{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZNOTZYMU56JPT6CUVAFGJHMWW3","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":"5c1495c8fac5e39ac037785c8d4c8edd5dc2eab2640beb816a1c3a157196d980","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-08-07T09:07:59Z","title_canon_sha256":"e478f38a841133ebaad60e5025b55ddc030f2a1e0d2b903433926e06219e4c81"},"schema_version":"1.0","source":{"id":"1208.1374","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1374","created_at":"2026-05-18T01:55:22Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1374v2","created_at":"2026-05-18T01:55:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1374","created_at":"2026-05-18T01:55:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZNOTZYMU56JP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZNOTZYMU56JPT6CU","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZNOTZYMU","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:3552959af746cbabb2d003dd9d7d9bed053d48d0d57f9868ab724577047ed7f9","target":"graph","created_at":"2026-05-18T01:55:22Z","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"},"paper":{"abstract_excerpt":"We introduce a single tau function that represents the CKP hierarchy into a generalized Hirota \"bilinear\" equation. The actions on the tau function by additional symmetries for the hierarchy are calculated, which involve strictly more than a central extension of the $w^C_\\infty$-algebra. As an application, for Drinfeld-Sokolov hierarchies of type C that are equivalent to certain reductions of the CKP hierarchy, their Virasoro symmetries are proved to be non-linearizable when acting on the tau function.","authors_text":"Chao-Zhong Wu, Liang Chang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-08-07T09:07:59Z","title":"Tau function of the CKP hierarchy and non-linearizable Virasoro symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1374","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":"sha256:2c8ffbbc67fdb84d6bb95acdf1e84886d7239d7b461972391db8c0d64d467876","target":"record","created_at":"2026-05-18T01:55:22Z","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":"5c1495c8fac5e39ac037785c8d4c8edd5dc2eab2640beb816a1c3a157196d980","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-08-07T09:07:59Z","title_canon_sha256":"e478f38a841133ebaad60e5025b55ddc030f2a1e0d2b903433926e06219e4c81"},"schema_version":"1.0","source":{"id":"1208.1374","kind":"arxiv","version":2}},"canonical_sha256":"cb5d3ce194ef92f9f854a80a649d96b6e9014a0db2436b907fe0305ddc9ff460","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb5d3ce194ef92f9f854a80a649d96b6e9014a0db2436b907fe0305ddc9ff460","first_computed_at":"2026-05-18T01:55:22.283897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:22.283897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m970GCGXhPQ3PjvJuMg7R643Egvv5bbAwVV0NIo51iQCSl4IECUNuVYbWVFOUw++oBg9VvbaYR2Kl8a2nrkkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:22.284270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1374","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c8ffbbc67fdb84d6bb95acdf1e84886d7239d7b461972391db8c0d64d467876","sha256:3552959af746cbabb2d003dd9d7d9bed053d48d0d57f9868ab724577047ed7f9"],"state_sha256":"da915911c2869ee6e24b3da921be947f8bcf9c640f0efcb641c8a2a336edf647"}