{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CE6SUHOFVWLHEVF73LLP4Q3T63","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":"c73b742b742a24e3d15291d6744c425b69a88fa8acbdb52524da8ad338980fe8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-16T09:53:59Z","title_canon_sha256":"316718d3f905098b1de44bec540afd762822a8f2a58b62cd472516225a7ffd79"},"schema_version":"1.0","source":{"id":"1703.05538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05538","created_at":"2026-05-18T00:48:33Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05538v1","created_at":"2026-05-18T00:48:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05538","created_at":"2026-05-18T00:48:33Z"},{"alias_kind":"pith_short_12","alias_value":"CE6SUHOFVWLH","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CE6SUHOFVWLHEVF7","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CE6SUHOF","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:58f5d836d4fec756ed2f5456b619d5bf94a84d484142e64460c9b734fe222c00","target":"graph","created_at":"2026-05-18T00:48:33Z","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":"This paper is concerned with the long-time behavior of solutions for the three dimensional globally modified Navier-Stokes equations in a three-dimensional bounded domain. We prove the existence of a global attractor $\\mathcal{A}_0$ in $H$ and investigate the regularity of the global attractors by proving that $\\mathcal{A}_0=\\mathcal{A}$ established in \\cite{ct}, which implies the asymptotic smoothing effect of solutions for the three dimensional globally modified Navier-Stokes equations in the sense that the solutions will eventually become more regular than the initial data. Furthermore, we ","authors_text":"Bo You, Fang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-16T09:53:59Z","title":"Long-time behavior of the three dimensional globally modified Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05538","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":"sha256:05885d0adbf50d64aa274c2cd7dfb01dcc9ec337019c4bcf64f6845fc3c9fd1d","target":"record","created_at":"2026-05-18T00:48:33Z","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":"c73b742b742a24e3d15291d6744c425b69a88fa8acbdb52524da8ad338980fe8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-16T09:53:59Z","title_canon_sha256":"316718d3f905098b1de44bec540afd762822a8f2a58b62cd472516225a7ffd79"},"schema_version":"1.0","source":{"id":"1703.05538","kind":"arxiv","version":1}},"canonical_sha256":"113d2a1dc5ad967254bfdad6fe4373f6dce684dccbc3e337c66d460307a9fe24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"113d2a1dc5ad967254bfdad6fe4373f6dce684dccbc3e337c66d460307a9fe24","first_computed_at":"2026-05-18T00:48:33.996737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:33.996737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LLY/tLx81CB8ZeLTwl4F4jl06r2Uw5ryvz2LnwkLF0wcIxymU8TI7GMHCJsUXjYx02wwrLQZ91jnUgeeaTMWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:33.997382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05885d0adbf50d64aa274c2cd7dfb01dcc9ec337019c4bcf64f6845fc3c9fd1d","sha256:58f5d836d4fec756ed2f5456b619d5bf94a84d484142e64460c9b734fe222c00"],"state_sha256":"ff3a2593083b1061f54264704c3169637e456f3cba376621cd3ba5d094a02d0b"}