{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:C6YBNGA7GVSQ53M6HJR2LHXFSE","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":"8eab717f4e3f71be76e09178ee15893234e7716887cbe22ac62add8ebf76a61b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-05-14T08:52:38Z","title_canon_sha256":"5d22e6e8d56866750f295e4912931e36ab72e0e547c8fd58311533d67fff90ab"},"schema_version":"1.0","source":{"id":"2005.06813","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.06813","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"2005.06813v3","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.06813","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"C6YBNGA7GVSQ","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"pith_short_16","alias_value":"C6YBNGA7GVSQ53M6","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"pith_short_8","alias_value":"C6YBNGA7","created_at":"2026-06-02T01:03:27Z"}],"graph_snapshots":[{"event_id":"sha256:d5c51e82333e2c2fea9618224c132af7dad318c9c7ed223a5225236945ab3902","target":"graph","created_at":"2026-06-02T01:03:27Z","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/2005.06813/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a proof that the classes of finitely generated Kleinian groups and of three-manifold groups are quasi-isometrically rigid.","authors_text":"Cyril Lecuire (IMT), Peter Ha\\\"issinsky (I2M)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-05-14T08:52:38Z","title":"Quasi-isometric rigidity of three manifold groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.06813","kind":"arxiv","version":3},"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":"sha256:9ceec6d40f7583644b8a1e669b169ab5b6bb1cdfa2d705e8a6f6b63b83775f09","target":"record","created_at":"2026-06-02T01:03:27Z","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":"8eab717f4e3f71be76e09178ee15893234e7716887cbe22ac62add8ebf76a61b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-05-14T08:52:38Z","title_canon_sha256":"5d22e6e8d56866750f295e4912931e36ab72e0e547c8fd58311533d67fff90ab"},"schema_version":"1.0","source":{"id":"2005.06813","kind":"arxiv","version":3}},"canonical_sha256":"17b016981f35650eed9e3a63a59ee59109c29d615c5bbca61da4b79ddea08a68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17b016981f35650eed9e3a63a59ee59109c29d615c5bbca61da4b79ddea08a68","first_computed_at":"2026-06-02T01:03:27.453838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:27.453838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m64+FXgZdZI4AnNI66/iP/u7xRsrb42fNe8c+p7k0RmHkiy2ukmCV4Xn9a06pKp5CwC0FJ0uFqFgSM3rFNrMBg==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:27.454288Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.06813","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ceec6d40f7583644b8a1e669b169ab5b6bb1cdfa2d705e8a6f6b63b83775f09","sha256:d5c51e82333e2c2fea9618224c132af7dad318c9c7ed223a5225236945ab3902"],"state_sha256":"bd45f5c108a62d6363fdb6c305e143a3ae67994962931d5eb39198a9df56ecf0"}