{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5TLKWV2ZFO3FSW7HGWC7XRFQHF","short_pith_number":"pith:5TLKWV2Z","canonical_record":{"source":{"id":"2405.03539","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2024-05-06T14:58:45Z","cross_cats_sorted":[],"title_canon_sha256":"0db61e22f8ed2d89520019eae002c8bea5e8ad914afef211915dcfaa3032755e","abstract_canon_sha256":"8bc707b8bbe1ab2b0a45ae3cc3bd85ec2f8abf22b83b6c8accb51e2ad8f1a3d2"},"schema_version":"1.0"},"canonical_sha256":"ecd6ab57592bb6595be73585fbc4b03954b6a77069a5d774ce01526187debf41","source":{"kind":"arxiv","id":"2405.03539","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03539","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03539v1","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03539","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"5TLKWV2ZFO3F","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"pith_short_16","alias_value":"5TLKWV2ZFO3FSW7H","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"pith_short_8","alias_value":"5TLKWV2Z","created_at":"2026-07-05T08:16:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5TLKWV2ZFO3FSW7HGWC7XRFQHF","target":"record","payload":{"canonical_record":{"source":{"id":"2405.03539","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2024-05-06T14:58:45Z","cross_cats_sorted":[],"title_canon_sha256":"0db61e22f8ed2d89520019eae002c8bea5e8ad914afef211915dcfaa3032755e","abstract_canon_sha256":"8bc707b8bbe1ab2b0a45ae3cc3bd85ec2f8abf22b83b6c8accb51e2ad8f1a3d2"},"schema_version":"1.0"},"canonical_sha256":"ecd6ab57592bb6595be73585fbc4b03954b6a77069a5d774ce01526187debf41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:16:04.265046Z","signature_b64":"cQfvstw0cowbRgy7qE58eRyunKe7Zlqy8FaXffQFAhSgAaAs0+yAoum9c6C69YFzEUnAxtnjqmrntd40VBALAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecd6ab57592bb6595be73585fbc4b03954b6a77069a5d774ce01526187debf41","last_reissued_at":"2026-07-05T08:16:04.264557Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:16:04.264557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.03539","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":"2026-07-05T08:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5VwScD+WRh4jhTPSw3UKPmiR6ldB6jDc39/iFw5+6Nvn/Muz88Y5basGZPM+FRCqkQerwi0k2oUePVgUJvMUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:19:33.702989Z"},"content_sha256":"be6659d2cba33b7278a1031d70d9b4a5054cf26cd3cbcfebef9342ebe127292e","schema_version":"1.0","event_id":"sha256:be6659d2cba33b7278a1031d70d9b4a5054cf26cd3cbcfebef9342ebe127292e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5TLKWV2ZFO3FSW7HGWC7XRFQHF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connecting essential triangulations I: via 2-3 and 0-2 moves","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Henry Segerman, Saul Schleimer, Tejas Kalelkar","submitted_at":"2024-05-06T14:58:45Z","abstract_excerpt":"Suppose that $M$ is a compact, connected three-manifold with boundary. We show that if the universal cover has infinitely many boundary components then $M$ has an ideal triangulation which is essential: no edge can be homotoped into the boundary. Under the same hypotheses, we show that the set of essential triangulations of $M$ is connected via 2-3, 3-2, 0-2, and 2-0 moves.\n  The above results are special cases of our general theory. We introduce $L$-essential triangulations: boundary components of the universal cover receive labels and no edge has the same label at both ends. As an applicatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03539","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/2405.03539/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":"2026-07-05T08:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZApI7quN+G1JW9QqGah4OtJ3DQtoNU83GHJVn2tJtc62HGZeIAiYPZIKgSV/OF3VFFHFc7HYGRL9mw0keaxpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:19:33.704161Z"},"content_sha256":"05ed83132a41353a24f12c8cb5a10827e8e6bc86cadcab9c9f8b4c2b9844b021","schema_version":"1.0","event_id":"sha256:05ed83132a41353a24f12c8cb5a10827e8e6bc86cadcab9c9f8b4c2b9844b021"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5TLKWV2ZFO3FSW7HGWC7XRFQHF/bundle.json","state_url":"https://pith.science/pith/5TLKWV2ZFO3FSW7HGWC7XRFQHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5TLKWV2ZFO3FSW7HGWC7XRFQHF/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":"2026-08-10T23:19:33Z","links":{"resolver":"https://pith.science/pith/5TLKWV2ZFO3FSW7HGWC7XRFQHF","bundle":"https://pith.science/pith/5TLKWV2ZFO3FSW7HGWC7XRFQHF/bundle.json","state":"https://pith.science/pith/5TLKWV2ZFO3FSW7HGWC7XRFQHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5TLKWV2ZFO3FSW7HGWC7XRFQHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5TLKWV2ZFO3FSW7HGWC7XRFQHF","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":"8bc707b8bbe1ab2b0a45ae3cc3bd85ec2f8abf22b83b6c8accb51e2ad8f1a3d2","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2024-05-06T14:58:45Z","title_canon_sha256":"0db61e22f8ed2d89520019eae002c8bea5e8ad914afef211915dcfaa3032755e"},"schema_version":"1.0","source":{"id":"2405.03539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03539","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03539v1","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03539","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"5TLKWV2ZFO3F","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"pith_short_16","alias_value":"5TLKWV2ZFO3FSW7H","created_at":"2026-07-05T08:16:04Z"},{"alias_kind":"pith_short_8","alias_value":"5TLKWV2Z","created_at":"2026-07-05T08:16:04Z"}],"graph_snapshots":[{"event_id":"sha256:05ed83132a41353a24f12c8cb5a10827e8e6bc86cadcab9c9f8b4c2b9844b021","target":"graph","created_at":"2026-07-05T08:16:04Z","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/2405.03539/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose that $M$ is a compact, connected three-manifold with boundary. We show that if the universal cover has infinitely many boundary components then $M$ has an ideal triangulation which is essential: no edge can be homotoped into the boundary. Under the same hypotheses, we show that the set of essential triangulations of $M$ is connected via 2-3, 3-2, 0-2, and 2-0 moves.\n  The above results are special cases of our general theory. We introduce $L$-essential triangulations: boundary components of the universal cover receive labels and no edge has the same label at both ends. As an applicatio","authors_text":"Henry Segerman, Saul Schleimer, Tejas Kalelkar","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2024-05-06T14:58:45Z","title":"Connecting essential triangulations I: via 2-3 and 0-2 moves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03539","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:be6659d2cba33b7278a1031d70d9b4a5054cf26cd3cbcfebef9342ebe127292e","target":"record","created_at":"2026-07-05T08:16:04Z","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":"8bc707b8bbe1ab2b0a45ae3cc3bd85ec2f8abf22b83b6c8accb51e2ad8f1a3d2","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2024-05-06T14:58:45Z","title_canon_sha256":"0db61e22f8ed2d89520019eae002c8bea5e8ad914afef211915dcfaa3032755e"},"schema_version":"1.0","source":{"id":"2405.03539","kind":"arxiv","version":1}},"canonical_sha256":"ecd6ab57592bb6595be73585fbc4b03954b6a77069a5d774ce01526187debf41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecd6ab57592bb6595be73585fbc4b03954b6a77069a5d774ce01526187debf41","first_computed_at":"2026-07-05T08:16:04.264557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:16:04.264557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQfvstw0cowbRgy7qE58eRyunKe7Zlqy8FaXffQFAhSgAaAs0+yAoum9c6C69YFzEUnAxtnjqmrntd40VBALAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:16:04.265046Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.03539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be6659d2cba33b7278a1031d70d9b4a5054cf26cd3cbcfebef9342ebe127292e","sha256:05ed83132a41353a24f12c8cb5a10827e8e6bc86cadcab9c9f8b4c2b9844b021"],"state_sha256":"965901b6ddef03d2f988aa59ea929c9ad471b94469469f100b350a942d8ed0b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wIUaE3C1AnvUFvh8x221BNbIYgbRPNtgX9ZWYPBcGQ9f2Luq0wK06VGrA7nk24atoHL5qF0iSHJ4gBqOEno9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T23:19:33.710179Z","bundle_sha256":"a49d122511afcde8f0c0a588174376036dfc76900dc66a92434cba9781620d34"}}