{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OLEJOIHBB7U23ASKUOAOPHCX7C","short_pith_number":"pith:OLEJOIHB","canonical_record":{"source":{"id":"1202.0263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-01T20:25:46Z","cross_cats_sorted":[],"title_canon_sha256":"0e1fa40ec1d41892096b57f1acd301d4bc2c60e493af02610932a82b84cd1b02","abstract_canon_sha256":"7b0450dd6b498b5da8829dac7b94a7962222678826f2b3525d7ba8a6317dcbd9"},"schema_version":"1.0"},"canonical_sha256":"72c89720e10fe9ad824aa380e79c57f8a05e55d0791d6667b4d62ffb26b7123f","source":{"kind":"arxiv","id":"1202.0263","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0263","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0263v2","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0263","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"OLEJOIHBB7U2","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OLEJOIHBB7U23ASK","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OLEJOIHB","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OLEJOIHBB7U23ASKUOAOPHCX7C","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-01T20:25:46Z","cross_cats_sorted":[],"title_canon_sha256":"0e1fa40ec1d41892096b57f1acd301d4bc2c60e493af02610932a82b84cd1b02","abstract_canon_sha256":"7b0450dd6b498b5da8829dac7b94a7962222678826f2b3525d7ba8a6317dcbd9"},"schema_version":"1.0"},"canonical_sha256":"72c89720e10fe9ad824aa380e79c57f8a05e55d0791d6667b4d62ffb26b7123f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:52.056419Z","signature_b64":"zjE47yUzavRVLHfM4L+XxodgHLl9C+osWKxPbQ5OChLnw0cJ6qmmRN8lZZngTvjA47JONInaX/jY+Ckfy7yjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72c89720e10fe9ad824aa380e79c57f8a05e55d0791d6667b4d62ffb26b7123f","last_reissued_at":"2026-05-18T03:06:52.055794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:52.055794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0263","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":"2026-05-18T03:06:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hjabe43mL9kVWW/tYCyp7uTN/GGs7pQSlYNgh1BnhnjcCXrB7TcL2NMCOzc0Dc8jZlIvlU+0J5l2KnBokWYxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:05:04.669568Z"},"content_sha256":"7e81b517a2b2e28b65a0f91a9447c3503dc8a109baa1e0319744bf58c0681be3","schema_version":"1.0","event_id":"sha256:7e81b517a2b2e28b65a0f91a9447c3503dc8a109baa1e0319744bf58c0681be3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OLEJOIHBB7U23ASKUOAOPHCX7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bridge number, Heegaard genus and non-integral Dehn surgery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Cameron Gordon, John Luecke, Kenneth L. Baker","submitted_at":"2012-02-01T20:25:46Z","abstract_excerpt":"We show there exists a linear function w: N->N with the following property. Let K be a hyperbolic knot in a hyperbolic 3-manifold M admitting a non-longitudinal S^3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g-1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0263","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":"2026-05-18T03:06:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8nZOwLGteVJkx+63QL/HwtMqHBv+ep9elOWgGuUrb2RgsngFbX/7+7pBVpHvy6jebKq9qUOgCNce0XbYJ/1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:05:04.670184Z"},"content_sha256":"02be4667cfab233e34cd76ff9f9b3b80d7b4d62364eadb278672c5dd449cfcb6","schema_version":"1.0","event_id":"sha256:02be4667cfab233e34cd76ff9f9b3b80d7b4d62364eadb278672c5dd449cfcb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLEJOIHBB7U23ASKUOAOPHCX7C/bundle.json","state_url":"https://pith.science/pith/OLEJOIHBB7U23ASKUOAOPHCX7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLEJOIHBB7U23ASKUOAOPHCX7C/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":"2026-05-27T08:05:04Z","links":{"resolver":"https://pith.science/pith/OLEJOIHBB7U23ASKUOAOPHCX7C","bundle":"https://pith.science/pith/OLEJOIHBB7U23ASKUOAOPHCX7C/bundle.json","state":"https://pith.science/pith/OLEJOIHBB7U23ASKUOAOPHCX7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLEJOIHBB7U23ASKUOAOPHCX7C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OLEJOIHBB7U23ASKUOAOPHCX7C","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":"7b0450dd6b498b5da8829dac7b94a7962222678826f2b3525d7ba8a6317dcbd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-01T20:25:46Z","title_canon_sha256":"0e1fa40ec1d41892096b57f1acd301d4bc2c60e493af02610932a82b84cd1b02"},"schema_version":"1.0","source":{"id":"1202.0263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0263","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0263v2","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0263","created_at":"2026-05-18T03:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"OLEJOIHBB7U2","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OLEJOIHBB7U23ASK","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OLEJOIHB","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:02be4667cfab233e34cd76ff9f9b3b80d7b4d62364eadb278672c5dd449cfcb6","target":"graph","created_at":"2026-05-18T03:06:52Z","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 there exists a linear function w: N->N with the following property. Let K be a hyperbolic knot in a hyperbolic 3-manifold M admitting a non-longitudinal S^3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g-1.","authors_text":"Cameron Gordon, John Luecke, Kenneth L. Baker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-01T20:25:46Z","title":"Bridge number, Heegaard genus and non-integral Dehn surgery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0263","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":"sha256:7e81b517a2b2e28b65a0f91a9447c3503dc8a109baa1e0319744bf58c0681be3","target":"record","created_at":"2026-05-18T03:06:52Z","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":"7b0450dd6b498b5da8829dac7b94a7962222678826f2b3525d7ba8a6317dcbd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-01T20:25:46Z","title_canon_sha256":"0e1fa40ec1d41892096b57f1acd301d4bc2c60e493af02610932a82b84cd1b02"},"schema_version":"1.0","source":{"id":"1202.0263","kind":"arxiv","version":2}},"canonical_sha256":"72c89720e10fe9ad824aa380e79c57f8a05e55d0791d6667b4d62ffb26b7123f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72c89720e10fe9ad824aa380e79c57f8a05e55d0791d6667b4d62ffb26b7123f","first_computed_at":"2026-05-18T03:06:52.055794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:52.055794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zjE47yUzavRVLHfM4L+XxodgHLl9C+osWKxPbQ5OChLnw0cJ6qmmRN8lZZngTvjA47JONInaX/jY+Ckfy7yjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:52.056419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e81b517a2b2e28b65a0f91a9447c3503dc8a109baa1e0319744bf58c0681be3","sha256:02be4667cfab233e34cd76ff9f9b3b80d7b4d62364eadb278672c5dd449cfcb6"],"state_sha256":"1385c6cf78929dd763c00ec86218864bb08b099d5c317a07d2d88dbab153f983"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sDLVTVe8aMTth9YMoC7Boy7j1w4uKtO8l3nTfqTbezHqVc6MM7elDNGwtxf8m5grW1zL+s8QwGZ8H+vX2pL+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:05:04.673971Z","bundle_sha256":"f9dd64a0d8d356a4f776c9f8d5d1434a77ee6e7809fbf3e1289f1c2f09a0da1a"}}