{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZAGXDNRXVR35CGEOE4VVXBA6GV","short_pith_number":"pith:ZAGXDNRX","schema_version":"1.0","canonical_sha256":"c80d71b637ac77d1188e272b5b841e357803cab7a6a0291a7e1fddae88dcd2f1","source":{"kind":"arxiv","id":"1511.09469","version":3},"attestation_state":"computed","paper":{"title":"The Writhe of Permutations and Random Framed Knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Chaim Even-Zohar","submitted_at":"2015-11-30T20:53:46Z","abstract_excerpt":"We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non-Gaussian limit distribution.\n  This work is motivated by the study of random knots. A model for random framed knots is described, which refines the Petaluma model. The distribution of the framing in this model is equivalent to the writhe of random permutations."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.09469","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-30T20:53:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"a72f7f320ac11242d894c5d4c3e77d873eccfc1ee8602445c139183112e21ecd","abstract_canon_sha256":"4caad1817f30b107e99aade431906d6cce48397999e9d46c5b2cb13a71aba3e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:21.355759Z","signature_b64":"4K3S7Hudb0FXaifVLK3sj4K51hVq3/PG7Lk8N1QpJ4KSVchDkJi21n2tjyfMzDRkk68vPP+xbA8LUeVSvopUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c80d71b637ac77d1188e272b5b841e357803cab7a6a0291a7e1fddae88dcd2f1","last_reissued_at":"2026-05-18T00:29:21.354826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:21.354826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Writhe of Permutations and Random Framed Knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Chaim Even-Zohar","submitted_at":"2015-11-30T20:53:46Z","abstract_excerpt":"We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non-Gaussian limit distribution.\n  This work is motivated by the study of random knots. A model for random framed knots is described, which refines the Petaluma model. The distribution of the framing in this model is equivalent to the writhe of random permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09469","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.09469","created_at":"2026-05-18T00:29:21.355004+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.09469v3","created_at":"2026-05-18T00:29:21.355004+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09469","created_at":"2026-05-18T00:29:21.355004+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZAGXDNRXVR35","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZAGXDNRXVR35CGEO","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZAGXDNRX","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV","json":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV.json","graph_json":"https://pith.science/api/pith-number/ZAGXDNRXVR35CGEOE4VVXBA6GV/graph.json","events_json":"https://pith.science/api/pith-number/ZAGXDNRXVR35CGEOE4VVXBA6GV/events.json","paper":"https://pith.science/paper/ZAGXDNRX"},"agent_actions":{"view_html":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV","download_json":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV.json","view_paper":"https://pith.science/paper/ZAGXDNRX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.09469&json=true","fetch_graph":"https://pith.science/api/pith-number/ZAGXDNRXVR35CGEOE4VVXBA6GV/graph.json","fetch_events":"https://pith.science/api/pith-number/ZAGXDNRXVR35CGEOE4VVXBA6GV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/action/storage_attestation","attest_author":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/action/author_attestation","sign_citation":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/action/citation_signature","submit_replication":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/action/replication_record"}},"created_at":"2026-05-18T00:29:21.355004+00:00","updated_at":"2026-05-18T00:29:21.355004+00:00"}