "statement": "exchange statistics, spacetime parity, Hermitian conjugation, and fixed phases are distinct and consistent" }, { "id": "positive_metric_congruence", "statement": "every OPE Gram matrix and basis congruence uses the declared positive two-point metric" }, { "id": "block_continuum", "statement": "spinning blocks and continuous-dimension positivity are enclosed on the full represented domain" } ], "failure_action": "Stop before solving. No downstream certificate, bound, island, navigator result, reconstruction, or model-compatibility statement remains supportable." } ], "rows": [ { "id": "certified_exclusion", "label": "Certified exclusion", "verified_output": "An independently verified infeasibility certificate for the declared finite represented problem.", "supported_interpretation": "The tested spectral hypothesis fails in that represented problem.", "required_assumptions": "External data, sectors, gaps, block and tail representation, positivity basis, and sign convention.", "convergence_study": "Certificate residuals and positivity margins across block, functional, spin, and precision settings.", "failure_or_downgrade_trigger": "An independently verified feasible witness, failed sign check, or failed positivity enclosure.", "evidence_record": "Serialized input, certificate, unscaled residuals, independent-verifier result, release date, and software environment.", "unsupported_inference": "“No exact CFT” without complete approximation control." }, { "id": "conditional_bound", "label": "Conditional bound", "verified_output": "One-sided certified exclusions establish a bound in the represented problem; a quoted boundary location also requires a declared unresolved or feasible-side bracket.", "supported_interpretation": "A finite conditional upper or lower limit under the stated assumptions.", "required_assumptions": "Normalization, spectral assumptions, monotonicity of the tested hypothesis, search protocol, and represented parameter domain.", "convergence_study": "For a one-sided exclusion bound, verify certificate margins across functional, block, spin-tail, and precision refinements; for a quoted boundary location, also require bracket and interpolation stability.", "failure_or_downgrade_trigger": "A feasible witness in the excluded region or motion outside the reported refinement envelope.", "evidence_record": "Retain the trial record, exclusion certificates, and full refinement table; when quoting a boundary location, also retain its feasible-side or unresolved bracket history and cutoff date.", "unsupported_inference": "“The boundary point exists” or an assumption-free universal number." }, { "id": "stable_feature", "label": "Stable feature or kink", "verified_output": "A dated, algorithmically defined feature persists within its reported envelope under the declared numerical and representation refinements.", "supported_interpretation": "A reproducible geometric feature and possible change of the active spectrum.", "required_assumptions": "Curve definition, interpolation, parameterization, and complete represented system.", "convergence_study": "Location and shape remain within the stated envelope as the mesh, functional, blocks, spin tail, and precision are refined.", "failure_or_downgrade_trigger": "The feature smooths, drifts beyond its envelope, or disappears after a missing sector is restored.", "evidence_record": "Dated curve data, underlying certificates, feature definition, and current independent physics checks with an evidence cutoff.", "unsupported_inference": "Automatic identification with a named model." }, { "id": "scan_delimited_component", "label": "Scan-delimited component", "verified_output": "A certified connected barrier or excluded-cell cover encloses a declared not-excluded component, with every unresolved boundary cell recorded.", "supported_interpretation": "A conditional component within the scanned domain and resolution.", "required_assumptions": "Correlator closure, shared-operator assumptions, search domain, and topology protocol.", "convergence_study": "Adaptive boundary refinement, topology checks, and assumption-removal scans.", "failure_or_downgrade_trigger": "A missed passage or component, failed enclosing certificate, or an opened region after relaxing an assumption.", "evidence_record": "Boundary certificates, dated scan map, unresolved cells, topology diagnostics, and search environment.", "unsupported_inference": "“Complete island,” realization of every interior point, or uniqueness without separate proof." }, { "id": "navigator_evaluation", "label": "Navigator evaluation", "verified_output": "The value or sign of a declared finite navigator objective.", "supported_interpretation": "Position relative to that deformed finite feasible set.", "required_assumptions": "Objective, deformation, normalization, finite representation, and sign convention.", "convergence_study": "Precision and cutoff studies plus direct feasibility checks near sign changes.", "failure_or_downgrade_trigger": "A direct certificate contradicts the sign or a convention round trip changes it.", "evidence_record": "Objective definition, evaluation point, dated solver record, environment, and feasibility cross-check.", "unsupported_inference": "A physical distance to exact theory space." }, { "id": "navigator_search", "label": "Navigator search or optimum", "verified_output": "A declared search returned a termination point satisfying its recorded termination tolerances; stationarity or local optimality only if independently checked.", "supported_interpretation": "A candidate region for more direct feasibility and reconstruction tests.", "required_assumptions": "Search domain, starting points, optimizer, stopping rule, and navigator definition.", "convergence_study": "Multiple starts, boundary traces, objective variations, and direct certificate checks.", "failure_or_downgrade_trigger": "A lower point, missed component, unstable active set, or failed direct feasibility check.", "evidence_record": "Dated search trajectories, starts, gradients, termination data, environment, and nearby certificates.", "unsupported_inference": "A unique theory or globally closest exact CFT without proof." }, { "id": "extremal_support", "label": "Extremal-functional support", "verified_output": "Zeros and support conditions of a finite extremal functional.", "supported_interpretation": "Candidate exchanged dimensions and active constraints at a represented boundary.", "required_assumptions": "Extremality, functional basis, sector convention, and endpoint or tangency rule.", "convergence_study": "Zero positions, multiplicities, derivative conditions, and positivity persist across cutoffs.", "failure_or_downgrade_trigger": "Zero drift, lost tangency, failed positivity, or incompatible primal data.", "evidence_record": "Saved functional, dated zero-finding record, derivative tests, cutoff sequence, and software environment.", "unsupported_inference": "An exact operator spectrum." }, { "id": "primal_spectrum_estimate", "label": "Primal spectrum or OPE reconstruction", "verified_output": "A scalar-nonnegative or matrix-PSD finite truncated solution with a verified residual in the original unscaled equations.", "supported_interpretation": "Approximate low-lying dimensions and invariant OPE data.", "required_assumptions": "Selected support, degeneracy treatment, basis convention, and tail model.", "convergence_study": "Unscaled residuals and low invariant data remain stable across cutoffs and support changes.", "failure_or_downgrade_trigger": "A negative OPE-matrix eigenvalue, ill-conditioned instability, or nondecreasing controlled residual.", "evidence_record": "Dated primal-dual record, residual in the original basis, conditioning data, environment, and external checks.", "unsupported_inference": "A full exact crossing solution or proof of model identity." }, { "id": "model_compatibility", "label": "Model compatibility", "verified_output": "Named-model predictions and the underlying verified exclusions, bounds, or reconstructed observables agree within declared tolerances after applying an explicit convention map.", "supported_interpretation": "A named model is compatible with the tested data and conventions.", "required_assumptions": "An explicit convention dictionary and a declared identification hypothesis.", "convergence_study": "Several observables, correlator systems, and independent methods remain compatible.", "failure_or_downgrade_trigger": "Conflicting symmetry, spectrum, OPE data, anomaly, or independently measured observable.", "evidence_record": "Current analytic, lattice, experimental, or independent bootstrap evidence with an explicit cutoff and convention map.", "unsupported_inference": "An existence or uniqueness theorem." } ], "global_stop_rule": "Every conclusion stops at the declared finite represented problem. Failure to exclude, primal feasibility, a scan-delimited component, a navigator minimum, stable extremal data, or agreement with a candidate model does not establish realization, existence, uniqueness, completeness, or model identity. Any stronger conclusion requires separate evidence whose hypotheses and conventions are stated alongside it." }