{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FUQHR6IU4AXSEPQTCEQOCKGHTP","short_pith_number":"pith:FUQHR6IU","schema_version":"1.0","canonical_sha256":"2d2078f914e02f223e131120e128c79be7d9f7969c7de4fa1216f85d5ba37ba2","source":{"kind":"arxiv","id":"1508.04156","version":1},"attestation_state":"computed","paper":{"title":"An extension problem for the fractional derivative defined by Marchaud","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudia Bucur, Fausto Ferrari","submitted_at":"2015-08-17T20:54:02Z","abstract_excerpt":"We prove that the (nonlocal) Marchaud fractional derivative in $\\mathbb{R}$ can be obtained from a parabolic extension problem with an extra (positive) variable, as the operator that maps the heat conduction equation to the Neumann condition. Some properties of the fractional derivative are deduced from those of the local operator. In particular we prove a Harnack principle for Marchaud-stationary functions."},"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":"1508.04156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-17T20:54:02Z","cross_cats_sorted":[],"title_canon_sha256":"41d702cea460b226a534b0c0b3116a4554fc2c050d6c29cc219088e2cef6237d","abstract_canon_sha256":"548b653d1b38cffa8d41d0813667dca4b8b877452310307b8b8a9de4af1e1127"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:42.144624Z","signature_b64":"Y3NHRRi5OWpTO8xdOnK+RHHCerxIZganyMgrjdkgRX/FAcuxRCs00QNvMBQ96dxI/dCqkqX2Uqco/eDZWVRuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d2078f914e02f223e131120e128c79be7d9f7969c7de4fa1216f85d5ba37ba2","last_reissued_at":"2026-05-18T01:09:42.144219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:42.144219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An extension problem for the fractional derivative defined by Marchaud","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudia Bucur, Fausto Ferrari","submitted_at":"2015-08-17T20:54:02Z","abstract_excerpt":"We prove that the (nonlocal) Marchaud fractional derivative in $\\mathbb{R}$ can be obtained from a parabolic extension problem with an extra (positive) variable, as the operator that maps the heat conduction equation to the Neumann condition. Some properties of the fractional derivative are deduced from those of the local operator. In particular we prove a Harnack principle for Marchaud-stationary functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04156","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":"1508.04156","created_at":"2026-05-18T01:09:42.144277+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.04156v1","created_at":"2026-05-18T01:09:42.144277+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04156","created_at":"2026-05-18T01:09:42.144277+00:00"},{"alias_kind":"pith_short_12","alias_value":"FUQHR6IU4AXS","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"FUQHR6IU4AXSEPQT","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"FUQHR6IU","created_at":"2026-05-18T12:29:22.688609+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/FUQHR6IU4AXSEPQTCEQOCKGHTP","json":"https://pith.science/pith/FUQHR6IU4AXSEPQTCEQOCKGHTP.json","graph_json":"https://pith.science/api/pith-number/FUQHR6IU4AXSEPQTCEQOCKGHTP/graph.json","events_json":"https://pith.science/api/pith-number/FUQHR6IU4AXSEPQTCEQOCKGHTP/events.json","paper":"https://pith.science/paper/FUQHR6IU"},"agent_actions":{"view_html":"https://pith.science/pith/FUQHR6IU4AXSEPQTCEQOCKGHTP","download_json":"https://pith.science/pith/FUQHR6IU4AXSEPQTCEQOCKGHTP.json","view_paper":"https://pith.science/paper/FUQHR6IU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.04156&json=true","fetch_graph":"https://pith.science/api/pith-number/FUQHR6IU4AXSEPQTCEQOCKGHTP/graph.json","fetch_events":"https://pith.science/api/pith-number/FUQHR6IU4AXSEPQTCEQOCKGHTP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FUQHR6IU4AXSEPQTCEQOCKGHTP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FUQHR6IU4AXSEPQTCEQOCKGHTP/action/storage_attestation","attest_author":"https://pith.science/pith/FUQHR6IU4AXSEPQTCEQOCKGHTP/action/author_attestation","sign_citation":"https://pith.science/pith/FUQHR6IU4AXSEPQTCEQOCKGHTP/action/citation_signature","submit_replication":"https://pith.science/pith/FUQHR6IU4AXSEPQTCEQOCKGHTP/action/replication_record"}},"created_at":"2026-05-18T01:09:42.144277+00:00","updated_at":"2026-05-18T01:09:42.144277+00:00"}