{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P7QJVOY2677GJI7Q7AMNFFN7MK","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":"ea050a80cd60e8636422eee90a2908b74da9035c1723afc1c7f1e501c19632cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-17T19:22:02Z","title_canon_sha256":"1c721fa8b160a415e12b0e07fe0c2f21b4448b4d5c550beaa5e70b0c4b5890df"},"schema_version":"1.0","source":{"id":"1311.4204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4204","created_at":"2026-05-18T01:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4204v1","created_at":"2026-05-18T01:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4204","created_at":"2026-05-18T01:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"P7QJVOY2677G","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P7QJVOY2677GJI7Q","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P7QJVOY2","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:01cc9b6c6a5dcb988a4f81dbda979f496f394a346ff16ebd72d71dd4477ce2ca","target":"graph","created_at":"2026-05-18T01:46:23Z","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 establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The proof is based on new moment bounds for strong solutions. The invariant measure is supported on strong solutions, but is furthermore shown to have higher regularity properties.","authors_text":"Igor Kukavica, Mohammed Ziane, Nathan Glatt-Holtz, Vlad Vicol","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-17T19:22:02Z","title":"Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4204","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":"sha256:3e0a6df96540a75bb617ae9613a5512ab2b307e16f014c088d32d9316ed3bfa8","target":"record","created_at":"2026-05-18T01:46:23Z","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":"ea050a80cd60e8636422eee90a2908b74da9035c1723afc1c7f1e501c19632cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-17T19:22:02Z","title_canon_sha256":"1c721fa8b160a415e12b0e07fe0c2f21b4448b4d5c550beaa5e70b0c4b5890df"},"schema_version":"1.0","source":{"id":"1311.4204","kind":"arxiv","version":1}},"canonical_sha256":"7fe09abb1af7fe64a3f0f818d295bf62bdacb33b13a21772eccda701ae152b91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fe09abb1af7fe64a3f0f818d295bf62bdacb33b13a21772eccda701ae152b91","first_computed_at":"2026-05-18T01:46:23.961275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:46:23.961275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3UwpQn2z5EhwpqIkUaLCjgRnP6RSIQ3by21L4VRigq/klAZS087qa3neBIPlkQ+p3xArk2kvttSH0HHXd6SpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:46:23.961801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e0a6df96540a75bb617ae9613a5512ab2b307e16f014c088d32d9316ed3bfa8","sha256:01cc9b6c6a5dcb988a4f81dbda979f496f394a346ff16ebd72d71dd4477ce2ca"],"state_sha256":"1ba75d032cccdef5af49ef0b01f146b64681fedd17870d8a08a68c070150a21e"}