{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BQVTHRWL24P4DMXCMG5HULGCP5","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":"581df53bfab8e79c79bf7eef21c16bcab3aca95f7baa217e43691e37955fefd9","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.AP","submitted_at":"2007-10-20T13:42:14Z","title_canon_sha256":"4cb31eb1fdb968b4746ec67bb94ff6f8ec301cb9eba2d1bce4d75db8ffee99fe"},"schema_version":"1.0","source":{"id":"0710.3842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3842","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3842v1","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3842","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"BQVTHRWL24P4","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BQVTHRWL24P4DMXC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BQVTHRWL","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:7c0e63a76cef9a685982425edca3c35c3f56b3e036f3c509fae2d467253aa32f","target":"graph","created_at":"2026-05-18T03:20:36Z","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 consider 3d Navier-Stokes system with periodic boundary conditions for small initial data from the space of Pseudomeasures. We provide asymptotic behavior for the coefficients in the perturbation series for the solution of this system.","authors_text":"M. D. Arnold, Ya. G. Sinai","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-10-20T13:42:14Z","title":"Global Existence Theorem for the Solutions of 3d Navier-Stokes System on T3 for small initial data from the space P(a)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3842","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":"sha256:273f5d0a386a26ac2e80999d367d67a8dbbfd617418800851f2d401d77f51662","target":"record","created_at":"2026-05-18T03:20:36Z","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":"581df53bfab8e79c79bf7eef21c16bcab3aca95f7baa217e43691e37955fefd9","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.AP","submitted_at":"2007-10-20T13:42:14Z","title_canon_sha256":"4cb31eb1fdb968b4746ec67bb94ff6f8ec301cb9eba2d1bce4d75db8ffee99fe"},"schema_version":"1.0","source":{"id":"0710.3842","kind":"arxiv","version":1}},"canonical_sha256":"0c2b33c6cbd71fc1b2e261ba7a2cc27f51e1c0fe180f4cb352434bd6a903d05a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c2b33c6cbd71fc1b2e261ba7a2cc27f51e1c0fe180f4cb352434bd6a903d05a","first_computed_at":"2026-05-18T03:20:36.083894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:36.083894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jcvfwzr95rEeclegAhRdY8aGUrCCG9j3UoE8U4CrtuT5eLMAGK1mIdHuHKpkEapoe1pWTinFe3iCvjb5D0V9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:36.084685Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:273f5d0a386a26ac2e80999d367d67a8dbbfd617418800851f2d401d77f51662","sha256:7c0e63a76cef9a685982425edca3c35c3f56b3e036f3c509fae2d467253aa32f"],"state_sha256":"d712e28c0dc556a294255a56247e25b77ed0306ef0c73a9c1f37d71dff3530d5"}