{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AO5CXTYAEBSUBN5BCT7OYOESFA","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":"7d65df7c3bb8d4bd14e3d3946bac27874d422f9e64e3c3f015bca8800cee4fef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-08T08:28:50Z","title_canon_sha256":"ec0aca1b5442bfeab4514b1dff19502a24b4679ddeb7c43872f4f74bb26c1686"},"schema_version":"1.0","source":{"id":"1009.1480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1480","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1480v1","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1480","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"AO5CXTYAEBSU","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AO5CXTYAEBSUBN5B","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AO5CXTYA","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:5ae233316fa6d334ca09081d753d4aa2f42d803420f666be078989de40f7e649","target":"graph","created_at":"2026-05-18T04:41:14Z","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":"In this paper we establish three basic equations for a general soliton structure on the Riemannian manifold $(M, <, >)$. We then draw some geometric conclusions with the aid of the maximum principle.","authors_text":"Marco Rigoli, Paolo Mastrolia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-08T08:28:50Z","title":"On the Geometry of complete Ricci Solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1480","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":"sha256:15b8ee1a7283f0f24508c5b6d083d3fe0ce49fe5b687e5d113737018d2180650","target":"record","created_at":"2026-05-18T04:41:14Z","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":"7d65df7c3bb8d4bd14e3d3946bac27874d422f9e64e3c3f015bca8800cee4fef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-08T08:28:50Z","title_canon_sha256":"ec0aca1b5442bfeab4514b1dff19502a24b4679ddeb7c43872f4f74bb26c1686"},"schema_version":"1.0","source":{"id":"1009.1480","kind":"arxiv","version":1}},"canonical_sha256":"03ba2bcf00206540b7a114feec3892283e3d5338077fcae5566206ed18eb016d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03ba2bcf00206540b7a114feec3892283e3d5338077fcae5566206ed18eb016d","first_computed_at":"2026-05-18T04:41:14.682910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:14.682910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RBC0HDeyIKcUQYMz8QrUNOFLWKYArrTCpGXLuq/ykT64ZkktPUttIwWCaxfr1mvDQjOVhoCmp51RX6S4xiNbBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:14.683668Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15b8ee1a7283f0f24508c5b6d083d3fe0ce49fe5b687e5d113737018d2180650","sha256:5ae233316fa6d334ca09081d753d4aa2f42d803420f666be078989de40f7e649"],"state_sha256":"7bc0f5bd32f9db763f9ee80e0f5e7985b8fb9fa192d411711bb6aa102a1c367c"}