{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:C37FSB7ZFKCIEIY4K7STZ7I7AH","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":"11ed2239898a57734ba78472debd4295ae06b841c9430eccc44336e0de7c2b4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-02-26T07:41:04Z","title_canon_sha256":"4901a35348482bb4c76171d9ccc2d40e8e779a24a1f6d37eca4f005cb0ced1c7"},"schema_version":"1.0","source":{"id":"2102.13341","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.13341","created_at":"2026-07-05T04:08:38Z"},{"alias_kind":"arxiv_version","alias_value":"2102.13341v2","created_at":"2026-07-05T04:08:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.13341","created_at":"2026-07-05T04:08:38Z"},{"alias_kind":"pith_short_12","alias_value":"C37FSB7ZFKCI","created_at":"2026-07-05T04:08:38Z"},{"alias_kind":"pith_short_16","alias_value":"C37FSB7ZFKCIEIY4","created_at":"2026-07-05T04:08:38Z"},{"alias_kind":"pith_short_8","alias_value":"C37FSB7Z","created_at":"2026-07-05T04:08:38Z"}],"graph_snapshots":[{"event_id":"sha256:d4d6057a9679196a09f40ac41e2b98e2191e26802ce04e996d9be7dea3e8b7d8","target":"graph","created_at":"2026-07-05T04:08:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.13341/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the nonhomogeneous boundary value problem for the steady Navier-Stokes equations in a helically symmetric spatial domain. When data is assumed to be helical invariant and satisfies the compatibility condition, we prove this problem has at least one helical invariant solution.","authors_text":"Mikhail Korobkov, Shangkun Weng, Wenqi Lyu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-02-26T07:41:04Z","title":"On the existence of helical invariant solutions to steady Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.13341","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":"sha256:8dd9f5eef403edb40702182e8a9ccdf9c835a38b6c594e53f7cdb90bafa12bf0","target":"record","created_at":"2026-07-05T04:08:38Z","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":"11ed2239898a57734ba78472debd4295ae06b841c9430eccc44336e0de7c2b4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-02-26T07:41:04Z","title_canon_sha256":"4901a35348482bb4c76171d9ccc2d40e8e779a24a1f6d37eca4f005cb0ced1c7"},"schema_version":"1.0","source":{"id":"2102.13341","kind":"arxiv","version":2}},"canonical_sha256":"16fe5907f92a8482231c57e53cfd1f01e021b931fe43b14e51ce803e9be4af65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16fe5907f92a8482231c57e53cfd1f01e021b931fe43b14e51ce803e9be4af65","first_computed_at":"2026-07-05T04:08:38.755307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:08:38.755307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sGDlsDtNz2iiagqvF1H1/+XTPVQcyw4hrfOfYJ/bE2HcEvsMLUlXNYIOr9movCtQEyzdtHdXONMwf0FWLAoABA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:08:38.755698Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.13341","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dd9f5eef403edb40702182e8a9ccdf9c835a38b6c594e53f7cdb90bafa12bf0","sha256:d4d6057a9679196a09f40ac41e2b98e2191e26802ce04e996d9be7dea3e8b7d8"],"state_sha256":"a93c2ae46212c86ba6bd8dd1c88975b60f15f16078386e11480f8f9da8066cf4"}