{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:J2266UAGP2VMBHHXPYYBLUDGW4","short_pith_number":"pith:J2266UAG","schema_version":"1.0","canonical_sha256":"4eb5ef50067eaac09cf77e3015d066b7053ba0c8db992a2ec3eee1d927d3b25b","source":{"kind":"arxiv","id":"2503.06904","version":1},"attestation_state":"computed","paper":{"title":"On Brezis' First Open Problem: A Complete Solution","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Liming Sun, Wen Yang","submitted_at":"2025-03-10T04:15:26Z","abstract_excerpt":"In 2023, H.\\,Brezis published a list of his ``favorite open problems\", which he described as challenges he had ``raised throughout his career and has resisted so far\". We provide a complete resolution to the first one--Open Problem 1.1--in Brezis's favorite open problems list: the existence of solutions to the long-standing Brezis-Nirenberg problem on a three-dimensional ball. Furthermore, using the building blocks of Del Pino-Musso-Pacard-Pistoia sign-changing solutions to the Yamabe problem, we establish the existence of infinitely many sign-changing, nonradial solutions for the full range o"},"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":"2503.06904","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-03-10T04:15:26Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c7596f94755a10a4054561d15517590d80601ae2e278ac4916ee47fe0a2fce2e","abstract_canon_sha256":"260b7e7a779538422342db2cbfc8ad8a56d85309810cef23078df5acc10c9057"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:27:45.563042Z","signature_b64":"OS96ThDKr3rSVisAjR4rtbHM7vIJ7C8sby1tA/OvIU70GUWSrqvGgDvPLu37Lk93MyDDnSxbQQPI8hkuvUCNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eb5ef50067eaac09cf77e3015d066b7053ba0c8db992a2ec3eee1d927d3b25b","last_reissued_at":"2026-07-05T10:27:45.562528Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:27:45.562528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Brezis' First Open Problem: A Complete Solution","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Liming Sun, Wen Yang","submitted_at":"2025-03-10T04:15:26Z","abstract_excerpt":"In 2023, H.\\,Brezis published a list of his ``favorite open problems\", which he described as challenges he had ``raised throughout his career and has resisted so far\". We provide a complete resolution to the first one--Open Problem 1.1--in Brezis's favorite open problems list: the existence of solutions to the long-standing Brezis-Nirenberg problem on a three-dimensional ball. Furthermore, using the building blocks of Del Pino-Musso-Pacard-Pistoia sign-changing solutions to the Yamabe problem, we establish the existence of infinitely many sign-changing, nonradial solutions for the full range o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06904","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/2503.06904/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":"2503.06904","created_at":"2026-07-05T10:27:45.562600+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.06904v1","created_at":"2026-07-05T10:27:45.562600+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.06904","created_at":"2026-07-05T10:27:45.562600+00:00"},{"alias_kind":"pith_short_12","alias_value":"J2266UAGP2VM","created_at":"2026-07-05T10:27:45.562600+00:00"},{"alias_kind":"pith_short_16","alias_value":"J2266UAGP2VMBHHX","created_at":"2026-07-05T10:27:45.562600+00:00"},{"alias_kind":"pith_short_8","alias_value":"J2266UAG","created_at":"2026-07-05T10:27:45.562600+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.22355","citing_title":"Uncountably many non-rotationally symmetric type II ancient Yamabe flows on the sphere","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2604.02978","citing_title":"Planar doubling nodal solutions to the Yamabe equation with maximal rank","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J2266UAGP2VMBHHXPYYBLUDGW4","json":"https://pith.science/pith/J2266UAGP2VMBHHXPYYBLUDGW4.json","graph_json":"https://pith.science/api/pith-number/J2266UAGP2VMBHHXPYYBLUDGW4/graph.json","events_json":"https://pith.science/api/pith-number/J2266UAGP2VMBHHXPYYBLUDGW4/events.json","paper":"https://pith.science/paper/J2266UAG"},"agent_actions":{"view_html":"https://pith.science/pith/J2266UAGP2VMBHHXPYYBLUDGW4","download_json":"https://pith.science/pith/J2266UAGP2VMBHHXPYYBLUDGW4.json","view_paper":"https://pith.science/paper/J2266UAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.06904&json=true","fetch_graph":"https://pith.science/api/pith-number/J2266UAGP2VMBHHXPYYBLUDGW4/graph.json","fetch_events":"https://pith.science/api/pith-number/J2266UAGP2VMBHHXPYYBLUDGW4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J2266UAGP2VMBHHXPYYBLUDGW4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J2266UAGP2VMBHHXPYYBLUDGW4/action/storage_attestation","attest_author":"https://pith.science/pith/J2266UAGP2VMBHHXPYYBLUDGW4/action/author_attestation","sign_citation":"https://pith.science/pith/J2266UAGP2VMBHHXPYYBLUDGW4/action/citation_signature","submit_replication":"https://pith.science/pith/J2266UAGP2VMBHHXPYYBLUDGW4/action/replication_record"}},"created_at":"2026-07-05T10:27:45.562600+00:00","updated_at":"2026-07-05T10:27:45.562600+00:00"}