{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YES33PC25CXN7CCM6AJVTXGDWO","short_pith_number":"pith:YES33PC2","schema_version":"1.0","canonical_sha256":"c125bdbc5ae8aedf884cf01359dcc3b39a42d3f5086701ac5a92462837708744","source":{"kind":"arxiv","id":"1011.1104","version":1},"attestation_state":"computed","paper":{"title":"Remarks on the Minimizing Geodesic Problem in Inviscid Incompressible Fluid Mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yann Brenier","submitted_at":"2010-11-04T10:35:22Z","abstract_excerpt":"We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally) solutions of the Euler equations. It is known that there is a unique possible pressure gradient for these curves whenever their end points are fixed. In addition, this pressure field has a limited but unconditional (internal) regularity. The present paper completes these results by showing: 1) the uniqueness property can be viewed as an infinite dimensional phe"},"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":"1011.1104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-04T10:35:22Z","cross_cats_sorted":[],"title_canon_sha256":"415030e7d013dac9197995648eb1f5396e151ed6d86e468a82478b335ef084db","abstract_canon_sha256":"898c063090767786c9a4f19eed577c5ab91bc4209a51f421c7a5a81365d02c1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:02.003656Z","signature_b64":"LlJlJYkYqvCcV46HWVw9pSqhiX3sbKHHdmPDn5c1MfF0D3fYL161i1I2ae5CjcL/X3z82obuLnrp9HmVzRmmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c125bdbc5ae8aedf884cf01359dcc3b39a42d3f5086701ac5a92462837708744","last_reissued_at":"2026-05-18T04:37:02.003062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:02.003062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on the Minimizing Geodesic Problem in Inviscid Incompressible Fluid Mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yann Brenier","submitted_at":"2010-11-04T10:35:22Z","abstract_excerpt":"We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally) solutions of the Euler equations. It is known that there is a unique possible pressure gradient for these curves whenever their end points are fixed. In addition, this pressure field has a limited but unconditional (internal) regularity. The present paper completes these results by showing: 1) the uniqueness property can be viewed as an infinite dimensional phe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1104","kind":"arxiv","version":1},"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":"1011.1104","created_at":"2026-05-18T04:37:02.003159+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.1104v1","created_at":"2026-05-18T04:37:02.003159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1104","created_at":"2026-05-18T04:37:02.003159+00:00"},{"alias_kind":"pith_short_12","alias_value":"YES33PC25CXN","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YES33PC25CXN7CCM","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YES33PC2","created_at":"2026-05-18T12:26:17.028572+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/YES33PC25CXN7CCM6AJVTXGDWO","json":"https://pith.science/pith/YES33PC25CXN7CCM6AJVTXGDWO.json","graph_json":"https://pith.science/api/pith-number/YES33PC25CXN7CCM6AJVTXGDWO/graph.json","events_json":"https://pith.science/api/pith-number/YES33PC25CXN7CCM6AJVTXGDWO/events.json","paper":"https://pith.science/paper/YES33PC2"},"agent_actions":{"view_html":"https://pith.science/pith/YES33PC25CXN7CCM6AJVTXGDWO","download_json":"https://pith.science/pith/YES33PC25CXN7CCM6AJVTXGDWO.json","view_paper":"https://pith.science/paper/YES33PC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.1104&json=true","fetch_graph":"https://pith.science/api/pith-number/YES33PC25CXN7CCM6AJVTXGDWO/graph.json","fetch_events":"https://pith.science/api/pith-number/YES33PC25CXN7CCM6AJVTXGDWO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YES33PC25CXN7CCM6AJVTXGDWO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YES33PC25CXN7CCM6AJVTXGDWO/action/storage_attestation","attest_author":"https://pith.science/pith/YES33PC25CXN7CCM6AJVTXGDWO/action/author_attestation","sign_citation":"https://pith.science/pith/YES33PC25CXN7CCM6AJVTXGDWO/action/citation_signature","submit_replication":"https://pith.science/pith/YES33PC25CXN7CCM6AJVTXGDWO/action/replication_record"}},"created_at":"2026-05-18T04:37:02.003159+00:00","updated_at":"2026-05-18T04:37:02.003159+00:00"}