{"authors":[],"bibtex":null,"citations":[],"columns":[{"description":"Catalogue identifier; a reference, not a knot diagram.","encoding":{"element":{"kind":"string"},"kind":"nominal","name":"KnotId"},"name":"knot_id","type":"Nominal(KnotId, string)"},{"description":"Display name of the oriented knot.","encoding":{"kind":"string"},"name":"name","type":"string"},{"description":"Optional DT catalogue alias.","encoding":{"element":{"kind":"string"},"kind":"option"},"name":"dt_name","type":"Option(string)"},{"description":"Minimal crossing number, when known.","encoding":{"element":{"kind":"int"},"kind":"option"},"name":"crossing_number","type":"Option(int)"},{"description":"Whether the catalogue marks the knot as alternating.","encoding":{"kind":"bool"},"name":"alternating","type":"bool"},{"description":"Current values: unknot, prime, composite.","encoding":{"kind":"string"},"name":"kind","type":"string"},{"description":"Number of components; always one in this dataset.","encoding":{"kind":"int"},"name":"component_count","type":"int"},{"description":"Oriented PD presentation, represented by a list of integer quadruples; [] denotes the unknot.","encoding":{"element":{"element":{"fields":[{"kind":"int"},{"kind":"int"},{"kind":"int"},{"kind":"int"}],"kind":"product"},"kind":"list"},"kind":"nominal","name":"PDCode"},"name":"pd_code","type":"Nominal(PDCode, List(Product(int, int, int, int)))"},{"description":"Source or derivation of the PD presentation.","encoding":{"kind":"string"},"name":"pd_source","type":"string"},{"description":"Locator or serialized source description.","encoding":{"kind":"string"},"name":"source_record","type":"string"},{"description":"Combined amphichirality status; None means unknown.","encoding":{"element":{"kind":"bool"},"kind":"option"},"name":"amphichiral","type":"Option(bool)"},{"description":"Reversibility status; None means unknown.","encoding":{"element":{"kind":"bool"},"kind":"option"},"name":"reversible","type":"Option(bool)"},{"description":"Imported symmetry category, when available.","encoding":{"element":{"kind":"string"},"kind":"option"},"name":"symmetry_type","type":"Option(string)"},{"description":"Catalogue references to unresolved possible duplicates.","encoding":{"element":{"element":{"kind":"string"},"kind":"nominal","name":"KnotId"},"kind":"list"},"name":"possible_duplicates","type":"List(Nominal(KnotId, string))"}],"completeness":"See source manifest; symmetry and equivalence may remain unresolved.","data_version":"8cb3ba370b31630457dc3734f58f9f1eba7882b741bfee7c75c019abb928faa9","description":"YakDB catalogue with explicit orientation and mirror conventions. Unresolved equivalences are retained.","id":"OrientedKnots","license":null,"methodology":"Imported catalogue presentations and existing normalization; name-based references are uncertified.","operations":["rows","count","filter","sort","export","entity"],"primary_key":"name","provenance":"YakDB source import; see integrations/YAKDB_SOURCE.json and integrations/yaksite/data/manifest.json.","public":true,"relationships":"References associate records by name.","schema_version":"b8754b7fe0915fd1546e20bbe7cf7c91e88713aee2abd8ad0cc071fd8420d5f3","title":"Oriented Knots","verification":{"explanation":"Snapshot changed; rerun validation.","mathematically_certified":false,"report":null,"status":"Unverified"}}