{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:F5Q2XVIYOOFAQ6AEOMRC2TRLRT","short_pith_number":"pith:F5Q2XVIY","schema_version":"1.0","canonical_sha256":"2f61abd518738a08780473222d4e2b8cf8a464f9af7349fa2f0e3cf73637ab14","source":{"kind":"arxiv","id":"2301.00804","version":1},"attestation_state":"computed","paper":{"title":"Convex integration above the Onsager exponent for the forced Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aynur Bulut, Manh Khang Huynh, Stan Palasek","submitted_at":"2023-01-02T18:50:46Z","abstract_excerpt":"We establish new non-uniqueness results for the Euler equations with external force on $\\mathbb{T}^{d}$ $(d\\geq3)$. By introducing a novel alternating convex integration scheme, we construct non-unique, almost-everywhere smooth, H\\\"older-continuous solutions with regularity $\\frac{1}{2}-$, which is notably above the Onsager threshold of $\\frac{1}{3}$.\n  The solutions we construct differ significantly in nature from those which arise from the recent unstable vortex construction of Vishik; in particular, our solutions are genuinely $d$-dimensional ($d\\geq3$), and give non-uniqueness results for "},"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":"2301.00804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-01-02T18:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"379b3f51a65b781dc6a73626671c7e86bea855a7600999c23c82c9431059be61","abstract_canon_sha256":"a4cf886e5d570b094a0660b74e848d24ecda4b51a50453ba2824f22d329887ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:29:50.348965Z","signature_b64":"8x7alpyDP7pFv5aao8hSVO0PPG28nnH6pi3XT/lOn7mzBqzq5wwuyL8vDwUJ9wpv2dxl3fwh3JV+b/G6pG1RCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f61abd518738a08780473222d4e2b8cf8a464f9af7349fa2f0e3cf73637ab14","last_reissued_at":"2026-07-05T05:29:50.348478Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:29:50.348478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex integration above the Onsager exponent for the forced Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aynur Bulut, Manh Khang Huynh, Stan Palasek","submitted_at":"2023-01-02T18:50:46Z","abstract_excerpt":"We establish new non-uniqueness results for the Euler equations with external force on $\\mathbb{T}^{d}$ $(d\\geq3)$. By introducing a novel alternating convex integration scheme, we construct non-unique, almost-everywhere smooth, H\\\"older-continuous solutions with regularity $\\frac{1}{2}-$, which is notably above the Onsager threshold of $\\frac{1}{3}$.\n  The solutions we construct differ significantly in nature from those which arise from the recent unstable vortex construction of Vishik; in particular, our solutions are genuinely $d$-dimensional ($d\\geq3$), and give non-uniqueness results for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.00804","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.00804/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2301.00804","created_at":"2026-07-05T05:29:50.348537+00:00"},{"alias_kind":"arxiv_version","alias_value":"2301.00804v1","created_at":"2026-07-05T05:29:50.348537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.00804","created_at":"2026-07-05T05:29:50.348537+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5Q2XVIYOOFA","created_at":"2026-07-05T05:29:50.348537+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5Q2XVIYOOFAQ6AE","created_at":"2026-07-05T05:29:50.348537+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5Q2XVIY","created_at":"2026-07-05T05:29:50.348537+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2404.15995","citing_title":"A proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT","json":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT.json","graph_json":"https://pith.science/api/pith-number/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/graph.json","events_json":"https://pith.science/api/pith-number/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/events.json","paper":"https://pith.science/paper/F5Q2XVIY"},"agent_actions":{"view_html":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT","download_json":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT.json","view_paper":"https://pith.science/paper/F5Q2XVIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2301.00804&json=true","fetch_graph":"https://pith.science/api/pith-number/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/graph.json","fetch_events":"https://pith.science/api/pith-number/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/action/storage_attestation","attest_author":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/action/author_attestation","sign_citation":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/action/citation_signature","submit_replication":"https://pith.science/pith/F5Q2XVIYOOFAQ6AEOMRC2TRLRT/action/replication_record"}},"created_at":"2026-07-05T05:29:50.348537+00:00","updated_at":"2026-07-05T05:29:50.348537+00:00"}