{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4I7SHRYOAL7FO36FNWYY3ELBCJ","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":"266b36d0611397d70f24bb010143891009e3cef0a9cce1d280c5d01537f9bc94","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-31T13:50:42Z","title_canon_sha256":"90c931f9a77625f99cad48dda5a44502d29f71dbe637ecece457d62f30dd7be3"},"schema_version":"1.0","source":{"id":"1608.08850","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08850","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08850v8","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08850","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"4I7SHRYOAL7F","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4I7SHRYOAL7FO36F","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4I7SHRYO","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:dbcacea9aeb7cf47948f63d3d90194d8ccce70bd18762314cbce4376e448c190","target":"graph","created_at":"2026-05-18T00:24:31Z","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 develop an integral geometry of stationary Euler equations defining some function $w$ on the Grassmannian of affine lines in the space. This function depends on a putative compactly supported solution $v$ of the system, and we deduce a linear differential equation for $w$. We prove also that the purported annulation of $w$ implies that locally supported solutions of the steady Euler equation in $\\mathbb R^3$ are zero.","authors_text":"Nikolai Nadirashvili, Serge Vl\\u{a}du\\c{t}","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-31T13:50:42Z","title":"Integral geometry of Euler equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08850","kind":"arxiv","version":8},"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":"sha256:993cfbf7df7b1c4577323205982faf3261e7fd7c4e9b56d293cd9ced4aaea093","target":"record","created_at":"2026-05-18T00:24:31Z","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":"266b36d0611397d70f24bb010143891009e3cef0a9cce1d280c5d01537f9bc94","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-31T13:50:42Z","title_canon_sha256":"90c931f9a77625f99cad48dda5a44502d29f71dbe637ecece457d62f30dd7be3"},"schema_version":"1.0","source":{"id":"1608.08850","kind":"arxiv","version":8}},"canonical_sha256":"e23f23c70e02fe576fc56db18d91611243a68e1cafdd890262ec62b0cdeb0412","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e23f23c70e02fe576fc56db18d91611243a68e1cafdd890262ec62b0cdeb0412","first_computed_at":"2026-05-18T00:24:31.729238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:31.729238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6GFr+c2oYmjLTGIm/WJO+Pco9G1uXgM8oc6KHCGxJVwZhO0bGrFMwVJH1MhP74NoseVlt4BA2UDfV8qwUjqHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:31.729823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08850","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:993cfbf7df7b1c4577323205982faf3261e7fd7c4e9b56d293cd9ced4aaea093","sha256:dbcacea9aeb7cf47948f63d3d90194d8ccce70bd18762314cbce4376e448c190"],"state_sha256":"11edac3f37c55ea285e518bce1c8af72c951177ecc4266c9b7af799a8408b502"}