{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5LCG7AZPLPMMGS7AGN7K4UYXRL","short_pith_number":"pith:5LCG7AZP","schema_version":"1.0","canonical_sha256":"eac46f832f5bd8c34be0337eae53178addedb5d34c4981d911e2748ad2d2636d","source":{"kind":"arxiv","id":"1512.09123","version":3},"attestation_state":"computed","paper":{"title":"Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"nlin.SI","authors_text":"George Berkeley, Sergei Igonin","submitted_at":"2015-12-30T20:53:17Z","abstract_excerpt":"Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations.\n  The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs.\n  Using this construction, from a given suitable DLR one can obtain many MTs of different "},"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":"1512.09123","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-12-30T20:53:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"75ff63ec5265805d192ca259e2d1ad4c1ecce9587b8b7213bbf827c717f7311d","abstract_canon_sha256":"641c1d8dfe568861b3321e3e6aa71c0a5623b37823ce4c495e0555f9052f38c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:49.938147Z","signature_b64":"z4N+0QnQnhQdTvht+suF1cx5Aq2FEWSG0KnfpjHEx5Z5udgVEBtfXgRYFUgBUPC8D9Fh721N12rS/DdoSBzSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eac46f832f5bd8c34be0337eae53178addedb5d34c4981d911e2748ad2d2636d","last_reissued_at":"2026-05-18T01:11:49.937800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:49.937800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"nlin.SI","authors_text":"George Berkeley, Sergei Igonin","submitted_at":"2015-12-30T20:53:17Z","abstract_excerpt":"Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations.\n  The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs.\n  Using this construction, from a given suitable DLR one can obtain many MTs of different "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09123","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":"1512.09123","created_at":"2026-05-18T01:11:49.937854+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.09123v3","created_at":"2026-05-18T01:11:49.937854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09123","created_at":"2026-05-18T01:11:49.937854+00:00"},{"alias_kind":"pith_short_12","alias_value":"5LCG7AZPLPMM","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5LCG7AZPLPMMGS7A","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5LCG7AZP","created_at":"2026-05-18T12:29:05.191682+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/5LCG7AZPLPMMGS7AGN7K4UYXRL","json":"https://pith.science/pith/5LCG7AZPLPMMGS7AGN7K4UYXRL.json","graph_json":"https://pith.science/api/pith-number/5LCG7AZPLPMMGS7AGN7K4UYXRL/graph.json","events_json":"https://pith.science/api/pith-number/5LCG7AZPLPMMGS7AGN7K4UYXRL/events.json","paper":"https://pith.science/paper/5LCG7AZP"},"agent_actions":{"view_html":"https://pith.science/pith/5LCG7AZPLPMMGS7AGN7K4UYXRL","download_json":"https://pith.science/pith/5LCG7AZPLPMMGS7AGN7K4UYXRL.json","view_paper":"https://pith.science/paper/5LCG7AZP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.09123&json=true","fetch_graph":"https://pith.science/api/pith-number/5LCG7AZPLPMMGS7AGN7K4UYXRL/graph.json","fetch_events":"https://pith.science/api/pith-number/5LCG7AZPLPMMGS7AGN7K4UYXRL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5LCG7AZPLPMMGS7AGN7K4UYXRL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5LCG7AZPLPMMGS7AGN7K4UYXRL/action/storage_attestation","attest_author":"https://pith.science/pith/5LCG7AZPLPMMGS7AGN7K4UYXRL/action/author_attestation","sign_citation":"https://pith.science/pith/5LCG7AZPLPMMGS7AGN7K4UYXRL/action/citation_signature","submit_replication":"https://pith.science/pith/5LCG7AZPLPMMGS7AGN7K4UYXRL/action/replication_record"}},"created_at":"2026-05-18T01:11:49.937854+00:00","updated_at":"2026-05-18T01:11:49.937854+00:00"}