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The system of EPD arises naturally from the differential equations which form a main body of the system characterizing the Gelfand hypergeometric function (Gelfand HGF) on the Grassmannian GM$(2,N)$. Using this link and the contiguity relations for the Gelfand HGF, which are constructed from root vectors for the root $\\epsilon_i-\\epsilon_j$ for $\\mathfrak{gl}(N)$, we show that the Gelfand HGF gives solutions"},"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":"2506.04638","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-06-05T05:18:22Z","cross_cats_sorted":[],"title_canon_sha256":"76c51b671de178b8c5644fd1ea321f7c23d8d228f7e873636212bb913274d0bf","abstract_canon_sha256":"7ec3594db75a314e72f53dc4e175739e7cc0a5e13b0e694545235cadf6133b9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:18.281359Z","signature_b64":"wIqh5T6CQKL8kRk/Ir9NUmrLsjrximaD8apJAxO4bF5DD11EtroQzPTyfm84WlYzivgqMLtJ+r/Psxy4ZQv5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f12fd85037e7dbe2b9ad64e4dc48556bac54c5a7960d32e7e3499f26f47792eb","last_reissued_at":"2026-07-05T11:16:18.280855Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:18.280855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hironobu Kimura","submitted_at":"2025-06-05T05:18:22Z","abstract_excerpt":"We construct solutions of the 2-dimensional Toda-Hirota equation (2dTHE) expressed by the solutions of the system of so-called Euler-Poisson-Darboux equations (EPD) in N complex variables. The system of EPD arises naturally from the differential equations which form a main body of the system characterizing the Gelfand hypergeometric function (Gelfand HGF) on the Grassmannian GM$(2,N)$. Using this link and the contiguity relations for the Gelfand HGF, which are constructed from root vectors for the root $\\epsilon_i-\\epsilon_j$ for $\\mathfrak{gl}(N)$, we show that the Gelfand HGF gives solutions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04638","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.04638/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.04638","created_at":"2026-07-05T11:16:18.280915+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.04638v1","created_at":"2026-07-05T11:16:18.280915+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04638","created_at":"2026-07-05T11:16:18.280915+00:00"},{"alias_kind":"pith_short_12","alias_value":"6EX5QUBX47N6","created_at":"2026-07-05T11:16:18.280915+00:00"},{"alias_kind":"pith_short_16","alias_value":"6EX5QUBX47N6FONN","created_at":"2026-07-05T11:16:18.280915+00:00"},{"alias_kind":"pith_short_8","alias_value":"6EX5QUBX","created_at":"2026-07-05T11:16:18.280915+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.11426","citing_title":"Gelfand hypergeometric functions as solutions to the 2-dimensional Toda-Hirota equations II","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6EX5QUBX47N6FONNMTSNYSCVNO","json":"https://pith.science/pith/6EX5QUBX47N6FONNMTSNYSCVNO.json","graph_json":"https://pith.science/api/pith-number/6EX5QUBX47N6FONNMTSNYSCVNO/graph.json","events_json":"https://pith.science/api/pith-number/6EX5QUBX47N6FONNMTSNYSCVNO/events.json","paper":"https://pith.science/paper/6EX5QUBX"},"agent_actions":{"view_html":"https://pith.science/pith/6EX5QUBX47N6FONNMTSNYSCVNO","download_json":"https://pith.science/pith/6EX5QUBX47N6FONNMTSNYSCVNO.json","view_paper":"https://pith.science/paper/6EX5QUBX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.04638&json=true","fetch_graph":"https://pith.science/api/pith-number/6EX5QUBX47N6FONNMTSNYSCVNO/graph.json","fetch_events":"https://pith.science/api/pith-number/6EX5QUBX47N6FONNMTSNYSCVNO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6EX5QUBX47N6FONNMTSNYSCVNO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6EX5QUBX47N6FONNMTSNYSCVNO/action/storage_attestation","attest_author":"https://pith.science/pith/6EX5QUBX47N6FONNMTSNYSCVNO/action/author_attestation","sign_citation":"https://pith.science/pith/6EX5QUBX47N6FONNMTSNYSCVNO/action/citation_signature","submit_replication":"https://pith.science/pith/6EX5QUBX47N6FONNMTSNYSCVNO/action/replication_record"}},"created_at":"2026-07-05T11:16:18.280915+00:00","updated_at":"2026-07-05T11:16:18.280915+00:00"}