{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BCHBCKJ26J34MH3SN64H656YBX","short_pith_number":"pith:BCHBCKJ2","schema_version":"1.0","canonical_sha256":"088e11293af277c61f726fb87f77d80dcf2e721df843d2ed1bb0b6c0ffe0ea83","source":{"kind":"arxiv","id":"2504.16909","version":1},"attestation_state":"computed","paper":{"title":"The CKN inequality for spinors: symmetry and symmetry breaking","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Jean Dolbeault, Maria J. Esteban, Michael Loss, Rupert L. Frank","submitted_at":"2025-04-23T17:37:38Z","abstract_excerpt":"This paper is devoted to Sobolev interpolation inequalities for spinors, with weights of Caffarelli-Kohn-Nirenberg (CKN) type. In view of the corresponding results for scalar functions, a natural question is to determine whether optimal spinors have symmetry properties, or whether spinors with symmetry properties are linearly unstable, in which case we shall say that symmetry breaking occurs. What symmetry means has to be carefully defined and the overall picture turns out to be richer than in the scalar case. So far, no symmetrization technique is available in the spinorial case. We can howev"},"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":"2504.16909","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-04-23T17:37:38Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"4dff3c66b482f1c7472ba8c45bb86517bc5e64388d8a8709731bd9e20d2039b0","abstract_canon_sha256":"a9ba846203b44d663f00c2c0b15017e50bc0fd8ef68c2c20bec0d6595240b8d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:53:06.229929Z","signature_b64":"UwOB/jTvIzRkE6axfe2WqVBfjfBqHgTKWLqtE2vv0q4spTW3/toWpHpi3vwhme97v/WMcB3zhvz/Cr3C4+jiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"088e11293af277c61f726fb87f77d80dcf2e721df843d2ed1bb0b6c0ffe0ea83","last_reissued_at":"2026-07-05T10:53:06.229512Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:53:06.229512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The CKN inequality for spinors: symmetry and symmetry breaking","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Jean Dolbeault, Maria J. Esteban, Michael Loss, Rupert L. Frank","submitted_at":"2025-04-23T17:37:38Z","abstract_excerpt":"This paper is devoted to Sobolev interpolation inequalities for spinors, with weights of Caffarelli-Kohn-Nirenberg (CKN) type. In view of the corresponding results for scalar functions, a natural question is to determine whether optimal spinors have symmetry properties, or whether spinors with symmetry properties are linearly unstable, in which case we shall say that symmetry breaking occurs. What symmetry means has to be carefully defined and the overall picture turns out to be richer than in the scalar case. So far, no symmetrization technique is available in the spinorial case. We can howev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16909","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/2504.16909/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":"2504.16909","created_at":"2026-07-05T10:53:06.229567+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.16909v1","created_at":"2026-07-05T10:53:06.229567+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16909","created_at":"2026-07-05T10:53:06.229567+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCHBCKJ26J34","created_at":"2026-07-05T10:53:06.229567+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCHBCKJ26J34MH3S","created_at":"2026-07-05T10:53:06.229567+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCHBCKJ2","created_at":"2026-07-05T10:53:06.229567+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.04010","citing_title":"Sharp upper bounds for the density of relativistic atoms: Noninteracting case","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BCHBCKJ26J34MH3SN64H656YBX","json":"https://pith.science/pith/BCHBCKJ26J34MH3SN64H656YBX.json","graph_json":"https://pith.science/api/pith-number/BCHBCKJ26J34MH3SN64H656YBX/graph.json","events_json":"https://pith.science/api/pith-number/BCHBCKJ26J34MH3SN64H656YBX/events.json","paper":"https://pith.science/paper/BCHBCKJ2"},"agent_actions":{"view_html":"https://pith.science/pith/BCHBCKJ26J34MH3SN64H656YBX","download_json":"https://pith.science/pith/BCHBCKJ26J34MH3SN64H656YBX.json","view_paper":"https://pith.science/paper/BCHBCKJ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.16909&json=true","fetch_graph":"https://pith.science/api/pith-number/BCHBCKJ26J34MH3SN64H656YBX/graph.json","fetch_events":"https://pith.science/api/pith-number/BCHBCKJ26J34MH3SN64H656YBX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCHBCKJ26J34MH3SN64H656YBX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCHBCKJ26J34MH3SN64H656YBX/action/storage_attestation","attest_author":"https://pith.science/pith/BCHBCKJ26J34MH3SN64H656YBX/action/author_attestation","sign_citation":"https://pith.science/pith/BCHBCKJ26J34MH3SN64H656YBX/action/citation_signature","submit_replication":"https://pith.science/pith/BCHBCKJ26J34MH3SN64H656YBX/action/replication_record"}},"created_at":"2026-07-05T10:53:06.229567+00:00","updated_at":"2026-07-05T10:53:06.229567+00:00"}