{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:6YJRAULHCL23BQCJJIYZMX27EM","short_pith_number":"pith:6YJRAULH","schema_version":"1.0","canonical_sha256":"f61310516712f5b0c0494a31965f5f23119a8b40e40be66e41018c0b2dd27f1d","source":{"kind":"arxiv","id":"math/0703893","version":3},"attestation_state":"computed","paper":{"title":"Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Alexander Varchenko, Evgeny Mukhin, Vitaly Tarasov","submitted_at":"2007-03-29T17:27:28Z","abstract_excerpt":"Let $M$ be the tensor product of finite-dimensional polynomial evaluation Yangian $Y(gl_N)$-modules. Consider the universal difference operator $D = \\sum_{k=0}^N (-1)^k T_k(u) e^{-k\\partial_u}$ whose coefficients $T_k(u): M \\to M$ are the XXX transfer matrices associated with $M$. We show that the difference equation $Df = 0$ for an $M$-valued function $f$ has a basis of solutions consisting of quasi-exponentials. We prove the same for the universal differential operator $D = \\sum_{k=0}^N (-1)^k S_k(u) \\partial_u^{N-k}$ whose coefficients $S_k(u) : M \\to M$ are the Gaudin transfer matrices ass"},"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":"math/0703893","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2007-03-29T17:27:28Z","cross_cats_sorted":[],"title_canon_sha256":"08e516fcdb6f7559a45c5820b25f1df116a478767b8a8caab020ba598012f481","abstract_canon_sha256":"c655db5267be466ddb1c7226d7b3e8c52465a980c89fbfbef40249a4ddc4b2ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:38.555875Z","signature_b64":"eMXZJLKq1PVCCngDMos1JxF3/V8avaNHy6jsV70JXpgbhywG0u0Rv21kKGF1BdVjYKri36dgyqDAdvzmIJyQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f61310516712f5b0c0494a31965f5f23119a8b40e40be66e41018c0b2dd27f1d","last_reissued_at":"2026-05-18T03:30:38.555079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:38.555079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Alexander Varchenko, Evgeny Mukhin, Vitaly Tarasov","submitted_at":"2007-03-29T17:27:28Z","abstract_excerpt":"Let $M$ be the tensor product of finite-dimensional polynomial evaluation Yangian $Y(gl_N)$-modules. Consider the universal difference operator $D = \\sum_{k=0}^N (-1)^k T_k(u) e^{-k\\partial_u}$ whose coefficients $T_k(u): M \\to M$ are the XXX transfer matrices associated with $M$. We show that the difference equation $Df = 0$ for an $M$-valued function $f$ has a basis of solutions consisting of quasi-exponentials. We prove the same for the universal differential operator $D = \\sum_{k=0}^N (-1)^k S_k(u) \\partial_u^{N-k}$ whose coefficients $S_k(u) : M \\to M$ are the Gaudin transfer matrices ass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703893","kind":"arxiv","version":3},"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":"math/0703893","created_at":"2026-05-18T03:30:38.555208+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0703893v3","created_at":"2026-05-18T03:30:38.555208+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703893","created_at":"2026-05-18T03:30:38.555208+00:00"},{"alias_kind":"pith_short_12","alias_value":"6YJRAULHCL23","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6YJRAULHCL23BQCJ","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6YJRAULH","created_at":"2026-05-18T12:25:55.427421+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/6YJRAULHCL23BQCJJIYZMX27EM","json":"https://pith.science/pith/6YJRAULHCL23BQCJJIYZMX27EM.json","graph_json":"https://pith.science/api/pith-number/6YJRAULHCL23BQCJJIYZMX27EM/graph.json","events_json":"https://pith.science/api/pith-number/6YJRAULHCL23BQCJJIYZMX27EM/events.json","paper":"https://pith.science/paper/6YJRAULH"},"agent_actions":{"view_html":"https://pith.science/pith/6YJRAULHCL23BQCJJIYZMX27EM","download_json":"https://pith.science/pith/6YJRAULHCL23BQCJJIYZMX27EM.json","view_paper":"https://pith.science/paper/6YJRAULH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0703893&json=true","fetch_graph":"https://pith.science/api/pith-number/6YJRAULHCL23BQCJJIYZMX27EM/graph.json","fetch_events":"https://pith.science/api/pith-number/6YJRAULHCL23BQCJJIYZMX27EM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6YJRAULHCL23BQCJJIYZMX27EM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6YJRAULHCL23BQCJJIYZMX27EM/action/storage_attestation","attest_author":"https://pith.science/pith/6YJRAULHCL23BQCJJIYZMX27EM/action/author_attestation","sign_citation":"https://pith.science/pith/6YJRAULHCL23BQCJJIYZMX27EM/action/citation_signature","submit_replication":"https://pith.science/pith/6YJRAULHCL23BQCJJIYZMX27EM/action/replication_record"}},"created_at":"2026-05-18T03:30:38.555208+00:00","updated_at":"2026-05-18T03:30:38.555208+00:00"}