{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:AII4XGRESOH5KTYQPSFH6IGG4J","short_pith_number":"pith:AII4XGRE","schema_version":"1.0","canonical_sha256":"0211cb9a24938fd54f107c8a7f20c6e25a746794f9bf106ce5b7116fc40537de","source":{"kind":"arxiv","id":"2504.01359","version":4},"attestation_state":"computed","paper":{"title":"Monogenic functions over real alternative *-algebras: fundamental results and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guangbin Ren, Qinghai Huo, Zhenghua Xu","submitted_at":"2025-04-02T05:04:50Z","abstract_excerpt":"The concept of monogenic functions over real alternative $\\ast$-algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. This paper explores the fundamental properties of these monogenic functions, focusing on the Cauchy-Pompeiu integral formula and Taylor series expansion in hypercomplex subspaces, among which the non-commutativity and especially non-associativity of multiplications demand full considerations. The theory presented herein provides a robust fram"},"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":"2504.01359","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-04-02T05:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"cabf2a55074c6608d4e1758380f72672853e462f5a1115c4e8c92456cda27e81","abstract_canon_sha256":"92852b2ba6148f909c6022d83842385c0eeb93e2ac852c4bace8e209cc642554"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:49.352633Z","signature_b64":"Nbtvx1G+byoJBVFfknZfJjVY4iDt1bRJ3z0mDX0Ct+O51mMDyqaZ+DStyYbEdnvDjNCSHJ5UxNoVagfeAbIqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0211cb9a24938fd54f107c8a7f20c6e25a746794f9bf106ce5b7116fc40537de","last_reissued_at":"2026-05-20T00:02:49.351789Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:49.351789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monogenic functions over real alternative *-algebras: fundamental results and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guangbin Ren, Qinghai Huo, Zhenghua Xu","submitted_at":"2025-04-02T05:04:50Z","abstract_excerpt":"The concept of monogenic functions over real alternative $\\ast$-algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. This paper explores the fundamental properties of these monogenic functions, focusing on the Cauchy-Pompeiu integral formula and Taylor series expansion in hypercomplex subspaces, among which the non-commutativity and especially non-associativity of multiplications demand full considerations. The theory presented herein provides a robust fram"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.01359","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.01359/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":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":"2504.01359","created_at":"2026-05-20T00:02:49.351926+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.01359v4","created_at":"2026-05-20T00:02:49.351926+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.01359","created_at":"2026-05-20T00:02:49.351926+00:00"},{"alias_kind":"pith_short_12","alias_value":"AII4XGRESOH5","created_at":"2026-05-20T00:02:49.351926+00:00"},{"alias_kind":"pith_short_16","alias_value":"AII4XGRESOH5KTYQ","created_at":"2026-05-20T00:02:49.351926+00:00"},{"alias_kind":"pith_short_8","alias_value":"AII4XGRE","created_at":"2026-05-20T00:02:49.351926+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2506.08307","citing_title":"Monogenic functions over real alternative *-algebras: the several hypercomplex variables case","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2506.08307","citing_title":"Monogenic functions over real alternative *-algebras: the several hypercomplex variables case","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2604.12876","citing_title":"Fueter trees for Dunkl-regular functions over alternative *-algebras","ref_index":25,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AII4XGRESOH5KTYQPSFH6IGG4J","json":"https://pith.science/pith/AII4XGRESOH5KTYQPSFH6IGG4J.json","graph_json":"https://pith.science/api/pith-number/AII4XGRESOH5KTYQPSFH6IGG4J/graph.json","events_json":"https://pith.science/api/pith-number/AII4XGRESOH5KTYQPSFH6IGG4J/events.json","paper":"https://pith.science/paper/AII4XGRE"},"agent_actions":{"view_html":"https://pith.science/pith/AII4XGRESOH5KTYQPSFH6IGG4J","download_json":"https://pith.science/pith/AII4XGRESOH5KTYQPSFH6IGG4J.json","view_paper":"https://pith.science/paper/AII4XGRE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.01359&json=true","fetch_graph":"https://pith.science/api/pith-number/AII4XGRESOH5KTYQPSFH6IGG4J/graph.json","fetch_events":"https://pith.science/api/pith-number/AII4XGRESOH5KTYQPSFH6IGG4J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AII4XGRESOH5KTYQPSFH6IGG4J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AII4XGRESOH5KTYQPSFH6IGG4J/action/storage_attestation","attest_author":"https://pith.science/pith/AII4XGRESOH5KTYQPSFH6IGG4J/action/author_attestation","sign_citation":"https://pith.science/pith/AII4XGRESOH5KTYQPSFH6IGG4J/action/citation_signature","submit_replication":"https://pith.science/pith/AII4XGRESOH5KTYQPSFH6IGG4J/action/replication_record"}},"created_at":"2026-05-20T00:02:49.351926+00:00","updated_at":"2026-05-20T00:02:49.351926+00:00"}