{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:25M5LM2CON2XGY6WCPCQ5HVBLD","short_pith_number":"pith:25M5LM2C","schema_version":"1.0","canonical_sha256":"d759d5b34273757363d613c50e9ea158fd7f7b2d4cf7ac17fcdbd049391d2395","source":{"kind":"arxiv","id":"2409.02344","version":1},"attestation_state":"computed","paper":{"title":"A sparse resolution of the DiPerna-Majda gap problem for $2$D Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Daniel Spector, Oscar Dom\\'inguez","submitted_at":"2024-09-04T00:12:49Z","abstract_excerpt":"A central question which originates in the celebrated work in the 1980's of DiPerna and Majda asks what is the optimal decay $f > 0$ such that uniform rates $|\\omega|(Q) \\leq f(|Q|)$ of the vorticity maximal functions guarantee strong convergence without concentrations of approximate solutions to energy-conserving weak solutions of the $2$D Euler equations with vortex sheet initial data. A famous result of Majda (1993) shows $f(r) = [\\log (1/r)]^{-1/2}$, $r<1/2$, as the optimal decay for \\emph{distinguished} sign vortex sheets. In the general setting of \\emph{mixed} sign vortex sheets, DiPerna"},"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":"2409.02344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-04T00:12:49Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"defd718ab99de6e9f3dccaf5292548edfeced81cbd88b3d9966bfba193d2ba3d","abstract_canon_sha256":"796aaff135c24496c484990d9f29c9ace0974c2f0c8ef0883c3f84e09389f474"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:02:45.945362Z","signature_b64":"5t6tVqWRbW7ycquVI0YnN8+EESaUxuDGdNUKveybZZIvKYSXdVxhLMJBT39ISM8VEkylir8a/0XsLjrqD+OmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d759d5b34273757363d613c50e9ea158fd7f7b2d4cf7ac17fcdbd049391d2395","last_reissued_at":"2026-07-05T09:02:45.944845Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:02:45.944845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sparse resolution of the DiPerna-Majda gap problem for $2$D Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Daniel Spector, Oscar Dom\\'inguez","submitted_at":"2024-09-04T00:12:49Z","abstract_excerpt":"A central question which originates in the celebrated work in the 1980's of DiPerna and Majda asks what is the optimal decay $f > 0$ such that uniform rates $|\\omega|(Q) \\leq f(|Q|)$ of the vorticity maximal functions guarantee strong convergence without concentrations of approximate solutions to energy-conserving weak solutions of the $2$D Euler equations with vortex sheet initial data. A famous result of Majda (1993) shows $f(r) = [\\log (1/r)]^{-1/2}$, $r<1/2$, as the optimal decay for \\emph{distinguished} sign vortex sheets. In the general setting of \\emph{mixed} sign vortex sheets, DiPerna"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.02344","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/2409.02344/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":"2409.02344","created_at":"2026-07-05T09:02:45.944912+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.02344v1","created_at":"2026-07-05T09:02:45.944912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.02344","created_at":"2026-07-05T09:02:45.944912+00:00"},{"alias_kind":"pith_short_12","alias_value":"25M5LM2CON2X","created_at":"2026-07-05T09:02:45.944912+00:00"},{"alias_kind":"pith_short_16","alias_value":"25M5LM2CON2XGY6W","created_at":"2026-07-05T09:02:45.944912+00:00"},{"alias_kind":"pith_short_8","alias_value":"25M5LM2C","created_at":"2026-07-05T09:02:45.944912+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2508.01440","citing_title":"Dissipation concentration in two-dimensional fluids","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/25M5LM2CON2XGY6WCPCQ5HVBLD","json":"https://pith.science/pith/25M5LM2CON2XGY6WCPCQ5HVBLD.json","graph_json":"https://pith.science/api/pith-number/25M5LM2CON2XGY6WCPCQ5HVBLD/graph.json","events_json":"https://pith.science/api/pith-number/25M5LM2CON2XGY6WCPCQ5HVBLD/events.json","paper":"https://pith.science/paper/25M5LM2C"},"agent_actions":{"view_html":"https://pith.science/pith/25M5LM2CON2XGY6WCPCQ5HVBLD","download_json":"https://pith.science/pith/25M5LM2CON2XGY6WCPCQ5HVBLD.json","view_paper":"https://pith.science/paper/25M5LM2C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.02344&json=true","fetch_graph":"https://pith.science/api/pith-number/25M5LM2CON2XGY6WCPCQ5HVBLD/graph.json","fetch_events":"https://pith.science/api/pith-number/25M5LM2CON2XGY6WCPCQ5HVBLD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/25M5LM2CON2XGY6WCPCQ5HVBLD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/25M5LM2CON2XGY6WCPCQ5HVBLD/action/storage_attestation","attest_author":"https://pith.science/pith/25M5LM2CON2XGY6WCPCQ5HVBLD/action/author_attestation","sign_citation":"https://pith.science/pith/25M5LM2CON2XGY6WCPCQ5HVBLD/action/citation_signature","submit_replication":"https://pith.science/pith/25M5LM2CON2XGY6WCPCQ5HVBLD/action/replication_record"}},"created_at":"2026-07-05T09:02:45.944912+00:00","updated_at":"2026-07-05T09:02:45.944912+00:00"}