{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TNRWQEC6EQVW2JMFZSRC6BHXWX","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":"bb1dbcb7bfb9734eda6e4f3ab1331b1f500981f9542e27d99f15f18146d61363","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-15T20:31:26Z","title_canon_sha256":"772017242c0fe48da26823e27d4365e90cfdb319f6bb78a8c7d074f19b6f3872"},"schema_version":"1.0","source":{"id":"1106.3095","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3095","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3095v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3095","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"TNRWQEC6EQVW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNRWQEC6EQVW2JMF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNRWQEC6","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:e1fe383a781ba0483ee4eb74fc653a100a627fc32d2efb09e07d23bff5c4248b","target":"graph","created_at":"2026-05-18T02:38:18Z","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 show that the crossing number of a satellite knot is at least 10^{-13} times the crossing number of its companion knot.","authors_text":"Marc Lackenby","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-15T20:31:26Z","title":"The crossing number of satellite knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3095","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":"sha256:3b8fa109696b0856d060292fda656f25c545361c81218eca636be85e486eea10","target":"record","created_at":"2026-05-18T02:38:18Z","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":"bb1dbcb7bfb9734eda6e4f3ab1331b1f500981f9542e27d99f15f18146d61363","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-15T20:31:26Z","title_canon_sha256":"772017242c0fe48da26823e27d4365e90cfdb319f6bb78a8c7d074f19b6f3872"},"schema_version":"1.0","source":{"id":"1106.3095","kind":"arxiv","version":2}},"canonical_sha256":"9b6368105e242b6d2585cca22f04f7b5db13f3dccad60b7eeb3163f56071022d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b6368105e242b6d2585cca22f04f7b5db13f3dccad60b7eeb3163f56071022d","first_computed_at":"2026-05-18T02:38:18.108273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.108273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wNHoO2bHZWd6SOZ8pRorPAfIe/NkykbYkVWWhYVdWfdLgJP4kw5PF3M9Zjr4NU/tjbK0II0N/BT91EXTMzptCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.108946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3095","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b8fa109696b0856d060292fda656f25c545361c81218eca636be85e486eea10","sha256:e1fe383a781ba0483ee4eb74fc653a100a627fc32d2efb09e07d23bff5c4248b"],"state_sha256":"cab44aa4b4a647e65fc03e5737b4f6c2adb75612210b3031b06a7389f2404bd4"}