{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:L5KJYK3JUQLDSOMIPW575Z45HQ","short_pith_number":"pith:L5KJYK3J","canonical_record":{"source":{"id":"1008.0377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T19:00:14Z","cross_cats_sorted":[],"title_canon_sha256":"081cbe9d3f1eb4ed5fa50b4b23910116f79effb139cd89bab51fd5007665eeb5","abstract_canon_sha256":"1180bd5600e15d30c3857cb5fac2c247d7e3321c12b1c3e7cddc4341002ba716"},"schema_version":"1.0"},"canonical_sha256":"5f549c2b69a4163939887dbbfee79d3c2e0fbe394d12e05eb8aec49f327b238e","source":{"kind":"arxiv","id":"1008.0377","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0377","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0377v1","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0377","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"L5KJYK3JUQLD","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"L5KJYK3JUQLDSOMI","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"L5KJYK3J","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:L5KJYK3JUQLDSOMIPW575Z45HQ","target":"record","payload":{"canonical_record":{"source":{"id":"1008.0377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T19:00:14Z","cross_cats_sorted":[],"title_canon_sha256":"081cbe9d3f1eb4ed5fa50b4b23910116f79effb139cd89bab51fd5007665eeb5","abstract_canon_sha256":"1180bd5600e15d30c3857cb5fac2c247d7e3321c12b1c3e7cddc4341002ba716"},"schema_version":"1.0"},"canonical_sha256":"5f549c2b69a4163939887dbbfee79d3c2e0fbe394d12e05eb8aec49f327b238e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:43.476518Z","signature_b64":"xcG4AWYzhzwUs0b/rrrHT2KUeMsp50nQA1hMzCvxmvCpN2FdLJKLa5SUwWifm6kPr30mtpru6V+ahTC94uwYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f549c2b69a4163939887dbbfee79d3c2e0fbe394d12e05eb8aec49f327b238e","last_reissued_at":"2026-05-18T04:42:43.476043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:43.476043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.0377","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":"2026-05-18T04:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EChY/8cLgJQCEVr6l/EU/aXccnl8J+NyOc9K26cl5z5Oi+1tSyLPt/2r+g6ievSrrzdlFLK5RGNX+gw2cWqcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:33:49.696632Z"},"content_sha256":"5cc7b3ea52a89ef9983816d71d890ba9a7f44ebbee56d5dd836eda5fbbcec38e","schema_version":"1.0","event_id":"sha256:5cc7b3ea52a89ef9983816d71d890ba9a7f44ebbee56d5dd836eda5fbbcec38e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:L5KJYK3JUQLDSOMIPW575Z45HQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Knotting and linking in the Petersen family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Danielle O'Donnol","submitted_at":"2010-08-02T19:00:14Z","abstract_excerpt":"This paper focuses on the graphs in the Petersen family, the set of minor minimal intrinsically linked graphs. We prove there is a relationship between algebraic linking of an embedding and knotting in an embedding. We also present a more explicit relationship for the graph $K_{3,3,1}$ between knotting and linking, which relates the sum of the squares of linking numbers of links in the embedding and the second coefficient of the Conway polynomial of particular cycles in the embedding."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0377","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":"2026-05-18T04:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/My3bPSymIoVxJ5VaIgoTLkttW9ngw8eg8tKi20Ordomra5fiHpKZAibR2I1lFqLF7UWo/aj7MyhezLzE40DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:33:49.696976Z"},"content_sha256":"7616f54822da6f8ce6bcdbd8bfd4991ed6fb4f3581177247bbde5bc6e5e2e19d","schema_version":"1.0","event_id":"sha256:7616f54822da6f8ce6bcdbd8bfd4991ed6fb4f3581177247bbde5bc6e5e2e19d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5KJYK3JUQLDSOMIPW575Z45HQ/bundle.json","state_url":"https://pith.science/pith/L5KJYK3JUQLDSOMIPW575Z45HQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5KJYK3JUQLDSOMIPW575Z45HQ/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":"2026-06-01T11:33:49Z","links":{"resolver":"https://pith.science/pith/L5KJYK3JUQLDSOMIPW575Z45HQ","bundle":"https://pith.science/pith/L5KJYK3JUQLDSOMIPW575Z45HQ/bundle.json","state":"https://pith.science/pith/L5KJYK3JUQLDSOMIPW575Z45HQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5KJYK3JUQLDSOMIPW575Z45HQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:L5KJYK3JUQLDSOMIPW575Z45HQ","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":"1180bd5600e15d30c3857cb5fac2c247d7e3321c12b1c3e7cddc4341002ba716","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T19:00:14Z","title_canon_sha256":"081cbe9d3f1eb4ed5fa50b4b23910116f79effb139cd89bab51fd5007665eeb5"},"schema_version":"1.0","source":{"id":"1008.0377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0377","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0377v1","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0377","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"L5KJYK3JUQLD","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"L5KJYK3JUQLDSOMI","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"L5KJYK3J","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:7616f54822da6f8ce6bcdbd8bfd4991ed6fb4f3581177247bbde5bc6e5e2e19d","target":"graph","created_at":"2026-05-18T04:42:43Z","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":"This paper focuses on the graphs in the Petersen family, the set of minor minimal intrinsically linked graphs. We prove there is a relationship between algebraic linking of an embedding and knotting in an embedding. We also present a more explicit relationship for the graph $K_{3,3,1}$ between knotting and linking, which relates the sum of the squares of linking numbers of links in the embedding and the second coefficient of the Conway polynomial of particular cycles in the embedding.","authors_text":"Danielle O'Donnol","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T19:00:14Z","title":"Knotting and linking in the Petersen family"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0377","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":"sha256:5cc7b3ea52a89ef9983816d71d890ba9a7f44ebbee56d5dd836eda5fbbcec38e","target":"record","created_at":"2026-05-18T04:42:43Z","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":"1180bd5600e15d30c3857cb5fac2c247d7e3321c12b1c3e7cddc4341002ba716","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T19:00:14Z","title_canon_sha256":"081cbe9d3f1eb4ed5fa50b4b23910116f79effb139cd89bab51fd5007665eeb5"},"schema_version":"1.0","source":{"id":"1008.0377","kind":"arxiv","version":1}},"canonical_sha256":"5f549c2b69a4163939887dbbfee79d3c2e0fbe394d12e05eb8aec49f327b238e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f549c2b69a4163939887dbbfee79d3c2e0fbe394d12e05eb8aec49f327b238e","first_computed_at":"2026-05-18T04:42:43.476043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:43.476043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xcG4AWYzhzwUs0b/rrrHT2KUeMsp50nQA1hMzCvxmvCpN2FdLJKLa5SUwWifm6kPr30mtpru6V+ahTC94uwYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:43.476518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cc7b3ea52a89ef9983816d71d890ba9a7f44ebbee56d5dd836eda5fbbcec38e","sha256:7616f54822da6f8ce6bcdbd8bfd4991ed6fb4f3581177247bbde5bc6e5e2e19d"],"state_sha256":"b8a0474c222a96d46546da1b349c65a9168a95c82e423a87da1ebe0550354fe9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h+NBu6OJcW90umjVXvwsHyKyJ3otAasrMSDTNAJmQ6gqGCu2gmIeLLYFJ2Nth2O1Pkq+JqPDrs/4pBJSpr91DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:33:49.699003Z","bundle_sha256":"2cadd245b8842c27ed6729a3037e70a325a21220ebfe468d2cd5e82a08238ec5"}}