{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NVM3OSQOJWZV6JCUTULUFOZCAW","short_pith_number":"pith:NVM3OSQO","schema_version":"1.0","canonical_sha256":"6d59b74a0e4db35f24549d1742bb2205af35b27dd4f4ca981e1d5c435e4ccdb0","source":{"kind":"arxiv","id":"1210.5038","version":1},"attestation_state":"computed","paper":{"title":"Regular solution and lattice miura transformation of bigraded Toda Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Chuanzhong Li, Jingsong He","submitted_at":"2012-10-18T07:24:34Z","abstract_excerpt":"In this paper, we give finite dimensional exponential solutions of the bigraded Toda Hierarchy(BTH). As an specific example of exponential solutions of the BTH, we consider a regular solution for the $(1,2)$-BTH with $3\\times 3$-sized Lax matrix, and discuss some geometric structure of the solution from which the difference between $(1,2)$-BTH and original Toda hierarchy is shown. After this, we construct another kind of Lax representation of $(N,1)$-bigraded Toda hierarchy($(N,1)$-BTH) which does not use the fractional operator of Lax operator. Then we introduce lattice Miura transformation o"},"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":"1210.5038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-10-18T07:24:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a9a0dd4447fce3ff8cb31e1ebaa0609fe50079c3bc93be955ddfcc52b77719fe","abstract_canon_sha256":"387e4546353e4a9737e67d62ea020cb45c88cada96330a8bfab07fde2cacdaa8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:54.468089Z","signature_b64":"dDceruyRZoXt5gYuA8MoTn9U3KwUpuhjtsF57Rl8UtyH+NOXkA4gn6YQoCkpN7i2AJ+3LBLHcgG3x0LNhOO1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d59b74a0e4db35f24549d1742bb2205af35b27dd4f4ca981e1d5c435e4ccdb0","last_reissued_at":"2026-05-18T03:42:54.467519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:54.467519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regular solution and lattice miura transformation of bigraded Toda Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Chuanzhong Li, Jingsong He","submitted_at":"2012-10-18T07:24:34Z","abstract_excerpt":"In this paper, we give finite dimensional exponential solutions of the bigraded Toda Hierarchy(BTH). As an specific example of exponential solutions of the BTH, we consider a regular solution for the $(1,2)$-BTH with $3\\times 3$-sized Lax matrix, and discuss some geometric structure of the solution from which the difference between $(1,2)$-BTH and original Toda hierarchy is shown. After this, we construct another kind of Lax representation of $(N,1)$-bigraded Toda hierarchy($(N,1)$-BTH) which does not use the fractional operator of Lax operator. Then we introduce lattice Miura transformation o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5038","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":"1210.5038","created_at":"2026-05-18T03:42:54.467616+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.5038v1","created_at":"2026-05-18T03:42:54.467616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5038","created_at":"2026-05-18T03:42:54.467616+00:00"},{"alias_kind":"pith_short_12","alias_value":"NVM3OSQOJWZV","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NVM3OSQOJWZV6JCU","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NVM3OSQO","created_at":"2026-05-18T12:27:16.716162+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/NVM3OSQOJWZV6JCUTULUFOZCAW","json":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW.json","graph_json":"https://pith.science/api/pith-number/NVM3OSQOJWZV6JCUTULUFOZCAW/graph.json","events_json":"https://pith.science/api/pith-number/NVM3OSQOJWZV6JCUTULUFOZCAW/events.json","paper":"https://pith.science/paper/NVM3OSQO"},"agent_actions":{"view_html":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW","download_json":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW.json","view_paper":"https://pith.science/paper/NVM3OSQO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.5038&json=true","fetch_graph":"https://pith.science/api/pith-number/NVM3OSQOJWZV6JCUTULUFOZCAW/graph.json","fetch_events":"https://pith.science/api/pith-number/NVM3OSQOJWZV6JCUTULUFOZCAW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/action/storage_attestation","attest_author":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/action/author_attestation","sign_citation":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/action/citation_signature","submit_replication":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/action/replication_record"}},"created_at":"2026-05-18T03:42:54.467616+00:00","updated_at":"2026-05-18T03:42:54.467616+00:00"}