{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:FJK7PBPFQFSEPPASIUFUPXDXMK","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":"cfefcc122056d0740407cbef68afa44ae7080e0dfcfee4bca69df5769236c9e7","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.GT","submitted_at":"2004-05-29T02:35:53Z","title_canon_sha256":"ac07407a5c78b5e0b643530bddb789a65d314a4e1a1d26dae8b9425fb2fbba80"},"schema_version":"1.0","source":{"id":"math/0405568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0405568","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"arxiv_version","alias_value":"math/0405568v1","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0405568","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"pith_short_12","alias_value":"FJK7PBPFQFSE","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"pith_short_16","alias_value":"FJK7PBPFQFSEPPAS","created_at":"2026-07-04T14:38:40Z"},{"alias_kind":"pith_short_8","alias_value":"FJK7PBPF","created_at":"2026-07-04T14:38:40Z"}],"graph_snapshots":[{"event_id":"sha256:8cff7b8fb0a55984125b9288c78e9659b3e39ef025d89724142bcfcb4745b8ba","target":"graph","created_at":"2026-07-04T14:38:40Z","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/0405568/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that hyperbolic 3-manifolds with finitely generated fundamental group are tame, that is the ends are products. We actually work in slightly greater generality with pinched negatively curved manifolds with hyperbolic cusps. This answers a conjecture of Marden and implies the Ahlfors measure conjecture. Applications are given to other questions about Kleinian groups and 3-manifolds.","authors_text":"Ian Agol","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2004-05-29T02:35:53Z","title":"Tameness of hyperbolic 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405568","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":"sha256:00f997f8cf870d3f745c31dfc5342eade4bc90fc588e501ee86464864a11f46a","target":"record","created_at":"2026-07-04T14:38:40Z","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":"cfefcc122056d0740407cbef68afa44ae7080e0dfcfee4bca69df5769236c9e7","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.GT","submitted_at":"2004-05-29T02:35:53Z","title_canon_sha256":"ac07407a5c78b5e0b643530bddb789a65d314a4e1a1d26dae8b9425fb2fbba80"},"schema_version":"1.0","source":{"id":"math/0405568","kind":"arxiv","version":1}},"canonical_sha256":"2a55f785e5816447bc12450b47dc77629070bb5633ee9591544e08d18655e3f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a55f785e5816447bc12450b47dc77629070bb5633ee9591544e08d18655e3f4","first_computed_at":"2026-07-04T14:38:40.068001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:40.068001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1NNHbgKGm6eCHVExiOTnWl3Hq/cDoaZCDdq95gEP7yhusgCIHranY6TAF1C4OsGi+lTVVWJBp7J2GTAOU3Z+Bw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:40.068355Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0405568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00f997f8cf870d3f745c31dfc5342eade4bc90fc588e501ee86464864a11f46a","sha256:8cff7b8fb0a55984125b9288c78e9659b3e39ef025d89724142bcfcb4745b8ba"],"state_sha256":"76b0f4d5d18ee184ef817e35a7e9a49e063082176aa744c03ee52b9a10f0aef7"}