{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PFOPSGEQB4UHL3B3LNG33Y7UPC","short_pith_number":"pith:PFOPSGEQ","schema_version":"1.0","canonical_sha256":"795cf918900f2875ec3b5b4dbde3f478be13154528f588569533301ca42982e1","source":{"kind":"arxiv","id":"1707.02710","version":2},"attestation_state":"computed","paper":{"title":"Fractional Hardy-Sobolev inequalities on half spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander I. Nazarov, Roberta Musina","submitted_at":"2017-07-10T06:32:56Z","abstract_excerpt":"We investigate the existence of extremals for Hardy-Sobolev inequalities involving the Dirichlet fractional Laplacian of order s, 0<s<1, on half-spaces."},"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":"1707.02710","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-10T06:32:56Z","cross_cats_sorted":[],"title_canon_sha256":"a18d9d516e2c326e5add6fc1a6a641e85988f0d65030e4e1422f715ad8490c7a","abstract_canon_sha256":"d2a42e8760502e2a522b0917a72e700a8e4bed9a648cf63d1ae0f326bebb54fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:53.657914Z","signature_b64":"btjZ5+2lsRLvowfv17x6BzITY8N4YmRN4kgeygr9zu417P/bPqJqg1KWf5Q/LpriFpZSXMtscNYh/0BsZIBADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"795cf918900f2875ec3b5b4dbde3f478be13154528f588569533301ca42982e1","last_reissued_at":"2026-05-18T00:19:53.657197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:53.657197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional Hardy-Sobolev inequalities on half spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander I. Nazarov, Roberta Musina","submitted_at":"2017-07-10T06:32:56Z","abstract_excerpt":"We investigate the existence of extremals for Hardy-Sobolev inequalities involving the Dirichlet fractional Laplacian of order s, 0<s<1, on half-spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02710","kind":"arxiv","version":2},"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":"1707.02710","created_at":"2026-05-18T00:19:53.657337+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.02710v2","created_at":"2026-05-18T00:19:53.657337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02710","created_at":"2026-05-18T00:19:53.657337+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFOPSGEQB4UH","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFOPSGEQB4UHL3B3","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFOPSGEQ","created_at":"2026-05-18T12:31:37.085036+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/PFOPSGEQB4UHL3B3LNG33Y7UPC","json":"https://pith.science/pith/PFOPSGEQB4UHL3B3LNG33Y7UPC.json","graph_json":"https://pith.science/api/pith-number/PFOPSGEQB4UHL3B3LNG33Y7UPC/graph.json","events_json":"https://pith.science/api/pith-number/PFOPSGEQB4UHL3B3LNG33Y7UPC/events.json","paper":"https://pith.science/paper/PFOPSGEQ"},"agent_actions":{"view_html":"https://pith.science/pith/PFOPSGEQB4UHL3B3LNG33Y7UPC","download_json":"https://pith.science/pith/PFOPSGEQB4UHL3B3LNG33Y7UPC.json","view_paper":"https://pith.science/paper/PFOPSGEQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.02710&json=true","fetch_graph":"https://pith.science/api/pith-number/PFOPSGEQB4UHL3B3LNG33Y7UPC/graph.json","fetch_events":"https://pith.science/api/pith-number/PFOPSGEQB4UHL3B3LNG33Y7UPC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFOPSGEQB4UHL3B3LNG33Y7UPC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFOPSGEQB4UHL3B3LNG33Y7UPC/action/storage_attestation","attest_author":"https://pith.science/pith/PFOPSGEQB4UHL3B3LNG33Y7UPC/action/author_attestation","sign_citation":"https://pith.science/pith/PFOPSGEQB4UHL3B3LNG33Y7UPC/action/citation_signature","submit_replication":"https://pith.science/pith/PFOPSGEQB4UHL3B3LNG33Y7UPC/action/replication_record"}},"created_at":"2026-05-18T00:19:53.657337+00:00","updated_at":"2026-05-18T00:19:53.657337+00:00"}