{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FMUBBNKF3CDKMIO2KBVVAFHX7W","short_pith_number":"pith:FMUBBNKF","schema_version":"1.0","canonical_sha256":"2b2810b545d886a621da506b5014f7fd84c54eb256b345508733c9b12472298a","source":{"kind":"arxiv","id":"1111.1806","version":1},"attestation_state":"computed","paper":{"title":"Deformation Expression for Elements of Algebras (V) - Diagonal matrix calculus and $*$-special functions -","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Akira Yoshioka, Hideki Omori, Naoya Miyazaki, Yoshiaki Maeda","submitted_at":"2011-11-08T05:31:16Z","abstract_excerpt":"In this note, we are interested in the *-version of various special functions. Noting that many special functions are defined by integrals involving the exponential functions, we define *-special functions by similar integral formula replacing exponential functions by *-exponential functions."},"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":"1111.1806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-08T05:31:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"2134f450a711fa6a8d72478f0b43ecbaa5dfed0414cafdeab59c580e7658f729","abstract_canon_sha256":"5374ddbd8ca2f92db3d9fbb283c927b3b75f0147a8b7aee60501c1eb345c655c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:24.699044Z","signature_b64":"ldSw89KrQQl0RXMZ91+v1+0PBDxWBBKW7Ku5FfnsgGexY+LZ73dtd+l+Xvp1ToR67bBu0Fz9a/H4GOQwTo1vAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b2810b545d886a621da506b5014f7fd84c54eb256b345508733c9b12472298a","last_reissued_at":"2026-05-18T04:09:24.698472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:24.698472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformation Expression for Elements of Algebras (V) - Diagonal matrix calculus and $*$-special functions -","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Akira Yoshioka, Hideki Omori, Naoya Miyazaki, Yoshiaki Maeda","submitted_at":"2011-11-08T05:31:16Z","abstract_excerpt":"In this note, we are interested in the *-version of various special functions. Noting that many special functions are defined by integrals involving the exponential functions, we define *-special functions by similar integral formula replacing exponential functions by *-exponential functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1806","kind":"arxiv","version":1},"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":"1111.1806","created_at":"2026-05-18T04:09:24.698552+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.1806v1","created_at":"2026-05-18T04:09:24.698552+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1806","created_at":"2026-05-18T04:09:24.698552+00:00"},{"alias_kind":"pith_short_12","alias_value":"FMUBBNKF3CDK","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FMUBBNKF3CDKMIO2","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FMUBBNKF","created_at":"2026-05-18T12:26:28.662955+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/FMUBBNKF3CDKMIO2KBVVAFHX7W","json":"https://pith.science/pith/FMUBBNKF3CDKMIO2KBVVAFHX7W.json","graph_json":"https://pith.science/api/pith-number/FMUBBNKF3CDKMIO2KBVVAFHX7W/graph.json","events_json":"https://pith.science/api/pith-number/FMUBBNKF3CDKMIO2KBVVAFHX7W/events.json","paper":"https://pith.science/paper/FMUBBNKF"},"agent_actions":{"view_html":"https://pith.science/pith/FMUBBNKF3CDKMIO2KBVVAFHX7W","download_json":"https://pith.science/pith/FMUBBNKF3CDKMIO2KBVVAFHX7W.json","view_paper":"https://pith.science/paper/FMUBBNKF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.1806&json=true","fetch_graph":"https://pith.science/api/pith-number/FMUBBNKF3CDKMIO2KBVVAFHX7W/graph.json","fetch_events":"https://pith.science/api/pith-number/FMUBBNKF3CDKMIO2KBVVAFHX7W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FMUBBNKF3CDKMIO2KBVVAFHX7W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FMUBBNKF3CDKMIO2KBVVAFHX7W/action/storage_attestation","attest_author":"https://pith.science/pith/FMUBBNKF3CDKMIO2KBVVAFHX7W/action/author_attestation","sign_citation":"https://pith.science/pith/FMUBBNKF3CDKMIO2KBVVAFHX7W/action/citation_signature","submit_replication":"https://pith.science/pith/FMUBBNKF3CDKMIO2KBVVAFHX7W/action/replication_record"}},"created_at":"2026-05-18T04:09:24.698552+00:00","updated_at":"2026-05-18T04:09:24.698552+00:00"}