{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:S2UNO5X2U5O34ZHF56SGXWDUPQ","short_pith_number":"pith:S2UNO5X2","canonical_record":{"source":{"id":"2109.01846","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-09-04T11:37:10Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"81c3db248d1d435066ee0f266a89934e9821915634cd45ebfea64c4b21ad0d8b","abstract_canon_sha256":"8c49ad7e0abdd8cad4e77b539b6eab2916b8999579128801505ef6c560053e7f"},"schema_version":"1.0"},"canonical_sha256":"96a8d776faa75dbe64e5efa46bd8747c38c540a25edeab1caadbc93d74bd9788","source":{"kind":"arxiv","id":"2109.01846","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.01846","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"arxiv_version","alias_value":"2109.01846v2","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.01846","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"pith_short_12","alias_value":"S2UNO5X2U5O3","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"pith_short_16","alias_value":"S2UNO5X2U5O34ZHF","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"pith_short_8","alias_value":"S2UNO5X2","created_at":"2026-07-05T03:12:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:S2UNO5X2U5O34ZHF56SGXWDUPQ","target":"record","payload":{"canonical_record":{"source":{"id":"2109.01846","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-09-04T11:37:10Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"81c3db248d1d435066ee0f266a89934e9821915634cd45ebfea64c4b21ad0d8b","abstract_canon_sha256":"8c49ad7e0abdd8cad4e77b539b6eab2916b8999579128801505ef6c560053e7f"},"schema_version":"1.0"},"canonical_sha256":"96a8d776faa75dbe64e5efa46bd8747c38c540a25edeab1caadbc93d74bd9788","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:12:17.188217Z","signature_b64":"+YyyCW1A3q+Udr4LgBJChUKEA2nfJVOpfoY8JeadSXaMCS2ItiNwdR1iRyEimop6Pz3G6a7ug0bNQswmdNcsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96a8d776faa75dbe64e5efa46bd8747c38c540a25edeab1caadbc93d74bd9788","last_reissued_at":"2026-07-05T03:12:17.187782Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:12:17.187782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.01846","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:12:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Szx05Al0c1WyVR1dM24uXhtRZkd8iCqZwF89S3jv4c5auLttZP3etSSawSqIZSzeRQro01wkVyuzDnxTiyS8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:07:40.035589Z"},"content_sha256":"f8a5ff72a7c90fe25819e9b07a32d251b32597f77154dcea697a6a0f23263d9e","schema_version":"1.0","event_id":"sha256:f8a5ff72a7c90fe25819e9b07a32d251b32597f77154dcea697a6a0f23263d9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:S2UNO5X2U5O34ZHF56SGXWDUPQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linearization of Virasoro symmetries associated with semisimple Frobenius manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Si-Qi Liu, Youjin Zhang, Zhe Wang","submitted_at":"2021-09-04T11:37:10Z","abstract_excerpt":"For any semisimple Frobenius manifold, we prove that a tau-symmetric bihamiltonian deformation of its Principal Hierarchy admits an infinite family of linearizable Virasoro symmetries if and only if all the central invariants of the corresponding deformation of the bihamiltonian structure are equal to $\\frac{1}{24}$. As an important application of this result, we prove that the Dubrovin-Zhang hierarchy associated with the semisimple Frobenius manifold possesses a bihamiltonian structure which can be represented in terms of differential polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.01846","kind":"arxiv","version":2},"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/2109.01846/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":"2026-07-05T03:12:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r4ZPkSQw1j8WTsrllhM9xd2W79vN2oCCaNpu7UWpEwbQEUV6FTQreLJBYqZP/AyyIpjVdZnWLcbK1GrdUAJCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:07:40.090454Z"},"content_sha256":"581112916f0fbb47f5932fff30795947b847b86eb490ae49a2ef1dda7a9b0b5d","schema_version":"1.0","event_id":"sha256:581112916f0fbb47f5932fff30795947b847b86eb490ae49a2ef1dda7a9b0b5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2UNO5X2U5O34ZHF56SGXWDUPQ/bundle.json","state_url":"https://pith.science/pith/S2UNO5X2U5O34ZHF56SGXWDUPQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2UNO5X2U5O34ZHF56SGXWDUPQ/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":"2026-08-13T22:07:40Z","links":{"resolver":"https://pith.science/pith/S2UNO5X2U5O34ZHF56SGXWDUPQ","bundle":"https://pith.science/pith/S2UNO5X2U5O34ZHF56SGXWDUPQ/bundle.json","state":"https://pith.science/pith/S2UNO5X2U5O34ZHF56SGXWDUPQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2UNO5X2U5O34ZHF56SGXWDUPQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:S2UNO5X2U5O34ZHF56SGXWDUPQ","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":"8c49ad7e0abdd8cad4e77b539b6eab2916b8999579128801505ef6c560053e7f","cross_cats_sorted":["math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-09-04T11:37:10Z","title_canon_sha256":"81c3db248d1d435066ee0f266a89934e9821915634cd45ebfea64c4b21ad0d8b"},"schema_version":"1.0","source":{"id":"2109.01846","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.01846","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"arxiv_version","alias_value":"2109.01846v2","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.01846","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"pith_short_12","alias_value":"S2UNO5X2U5O3","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"pith_short_16","alias_value":"S2UNO5X2U5O34ZHF","created_at":"2026-07-05T03:12:17Z"},{"alias_kind":"pith_short_8","alias_value":"S2UNO5X2","created_at":"2026-07-05T03:12:17Z"}],"graph_snapshots":[{"event_id":"sha256:581112916f0fbb47f5932fff30795947b847b86eb490ae49a2ef1dda7a9b0b5d","target":"graph","created_at":"2026-07-05T03:12:17Z","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/2109.01846/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any semisimple Frobenius manifold, we prove that a tau-symmetric bihamiltonian deformation of its Principal Hierarchy admits an infinite family of linearizable Virasoro symmetries if and only if all the central invariants of the corresponding deformation of the bihamiltonian structure are equal to $\\frac{1}{24}$. As an important application of this result, we prove that the Dubrovin-Zhang hierarchy associated with the semisimple Frobenius manifold possesses a bihamiltonian structure which can be represented in terms of differential polynomials.","authors_text":"Si-Qi Liu, Youjin Zhang, Zhe Wang","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-09-04T11:37:10Z","title":"Linearization of Virasoro symmetries associated with semisimple Frobenius manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.01846","kind":"arxiv","version":2},"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:f8a5ff72a7c90fe25819e9b07a32d251b32597f77154dcea697a6a0f23263d9e","target":"record","created_at":"2026-07-05T03:12:17Z","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":"8c49ad7e0abdd8cad4e77b539b6eab2916b8999579128801505ef6c560053e7f","cross_cats_sorted":["math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-09-04T11:37:10Z","title_canon_sha256":"81c3db248d1d435066ee0f266a89934e9821915634cd45ebfea64c4b21ad0d8b"},"schema_version":"1.0","source":{"id":"2109.01846","kind":"arxiv","version":2}},"canonical_sha256":"96a8d776faa75dbe64e5efa46bd8747c38c540a25edeab1caadbc93d74bd9788","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96a8d776faa75dbe64e5efa46bd8747c38c540a25edeab1caadbc93d74bd9788","first_computed_at":"2026-07-05T03:12:17.187782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:12:17.187782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+YyyCW1A3q+Udr4LgBJChUKEA2nfJVOpfoY8JeadSXaMCS2ItiNwdR1iRyEimop6Pz3G6a7ug0bNQswmdNcsCA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:12:17.188217Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.01846","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8a5ff72a7c90fe25819e9b07a32d251b32597f77154dcea697a6a0f23263d9e","sha256:581112916f0fbb47f5932fff30795947b847b86eb490ae49a2ef1dda7a9b0b5d"],"state_sha256":"1a8bcecf634a46805ffc1835b14ccbb839267adea3ac71590b731de45f5c5e17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"URdFRGwvW6DLkoN3UNbIRavjr6MIR0nuz4StcX53Svb9bcnjga/wGnXqWMhZWcAbooVW/Y0/KBg+YaAqm98vAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T22:07:40.119608Z","bundle_sha256":"5990d0336bc13b50b24727d68dafde651ff8d2b18a6e660a7d0cbadb2f7d0f79"}}