{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZRASQYWM4ZQLMVFXR6OK7DKA32","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":"90117c5457c0c59af34808ceddec499cfe0be4e0e3dce8bcaf0fc2ae644f74ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-15T05:52:41Z","title_canon_sha256":"ed10d42c2ab286a9acc9ee4e5aa42f2d16cd2a28b9f21e4f675056abf1a935c5"},"schema_version":"1.0","source":{"id":"1108.2936","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2936","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2936v1","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2936","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"pith_short_12","alias_value":"ZRASQYWM4ZQL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZRASQYWM4ZQLMVFX","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZRASQYWM","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:cb18b20fdad8c8cf097c051719d36a8bb61a19de686630c739e0bd0c846a9210","target":"graph","created_at":"2026-05-18T04:15:28Z","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":"A triangulation of a compact 3-manifold is annular-efficient if it is 0-efficient and the only normal, incompressible annuli are thin edge-linking. If a compact 3-manifold has an annular-efficient triangulation, then it is irreducible, boundary-irreducible, and an-annular. Conversely, it is shown that for a compact, irreducible, boundary-irreducible, and an-annular 3-manifold, any triangulation can be modified to an annular-efficient triangulation. It follows that for a manifold satisfying this hypothesis, there are only a finite number of boundary slopes for incompressible and boundary-incomp","authors_text":"J.Hyam Rubinstein, William Jaco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-15T05:52:41Z","title":"Annular-Efficient Triangulations of 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2936","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:ea0a5241fd8542b1950a18fce475657df30b4b9548143348d666cffdfdb3dc28","target":"record","created_at":"2026-05-18T04:15:28Z","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":"90117c5457c0c59af34808ceddec499cfe0be4e0e3dce8bcaf0fc2ae644f74ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-15T05:52:41Z","title_canon_sha256":"ed10d42c2ab286a9acc9ee4e5aa42f2d16cd2a28b9f21e4f675056abf1a935c5"},"schema_version":"1.0","source":{"id":"1108.2936","kind":"arxiv","version":1}},"canonical_sha256":"cc412862cce660b654b78f9caf8d40de911eb8c58a4c780be9bf13489351455b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc412862cce660b654b78f9caf8d40de911eb8c58a4c780be9bf13489351455b","first_computed_at":"2026-05-18T04:15:28.947717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:28.947717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bcl9qwk50fPEK4RjP/g05OiGf+khHUtGKZvQp8t9BiHFybRDGV+LC5AdCRs9MVPmTWzODj17d446n2adb+CwCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:28.948198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2936","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea0a5241fd8542b1950a18fce475657df30b4b9548143348d666cffdfdb3dc28","sha256:cb18b20fdad8c8cf097c051719d36a8bb61a19de686630c739e0bd0c846a9210"],"state_sha256":"6cff890cb5bcf4c1ec32d7bbfc3069fdc20dd89aa224d24ea47bc53bd7273c3f"}