{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HNLPEVHJN7W3TOFZEJSLKXFPLX","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":"03c77dae3c14158ec76e90d155c0a8731d016a629b2223f496c1134d1793cc94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-22T00:44:18Z","title_canon_sha256":"d93776f2d8c53ed48c7e1152494bb8dee8ea549eac03bd7de01674a6dc3fcd33"},"schema_version":"1.0","source":{"id":"1411.6058","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6058","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6058v3","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6058","created_at":"2026-05-18T01:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"HNLPEVHJN7W3","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNLPEVHJN7W3TOFZ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNLPEVHJ","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:260426de09548b6654db3c19add78a2356b050c7437a60b6c61f955f27e60e9c","target":"graph","created_at":"2026-05-18T01:36:20Z","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":"We study the Ricci flow on Riemannian groupoids. We assume that these groupoids are closed and that the space of orbits is compact and connected. We prove the short time existence and uniqueness of the Ricci flow on these groupoids. We also define a F-functional and derive the corresponding results for steady breathers on these spaces.","authors_text":"Christian Hilaire","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-22T00:44:18Z","title":"Ricci flow on Riemannian groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6058","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":"sha256:94f451df00454c83bc16d19f776b487bcf0f3dff6e80b58ee6d90e246d92704e","target":"record","created_at":"2026-05-18T01:36:20Z","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":"03c77dae3c14158ec76e90d155c0a8731d016a629b2223f496c1134d1793cc94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-22T00:44:18Z","title_canon_sha256":"d93776f2d8c53ed48c7e1152494bb8dee8ea549eac03bd7de01674a6dc3fcd33"},"schema_version":"1.0","source":{"id":"1411.6058","kind":"arxiv","version":3}},"canonical_sha256":"3b56f254e96fedb9b8b92264b55caf5ddc5fb5b382a358d6c5644a869a266d7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b56f254e96fedb9b8b92264b55caf5ddc5fb5b382a358d6c5644a869a266d7a","first_computed_at":"2026-05-18T01:36:20.308390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:20.308390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Z15uTXYbJxjMY64dkUT0D4oE7Ik5FrWCZkUJ7ouekIYHI4U1Z6Uw4IGa4UVBpcYvOOZpWxRnf+S6+TVh7M1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:20.309195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6058","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94f451df00454c83bc16d19f776b487bcf0f3dff6e80b58ee6d90e246d92704e","sha256:260426de09548b6654db3c19add78a2356b050c7437a60b6c61f955f27e60e9c"],"state_sha256":"27b927d15a01ec10027628732f46fd49c5ba2ff8fa52fe52738ae9fed983f0ce"}