{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:I7M7MSYYWONTCXK2TGYYPQIDSP","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":"181d5d56c387f2f016930751082370c748abdf5a9d9dd08a176bddf23c15dfd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-03-17T04:46:43Z","title_canon_sha256":"c45717ce4e2ab98c63ae6100027533d62739881e2ff3e7befad19113274ce009"},"schema_version":"1.0","source":{"id":"2003.11419","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.11419","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"2003.11419v2","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.11419","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"I7M7MSYYWONT","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"pith_short_16","alias_value":"I7M7MSYYWONTCXK2","created_at":"2026-06-02T01:03:27Z"},{"alias_kind":"pith_short_8","alias_value":"I7M7MSYY","created_at":"2026-06-02T01:03:27Z"}],"graph_snapshots":[{"event_id":"sha256:dddede5836857c40a0df120efb9ccd4b87709eb0b4dd9403f313779e9cb12e4e","target":"graph","created_at":"2026-06-02T01:03:27Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2003.11419/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we introduce incomplete Lauricella matrix functions (ILMFs) of $n$ variables through application of the incomplete Pochhammer matrix symbols. Furthermore there is derivation of certain properties; matrix differential equation, integral formula, recursion formula and differentiation formula of the ILMFs. We also establish the connection between these matrix functions and other peculiar matrix functions; incomplete gamma matrix function, Laguerre, Bessel and modified Bessel matrix functions.","authors_text":"Ashish Verma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-03-17T04:46:43Z","title":"On the incomplete Lauricella matrix functions of several variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.11419","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4dac4b68e23a906b252ee8e12943908482ed4b81d5f1b0806d81fd6d55ce0797","target":"record","created_at":"2026-06-02T01:03:27Z","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":"181d5d56c387f2f016930751082370c748abdf5a9d9dd08a176bddf23c15dfd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-03-17T04:46:43Z","title_canon_sha256":"c45717ce4e2ab98c63ae6100027533d62739881e2ff3e7befad19113274ce009"},"schema_version":"1.0","source":{"id":"2003.11419","kind":"arxiv","version":2}},"canonical_sha256":"47d9f64b18b39b315d5a99b187c10393fdeba8f0121b657692b65130b0ff11e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47d9f64b18b39b315d5a99b187c10393fdeba8f0121b657692b65130b0ff11e2","first_computed_at":"2026-06-02T01:03:27.435259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:27.435259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1p9d1wsFl1fYPaUfn81D9A1tknqPMKzjb7PIJ8ejYo1xqSUhKpALAh/D02V/Yn46fS0xX7oaP3pfSyS5xu51CQ==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:27.435631Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.11419","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4dac4b68e23a906b252ee8e12943908482ed4b81d5f1b0806d81fd6d55ce0797","sha256:dddede5836857c40a0df120efb9ccd4b87709eb0b4dd9403f313779e9cb12e4e"],"state_sha256":"4333c25df401f4c003252ad79c88f54f5c92368527713b4ef9dbdfdfd3f1e7ee"}