{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RSHV5K73X75QN4WYOUGJOFYZNV","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":"3369c2f52e5c1af2e6a0cb3a1c251081b4af97e668152f460db99582d4af252c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-05T05:16:24Z","title_canon_sha256":"e12499db21e36b428e28d3f45698e7622a4f609e21bc8d759b475cf059bc8d5d"},"schema_version":"1.0","source":{"id":"1806.01498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01498","created_at":"2026-05-18T00:14:12Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01498v1","created_at":"2026-05-18T00:14:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01498","created_at":"2026-05-18T00:14:12Z"},{"alias_kind":"pith_short_12","alias_value":"RSHV5K73X75Q","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RSHV5K73X75QN4WY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RSHV5K73","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:9e5a8188d47049cb14dd8fc92910d43ee5e8f94646400ce87d7ee88614d866b5","target":"graph","created_at":"2026-05-18T00:14:12Z","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 investigate the convergence of the Galerkin approximation for the stochastic Navier-Stokes equations in an open bounded domain $\\mathcal{O}$ with the non-slip boundary condition. We prove that\n  \\begin{equation*}\n  \\mathbb{E} \\left[ \\sup_{t \\in [0,T]} \\phi_1(\\lVert (u(t)-u^n(t))\n  \\rVert^2_V) \\right] \\rightarrow 0\n  \\end{equation*} as $n \\rightarrow \\infty$ for any deterministic time $T > 0$ and for a specified moment function $\\phi_1(x)$ where $u^n(t,x)$ denotes the Galerkin approximation of the solution $u(t,x)$. Also, we provide a result on uniform boundedness of the moment $\\mathbb{E} [","authors_text":"Igor Kukavica, Kerem Ugurlu, Mohammed Ziane","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-05T05:16:24Z","title":"On the Galerkin approximation and strong norm bounds for the stochastic Navier-Stokes equations with multiplicative noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01498","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:eb907062d307167866eabe1ad9b3f4295934abc207139741a6f2043055d37236","target":"record","created_at":"2026-05-18T00:14:12Z","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":"3369c2f52e5c1af2e6a0cb3a1c251081b4af97e668152f460db99582d4af252c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-05T05:16:24Z","title_canon_sha256":"e12499db21e36b428e28d3f45698e7622a4f609e21bc8d759b475cf059bc8d5d"},"schema_version":"1.0","source":{"id":"1806.01498","kind":"arxiv","version":1}},"canonical_sha256":"8c8f5eabfbbffb06f2d8750c9717196d7a11386b3f2205ae904661b133ef0c02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c8f5eabfbbffb06f2d8750c9717196d7a11386b3f2205ae904661b133ef0c02","first_computed_at":"2026-05-18T00:14:12.773899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:12.773899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hO3QtMeDP0e3iqdEqeUGiCbMa4vt54cKaI8LVGWNRR/aMcnbvT4tkeiiK0AKLhIP+ztciRse9DCX8Wkz5pMIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:12.774388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.01498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb907062d307167866eabe1ad9b3f4295934abc207139741a6f2043055d37236","sha256:9e5a8188d47049cb14dd8fc92910d43ee5e8f94646400ce87d7ee88614d866b5"],"state_sha256":"7bc164195efe7671b2e730920c9d53758536609533e820891600881567c7a424"}