{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BYRGOBGF6LXZ7BER6NT5INPGYA","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":"49c9f2de98b43c53f2021daefb7ab16df8ec331c151c75bd2c42b39c75285606","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-26T14:59:25Z","title_canon_sha256":"4177b55657edf2abf81fe599f0d4fd111c6150f36a56a24deeb448e52fdd0c1e"},"schema_version":"1.0","source":{"id":"1807.10181","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10181","created_at":"2026-07-05T01:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10181v2","created_at":"2026-07-05T01:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10181","created_at":"2026-07-05T01:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"BYRGOBGF6LXZ","created_at":"2026-07-05T01:53:35Z"},{"alias_kind":"pith_short_16","alias_value":"BYRGOBGF6LXZ7BER","created_at":"2026-07-05T01:53:35Z"},{"alias_kind":"pith_short_8","alias_value":"BYRGOBGF","created_at":"2026-07-05T01:53:35Z"}],"graph_snapshots":[{"event_id":"sha256:de1df1271d7c012883b7453f88f8b45a15808032d15e7fa38225670982996a9c","target":"graph","created_at":"2026-07-05T01:53:35Z","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/1807.10181/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we prove gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians which satisfy an ellipticity assumption. As applications, we study completeness and finiteness of stochastically complete graphs under Bakry-Emery curvature bounds.","authors_text":"Florentin M\\\"unch, Matthias Keller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-26T14:59:25Z","title":"Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10181","kind":"arxiv","version":2},"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":"sha256:3b5159b6e3e482531835f93e1b034d63b7a8ce99687076c97fffe93ffaa9cdc1","target":"record","created_at":"2026-07-05T01:53:35Z","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":"49c9f2de98b43c53f2021daefb7ab16df8ec331c151c75bd2c42b39c75285606","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-26T14:59:25Z","title_canon_sha256":"4177b55657edf2abf81fe599f0d4fd111c6150f36a56a24deeb448e52fdd0c1e"},"schema_version":"1.0","source":{"id":"1807.10181","kind":"arxiv","version":2}},"canonical_sha256":"0e226704c5f2ef9f8491f367d435e6c016d1e657b1e6c00344c37b47fac843b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e226704c5f2ef9f8491f367d435e6c016d1e657b1e6c00344c37b47fac843b9","first_computed_at":"2026-07-05T01:53:35.370751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:53:35.370751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dQDlwIHahbP69UjP1BakPFY1lOwYZkBG0aARfzjQYVPnAxykjfSp9xpLy8/bYIn44DH8+64na5YDwOVkcIMrBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:53:35.371138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10181","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b5159b6e3e482531835f93e1b034d63b7a8ce99687076c97fffe93ffaa9cdc1","sha256:de1df1271d7c012883b7453f88f8b45a15808032d15e7fa38225670982996a9c"],"state_sha256":"25bf06efb1459ca16ae8c455867f955833f5f8b22dd692786b601daa8774b0b9"}