{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:E7ML5CYYCKPBIBO4QUXXND7TPU","short_pith_number":"pith:E7ML5CYY","canonical_record":{"source":{"id":"math/0205231","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2002-05-22T17:28:02Z","cross_cats_sorted":[],"title_canon_sha256":"6924891df49a07511e9d09d682fa85950d988c5eb73af2092f47d35ed98a6433","abstract_canon_sha256":"97af74c400fee9fdab9389494e85148e1f3b637833752e628a2ec8ba762ece2d"},"schema_version":"1.0"},"canonical_sha256":"27d8be8b18129e1405dc852f768ff37d02cf78602e2a23f83ae849d4cbdf7998","source":{"kind":"arxiv","id":"math/0205231","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205231","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205231v1","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205231","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"pith_short_12","alias_value":"E7ML5CYYCKPB","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"E7ML5CYYCKPBIBO4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"E7ML5CYY","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:E7ML5CYYCKPBIBO4QUXXND7TPU","target":"record","payload":{"canonical_record":{"source":{"id":"math/0205231","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2002-05-22T17:28:02Z","cross_cats_sorted":[],"title_canon_sha256":"6924891df49a07511e9d09d682fa85950d988c5eb73af2092f47d35ed98a6433","abstract_canon_sha256":"97af74c400fee9fdab9389494e85148e1f3b637833752e628a2ec8ba762ece2d"},"schema_version":"1.0"},"canonical_sha256":"27d8be8b18129e1405dc852f768ff37d02cf78602e2a23f83ae849d4cbdf7998","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:33.032949Z","signature_b64":"4i/b34dWJ/Awykw/+ghNyjA1lyiaIJzvNjhYWYKV0xlJR/lWgTN1YE1gcrm/dTwwTUysJDKwM2fshNHFQPBFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27d8be8b18129e1405dc852f768ff37d02cf78602e2a23f83ae849d4cbdf7998","last_reissued_at":"2026-05-18T02:41:33.032515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:33.032515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0205231","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rso/51aBX97LE5bnxbpHigETkPrmynYVNOx2b+wYcNHEPu97AzA93Sew7axIA9IxiDRRLHLeVOFk1mtlX1ZIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:35:50.935621Z"},"content_sha256":"704488d603af6e74731b119c6d90d8c148c386123216c92a6c4284ba0b7ae8bd","schema_version":"1.0","event_id":"sha256:704488d603af6e74731b119c6d90d8c148c386123216c92a6c4284ba0b7ae8bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:E7ML5CYYCKPBIBO4QUXXND7TPU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intrinsic knotting and linking of complete graphs","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Erica Flapan","submitted_at":"2002-05-22T17:28:02Z","abstract_excerpt":"We show that for every m in N, there exists an n in N such that every embedding of the complete graph K_n in R^3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r in N such that every embedding of K_r in R^3 contains a knot Q with |a_2(Q)| > m-1, where a_2(Q) denotes the second coefficient of the Conway polynomial of Q."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205231","kind":"arxiv","version":1},"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":"2026-05-18T02:41:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Djk+s9lVBQA0aU+IhYsoxfEwOIjUho/09W50pfvAahhLeFMDDLRRAarxE3bqym4FuSS+sXk0W3L29hPc8XlCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:35:50.936021Z"},"content_sha256":"aaada80ef41eb97b2cbb6955a4fc7b81e1783aeff46d4f026a02149501db07b0","schema_version":"1.0","event_id":"sha256:aaada80ef41eb97b2cbb6955a4fc7b81e1783aeff46d4f026a02149501db07b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7ML5CYYCKPBIBO4QUXXND7TPU/bundle.json","state_url":"https://pith.science/pith/E7ML5CYYCKPBIBO4QUXXND7TPU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7ML5CYYCKPBIBO4QUXXND7TPU/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":"2026-06-21T22:35:50Z","links":{"resolver":"https://pith.science/pith/E7ML5CYYCKPBIBO4QUXXND7TPU","bundle":"https://pith.science/pith/E7ML5CYYCKPBIBO4QUXXND7TPU/bundle.json","state":"https://pith.science/pith/E7ML5CYYCKPBIBO4QUXXND7TPU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7ML5CYYCKPBIBO4QUXXND7TPU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:E7ML5CYYCKPBIBO4QUXXND7TPU","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":"97af74c400fee9fdab9389494e85148e1f3b637833752e628a2ec8ba762ece2d","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2002-05-22T17:28:02Z","title_canon_sha256":"6924891df49a07511e9d09d682fa85950d988c5eb73af2092f47d35ed98a6433"},"schema_version":"1.0","source":{"id":"math/0205231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205231","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205231v1","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205231","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"pith_short_12","alias_value":"E7ML5CYYCKPB","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"E7ML5CYYCKPBIBO4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"E7ML5CYY","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:aaada80ef41eb97b2cbb6955a4fc7b81e1783aeff46d4f026a02149501db07b0","target":"graph","created_at":"2026-05-18T02:41:33Z","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 show that for every m in N, there exists an n in N such that every embedding of the complete graph K_n in R^3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r in N such that every embedding of K_r in R^3 contains a knot Q with |a_2(Q)| > m-1, where a_2(Q) denotes the second coefficient of the Conway polynomial of Q.","authors_text":"Erica Flapan","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2002-05-22T17:28:02Z","title":"Intrinsic knotting and linking of complete graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205231","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":"sha256:704488d603af6e74731b119c6d90d8c148c386123216c92a6c4284ba0b7ae8bd","target":"record","created_at":"2026-05-18T02:41:33Z","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":"97af74c400fee9fdab9389494e85148e1f3b637833752e628a2ec8ba762ece2d","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2002-05-22T17:28:02Z","title_canon_sha256":"6924891df49a07511e9d09d682fa85950d988c5eb73af2092f47d35ed98a6433"},"schema_version":"1.0","source":{"id":"math/0205231","kind":"arxiv","version":1}},"canonical_sha256":"27d8be8b18129e1405dc852f768ff37d02cf78602e2a23f83ae849d4cbdf7998","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27d8be8b18129e1405dc852f768ff37d02cf78602e2a23f83ae849d4cbdf7998","first_computed_at":"2026-05-18T02:41:33.032515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:33.032515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4i/b34dWJ/Awykw/+ghNyjA1lyiaIJzvNjhYWYKV0xlJR/lWgTN1YE1gcrm/dTwwTUysJDKwM2fshNHFQPBFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:33.032949Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0205231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:704488d603af6e74731b119c6d90d8c148c386123216c92a6c4284ba0b7ae8bd","sha256:aaada80ef41eb97b2cbb6955a4fc7b81e1783aeff46d4f026a02149501db07b0"],"state_sha256":"57f7401fda4bd721d359373c7b1d48bb782ee6cf2e0a5f6aa8c7c24162e6e0d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLxUryDW0CY2x8hXSTegnjc+p2uuHJ8uoOg4py6mo/2idKy9+N6m8byAzZiqaR94/buQfYDaV2S5wLqiMhzXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:35:50.938023Z","bundle_sha256":"a4fa8949aa1fe57b0d4c7d934ca19ffd23e2a9f6f89cba4782030855d3490a9d"}}