{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:47FVXV4SLCHSFZKNK7ZF2VTCSN","short_pith_number":"pith:47FVXV4S","canonical_record":{"source":{"id":"math/0301219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2003-01-20T18:46:51Z","cross_cats_sorted":[],"title_canon_sha256":"82bb0bb23d63db463a8abdab1525a2f78705ebfda64cb466b7a326242870f8c9","abstract_canon_sha256":"ab2c83a5490ed6ea70b837a68079a6bb0521fb00c6f767bdb129556c28e209d3"},"schema_version":"1.0"},"canonical_sha256":"e7cb5bd792588f22e54d57f25d5662935e35c94be95019a0b73dc7d0a544e150","source":{"kind":"arxiv","id":"math/0301219","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301219","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301219v1","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301219","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"47FVXV4SLCHS","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"47FVXV4SLCHSFZKN","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"47FVXV4S","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:47FVXV4SLCHSFZKNK7ZF2VTCSN","target":"record","payload":{"canonical_record":{"source":{"id":"math/0301219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2003-01-20T18:46:51Z","cross_cats_sorted":[],"title_canon_sha256":"82bb0bb23d63db463a8abdab1525a2f78705ebfda64cb466b7a326242870f8c9","abstract_canon_sha256":"ab2c83a5490ed6ea70b837a68079a6bb0521fb00c6f767bdb129556c28e209d3"},"schema_version":"1.0"},"canonical_sha256":"e7cb5bd792588f22e54d57f25d5662935e35c94be95019a0b73dc7d0a544e150","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:15.331748Z","signature_b64":"hhuaAesaEWMOWBB7au1lDqb2h5frJpaRY29TqwEd5YEW3xSotThlG4DeMtgnugsnrezXN9//MxdX1SzPxSQWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7cb5bd792588f22e54d57f25d5662935e35c94be95019a0b73dc7d0a544e150","last_reissued_at":"2026-05-17T23:55:15.331247Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:15.331247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0301219","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":"2026-05-17T23:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8GxFt4GVpe564TYYtCsDeiJHBDxyi1+EPQ1CNjkN+HNx0gzpJNXvQ8XEC2bUU+QVWkcf9EnefD7HaGT5SzUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:21:37.722845Z"},"content_sha256":"abca11c7761347fca39d66b93e67f98465197ed0b8da16d7e661557df73b4575","schema_version":"1.0","event_id":"sha256:abca11c7761347fca39d66b93e67f98465197ed0b8da16d7e661557df73b4575"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:47FVXV4SLCHSFZKNK7ZF2VTCSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A calculus for ideal triangulations of three-manifolds with embedded arcs","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gennaro Amendola","submitted_at":"2003-01-20T18:46:51Z","abstract_excerpt":"Refining the notion of an ideal triangulation of a compact three-manifold, we provide in this paper a combinatorial presentation of the set of pairs (M,a), where M is a three-manifold and a is a collection of properly embedded arcs. We also show that certain well-understood combinatorial moves are sufficient to relate to each other any two refined triangulations representing the same (M,a). Our proof does not assume the Matveev-Pergallini calculus for ideal triangulations, and actually easily implies this calculus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301219","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":"2026-05-17T23:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jgxlETcLshg2QLGcWv0e+0dCeV9lIM8EUZwp5V8tRkft+DmTah7XCi+W0txpxIsAErkh6ndpKAgi0hmWxY09Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:21:37.723180Z"},"content_sha256":"586fb9c09529c9059a7a3eedb08f244b215d908012d75625ba3de886d50ea9ac","schema_version":"1.0","event_id":"sha256:586fb9c09529c9059a7a3eedb08f244b215d908012d75625ba3de886d50ea9ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/47FVXV4SLCHSFZKNK7ZF2VTCSN/bundle.json","state_url":"https://pith.science/pith/47FVXV4SLCHSFZKNK7ZF2VTCSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/47FVXV4SLCHSFZKNK7ZF2VTCSN/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":"2026-06-26T22:21:37Z","links":{"resolver":"https://pith.science/pith/47FVXV4SLCHSFZKNK7ZF2VTCSN","bundle":"https://pith.science/pith/47FVXV4SLCHSFZKNK7ZF2VTCSN/bundle.json","state":"https://pith.science/pith/47FVXV4SLCHSFZKNK7ZF2VTCSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/47FVXV4SLCHSFZKNK7ZF2VTCSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:47FVXV4SLCHSFZKNK7ZF2VTCSN","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":"ab2c83a5490ed6ea70b837a68079a6bb0521fb00c6f767bdb129556c28e209d3","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2003-01-20T18:46:51Z","title_canon_sha256":"82bb0bb23d63db463a8abdab1525a2f78705ebfda64cb466b7a326242870f8c9"},"schema_version":"1.0","source":{"id":"math/0301219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301219","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301219v1","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301219","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"47FVXV4SLCHS","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"47FVXV4SLCHSFZKN","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"47FVXV4S","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:586fb9c09529c9059a7a3eedb08f244b215d908012d75625ba3de886d50ea9ac","target":"graph","created_at":"2026-05-17T23:55:15Z","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":"Refining the notion of an ideal triangulation of a compact three-manifold, we provide in this paper a combinatorial presentation of the set of pairs (M,a), where M is a three-manifold and a is a collection of properly embedded arcs. We also show that certain well-understood combinatorial moves are sufficient to relate to each other any two refined triangulations representing the same (M,a). Our proof does not assume the Matveev-Pergallini calculus for ideal triangulations, and actually easily implies this calculus.","authors_text":"Gennaro Amendola","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2003-01-20T18:46:51Z","title":"A calculus for ideal triangulations of three-manifolds with embedded arcs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301219","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:abca11c7761347fca39d66b93e67f98465197ed0b8da16d7e661557df73b4575","target":"record","created_at":"2026-05-17T23:55:15Z","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":"ab2c83a5490ed6ea70b837a68079a6bb0521fb00c6f767bdb129556c28e209d3","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2003-01-20T18:46:51Z","title_canon_sha256":"82bb0bb23d63db463a8abdab1525a2f78705ebfda64cb466b7a326242870f8c9"},"schema_version":"1.0","source":{"id":"math/0301219","kind":"arxiv","version":1}},"canonical_sha256":"e7cb5bd792588f22e54d57f25d5662935e35c94be95019a0b73dc7d0a544e150","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7cb5bd792588f22e54d57f25d5662935e35c94be95019a0b73dc7d0a544e150","first_computed_at":"2026-05-17T23:55:15.331247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:15.331247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hhuaAesaEWMOWBB7au1lDqb2h5frJpaRY29TqwEd5YEW3xSotThlG4DeMtgnugsnrezXN9//MxdX1SzPxSQWAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:15.331748Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0301219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abca11c7761347fca39d66b93e67f98465197ed0b8da16d7e661557df73b4575","sha256:586fb9c09529c9059a7a3eedb08f244b215d908012d75625ba3de886d50ea9ac"],"state_sha256":"f67f1ae8b834fcbc4a6e906a04d63be820f7f5a0382a6386d24c6c29e5b506cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"euVJQ5icK0J4FxHkigMoQJE+RLB2vcYrREe9Itb8Hl7+KcaO5wZiUYfbKwX3zKVkwkxDtaDwNuU4aaiM3C2sAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T22:21:37.725016Z","bundle_sha256":"4ab9a6c6b261135f66f19602826cfdec056f8968f2709ac60e711e10b57702ad"}}