{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OVL6FRUP7U4PSAGDECIDMPEFOR","short_pith_number":"pith:OVL6FRUP","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"},"canonical_sha256":"7557e2c68ffd38f900c32090363c857454b6913d2af633e791aa9d57bbea53a2","source":{"kind":"arxiv","id":"2506.08307","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08307","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08307v3","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08307","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"pith_short_12","alias_value":"OVL6FRUP7U4P","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"pith_short_16","alias_value":"OVL6FRUP7U4PSAGD","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"pith_short_8","alias_value":"OVL6FRUP","created_at":"2026-05-20T00:02:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OVL6FRUP7U4PSAGDECIDMPEFOR","target":"record","payload":{"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"},"canonical_sha256":"7557e2c68ffd38f900c32090363c857454b6913d2af633e791aa9d57bbea53a2","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"},"source_kind":"arxiv","source_id":"2506.08307","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"irl4XN7fYCJ3S0kjyFC/fMdIaGQBrI08F5MwL10+YXTg/4lN4koz0QALeicEW188injFL2v7xdQJupZIvhRUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:10:41.776794Z"},"content_sha256":"04248992b41a7d402e98156ca0724a9886383cfa715bf8aa35628bedb65664b9","schema_version":"1.0","event_id":"sha256:04248992b41a7d402e98156ca0724a9886383cfa715bf8aa35628bedb65664b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OVL6FRUP7U4PSAGDECIDMPEFOR","target":"graph","payload":{"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"},"verdict_id":"4e18f0ee-655a-485e-bfe0-a356765970e2"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZmH6NFU7XAZckAR1VVwI1fFBJoWs20od2P2XMwCri6QlWL4Ul5DXLDx7xJLFkHiQYlkbGVKOfcWQirQ/vT44AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:10:41.777806Z"},"content_sha256":"38f01496b9952438b1b615073e7ee635f6dbf44862a857c668b98ca6e4804c07","schema_version":"1.0","event_id":"sha256:38f01496b9952438b1b615073e7ee635f6dbf44862a857c668b98ca6e4804c07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/bundle.json","state_url":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T01:10:41Z","links":{"resolver":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR","bundle":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/bundle.json","state":"https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVL6FRUP7U4PSAGDECIDMPEFOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OVL6FRUP7U4PSAGDECIDMPEFOR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a0f860f9d237ec421325610340ab1bf717dc5c438cbde5785428f4b723208c5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-10T00:33:46Z","title_canon_sha256":"a4d65e020a91a908c8084f44bea96284202eaf5409b3a1d069a12f7b8970988e"},"schema_version":"1.0","source":{"id":"2506.08307","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08307","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08307v3","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08307","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"pith_short_12","alias_value":"OVL6FRUP7U4P","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"pith_short_16","alias_value":"OVL6FRUP7U4PSAGD","created_at":"2026-05-20T00:02:51Z"},{"alias_kind":"pith_short_8","alias_value":"OVL6FRUP","created_at":"2026-05-20T00:02:51Z"}],"graph_snapshots":[{"event_id":"sha256:38f01496b9952438b1b615073e7ee635f6dbf44862a857c668b98ca6e4804c07","target":"graph","created_at":"2026-05-20T00:02:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Introduces monogenic functions of several hypercomplex variables over real alternative *-algebras and establishes Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem."}],"snapshot_sha256":"434c0b409eeaf452c00f32be645ab2ee3a7928f0b261d070f1fee7c871781140"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8002aec0d1256210ce5be507c1363397daa970abe2a5f19884faded4474e911b"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.08307/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Chao Ding, Haiyan Wang, Zhenghua Xu","cross_cats":[],"headline":"Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-10T00:33:46Z","title":"Monogenic functions over real alternative *-algebras: the several hypercomplex variables case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08307","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-19T10:35:01.344546Z","id":"4e18f0ee-655a-485e-bfe0-a356765970e2","model_set":{"reader":"grok-4.3"},"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","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.","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.","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."}},"verdict_id":"4e18f0ee-655a-485e-bfe0-a356765970e2"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:04248992b41a7d402e98156ca0724a9886383cfa715bf8aa35628bedb65664b9","target":"record","created_at":"2026-05-20T00:02:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a0f860f9d237ec421325610340ab1bf717dc5c438cbde5785428f4b723208c5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-10T00:33:46Z","title_canon_sha256":"a4d65e020a91a908c8084f44bea96284202eaf5409b3a1d069a12f7b8970988e"},"schema_version":"1.0","source":{"id":"2506.08307","kind":"arxiv","version":3}},"canonical_sha256":"7557e2c68ffd38f900c32090363c857454b6913d2af633e791aa9d57bbea53a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7557e2c68ffd38f900c32090363c857454b6913d2af633e791aa9d57bbea53a2","first_computed_at":"2026-05-20T00:02:51.037427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:51.037427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qv2V4RSgQF67CnRSh/JH2eNbXsYwh4+tfj0PgCGyaIghQyxjfbOQs6Z36VpouTqjMpTytUy+RNZTmO0vA793CA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:51.038472Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08307","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04248992b41a7d402e98156ca0724a9886383cfa715bf8aa35628bedb65664b9","sha256:38f01496b9952438b1b615073e7ee635f6dbf44862a857c668b98ca6e4804c07"],"state_sha256":"47778eb0a17ca1d78073e2ab0ce51f6fdc535d76c79dbcb21d7fde5ba2fb01e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sB2dVhTwKooxCs3NtyXXdDz6v7Pzp6JzY80YfTtClU4VW3MPFAkf6IQ5u+2wCMzIYhf+xKIL0c0bD+IqGJd7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:10:41.781775Z","bundle_sha256":"fbaa02d5bca9ebe7f22cd249076a1f9e514130ed7326a63aa9af63eaae43cc84"}}