{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OVL6FRUP7U4PSAGDECIDMPEFOR","short_pith_number":"pith:OVL6FRUP","schema_version":"1.0","canonical_sha256":"7557e2c68ffd38f900c32090363c857454b6913d2af633e791aa9d57bbea53a2","source":{"kind":"arxiv","id":"2506.08307","version":3},"attestation_state":"computed","paper":{"title":"Monogenic functions over real alternative *-algebras: the several hypercomplex variables case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","cross_cats":[],"primary_cat":"math.CV","authors_text":"Chao Ding, Haiyan Wang, Zhenghua Xu","submitted_at":"2025-06-10T00:33:46Z","abstract_excerpt":"The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative $\\ast$-algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative $\\ast$-algebras, which naturally extends the theory of several complex variables to a very general setting. In"},"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":true},"canonical_record":{"source":{"id":"2506.08307","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-10T00:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"a4d65e020a91a908c8084f44bea96284202eaf5409b3a1d069a12f7b8970988e","abstract_canon_sha256":"a0f860f9d237ec421325610340ab1bf717dc5c438cbde5785428f4b723208c5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:51.038472Z","signature_b64":"Qv2V4RSgQF67CnRSh/JH2eNbXsYwh4+tfj0PgCGyaIghQyxjfbOQs6Z36VpouTqjMpTytUy+RNZTmO0vA793CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7557e2c68ffd38f900c32090363c857454b6913d2af633e791aa9d57bbea53a2","last_reissued_at":"2026-05-20T00:02:51.037427Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:51.037427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monogenic functions over real alternative *-algebras: the several hypercomplex variables case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","cross_cats":[],"primary_cat":"math.CV","authors_text":"Chao Ding, Haiyan Wang, Zhenghua Xu","submitted_at":"2025-06-10T00:33:46Z","abstract_excerpt":"The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative $\\ast$-algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative $\\ast$-algebras, which naturally extends the theory of several complex variables to a very general setting. In"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We initiate the study of monogenic functions of several hypercomplex variables over real alternative *-algebras and develop fundamental properties such as the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the single-variable monogenic theory over real alternative *-algebras extends directly to the several-variable case while preserving the listed integral and extension properties without additional structural restrictions on the algebra or the functions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces monogenic functions of several hypercomplex variables over real alternative *-algebras and establishes Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"434c0b409eeaf452c00f32be645ab2ee3a7928f0b261d070f1fee7c871781140"},"source":{"id":"2506.08307","kind":"arxiv","version":3},"verdict":{"id":"4e18f0ee-655a-485e-bfe0-a356765970e2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T10:35:01.344546Z","strongest_claim":"We initiate the study of monogenic functions of several hypercomplex variables over real alternative *-algebras and develop fundamental properties such as the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","one_line_summary":"Introduces monogenic functions of several hypercomplex variables over real alternative *-algebras and establishes Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the single-variable monogenic theory over real alternative *-algebras extends directly to the several-variable case while preserving the listed integral and extension properties without additional structural restrictions on the algebra or the functions.","pith_extraction_headline":"Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08307/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8002aec0d1256210ce5be507c1363397daa970abe2a5f19884faded4474e911b"},"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":"2506.08307","created_at":"2026-05-20T00:02:51.037566+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.08307v3","created_at":"2026-05-20T00:02:51.037566+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08307","created_at":"2026-05-20T00:02:51.037566+00:00"},{"alias_kind":"pith_short_12","alias_value":"OVL6FRUP7U4P","created_at":"2026-05-20T00:02:51.037566+00:00"},{"alias_kind":"pith_short_16","alias_value":"OVL6FRUP7U4PSAGD","created_at":"2026-05-20T00:02:51.037566+00:00"},{"alias_kind":"pith_short_8","alias_value":"OVL6FRUP","created_at":"2026-05-20T00:02:51.037566+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR","json":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR.json","graph_json":"https://pith.science/api/pith-number/OVL6FRUP7U4PSAGDECIDMPEFOR/graph.json","events_json":"https://pith.science/api/pith-number/OVL6FRUP7U4PSAGDECIDMPEFOR/events.json","paper":"https://pith.science/paper/OVL6FRUP"},"agent_actions":{"view_html":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR","download_json":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR.json","view_paper":"https://pith.science/paper/OVL6FRUP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.08307&json=true","fetch_graph":"https://pith.science/api/pith-number/OVL6FRUP7U4PSAGDECIDMPEFOR/graph.json","fetch_events":"https://pith.science/api/pith-number/OVL6FRUP7U4PSAGDECIDMPEFOR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/action/storage_attestation","attest_author":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/action/author_attestation","sign_citation":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/action/citation_signature","submit_replication":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/action/replication_record"}},"created_at":"2026-05-20T00:02:51.037566+00:00","updated_at":"2026-05-20T00:02:51.037566+00:00"}