{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:C7NE5NVOTEUEPMMW4OWZPWRTKI","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":"4dfd9a7b37a14d18805ca68744bc0609aac405b958abbebae66b07b6bfd85867","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2000-10-31T22:06:14Z","title_canon_sha256":"bdcf3eeeabbcebb703fdaa9d427f175228ff0bb9963a5f21dcd9c7b7b1fa73fd"},"schema_version":"1.0","source":{"id":"math/0010327","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0010327","created_at":"2026-07-04T14:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0010327v1","created_at":"2026-07-04T14:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0010327","created_at":"2026-07-04T14:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"C7NE5NVOTEUE","created_at":"2026-07-04T14:34:54Z"},{"alias_kind":"pith_short_16","alias_value":"C7NE5NVOTEUEPMMW","created_at":"2026-07-04T14:34:54Z"},{"alias_kind":"pith_short_8","alias_value":"C7NE5NVO","created_at":"2026-07-04T14:34:54Z"}],"graph_snapshots":[{"event_id":"sha256:99a64ef6127182537a483b102f3c753c20d271251b20c3d82fedd017002b9771","target":"graph","created_at":"2026-07-04T14:34:54Z","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/0010327/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that if a simple 3-manifold $M$ has two Dehn fillings at distance $\\Delta \\geq 4$, each of which contains an essential annulus, then $M$ is one of three specific 2-component link exteriors in $S^3$. One of these has such a pair of annular fillings with $\\Delta = 5$, and the other two have pairs with $\\Delta = 4$.","authors_text":"Cameron McA. Gordon, Ying-Qing Wu","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2000-10-31T22:06:14Z","title":"Annular Dehn fillings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0010327","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":"sha256:44d900789434bcd4734ee28c6c4d87ce607fb9021f9898691e8613c8bf015afb","target":"record","created_at":"2026-07-04T14:34:54Z","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":"4dfd9a7b37a14d18805ca68744bc0609aac405b958abbebae66b07b6bfd85867","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2000-10-31T22:06:14Z","title_canon_sha256":"bdcf3eeeabbcebb703fdaa9d427f175228ff0bb9963a5f21dcd9c7b7b1fa73fd"},"schema_version":"1.0","source":{"id":"math/0010327","kind":"arxiv","version":1}},"canonical_sha256":"17da4eb6ae992847b196e3ad97da33522145079d665e99fee4b47df53c33b9a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17da4eb6ae992847b196e3ad97da33522145079d665e99fee4b47df53c33b9a9","first_computed_at":"2026-07-04T14:34:54.035900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:54.035900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pgV+9SNBq95ISA32OKr8ORxqy8CgOe9M/FYfquLvbBW9UTkP9cLqUTOWfovKiXB83Xn1u03nENGE4/WaoOpSBA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:54.036259Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0010327","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44d900789434bcd4734ee28c6c4d87ce607fb9021f9898691e8613c8bf015afb","sha256:99a64ef6127182537a483b102f3c753c20d271251b20c3d82fedd017002b9771"],"state_sha256":"15d99e9722d03ccc141759676309777fe81a240e85cb84f96d20b9989830bafc"}