{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:4V7WGUVHZKGAEMYV6OPMZJBMOC","short_pith_number":"pith:4V7WGUVH","canonical_record":{"source":{"id":"2209.00483","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2022-09-01T14:13:02Z","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"title_canon_sha256":"b498dd1e37815bc0ca63720388cbc08b9ba3203772da6157daa9623d8dc3568a","abstract_canon_sha256":"11deb76bb238a0e5f42c15263d94e0ce86f728d8f4a6d39b30a9bc53c24dca25"},"schema_version":"1.0"},"canonical_sha256":"e57f6352a7ca8c023315f39ecca42c7095e139e641df0be3d1a3013156adda36","source":{"kind":"arxiv","id":"2209.00483","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.00483","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"2209.00483v3","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.00483","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"4V7WGUVHZKGA","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"pith_short_16","alias_value":"4V7WGUVHZKGAEMYV","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"pith_short_8","alias_value":"4V7WGUVH","created_at":"2026-07-05T08:57:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:4V7WGUVHZKGAEMYV6OPMZJBMOC","target":"record","payload":{"canonical_record":{"source":{"id":"2209.00483","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2022-09-01T14:13:02Z","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"title_canon_sha256":"b498dd1e37815bc0ca63720388cbc08b9ba3203772da6157daa9623d8dc3568a","abstract_canon_sha256":"11deb76bb238a0e5f42c15263d94e0ce86f728d8f4a6d39b30a9bc53c24dca25"},"schema_version":"1.0"},"canonical_sha256":"e57f6352a7ca8c023315f39ecca42c7095e139e641df0be3d1a3013156adda36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:57:32.557073Z","signature_b64":"yKCPV9d1R1B8/MG5MNZz7FuY4rmmi1CBM8/dFMA5w2tFbJjEJ8HcKvdUcKXa5C1V9fHYHrdthZ4hxqONX52sCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e57f6352a7ca8c023315f39ecca42c7095e139e641df0be3d1a3013156adda36","last_reissued_at":"2026-07-05T08:57:32.556597Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:57:32.556597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.00483","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:57:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUOrlmO2DknCOhDhUpCW0mrHJrw3cifWKyE1u9wHcNwf4qBspFpAYv+hfJrlUkbbZmTnO9EPszgo/SbkXl8jCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:50:35.931693Z"},"content_sha256":"1abe2155bd87ea6cfa9d8be4fdad482e3a4d1175b40a42b195a6ea040c6ceb75","schema_version":"1.0","event_id":"sha256:1abe2155bd87ea6cfa9d8be4fdad482e3a4d1175b40a42b195a6ea040c6ceb75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:4V7WGUVHZKGAEMYV6OPMZJBMOC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Frobenius Manifolds with Non-flat Unity and Integrable Hierarchies","license":"http://creativecommons.org/licenses/by-nc-sa/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":"2022-09-01T14:13:02Z","abstract_excerpt":"For any generalized Frobenius manifold with non-flat unity, we construct a bihamiltonian integrable hierarchy of hydrodynamic type which is an analogue of the Principal Hierarchy of a Frobenius manifold. We show that such an integrable hierarchy, which we also call the Principal Hierarchy, possesses Virasoro symmetries and a tau structure, and the Virasoro symmetries can be lifted to symmetries of the tau-cover of the integrable hierarchy. We derive the loop equation from the condition of linearization of actions of the Virasoro symmetries on the tau function, and construct the topological def"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00483","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.00483/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":"2026-07-05T08:57:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AWttavLJP8k0TiK2OO8DVuqwkYfSXDFe+Jp3S2bcZyxt6tyTuQ1lf001keMzv9USHEdlPBhNxhFwdxQZANAdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:50:35.932078Z"},"content_sha256":"23c6a4b7c25f05119b8d70cdb7fa0c8c8b834ae4784fdc5e7525389c4ab60137","schema_version":"1.0","event_id":"sha256:23c6a4b7c25f05119b8d70cdb7fa0c8c8b834ae4784fdc5e7525389c4ab60137"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4V7WGUVHZKGAEMYV6OPMZJBMOC/bundle.json","state_url":"https://pith.science/pith/4V7WGUVHZKGAEMYV6OPMZJBMOC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4V7WGUVHZKGAEMYV6OPMZJBMOC/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":"2026-08-13T02:50:35Z","links":{"resolver":"https://pith.science/pith/4V7WGUVHZKGAEMYV6OPMZJBMOC","bundle":"https://pith.science/pith/4V7WGUVHZKGAEMYV6OPMZJBMOC/bundle.json","state":"https://pith.science/pith/4V7WGUVHZKGAEMYV6OPMZJBMOC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4V7WGUVHZKGAEMYV6OPMZJBMOC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:4V7WGUVHZKGAEMYV6OPMZJBMOC","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":"11deb76bb238a0e5f42c15263d94e0ce86f728d8f4a6d39b30a9bc53c24dca25","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2022-09-01T14:13:02Z","title_canon_sha256":"b498dd1e37815bc0ca63720388cbc08b9ba3203772da6157daa9623d8dc3568a"},"schema_version":"1.0","source":{"id":"2209.00483","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.00483","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"2209.00483v3","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.00483","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"4V7WGUVHZKGA","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"pith_short_16","alias_value":"4V7WGUVHZKGAEMYV","created_at":"2026-07-05T08:57:32Z"},{"alias_kind":"pith_short_8","alias_value":"4V7WGUVH","created_at":"2026-07-05T08:57:32Z"}],"graph_snapshots":[{"event_id":"sha256:23c6a4b7c25f05119b8d70cdb7fa0c8c8b834ae4784fdc5e7525389c4ab60137","target":"graph","created_at":"2026-07-05T08:57:32Z","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/2209.00483/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any generalized Frobenius manifold with non-flat unity, we construct a bihamiltonian integrable hierarchy of hydrodynamic type which is an analogue of the Principal Hierarchy of a Frobenius manifold. We show that such an integrable hierarchy, which we also call the Principal Hierarchy, possesses Virasoro symmetries and a tau structure, and the Virasoro symmetries can be lifted to symmetries of the tau-cover of the integrable hierarchy. We derive the loop equation from the condition of linearization of actions of the Virasoro symmetries on the tau function, and construct the topological def","authors_text":"Haonan Qu, Si-Qi Liu, Youjin Zhang","cross_cats":["math.DG","math.MP","nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2022-09-01T14:13:02Z","title":"Generalized Frobenius Manifolds with Non-flat Unity and Integrable Hierarchies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00483","kind":"arxiv","version":3},"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":"sha256:1abe2155bd87ea6cfa9d8be4fdad482e3a4d1175b40a42b195a6ea040c6ceb75","target":"record","created_at":"2026-07-05T08:57:32Z","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":"11deb76bb238a0e5f42c15263d94e0ce86f728d8f4a6d39b30a9bc53c24dca25","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2022-09-01T14:13:02Z","title_canon_sha256":"b498dd1e37815bc0ca63720388cbc08b9ba3203772da6157daa9623d8dc3568a"},"schema_version":"1.0","source":{"id":"2209.00483","kind":"arxiv","version":3}},"canonical_sha256":"e57f6352a7ca8c023315f39ecca42c7095e139e641df0be3d1a3013156adda36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e57f6352a7ca8c023315f39ecca42c7095e139e641df0be3d1a3013156adda36","first_computed_at":"2026-07-05T08:57:32.556597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:57:32.556597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yKCPV9d1R1B8/MG5MNZz7FuY4rmmi1CBM8/dFMA5w2tFbJjEJ8HcKvdUcKXa5C1V9fHYHrdthZ4hxqONX52sCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:57:32.557073Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.00483","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1abe2155bd87ea6cfa9d8be4fdad482e3a4d1175b40a42b195a6ea040c6ceb75","sha256:23c6a4b7c25f05119b8d70cdb7fa0c8c8b834ae4784fdc5e7525389c4ab60137"],"state_sha256":"1b0b083dbb00e4f483fd344e4a89273d77f07b999479a7693fee0c9f66953366"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MR1SG3cOl4uVkANQHpVZTaBjp4Lsgwuc6fSwZmI3KulkQmtkPp+3Q6SCuklVJtGYJEg0j8xOoFvsvVHnH8NGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T02:50:35.934457Z","bundle_sha256":"c6bce081343921d2c9ed38b216ad816b6f67644ad30239a4b04c07983aa294bb"}}