{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YZQKUDMHXBB2IWRTZLZVPF2L3Z","short_pith_number":"pith:YZQKUDMH","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"},"canonical_sha256":"c660aa0d87b843a45a33caf357974bde4a040b4a21561bcf769987602405dc6b","source":{"kind":"arxiv","id":"2411.15496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15496","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15496v1","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15496","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_12","alias_value":"YZQKUDMHXBB2","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_16","alias_value":"YZQKUDMHXBB2IWRT","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_8","alias_value":"YZQKUDMH","created_at":"2026-07-05T09:39:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YZQKUDMHXBB2IWRTZLZVPF2L3Z","target":"record","payload":{"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"},"canonical_sha256":"c660aa0d87b843a45a33caf357974bde4a040b4a21561bcf769987602405dc6b","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"},"source_kind":"arxiv","source_id":"2411.15496","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:39:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HefA1gFmnSJLjBYxcet/fC2WEyG+6y0t5epxFIDHiBw8Oc+I3ZzXJPshymjrn2Zg0o5pauvlE1Tic5cg3dBMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:36:51.565552Z"},"content_sha256":"aa865cc585307c4fc836a3cd6fad39669bfd66082e6ef831650e3ec8439ebc89","schema_version":"1.0","event_id":"sha256:aa865cc585307c4fc836a3cd6fad39669bfd66082e6ef831650e3ec8439ebc89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YZQKUDMHXBB2IWRTZLZVPF2L3Z","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:39:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z3k2VM3cNcTlQt9KHKFvTS+F/8K/C8fZmDO74lYnye/C81dcJ6DnybKD4haUbUDXMI7EGXnc0sZCkO+ue45kDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:36:51.566442Z"},"content_sha256":"d5b86220e9a2ad2046edef83e92755781b8c1a42d1f0a1f32a222d2377273191","schema_version":"1.0","event_id":"sha256:d5b86220e9a2ad2046edef83e92755781b8c1a42d1f0a1f32a222d2377273191"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/bundle.json","state_url":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T22:36:51Z","links":{"resolver":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z","bundle":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/bundle.json","state":"https://pith.science/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZQKUDMHXBB2IWRTZLZVPF2L3Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YZQKUDMHXBB2IWRTZLZVPF2L3Z","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fa4416403e349bb5870f587823779e193b8d73b54b5709ef96ac540dee880ac0","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-11-23T09:00:35Z","title_canon_sha256":"d2a0399fbc2a0aae7cb58ed1c841379b0fd3a04338e5c22d4708d8e69127c9c7"},"schema_version":"1.0","source":{"id":"2411.15496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15496","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15496v1","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15496","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_12","alias_value":"YZQKUDMHXBB2","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_16","alias_value":"YZQKUDMHXBB2IWRT","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_8","alias_value":"YZQKUDMH","created_at":"2026-07-05T09:39:35Z"}],"graph_snapshots":[{"event_id":"sha256:d5b86220e9a2ad2046edef83e92755781b8c1a42d1f0a1f32a222d2377273191","target":"graph","created_at":"2026-07-05T09:39:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.15496/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Haonan Qu, Si-Qi Liu, Youjin Zhang","cross_cats":["math.DG","math.MP","nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-11-23T09:00:35Z","title":"Legendre transformations of a class of generalized Frobenius manifolds and the associated integrable hierarchies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15496","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aa865cc585307c4fc836a3cd6fad39669bfd66082e6ef831650e3ec8439ebc89","target":"record","created_at":"2026-07-05T09:39:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fa4416403e349bb5870f587823779e193b8d73b54b5709ef96ac540dee880ac0","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-11-23T09:00:35Z","title_canon_sha256":"d2a0399fbc2a0aae7cb58ed1c841379b0fd3a04338e5c22d4708d8e69127c9c7"},"schema_version":"1.0","source":{"id":"2411.15496","kind":"arxiv","version":1}},"canonical_sha256":"c660aa0d87b843a45a33caf357974bde4a040b4a21561bcf769987602405dc6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c660aa0d87b843a45a33caf357974bde4a040b4a21561bcf769987602405dc6b","first_computed_at":"2026-07-05T09:39:35.877637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:35.877637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jW6LfPAMswtgJ2mqu3o+xKwJzuIeWd1+tQN6uW4m8P27kjAFCRdpt6qSXystv82QXprAZre270RQTzEGM+v7CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:35.878038Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa865cc585307c4fc836a3cd6fad39669bfd66082e6ef831650e3ec8439ebc89","sha256:d5b86220e9a2ad2046edef83e92755781b8c1a42d1f0a1f32a222d2377273191"],"state_sha256":"5e204d059aead7ebaa92956fa5fd7345d70b2c9f7664d47b831442260ef97655"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gGmRsPSBguHpOU7T8oFYkuoRRRuNVdn6QPjRX0q+DzUCzPY36ACgtUj7vSurzPhMcf/IkhB4nHvB95MngF9GBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:36:51.574984Z","bundle_sha256":"9844d9b1b432a87f385e4d3dfc3d9fe97047427c9e0814dcde20cf66275c4741"}}