{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:67J6MUMZALZE2HSYT7QQPIHTQI","short_pith_number":"pith:67J6MUMZ","schema_version":"1.0","canonical_sha256":"f7d3e6519902f24d1e589fe107a0f38234a528c0dac0584cec710b2ead8abdfc","source":{"kind":"arxiv","id":"1308.3606","version":2},"attestation_state":"computed","paper":{"title":"On fractional Laplacians","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":"2013-08-16T11:29:25Z","abstract_excerpt":"We compare two natural types of fractional Laplacians $(-\\Delta)^s$, \"Navier\" and \"Dirichlet\" ones. We show that for $0<s<1$ their difference is positive definite and positivity preserving. Then we prove the coincidence of the Sobolev constants for these two fractional Laplacians."},"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":"1308.3606","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-16T11:29:25Z","cross_cats_sorted":[],"title_canon_sha256":"f6196e232e69bfaf174b134bc6074a366611482d963f2bc97853c76d8ba356ae","abstract_canon_sha256":"4d163fc60a74f81c94f7b279c60568445f687b01940d8214a2435e6a546d828b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:12.605385Z","signature_b64":"nG2gIJlcZy21F5xB0nlzOKl8V5jnYsg7XK1/qfWJCnSzXxX+hQ95V5yH2u3zzvpEn+58e5TPwpqQIVylsVbUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7d3e6519902f24d1e589fe107a0f38234a528c0dac0584cec710b2ead8abdfc","last_reissued_at":"2026-05-18T03:11:12.604717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:12.604717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On fractional Laplacians","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":"2013-08-16T11:29:25Z","abstract_excerpt":"We compare two natural types of fractional Laplacians $(-\\Delta)^s$, \"Navier\" and \"Dirichlet\" ones. We show that for $0<s<1$ their difference is positive definite and positivity preserving. Then we prove the coincidence of the Sobolev constants for these two fractional Laplacians."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3606","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":"1308.3606","created_at":"2026-05-18T03:11:12.604840+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.3606v2","created_at":"2026-05-18T03:11:12.604840+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3606","created_at":"2026-05-18T03:11:12.604840+00:00"},{"alias_kind":"pith_short_12","alias_value":"67J6MUMZALZE","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"67J6MUMZALZE2HSY","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"67J6MUMZ","created_at":"2026-05-18T12:27:36.564083+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/67J6MUMZALZE2HSYT7QQPIHTQI","json":"https://pith.science/pith/67J6MUMZALZE2HSYT7QQPIHTQI.json","graph_json":"https://pith.science/api/pith-number/67J6MUMZALZE2HSYT7QQPIHTQI/graph.json","events_json":"https://pith.science/api/pith-number/67J6MUMZALZE2HSYT7QQPIHTQI/events.json","paper":"https://pith.science/paper/67J6MUMZ"},"agent_actions":{"view_html":"https://pith.science/pith/67J6MUMZALZE2HSYT7QQPIHTQI","download_json":"https://pith.science/pith/67J6MUMZALZE2HSYT7QQPIHTQI.json","view_paper":"https://pith.science/paper/67J6MUMZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.3606&json=true","fetch_graph":"https://pith.science/api/pith-number/67J6MUMZALZE2HSYT7QQPIHTQI/graph.json","fetch_events":"https://pith.science/api/pith-number/67J6MUMZALZE2HSYT7QQPIHTQI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/67J6MUMZALZE2HSYT7QQPIHTQI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/67J6MUMZALZE2HSYT7QQPIHTQI/action/storage_attestation","attest_author":"https://pith.science/pith/67J6MUMZALZE2HSYT7QQPIHTQI/action/author_attestation","sign_citation":"https://pith.science/pith/67J6MUMZALZE2HSYT7QQPIHTQI/action/citation_signature","submit_replication":"https://pith.science/pith/67J6MUMZALZE2HSYT7QQPIHTQI/action/replication_record"}},"created_at":"2026-05-18T03:11:12.604840+00:00","updated_at":"2026-05-18T03:11:12.604840+00:00"}