{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4RRXNEPRQZNK3UZKUICNRTT2LM","short_pith_number":"pith:4RRXNEPR","schema_version":"1.0","canonical_sha256":"e4637691f1865aadd32aa204d8ce7a5b0138ae08f9589a426ac797facf503b6b","source":{"kind":"arxiv","id":"1302.0276","version":1},"attestation_state":"computed","paper":{"title":"Non degeneracy of the bubble in the critical case for non local equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan Davila, Manuel del Pino, Yannick Sire","submitted_at":"2013-02-01T20:47:15Z","abstract_excerpt":"We prove the nondegeneracy of the extremals of the fractional Sobolev inequality as solutions of a critical semilinear nonlocal equation involving the fractional Laplacian."},"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":"1302.0276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T20:47:15Z","cross_cats_sorted":[],"title_canon_sha256":"07b33eafff1bd278538c037a6585e97ce44b827624b7780ff3350079af7ff953","abstract_canon_sha256":"8dc2d8aaf2af7ed9f6980491cd12b5f4affcb051ea8d70d20d2ce83ad94aa7eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:46.873963Z","signature_b64":"91o/1mDBsmzCa/aUH3IfyP9U9pApfKkD/4ccr20T0NPYwiAGW/fqZIaySqtZ2rZxzBwpSeeMPetpMKKljpDXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4637691f1865aadd32aa204d8ce7a5b0138ae08f9589a426ac797facf503b6b","last_reissued_at":"2026-05-18T03:34:46.873263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:46.873263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non degeneracy of the bubble in the critical case for non local equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan Davila, Manuel del Pino, Yannick Sire","submitted_at":"2013-02-01T20:47:15Z","abstract_excerpt":"We prove the nondegeneracy of the extremals of the fractional Sobolev inequality as solutions of a critical semilinear nonlocal equation involving the fractional Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0276","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":"1302.0276","created_at":"2026-05-18T03:34:46.873366+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.0276v1","created_at":"2026-05-18T03:34:46.873366+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0276","created_at":"2026-05-18T03:34:46.873366+00:00"},{"alias_kind":"pith_short_12","alias_value":"4RRXNEPRQZNK","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"4RRXNEPRQZNK3UZK","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"4RRXNEPR","created_at":"2026-05-18T12:27:34.582898+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/4RRXNEPRQZNK3UZKUICNRTT2LM","json":"https://pith.science/pith/4RRXNEPRQZNK3UZKUICNRTT2LM.json","graph_json":"https://pith.science/api/pith-number/4RRXNEPRQZNK3UZKUICNRTT2LM/graph.json","events_json":"https://pith.science/api/pith-number/4RRXNEPRQZNK3UZKUICNRTT2LM/events.json","paper":"https://pith.science/paper/4RRXNEPR"},"agent_actions":{"view_html":"https://pith.science/pith/4RRXNEPRQZNK3UZKUICNRTT2LM","download_json":"https://pith.science/pith/4RRXNEPRQZNK3UZKUICNRTT2LM.json","view_paper":"https://pith.science/paper/4RRXNEPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.0276&json=true","fetch_graph":"https://pith.science/api/pith-number/4RRXNEPRQZNK3UZKUICNRTT2LM/graph.json","fetch_events":"https://pith.science/api/pith-number/4RRXNEPRQZNK3UZKUICNRTT2LM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4RRXNEPRQZNK3UZKUICNRTT2LM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4RRXNEPRQZNK3UZKUICNRTT2LM/action/storage_attestation","attest_author":"https://pith.science/pith/4RRXNEPRQZNK3UZKUICNRTT2LM/action/author_attestation","sign_citation":"https://pith.science/pith/4RRXNEPRQZNK3UZKUICNRTT2LM/action/citation_signature","submit_replication":"https://pith.science/pith/4RRXNEPRQZNK3UZKUICNRTT2LM/action/replication_record"}},"created_at":"2026-05-18T03:34:46.873366+00:00","updated_at":"2026-05-18T03:34:46.873366+00:00"}