{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:S33WYGTW7OL7GNOTXYLAHPZVW4","short_pith_number":"pith:S33WYGTW","canonical_record":{"source":{"id":"math/0608700","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2006-08-28T21:17:58Z","cross_cats_sorted":[],"title_canon_sha256":"b02c8b142095dfcc477650b8e451056d2cbd36f0bcec7a1e2c1c9130dfb7ca40","abstract_canon_sha256":"1cc24289dd3e5f2a4146ff700523dc386c822114099eb1022414a4ea7e2003f7"},"schema_version":"1.0"},"canonical_sha256":"96f76c1a76fb97f335d3be1603bf35b71dbfb469b3b0595d014dc15370e05780","source":{"kind":"arxiv","id":"math/0608700","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608700","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608700v1","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608700","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"S33WYGTW7OL7","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"pith_short_16","alias_value":"S33WYGTW7OL7GNOT","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"pith_short_8","alias_value":"S33WYGTW","created_at":"2026-07-04T14:56:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:S33WYGTW7OL7GNOTXYLAHPZVW4","target":"record","payload":{"canonical_record":{"source":{"id":"math/0608700","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2006-08-28T21:17:58Z","cross_cats_sorted":[],"title_canon_sha256":"b02c8b142095dfcc477650b8e451056d2cbd36f0bcec7a1e2c1c9130dfb7ca40","abstract_canon_sha256":"1cc24289dd3e5f2a4146ff700523dc386c822114099eb1022414a4ea7e2003f7"},"schema_version":"1.0"},"canonical_sha256":"96f76c1a76fb97f335d3be1603bf35b71dbfb469b3b0595d014dc15370e05780","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:56:09.694147Z","signature_b64":"WzOBuh/IzU8lfBnoJPg4bcio0vN4zhgBTvcFRuBkdfwMzag+HI0rOyDV39Lb6ezMmvZ35KitBU0DxJcegC0uDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96f76c1a76fb97f335d3be1603bf35b71dbfb469b3b0595d014dc15370e05780","last_reissued_at":"2026-07-04T14:56:09.693685Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:56:09.693685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0608700","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":"2026-07-04T14:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jyDL+3st3dGBKDf6yX6T1ibUwsAdkzDvySXTME3L3RHmlojE+93UO4+vsHAfCs9UjMty2qt0z/6oZQFyU/N8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T20:53:53.052553Z"},"content_sha256":"ba76986190316c5483e7bfef53c8688c23080e5f8fc6e5ef21d7c7b0666835b7","schema_version":"1.0","event_id":"sha256:ba76986190316c5483e7bfef53c8688c23080e5f8fc6e5ef21d7c7b0666835b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:S33WYGTW7OL7GNOTXYLAHPZVW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding planar surfaces in knot- and link-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eric Sedgwick, J. Hyam Rubinstein, William Jaco","submitted_at":"2006-08-28T21:17:58Z","abstract_excerpt":"It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. If a slope on the boundary of the link-manifold is given, there is an algorithm to determine if the slope bounds an embedded punctured-disk; if a meridian slope is given, then it can be determined if a longitude bounds an embedded punctured-disk. The methods use normal surface theory but do not follow the classical approach. Properties of minimal vertex triangulations, layered-triangulations, 0--efficient triangu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608700","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0608700/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lTHOuPX30p+Yx7hL07AR+RNxxydcU0Rbcmp5RcsQXJ8dFJAAueXAGjRqmiPP0EKUR7E6Nzd1r32+zbVlFZumAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T20:53:53.052928Z"},"content_sha256":"df587c87049685a1bdf6bd12ee1bfd189527e0a98fce76ef267a8fc747365446","schema_version":"1.0","event_id":"sha256:df587c87049685a1bdf6bd12ee1bfd189527e0a98fce76ef267a8fc747365446"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S33WYGTW7OL7GNOTXYLAHPZVW4/bundle.json","state_url":"https://pith.science/pith/S33WYGTW7OL7GNOTXYLAHPZVW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S33WYGTW7OL7GNOTXYLAHPZVW4/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":"2026-07-04T20:53:53Z","links":{"resolver":"https://pith.science/pith/S33WYGTW7OL7GNOTXYLAHPZVW4","bundle":"https://pith.science/pith/S33WYGTW7OL7GNOTXYLAHPZVW4/bundle.json","state":"https://pith.science/pith/S33WYGTW7OL7GNOTXYLAHPZVW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S33WYGTW7OL7GNOTXYLAHPZVW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:S33WYGTW7OL7GNOTXYLAHPZVW4","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":"1cc24289dd3e5f2a4146ff700523dc386c822114099eb1022414a4ea7e2003f7","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2006-08-28T21:17:58Z","title_canon_sha256":"b02c8b142095dfcc477650b8e451056d2cbd36f0bcec7a1e2c1c9130dfb7ca40"},"schema_version":"1.0","source":{"id":"math/0608700","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608700","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608700v1","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608700","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"S33WYGTW7OL7","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"pith_short_16","alias_value":"S33WYGTW7OL7GNOT","created_at":"2026-07-04T14:56:09Z"},{"alias_kind":"pith_short_8","alias_value":"S33WYGTW","created_at":"2026-07-04T14:56:09Z"}],"graph_snapshots":[{"event_id":"sha256:df587c87049685a1bdf6bd12ee1bfd189527e0a98fce76ef267a8fc747365446","target":"graph","created_at":"2026-07-04T14:56:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0608700/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. If a slope on the boundary of the link-manifold is given, there is an algorithm to determine if the slope bounds an embedded punctured-disk; if a meridian slope is given, then it can be determined if a longitude bounds an embedded punctured-disk. The methods use normal surface theory but do not follow the classical approach. Properties of minimal vertex triangulations, layered-triangulations, 0--efficient triangu","authors_text":"Eric Sedgwick, J. Hyam Rubinstein, William Jaco","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2006-08-28T21:17:58Z","title":"Finding planar surfaces in knot- and link-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608700","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:ba76986190316c5483e7bfef53c8688c23080e5f8fc6e5ef21d7c7b0666835b7","target":"record","created_at":"2026-07-04T14:56:09Z","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":"1cc24289dd3e5f2a4146ff700523dc386c822114099eb1022414a4ea7e2003f7","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2006-08-28T21:17:58Z","title_canon_sha256":"b02c8b142095dfcc477650b8e451056d2cbd36f0bcec7a1e2c1c9130dfb7ca40"},"schema_version":"1.0","source":{"id":"math/0608700","kind":"arxiv","version":1}},"canonical_sha256":"96f76c1a76fb97f335d3be1603bf35b71dbfb469b3b0595d014dc15370e05780","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96f76c1a76fb97f335d3be1603bf35b71dbfb469b3b0595d014dc15370e05780","first_computed_at":"2026-07-04T14:56:09.693685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:56:09.693685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WzOBuh/IzU8lfBnoJPg4bcio0vN4zhgBTvcFRuBkdfwMzag+HI0rOyDV39Lb6ezMmvZ35KitBU0DxJcegC0uDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:56:09.694147Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0608700","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba76986190316c5483e7bfef53c8688c23080e5f8fc6e5ef21d7c7b0666835b7","sha256:df587c87049685a1bdf6bd12ee1bfd189527e0a98fce76ef267a8fc747365446"],"state_sha256":"2772cf714ec80a44bde06d8eb8831ac1c0e44b627efdaced28752ec73feb8181"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U3QUulkzXhB4KzeSfo/tl3DMbcd3MMr+NyErB40YZoL/nRNUsVqhuL4aSxsKmctE9H+r4keYdSeV97IUxEeODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T20:53:53.054880Z","bundle_sha256":"6588d251dfaf21933bfded6ab4c338e61383514e1de23139b4241a4c36a21faa"}}