{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3NPXEYRFL65LG2MRLJ7EESSM7X","short_pith_number":"pith:3NPXEYRF","canonical_record":{"source":{"id":"1212.1531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T05:48:05Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"02c79a8b67385ff56c08c14b139b34beec23770792ec5006724008f0989a036e","abstract_canon_sha256":"7868ae034aa4e745b8f54eb9119f2a6978529f7e94dba62bcd6ad1579cc6be14"},"schema_version":"1.0"},"canonical_sha256":"db5f7262255fbab369915a7e424a4cfdfc7592e26b3fa3a167bb0d1032904a0e","source":{"kind":"arxiv","id":"1212.1531","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1531","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1531v1","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1531","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"3NPXEYRFL65L","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3NPXEYRFL65LG2MR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3NPXEYRF","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3NPXEYRFL65LG2MRLJ7EESSM7X","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T05:48:05Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"02c79a8b67385ff56c08c14b139b34beec23770792ec5006724008f0989a036e","abstract_canon_sha256":"7868ae034aa4e745b8f54eb9119f2a6978529f7e94dba62bcd6ad1579cc6be14"},"schema_version":"1.0"},"canonical_sha256":"db5f7262255fbab369915a7e424a4cfdfc7592e26b3fa3a167bb0d1032904a0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:57.606196Z","signature_b64":"eTZlRb6mfa1kMjHBpyMqnZcBDk8U+10+mChb6FUFtIk2JoPp3eKvToWm2rpyIMxYKQY0TjWMKRDK/PsRsvTWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db5f7262255fbab369915a7e424a4cfdfc7592e26b3fa3a167bb0d1032904a0e","last_reissued_at":"2026-05-18T03:15:57.605433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:57.605433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1531","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":"2026-05-18T03:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6zy5XQdZX2jtw68qu2cOOKX5kj/9H+N+Y9ZWhjRa84pXjg2fQ9QrnNv3KmNsncOGIhSTUrqR787KP+lq+rgOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:26:41.947822Z"},"content_sha256":"9e179fb339dd683580a9b837aa1fb6aff5a3ccea5268bb34567c2a8bc9bc802a","schema_version":"1.0","event_id":"sha256:9e179fb339dd683580a9b837aa1fb6aff5a3ccea5268bb34567c2a8bc9bc802a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3NPXEYRFL65LG2MRLJ7EESSM7X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing closed essential surfaces in knot complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.GT","authors_text":"Alexander Coward, Benjamin A. Burton, Stephan Tillmann","submitted_at":"2012-12-07T05:48:05Z","abstract_excerpt":"We present a new, practical algorithm to test whether a knot complement contains a closed essential surface. This property has important theoretical and algorithmic consequences; however, systematically testing it has until now been infeasibly slow, and current techniques only apply to specific families of knots. As a testament to its practicality, we run the algorithm over a comprehensive body of 2979 knots, including the two 20-crossing dodecahedral knots, yielding results that were not previously known.\n  The algorithm derives from the original Jaco-Oertel framework, involves both enumerati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1531","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":"2026-05-18T03:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rXcak80fJQJrr0bVOKSJvTdm7iIF42bNhMgetPDAV+aUf+jpk+uopYt4GzIFc5IArq6WGPRyek+5hR4CKtWHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:26:41.948159Z"},"content_sha256":"a82493d508f2e3b1feeb3aea4a4442dd53307f4ad1a88c84f43f5c900535dd32","schema_version":"1.0","event_id":"sha256:a82493d508f2e3b1feeb3aea4a4442dd53307f4ad1a88c84f43f5c900535dd32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/bundle.json","state_url":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/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":"2026-06-01T10:26:41Z","links":{"resolver":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X","bundle":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/bundle.json","state":"https://pith.science/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3NPXEYRFL65LG2MRLJ7EESSM7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3NPXEYRFL65LG2MRLJ7EESSM7X","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":"7868ae034aa4e745b8f54eb9119f2a6978529f7e94dba62bcd6ad1579cc6be14","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T05:48:05Z","title_canon_sha256":"02c79a8b67385ff56c08c14b139b34beec23770792ec5006724008f0989a036e"},"schema_version":"1.0","source":{"id":"1212.1531","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1531","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1531v1","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1531","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"3NPXEYRFL65L","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3NPXEYRFL65LG2MR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3NPXEYRF","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:a82493d508f2e3b1feeb3aea4a4442dd53307f4ad1a88c84f43f5c900535dd32","target":"graph","created_at":"2026-05-18T03:15:57Z","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 present a new, practical algorithm to test whether a knot complement contains a closed essential surface. This property has important theoretical and algorithmic consequences; however, systematically testing it has until now been infeasibly slow, and current techniques only apply to specific families of knots. As a testament to its practicality, we run the algorithm over a comprehensive body of 2979 knots, including the two 20-crossing dodecahedral knots, yielding results that were not previously known.\n  The algorithm derives from the original Jaco-Oertel framework, involves both enumerati","authors_text":"Alexander Coward, Benjamin A. Burton, Stephan Tillmann","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T05:48:05Z","title":"Computing closed essential surfaces in knot complements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1531","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":"sha256:9e179fb339dd683580a9b837aa1fb6aff5a3ccea5268bb34567c2a8bc9bc802a","target":"record","created_at":"2026-05-18T03:15:57Z","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":"7868ae034aa4e745b8f54eb9119f2a6978529f7e94dba62bcd6ad1579cc6be14","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-07T05:48:05Z","title_canon_sha256":"02c79a8b67385ff56c08c14b139b34beec23770792ec5006724008f0989a036e"},"schema_version":"1.0","source":{"id":"1212.1531","kind":"arxiv","version":1}},"canonical_sha256":"db5f7262255fbab369915a7e424a4cfdfc7592e26b3fa3a167bb0d1032904a0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db5f7262255fbab369915a7e424a4cfdfc7592e26b3fa3a167bb0d1032904a0e","first_computed_at":"2026-05-18T03:15:57.605433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:57.605433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eTZlRb6mfa1kMjHBpyMqnZcBDk8U+10+mChb6FUFtIk2JoPp3eKvToWm2rpyIMxYKQY0TjWMKRDK/PsRsvTWDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:57.606196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1531","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e179fb339dd683580a9b837aa1fb6aff5a3ccea5268bb34567c2a8bc9bc802a","sha256:a82493d508f2e3b1feeb3aea4a4442dd53307f4ad1a88c84f43f5c900535dd32"],"state_sha256":"5dfe1283302a2e0ede98a987128948281a48a2595833f78eb04ac4e47922bc2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v2YKlos1KxpVSoCdrC7UCwHtbEZT4cGZ52i5DQHVR9S/OhU7vOfxcy8R5pJaJ5Onv05ZswNqsB/a1kbcdU+DDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:26:41.950081Z","bundle_sha256":"9c2499348958e1921a4661b77b5898c7c6b3263be92a0bc20263a3b982e76855"}}