{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:P4MKMGT24CBDKJVJMT2DXH4PZL","short_pith_number":"pith:P4MKMGT2","schema_version":"1.0","canonical_sha256":"7f18a61a7ae0823526a964f43b9f8fcacb57eac7ba29ed9e961cd4f041f0c2ae","source":{"kind":"arxiv","id":"1209.0400","version":2},"attestation_state":"computed","paper":{"title":"Definitions of complex order integrals and derivatives using operator approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Rakotoson Hanitriarivo, Raoelina Andriambololona, Tokiniaina Ranaivoson","submitted_at":"2012-08-31T08:16:52Z","abstract_excerpt":"For a complex number s, the s-order integral of function f fulfilling some conditions is defined as action of an operator, noted J^s, on f. The definition of the operator J^s is given firstly for the case of complex number s with positive real part. Then, using the fact that the operator of one order derivative, noted D^1, is the left- hand side inverse of the operator J^1, an s-order derivative operator, noted D^s, is also defined for all complex number s with positive real part. Finally, considering the relation J^s=D^(-s), the definition of the s-order integral and s-order derivative is ext"},"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":"1209.0400","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-08-31T08:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"04e7f4fda930f97c33410ba8480714b65d32b242b2b4fc1e404722dd4353c587","abstract_canon_sha256":"ff839c31af57f884c5e0435f55b2f2c9341debc95f30640e02123fe8576e172c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:29.482648Z","signature_b64":"FQb9VGIyVd/aZWJHbukpVPiu7SuQ82p3F/ub7CMc8acyWS7ZcT1f87hMJkBPefYeO64hszY8FbSmri+kux6QCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f18a61a7ae0823526a964f43b9f8fcacb57eac7ba29ed9e961cd4f041f0c2ae","last_reissued_at":"2026-05-18T03:31:29.482000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:29.482000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Definitions of complex order integrals and derivatives using operator approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Rakotoson Hanitriarivo, Raoelina Andriambololona, Tokiniaina Ranaivoson","submitted_at":"2012-08-31T08:16:52Z","abstract_excerpt":"For a complex number s, the s-order integral of function f fulfilling some conditions is defined as action of an operator, noted J^s, on f. The definition of the operator J^s is given firstly for the case of complex number s with positive real part. Then, using the fact that the operator of one order derivative, noted D^1, is the left- hand side inverse of the operator J^1, an s-order derivative operator, noted D^s, is also defined for all complex number s with positive real part. Finally, considering the relation J^s=D^(-s), the definition of the s-order integral and s-order derivative is ext"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0400","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":"1209.0400","created_at":"2026-05-18T03:31:29.482121+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.0400v2","created_at":"2026-05-18T03:31:29.482121+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0400","created_at":"2026-05-18T03:31:29.482121+00:00"},{"alias_kind":"pith_short_12","alias_value":"P4MKMGT24CBD","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"P4MKMGT24CBDKJVJ","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"P4MKMGT2","created_at":"2026-05-18T12:27:18.751474+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/P4MKMGT24CBDKJVJMT2DXH4PZL","json":"https://pith.science/pith/P4MKMGT24CBDKJVJMT2DXH4PZL.json","graph_json":"https://pith.science/api/pith-number/P4MKMGT24CBDKJVJMT2DXH4PZL/graph.json","events_json":"https://pith.science/api/pith-number/P4MKMGT24CBDKJVJMT2DXH4PZL/events.json","paper":"https://pith.science/paper/P4MKMGT2"},"agent_actions":{"view_html":"https://pith.science/pith/P4MKMGT24CBDKJVJMT2DXH4PZL","download_json":"https://pith.science/pith/P4MKMGT24CBDKJVJMT2DXH4PZL.json","view_paper":"https://pith.science/paper/P4MKMGT2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.0400&json=true","fetch_graph":"https://pith.science/api/pith-number/P4MKMGT24CBDKJVJMT2DXH4PZL/graph.json","fetch_events":"https://pith.science/api/pith-number/P4MKMGT24CBDKJVJMT2DXH4PZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P4MKMGT24CBDKJVJMT2DXH4PZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P4MKMGT24CBDKJVJMT2DXH4PZL/action/storage_attestation","attest_author":"https://pith.science/pith/P4MKMGT24CBDKJVJMT2DXH4PZL/action/author_attestation","sign_citation":"https://pith.science/pith/P4MKMGT24CBDKJVJMT2DXH4PZL/action/citation_signature","submit_replication":"https://pith.science/pith/P4MKMGT24CBDKJVJMT2DXH4PZL/action/replication_record"}},"created_at":"2026-05-18T03:31:29.482121+00:00","updated_at":"2026-05-18T03:31:29.482121+00:00"}