{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IF6CIU3Q2P6TM4VSWEDJZJO5Z6","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":"00cda32ec1b1cb70502b84aadf4929f0e3ca3c041ff1377e9f9a46e79a8fa69a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T15:50:34Z","title_canon_sha256":"b0623076edf2659c506c9d50594cacf4fd3fbc8127d624dbad1bf3d3044d3e2d"},"schema_version":"1.0","source":{"id":"2505.22500","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22500","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22500v1","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22500","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"IF6CIU3Q2P6T","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"pith_short_16","alias_value":"IF6CIU3Q2P6TM4VS","created_at":"2026-07-05T11:11:25Z"},{"alias_kind":"pith_short_8","alias_value":"IF6CIU3Q","created_at":"2026-07-05T11:11:25Z"}],"graph_snapshots":[{"event_id":"sha256:2555d362d70af572c4f8365a22de9a9e3cecd23539cac3fa2ea15b776fdc74ea","target":"graph","created_at":"2026-07-05T11:11:25Z","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/2505.22500/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce bivariate polynomial sets of deformed $q$-Appell type, and we study the algebraic properties of these sets. We show the relation between deformed bivariate $q$-Appell polynomials and deformed homogeneous polynomials. Next, we give some of their characterizations and algebraic structure. Then, we introduce the deformed $q$-Appell operators and obtain Mehler's and Rogers-type formulas of quasi-$q$-Appell polynomials. Finally, some examples of polynomial sequences of deformed $q$-Appell type are given: Bernoulli, Euler, and Genocchi types.","authors_text":"Ronald Orozco L\\'opez","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T15:50:34Z","title":"Deformed Bivariate $q$-Appell Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22500","kind":"arxiv","version":1},"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":"sha256:6072cb0d762a3c9ceb77f71cbb68ae0d6d1e5878bf2c91defe3dd960590f6c17","target":"record","created_at":"2026-07-05T11:11:25Z","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":"00cda32ec1b1cb70502b84aadf4929f0e3ca3c041ff1377e9f9a46e79a8fa69a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T15:50:34Z","title_canon_sha256":"b0623076edf2659c506c9d50594cacf4fd3fbc8127d624dbad1bf3d3044d3e2d"},"schema_version":"1.0","source":{"id":"2505.22500","kind":"arxiv","version":1}},"canonical_sha256":"417c245370d3fd3672b2b1069ca5ddcf9cca416ef9211390ba9c2e3c7e23f0d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"417c245370d3fd3672b2b1069ca5ddcf9cca416ef9211390ba9c2e3c7e23f0d5","first_computed_at":"2026-07-05T11:11:25.306297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:25.306297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y5A2TXQHg4DiAUIuEddmeoYuM46dbaH6bsPOCD8kotiwUFvcHj3Kx0iJsGeOSs08Ly2Szvj7s+8Jbk+kdUUTAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:25.306934Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22500","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6072cb0d762a3c9ceb77f71cbb68ae0d6d1e5878bf2c91defe3dd960590f6c17","sha256:2555d362d70af572c4f8365a22de9a9e3cecd23539cac3fa2ea15b776fdc74ea"],"state_sha256":"a1c503a7cd19cfe0c72e7a2a6b44798e07ad1baa1d0702c92eee783836a10d36"}