{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:YZQKUDMHXBB2IWRTZLZVPF2L3Z","short_pith_number":"pith:YZQKUDMH","schema_version":"1.0","canonical_sha256":"c660aa0d87b843a45a33caf357974bde4a040b4a21561bcf769987602405dc6b","source":{"kind":"arxiv","id":"2411.15496","version":1},"attestation_state":"computed","paper":{"title":"Legendre transformations of a class of generalized Frobenius manifolds and the associated integrable hierarchies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Haonan Qu, Si-Qi Liu, Youjin Zhang","submitted_at":"2024-11-23T09:00:35Z","abstract_excerpt":"For two generalized Frobenius manifolds related by a Legendre-type transformation, we show that the associated integrable hierarchies of hydrodynamic type, which are called the Legendre-extended Principal Hierarchies, are related by a certain linear reciprocal transformation; we also show, under the semisimplicity condition, that the topological deformations of these Legendre-extended Principal Hierarchies are related by the same linear reciprocal transformation."},"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":"2411.15496","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-11-23T09:00:35Z","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"title_canon_sha256":"d2a0399fbc2a0aae7cb58ed1c841379b0fd3a04338e5c22d4708d8e69127c9c7","abstract_canon_sha256":"fa4416403e349bb5870f587823779e193b8d73b54b5709ef96ac540dee880ac0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:35.878038Z","signature_b64":"jW6LfPAMswtgJ2mqu3o+xKwJzuIeWd1+tQN6uW4m8P27kjAFCRdpt6qSXystv82QXprAZre270RQTzEGM+v7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c660aa0d87b843a45a33caf357974bde4a040b4a21561bcf769987602405dc6b","last_reissued_at":"2026-07-05T09:39:35.877637Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:35.877637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Legendre transformations of a class of generalized Frobenius manifolds and the associated integrable hierarchies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Haonan Qu, Si-Qi Liu, Youjin Zhang","submitted_at":"2024-11-23T09:00:35Z","abstract_excerpt":"For two generalized Frobenius manifolds related by a Legendre-type transformation, we show that the associated integrable hierarchies of hydrodynamic type, which are called the Legendre-extended Principal Hierarchies, are related by a certain linear reciprocal transformation; we also show, under the semisimplicity condition, that the topological deformations of these Legendre-extended Principal Hierarchies are related by the same linear reciprocal transformation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15496","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/2411.15496/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":"2411.15496","created_at":"2026-07-05T09:39:35.877694+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.15496v1","created_at":"2026-07-05T09:39:35.877694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15496","created_at":"2026-07-05T09:39:35.877694+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZQKUDMHXBB2","created_at":"2026-07-05T09:39:35.877694+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZQKUDMHXBB2IWRT","created_at":"2026-07-05T09:39:35.877694+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZQKUDMH","created_at":"2026-07-05T09:39:35.877694+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.11902","citing_title":"Universal formulae for correlators of a broad class of models","ref_index":79,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z","json":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z.json","graph_json":"https://pith.science/api/pith-number/YZQKUDMHXBB2IWRTZLZVPF2L3Z/graph.json","events_json":"https://pith.science/api/pith-number/YZQKUDMHXBB2IWRTZLZVPF2L3Z/events.json","paper":"https://pith.science/paper/YZQKUDMH"},"agent_actions":{"view_html":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z","download_json":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z.json","view_paper":"https://pith.science/paper/YZQKUDMH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.15496&json=true","fetch_graph":"https://pith.science/api/pith-number/YZQKUDMHXBB2IWRTZLZVPF2L3Z/graph.json","fetch_events":"https://pith.science/api/pith-number/YZQKUDMHXBB2IWRTZLZVPF2L3Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/action/storage_attestation","attest_author":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/action/author_attestation","sign_citation":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/action/citation_signature","submit_replication":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/action/replication_record"}},"created_at":"2026-07-05T09:39:35.877694+00:00","updated_at":"2026-07-05T09:39:35.877694+00:00"}