{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MMTXZS3NJ56DPBHYENEC25D6XL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"82dcf1cd8d2b0010b9338e727b749e431a745b1a636d35a247fc433058ec0121","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.LO","submitted_at":"2012-09-17T06:49:35Z","title_canon_sha256":"557a288e5731dc36ee75d38aafb072c47f938f58740fc149389cfa62af003250"},"schema_version":"1.0","source":{"id":"1209.3562","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3562","created_at":"2026-05-18T03:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3562v1","created_at":"2026-05-18T03:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3562","created_at":"2026-05-18T03:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"MMTXZS3NJ56D","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MMTXZS3NJ56DPBHY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MMTXZS3N","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:556566c3efbf92b34209b722bc1d227b91f7b374537203efd2ddd9edd4f4ab73","target":"graph","created_at":"2026-05-18T03:45:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Determining when two knots are equivalent (more precisely isotopic) is a fundamental problem in topology. Here we formulate this problem in terms of Predicate Calculus, using the formulation of knots in terms of braids and some basic topological results.\n  Concretely, Knot theory is formulated in terms of a language with signature $(\\cdot,T,\\equiv, 1,\\sigma,\\bar\\sigma)$, with $\\cdot$ a 2-function, $T$ a 1-function, $\\equiv$ a 2-predicate and 1, $\\sigma$ and $\\bar\\sigma$ constants. We describe a finite set of axioms making the language into a (first order) theory. We show that every knot can be","authors_text":"Siddhartha Gadgil, T. V. H. Prathamesh","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.LO","submitted_at":"2012-09-17T06:49:35Z","title":"Knots, Braids and First Order Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3562","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b865ad9927d526c5e2b1d50310bfe17ccddb8964036eab6afb4823de8ea51223","target":"record","created_at":"2026-05-18T03:45:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"82dcf1cd8d2b0010b9338e727b749e431a745b1a636d35a247fc433058ec0121","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.LO","submitted_at":"2012-09-17T06:49:35Z","title_canon_sha256":"557a288e5731dc36ee75d38aafb072c47f938f58740fc149389cfa62af003250"},"schema_version":"1.0","source":{"id":"1209.3562","kind":"arxiv","version":1}},"canonical_sha256":"63277ccb6d4f7c3784f823482d747ebac5a192198a6f01b26baf889768aec57a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63277ccb6d4f7c3784f823482d747ebac5a192198a6f01b26baf889768aec57a","first_computed_at":"2026-05-18T03:45:30.628023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:30.628023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"obhLADOhHr6Ig24gieZgKfimgSeDyjIF1gmV04Jes+z/7E5aY7AnMXdtB4pNZKmWMwpFOSx925+O8CddEULjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:30.628489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3562","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b865ad9927d526c5e2b1d50310bfe17ccddb8964036eab6afb4823de8ea51223","sha256:556566c3efbf92b34209b722bc1d227b91f7b374537203efd2ddd9edd4f4ab73"],"state_sha256":"d9bb91239441ecebf87a3eb8e73123a40478b4ea95790ac6a130ca1fc44d4fc5"}