{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OT4YAD5EXEUBF47RAHFTJZQXIL","short_pith_number":"pith:OT4YAD5E","schema_version":"1.0","canonical_sha256":"74f9800fa4b92812f3f101cb34e61742e47f9ce901b7a7e89462ddb7a5a5ab3e","source":{"kind":"arxiv","id":"1408.3946","version":1},"attestation_state":"computed","paper":{"title":"On the Sobolev and Hardy constants for the fractional Navier Laplacian","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":"2014-08-18T09:24:45Z","abstract_excerpt":"We prove the coincidence of the Sobolev and Hardy constants relative to the \"Dirichlet\" and \"Navier\" fractional Laplacians of any real order $m\\in(0,\\frac{n}{2})$ over bounded domains in $\\mathbb R^n$."},"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":"1408.3946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-18T09:24:45Z","cross_cats_sorted":[],"title_canon_sha256":"ad0daaf5b2b114b158930740e3927c9c1c4068c737cb1a4cb8391b74029418e6","abstract_canon_sha256":"0a50647a2415eab4d346a92f79b958b162f79aef374a367878b9adf14cb38741"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:57.539644Z","signature_b64":"haC3SwJAuHTBwJ15E8dy1ao+DuwBv5KoPTYnzQ5XeIqF6QcJYqo/anxGvexTH2CrhWIeoSL3J5CzOx9JSWkvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74f9800fa4b92812f3f101cb34e61742e47f9ce901b7a7e89462ddb7a5a5ab3e","last_reissued_at":"2026-05-18T02:44:57.539218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:57.539218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Sobolev and Hardy constants for the fractional Navier Laplacian","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":"2014-08-18T09:24:45Z","abstract_excerpt":"We prove the coincidence of the Sobolev and Hardy constants relative to the \"Dirichlet\" and \"Navier\" fractional Laplacians of any real order $m\\in(0,\\frac{n}{2})$ over bounded domains in $\\mathbb R^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3946","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":"1408.3946","created_at":"2026-05-18T02:44:57.539275+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.3946v1","created_at":"2026-05-18T02:44:57.539275+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3946","created_at":"2026-05-18T02:44:57.539275+00:00"},{"alias_kind":"pith_short_12","alias_value":"OT4YAD5EXEUB","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OT4YAD5EXEUBF47R","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OT4YAD5E","created_at":"2026-05-18T12:28:43.426989+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/OT4YAD5EXEUBF47RAHFTJZQXIL","json":"https://pith.science/pith/OT4YAD5EXEUBF47RAHFTJZQXIL.json","graph_json":"https://pith.science/api/pith-number/OT4YAD5EXEUBF47RAHFTJZQXIL/graph.json","events_json":"https://pith.science/api/pith-number/OT4YAD5EXEUBF47RAHFTJZQXIL/events.json","paper":"https://pith.science/paper/OT4YAD5E"},"agent_actions":{"view_html":"https://pith.science/pith/OT4YAD5EXEUBF47RAHFTJZQXIL","download_json":"https://pith.science/pith/OT4YAD5EXEUBF47RAHFTJZQXIL.json","view_paper":"https://pith.science/paper/OT4YAD5E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.3946&json=true","fetch_graph":"https://pith.science/api/pith-number/OT4YAD5EXEUBF47RAHFTJZQXIL/graph.json","fetch_events":"https://pith.science/api/pith-number/OT4YAD5EXEUBF47RAHFTJZQXIL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OT4YAD5EXEUBF47RAHFTJZQXIL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OT4YAD5EXEUBF47RAHFTJZQXIL/action/storage_attestation","attest_author":"https://pith.science/pith/OT4YAD5EXEUBF47RAHFTJZQXIL/action/author_attestation","sign_citation":"https://pith.science/pith/OT4YAD5EXEUBF47RAHFTJZQXIL/action/citation_signature","submit_replication":"https://pith.science/pith/OT4YAD5EXEUBF47RAHFTJZQXIL/action/replication_record"}},"created_at":"2026-05-18T02:44:57.539275+00:00","updated_at":"2026-05-18T02:44:57.539275+00:00"}