{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NWOQANPDJDE7A54U6PC2TJLVYX","short_pith_number":"pith:NWOQANPD","canonical_record":{"source":{"id":"1704.07510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-04-25T01:33:59Z","cross_cats_sorted":[],"title_canon_sha256":"0aed092b09a457f4850641bc9812324aa6cf3dcbe74491a5208b404f8415668e","abstract_canon_sha256":"06855952c7cda163ff4f4eb52c60ff7050d9aa123be823c089fb38fe9e3c6ba2"},"schema_version":"1.0"},"canonical_sha256":"6d9d0035e348c9f07794f3c5a9a575c5c3075fbaeaabca4596b4b0b354d58f55","source":{"kind":"arxiv","id":"1704.07510","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07510","created_at":"2026-05-18T00:33:18Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07510v2","created_at":"2026-05-18T00:33:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07510","created_at":"2026-05-18T00:33:18Z"},{"alias_kind":"pith_short_12","alias_value":"NWOQANPDJDE7","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NWOQANPDJDE7A54U","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NWOQANPD","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NWOQANPDJDE7A54U6PC2TJLVYX","target":"record","payload":{"canonical_record":{"source":{"id":"1704.07510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-04-25T01:33:59Z","cross_cats_sorted":[],"title_canon_sha256":"0aed092b09a457f4850641bc9812324aa6cf3dcbe74491a5208b404f8415668e","abstract_canon_sha256":"06855952c7cda163ff4f4eb52c60ff7050d9aa123be823c089fb38fe9e3c6ba2"},"schema_version":"1.0"},"canonical_sha256":"6d9d0035e348c9f07794f3c5a9a575c5c3075fbaeaabca4596b4b0b354d58f55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:18.547628Z","signature_b64":"PCwTVYquZZAZGJ2QrxBmjNZvQCVLYBO1Q/C7FZAcjhMKeRi9hvXhDKf6ekEyQpuElHrh5oKWJBTYbmK3Qdj5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d9d0035e348c9f07794f3c5a9a575c5c3075fbaeaabca4596b4b0b354d58f55","last_reissued_at":"2026-05-18T00:33:18.546936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:18.546936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.07510","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sYrwxwtqh4+SmCmXueQvDZUHBPjYhCllxw7Uo8qY/4A+7XV0bRLAlfLifg75IstDAZsArRMTL4oao5CfnCVdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:55:49.312872Z"},"content_sha256":"6312fd2151cabba56eb038a726235d4d57eaaf0618bd3db3e84fe9e7bddeea6b","schema_version":"1.0","event_id":"sha256:6312fd2151cabba56eb038a726235d4d57eaaf0618bd3db3e84fe9e7bddeea6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NWOQANPDJDE7A54U6PC2TJLVYX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Knotting probability of self-avoiding polygons under a topological constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Erica Uehara, Tetsuo Deguchi","submitted_at":"2017-04-25T01:33:59Z","abstract_excerpt":"We define the knotting probability of a knot $K$ by the probability for a random polygon (RP) or self-avoiding polygon (SAP) of $N$ segments having the knot type $K$. We show fundamental and generic properties of the knotting probability particularly its dependence on the excluded volume. We investigate them for the SAP consisting of hard cylindrical segments of unit length and radius $r_{\\rm ex}$. For various prime and composite knots we numerically show that a compact formula describes the knotting probabilities for the cylindrical SAP as a function of segment number $N$ and radius $r_{\\rm e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07510","kind":"arxiv","version":2},"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":"2026-05-18T00:33:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"21OoxbW0EBH0v3CUmIBlkW2VfyGFjVjwd68gpAwY6OZhjZTGmUy+xJ8FpWti5bYQcLMfYOMKHLvfWVyEB5IcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:55:49.313614Z"},"content_sha256":"7280afbafd8f8e074871b11526e798b14837c409b82a085e61056b6d49706621","schema_version":"1.0","event_id":"sha256:7280afbafd8f8e074871b11526e798b14837c409b82a085e61056b6d49706621"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWOQANPDJDE7A54U6PC2TJLVYX/bundle.json","state_url":"https://pith.science/pith/NWOQANPDJDE7A54U6PC2TJLVYX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWOQANPDJDE7A54U6PC2TJLVYX/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":"2026-05-31T21:55:49Z","links":{"resolver":"https://pith.science/pith/NWOQANPDJDE7A54U6PC2TJLVYX","bundle":"https://pith.science/pith/NWOQANPDJDE7A54U6PC2TJLVYX/bundle.json","state":"https://pith.science/pith/NWOQANPDJDE7A54U6PC2TJLVYX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWOQANPDJDE7A54U6PC2TJLVYX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NWOQANPDJDE7A54U6PC2TJLVYX","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":"06855952c7cda163ff4f4eb52c60ff7050d9aa123be823c089fb38fe9e3c6ba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-04-25T01:33:59Z","title_canon_sha256":"0aed092b09a457f4850641bc9812324aa6cf3dcbe74491a5208b404f8415668e"},"schema_version":"1.0","source":{"id":"1704.07510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07510","created_at":"2026-05-18T00:33:18Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07510v2","created_at":"2026-05-18T00:33:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07510","created_at":"2026-05-18T00:33:18Z"},{"alias_kind":"pith_short_12","alias_value":"NWOQANPDJDE7","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NWOQANPDJDE7A54U","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NWOQANPD","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:7280afbafd8f8e074871b11526e798b14837c409b82a085e61056b6d49706621","target":"graph","created_at":"2026-05-18T00:33:18Z","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 define the knotting probability of a knot $K$ by the probability for a random polygon (RP) or self-avoiding polygon (SAP) of $N$ segments having the knot type $K$. We show fundamental and generic properties of the knotting probability particularly its dependence on the excluded volume. We investigate them for the SAP consisting of hard cylindrical segments of unit length and radius $r_{\\rm ex}$. For various prime and composite knots we numerically show that a compact formula describes the knotting probabilities for the cylindrical SAP as a function of segment number $N$ and radius $r_{\\rm e","authors_text":"Erica Uehara, Tetsuo Deguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-04-25T01:33:59Z","title":"Knotting probability of self-avoiding polygons under a topological constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07510","kind":"arxiv","version":2},"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":"sha256:6312fd2151cabba56eb038a726235d4d57eaaf0618bd3db3e84fe9e7bddeea6b","target":"record","created_at":"2026-05-18T00:33:18Z","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":"06855952c7cda163ff4f4eb52c60ff7050d9aa123be823c089fb38fe9e3c6ba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-04-25T01:33:59Z","title_canon_sha256":"0aed092b09a457f4850641bc9812324aa6cf3dcbe74491a5208b404f8415668e"},"schema_version":"1.0","source":{"id":"1704.07510","kind":"arxiv","version":2}},"canonical_sha256":"6d9d0035e348c9f07794f3c5a9a575c5c3075fbaeaabca4596b4b0b354d58f55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d9d0035e348c9f07794f3c5a9a575c5c3075fbaeaabca4596b4b0b354d58f55","first_computed_at":"2026-05-18T00:33:18.546936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:18.546936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PCwTVYquZZAZGJ2QrxBmjNZvQCVLYBO1Q/C7FZAcjhMKeRi9hvXhDKf6ekEyQpuElHrh5oKWJBTYbmK3Qdj5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:18.547628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6312fd2151cabba56eb038a726235d4d57eaaf0618bd3db3e84fe9e7bddeea6b","sha256:7280afbafd8f8e074871b11526e798b14837c409b82a085e61056b6d49706621"],"state_sha256":"bf55deff0e0b012884247d221c025f00af1b15cb8624f90496c3bc6a4da10dba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CB6GjWHRqSvLFAWPH96+Td/r8uf1gixF3aNb1OmcKQ+1TETjfqkt0qQ1ju91qwDJGDkhkQGVo57mw4ySOS6VCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:55:49.317951Z","bundle_sha256":"c28eab3446872f6fd3f5356ed3d63a191d83f7395f156650a8bdc535a5d40f06"}}