{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:P7MKB6JQLMH5R7W2BW5DNRB7TQ","short_pith_number":"pith:P7MKB6JQ","schema_version":"1.0","canonical_sha256":"7fd8a0f9305b0fd8feda0dba36c43f9c03a02bfd75d9e4cb00b6b3c3cda447e5","source":{"kind":"arxiv","id":"1606.08059","version":2},"attestation_state":"computed","paper":{"title":"Spatial asymptotic expansions in the incompressible Euler equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Peter Topalov, R. McOwen","submitted_at":"2016-06-26T17:34:10Z","abstract_excerpt":"In this paper we prove that the Euler equation describing the motion of an ideal fluid in $\\R^d$ is well-posed in a class of functions allowing spatial asymptotic expansions as $|x|\\to\\infty$ of any a priori given order. These asymptotic expansions can involve log terms and lead to a family of conservation laws. Typically, the solutions of the Euler equation with initial data in the Schwartz class develop non-trivial spatial asymptotic expansions of the type considered here."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.08059","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-26T17:34:10Z","cross_cats_sorted":[],"title_canon_sha256":"6d439f5242bae77e1c472955e5e848cd9ba5608b0cb8e4a5eb8be63b7bbd17c7","abstract_canon_sha256":"717d3e96136d0fb26e4d4793fc210cfbda93994a653205cddf26500e0cb6350b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:58.636293Z","signature_b64":"uH3JyOk6RRCiQ4tgbHaDm5gFS5iIkTkYgy72QbATOlsd+hD4MuZEATo6p9fpmVAmLukotIDxDQXE5eQwkePBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fd8a0f9305b0fd8feda0dba36c43f9c03a02bfd75d9e4cb00b6b3c3cda447e5","last_reissued_at":"2026-05-18T01:03:58.635428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:58.635428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spatial asymptotic expansions in the incompressible Euler equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Peter Topalov, R. McOwen","submitted_at":"2016-06-26T17:34:10Z","abstract_excerpt":"In this paper we prove that the Euler equation describing the motion of an ideal fluid in $\\R^d$ is well-posed in a class of functions allowing spatial asymptotic expansions as $|x|\\to\\infty$ of any a priori given order. These asymptotic expansions can involve log terms and lead to a family of conservation laws. Typically, the solutions of the Euler equation with initial data in the Schwartz class develop non-trivial spatial asymptotic expansions of the type considered here."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08059","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.08059","created_at":"2026-05-18T01:03:58.635586+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.08059v2","created_at":"2026-05-18T01:03:58.635586+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08059","created_at":"2026-05-18T01:03:58.635586+00:00"},{"alias_kind":"pith_short_12","alias_value":"P7MKB6JQLMH5","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"P7MKB6JQLMH5R7W2","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"P7MKB6JQ","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P7MKB6JQLMH5R7W2BW5DNRB7TQ","json":"https://pith.science/pith/P7MKB6JQLMH5R7W2BW5DNRB7TQ.json","graph_json":"https://pith.science/api/pith-number/P7MKB6JQLMH5R7W2BW5DNRB7TQ/graph.json","events_json":"https://pith.science/api/pith-number/P7MKB6JQLMH5R7W2BW5DNRB7TQ/events.json","paper":"https://pith.science/paper/P7MKB6JQ"},"agent_actions":{"view_html":"https://pith.science/pith/P7MKB6JQLMH5R7W2BW5DNRB7TQ","download_json":"https://pith.science/pith/P7MKB6JQLMH5R7W2BW5DNRB7TQ.json","view_paper":"https://pith.science/paper/P7MKB6JQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.08059&json=true","fetch_graph":"https://pith.science/api/pith-number/P7MKB6JQLMH5R7W2BW5DNRB7TQ/graph.json","fetch_events":"https://pith.science/api/pith-number/P7MKB6JQLMH5R7W2BW5DNRB7TQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P7MKB6JQLMH5R7W2BW5DNRB7TQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P7MKB6JQLMH5R7W2BW5DNRB7TQ/action/storage_attestation","attest_author":"https://pith.science/pith/P7MKB6JQLMH5R7W2BW5DNRB7TQ/action/author_attestation","sign_citation":"https://pith.science/pith/P7MKB6JQLMH5R7W2BW5DNRB7TQ/action/citation_signature","submit_replication":"https://pith.science/pith/P7MKB6JQLMH5R7W2BW5DNRB7TQ/action/replication_record"}},"created_at":"2026-05-18T01:03:58.635586+00:00","updated_at":"2026-05-18T01:03:58.635586+00:00"}