{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5OXYLQHPUUKPRUVALVRVFNSJ5E","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":"4d3397bde2ce28eee9808d23068745c8d1df93a27f1cdabb7ef48f968ea84c1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-11T16:55:26Z","title_canon_sha256":"75044ed2c54796aa7819185235dc4d057a0e2176b06fd4e12cb2f1d03bc9c57c"},"schema_version":"1.0","source":{"id":"1503.03415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03415","created_at":"2026-05-18T02:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03415v1","created_at":"2026-05-18T02:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03415","created_at":"2026-05-18T02:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"5OXYLQHPUUKP","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5OXYLQHPUUKPRUVA","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5OXYLQHP","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:30346a0a325b5874f31648933ab7ff6dd0811bb67ca8d10e29387c1f3a0405a2","target":"graph","created_at":"2026-05-18T02:24:58Z","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 finite energy solutions for the damped and driven two-dimensional Navier--Stokes equations in the plane and show that the corresponding dynamical system possesses a global attractor. We obtain upper bounds for its fractal dimension when the forcing term belongs to the whole scale of homogeneous Sobolev spaces from -1 to 1","authors_text":"Alexei Ilyin, Kavita Patni, Sergey Zelik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-11T16:55:26Z","title":"Upper bounds for the attractor dimension of damped Navier-Stokes equations in $\\mathbb R^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03415","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":"sha256:9c5297e7d6ad5488aa398f341a30f0c866d91fa10415da1a46602298a0626c9e","target":"record","created_at":"2026-05-18T02:24:58Z","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":"4d3397bde2ce28eee9808d23068745c8d1df93a27f1cdabb7ef48f968ea84c1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-11T16:55:26Z","title_canon_sha256":"75044ed2c54796aa7819185235dc4d057a0e2176b06fd4e12cb2f1d03bc9c57c"},"schema_version":"1.0","source":{"id":"1503.03415","kind":"arxiv","version":1}},"canonical_sha256":"ebaf85c0efa514f8d2a05d6352b649e936b379629d54ed932255d7dea7644d2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebaf85c0efa514f8d2a05d6352b649e936b379629d54ed932255d7dea7644d2f","first_computed_at":"2026-05-18T02:24:58.949124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:58.949124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ApaLv0xAMV2HS2JkiSQ8Bwv7R2a8lJ0HawnU3bkGAY6enKTcoHyUtyD2smwBj2F0nnk2JHrix5iudn0DZ+E8BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:58.949696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c5297e7d6ad5488aa398f341a30f0c866d91fa10415da1a46602298a0626c9e","sha256:30346a0a325b5874f31648933ab7ff6dd0811bb67ca8d10e29387c1f3a0405a2"],"state_sha256":"06e0878cd664f4fc61ae9a661905844b7f4a71161496af8163ed5416af7cb19d"}