{"authors":[],"bibtex":null,"citations":[],"columns":[{"description":"Length of the braid","encoding":{"kind":"int"},"name":"length","type":"int"},{"description":"Braid word used to compute $F_K$","encoding":{"kind":"mathematica_short_code"},"name":"braid","type":"mathematica_short_code"},{"description":"YakDB ID","encoding":{"kind":"string"},"name":"yakdb_id","type":"string"},{"description":"Is the braid positive?","encoding":{"kind":"bool"},"name":"positive","type":"bool"},{"description":"Is the braid homogeneous?","encoding":{"kind":"bool"},"name":"homogeneous","type":"bool"},{"description":"Is the braid a minimum braid?","encoding":{"kind":"bool"},"name":"is_minimum_braid","type":"bool"},{"description":"Shortest braid word for this knot","encoding":{"kind":"mathematica_short_code"},"name":"minimum_braid","type":"mathematica_short_code"}],"completeness":null,"data_version":"unversioned-synapse","description":"Canonical braids up to 10 crossings, lexicographically minimal among cyclic rotations and mirror images, with each generator appearing at least twice.","id":"hard_braids","license":null,"methodology":"Legacy schema requires audit. Source payloads are preserved; name-based joins are uncertified.","operations":["rows","count","filter","sort","export"],"primary_key":null,"provenance":null,"public":true,"relationships":"References associate records by name.","schema_version":"80a86895da2bbd7e6da60d9058976a8d842c24ee10273bb248c18cf30de8e616","title":"Normalized braids","verification":{"explanation":"Snapshot changed; rerun validation.","mathematically_certified":false,"report":null,"status":"Unverified"}}