{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:T5LVIO6GH4VFVETDN3CKBLFZ33","short_pith_number":"pith:T5LVIO6G","schema_version":"1.0","canonical_sha256":"9f57543bc63f2a5a92636ec4a0acb9deeabe0648431105a15049a9d93da4d0c2","source":{"kind":"arxiv","id":"1506.07071","version":4},"attestation_state":"computed","paper":{"title":"Generalized adjoint actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Arkady Berenstein, Vladimir Retakh","submitted_at":"2015-06-23T16:10:04Z","abstract_excerpt":"The aim of this paper is to generalize the classical formula $e^xye^{-x}=\\sum\\limits_{k\\ge 0} \\frac{1}{k!} (ad~x)^k(y)$ by replacing $e^x$ with any formal power series $\\displaystyle {f(x)=1+\\sum_{k\\ge 1} a_kx^k}$. We also obtain combinatorial applications to $q$-exponentials, $q$-binomials, and Hall-Littlewood polynomials."},"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":"1506.07071","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-23T16:10:04Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"3d6784d9c57c7c19946245b26c9deb50b61746df086658b32abafac779441a73","abstract_canon_sha256":"4c7a79e41dba04a39e03d91fe4a94afaab486b1902ddda170641a63113c16b04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:25.412478Z","signature_b64":"a4q/wK5XTph+Bytn9QxPOoDU4vp3mO+MpxP+t9u6Wc3k5n79yrO6nEieoNU+dWaMAsVKABn05eP3LNJ504tYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f57543bc63f2a5a92636ec4a0acb9deeabe0648431105a15049a9d93da4d0c2","last_reissued_at":"2026-05-18T01:36:25.412006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:25.412006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized adjoint actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Arkady Berenstein, Vladimir Retakh","submitted_at":"2015-06-23T16:10:04Z","abstract_excerpt":"The aim of this paper is to generalize the classical formula $e^xye^{-x}=\\sum\\limits_{k\\ge 0} \\frac{1}{k!} (ad~x)^k(y)$ by replacing $e^x$ with any formal power series $\\displaystyle {f(x)=1+\\sum_{k\\ge 1} a_kx^k}$. We also obtain combinatorial applications to $q$-exponentials, $q$-binomials, and Hall-Littlewood polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07071","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":""},"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":"1506.07071","created_at":"2026-05-18T01:36:25.412078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.07071v4","created_at":"2026-05-18T01:36:25.412078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07071","created_at":"2026-05-18T01:36:25.412078+00:00"},{"alias_kind":"pith_short_12","alias_value":"T5LVIO6GH4VF","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"T5LVIO6GH4VFVETD","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"T5LVIO6G","created_at":"2026-05-18T12:29:42.218222+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/T5LVIO6GH4VFVETDN3CKBLFZ33","json":"https://pith.science/pith/T5LVIO6GH4VFVETDN3CKBLFZ33.json","graph_json":"https://pith.science/api/pith-number/T5LVIO6GH4VFVETDN3CKBLFZ33/graph.json","events_json":"https://pith.science/api/pith-number/T5LVIO6GH4VFVETDN3CKBLFZ33/events.json","paper":"https://pith.science/paper/T5LVIO6G"},"agent_actions":{"view_html":"https://pith.science/pith/T5LVIO6GH4VFVETDN3CKBLFZ33","download_json":"https://pith.science/pith/T5LVIO6GH4VFVETDN3CKBLFZ33.json","view_paper":"https://pith.science/paper/T5LVIO6G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.07071&json=true","fetch_graph":"https://pith.science/api/pith-number/T5LVIO6GH4VFVETDN3CKBLFZ33/graph.json","fetch_events":"https://pith.science/api/pith-number/T5LVIO6GH4VFVETDN3CKBLFZ33/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T5LVIO6GH4VFVETDN3CKBLFZ33/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T5LVIO6GH4VFVETDN3CKBLFZ33/action/storage_attestation","attest_author":"https://pith.science/pith/T5LVIO6GH4VFVETDN3CKBLFZ33/action/author_attestation","sign_citation":"https://pith.science/pith/T5LVIO6GH4VFVETDN3CKBLFZ33/action/citation_signature","submit_replication":"https://pith.science/pith/T5LVIO6GH4VFVETDN3CKBLFZ33/action/replication_record"}},"created_at":"2026-05-18T01:36:25.412078+00:00","updated_at":"2026-05-18T01:36:25.412078+00:00"}