{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZAGXDNRXVR35CGEOE4VVXBA6GV","short_pith_number":"pith:ZAGXDNRX","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"},"canonical_sha256":"c80d71b637ac77d1188e272b5b841e357803cab7a6a0291a7e1fddae88dcd2f1","source":{"kind":"arxiv","id":"1511.09469","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09469","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09469v3","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09469","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZAGXDNRXVR35","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZAGXDNRXVR35CGEO","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZAGXDNRX","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZAGXDNRXVR35CGEOE4VVXBA6GV","target":"record","payload":{"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"},"canonical_sha256":"c80d71b637ac77d1188e272b5b841e357803cab7a6a0291a7e1fddae88dcd2f1","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"},"source_kind":"arxiv","source_id":"1511.09469","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GRCeQEb5SteIcD9WIlxYPdjaNrJFhVS1UaS4t6rhhhFBNUrouCGyEXnX1oWISOoHBNQt8J64GE7XgAYeV7/UDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:41:29.763498Z"},"content_sha256":"c5299d40eb72f568326f3ea251539af05f9ebd1c4a785b6097680f372c8e0078","schema_version":"1.0","event_id":"sha256:c5299d40eb72f568326f3ea251539af05f9ebd1c4a785b6097680f372c8e0078"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZAGXDNRXVR35CGEOE4VVXBA6GV","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dw7Z5s6NIluJy4w3WO4kNREF7C4xsSmnX5yQfFxgpA1uCkDESqQ4tf8UPmJOUgb87B3Y14R7Kv2onj9/4XI8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:41:29.764224Z"},"content_sha256":"87804ff80b265ade532f752bc123fc63cdfb1b43e60d2b9d9a862901502f8993","schema_version":"1.0","event_id":"sha256:87804ff80b265ade532f752bc123fc63cdfb1b43e60d2b9d9a862901502f8993"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/bundle.json","state_url":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T06:41:29Z","links":{"resolver":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV","bundle":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/bundle.json","state":"https://pith.science/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZAGXDNRXVR35CGEOE4VVXBA6GV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZAGXDNRXVR35CGEOE4VVXBA6GV","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":"4caad1817f30b107e99aade431906d6cce48397999e9d46c5b2cb13a71aba3e9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-30T20:53:46Z","title_canon_sha256":"a72f7f320ac11242d894c5d4c3e77d873eccfc1ee8602445c139183112e21ecd"},"schema_version":"1.0","source":{"id":"1511.09469","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09469","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09469v3","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09469","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZAGXDNRXVR35","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZAGXDNRXVR35CGEO","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZAGXDNRX","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:87804ff80b265ade532f752bc123fc63cdfb1b43e60d2b9d9a862901502f8993","target":"graph","created_at":"2026-05-18T00:29:21Z","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":"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.","authors_text":"Chaim Even-Zohar","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-30T20:53:46Z","title":"The Writhe of Permutations and Random Framed Knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09469","kind":"arxiv","version":3},"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:c5299d40eb72f568326f3ea251539af05f9ebd1c4a785b6097680f372c8e0078","target":"record","created_at":"2026-05-18T00:29:21Z","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":"4caad1817f30b107e99aade431906d6cce48397999e9d46c5b2cb13a71aba3e9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-30T20:53:46Z","title_canon_sha256":"a72f7f320ac11242d894c5d4c3e77d873eccfc1ee8602445c139183112e21ecd"},"schema_version":"1.0","source":{"id":"1511.09469","kind":"arxiv","version":3}},"canonical_sha256":"c80d71b637ac77d1188e272b5b841e357803cab7a6a0291a7e1fddae88dcd2f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c80d71b637ac77d1188e272b5b841e357803cab7a6a0291a7e1fddae88dcd2f1","first_computed_at":"2026-05-18T00:29:21.354826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:21.354826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4K3S7Hudb0FXaifVLK3sj4K51hVq3/PG7Lk8N1QpJ4KSVchDkJi21n2tjyfMzDRkk68vPP+xbA8LUeVSvopUCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:21.355759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.09469","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5299d40eb72f568326f3ea251539af05f9ebd1c4a785b6097680f372c8e0078","sha256:87804ff80b265ade532f752bc123fc63cdfb1b43e60d2b9d9a862901502f8993"],"state_sha256":"23764863f67ace75ddea0ff30e83e802a2a46a14535b13942c629055af308ee5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CCTXYGmTT3rPBAqPAS2LloOrGhYabk1gmt7QK0utEc/oj0YRNXdeGAQhnSIQQeOx2d7rbpeYxtXapiriHskJAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:41:29.768783Z","bundle_sha256":"1def08b736321b9bb578a4e90eb79715f8bd82e7d6e9f39de7f1e04774b9de53"}}