{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4TGWA46647OHKGVTZVABKRZKN4","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":"8c1b3edcbea800337b181120f53f0e29e6815301535f81356ef3b9e0d48d356f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-04T16:36:19Z","title_canon_sha256":"6c6eca80e184a61aa8f97bc3c990386da797105fd63912dea6ef1aac90b92134"},"schema_version":"1.0","source":{"id":"1104.0619","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0619","created_at":"2026-05-18T04:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0619v2","created_at":"2026-05-18T04:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0619","created_at":"2026-05-18T04:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"4TGWA46647OH","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4TGWA46647OHKGVT","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4TGWA466","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:b7751c04d0ba5a24da820ae12ec2abb02b1e57e8246fc745c3eba2f7be09a70d","target":"graph","created_at":"2026-05-18T04:11:51Z","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":"Let w be the vorticity of a stationary solution of the two-dimensional Navier-Stokes equations with a drift term parallel to the boundary in the half-plane -\\infty<x<\\infty, y>1, with zero Dirichlet boundary conditions at y=1 and at infinity, and with a small force term of compact support. Then, |xyw(x,y)| is uniformly bounded in the half-plane. The proof is given in a specially adapted functional framework and complements previous work.","authors_text":"Christoph Boeckle, Peter Wittwer","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-04T16:36:19Z","title":"Decay estimates for steady solutions of the Navier-Stokes equations in two dimensions in the presence of a wall"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0619","kind":"arxiv","version":2},"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":"sha256:94d0d60c62ef459e694ca824855a482871226a758361b719aa474709ef4c210f","target":"record","created_at":"2026-05-18T04:11:51Z","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":"8c1b3edcbea800337b181120f53f0e29e6815301535f81356ef3b9e0d48d356f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-04T16:36:19Z","title_canon_sha256":"6c6eca80e184a61aa8f97bc3c990386da797105fd63912dea6ef1aac90b92134"},"schema_version":"1.0","source":{"id":"1104.0619","kind":"arxiv","version":2}},"canonical_sha256":"e4cd6073dee7dc751ab3cd4015472a6f012a0a49fba25460a8ee8b8ea52c2a8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4cd6073dee7dc751ab3cd4015472a6f012a0a49fba25460a8ee8b8ea52c2a8d","first_computed_at":"2026-05-18T04:11:51.537403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:51.537403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0/wVurnts3FOJ+JVHD4eKnTA8aC5oAPNEDaPAXNzq3TfPXOEloaSlPsKEvexP/wY6giMQpPpwySX5GWrs/nbDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:51.538080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0619","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94d0d60c62ef459e694ca824855a482871226a758361b719aa474709ef4c210f","sha256:b7751c04d0ba5a24da820ae12ec2abb02b1e57e8246fc745c3eba2f7be09a70d"],"state_sha256":"3e1167a606fc8334d085efb27e5bda528c321b5dd00b9accd5bd2deb103a184e"}