{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:HFW36S6TTUITYELJKOVGZNXAEK","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":"7588e4117c66daab8a57daa682d21a4fbc89658bca1b29c8742b57b499056355","cross_cats_sorted":["math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2009-06-29T20:06:10Z","title_canon_sha256":"72f0344d5848e8fe73d46370b9ada998d19c2439dd3f788969ec1539dd4441ad"},"schema_version":"1.0","source":{"id":"0906.5360","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5360","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5360v2","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5360","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"HFW36S6TTUIT","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HFW36S6TTUITYELJ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HFW36S6T","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:a8ca35c43ce1e22d6c303de7e2aad19d06d9a04c9d1ba61ac49de0868ce67c23","target":"graph","created_at":"2026-05-18T02:13:11Z","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":"For the Kac-Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra $D_n^{(1)}$, we compute the coefficients of the corresponding Hirota bilinear equations, and verify the coincidence of these bilinear equations with the ones that are satisfied by Givental's total descendant potential of the $D_n$ singularity, as conjectured by Givental and Milanov in \\cite{GM}","authors_text":"Chao-Zhong Wu","cross_cats":["math.MP","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2009-06-29T20:06:10Z","title":"A Remark on Kac-Wakimoto Hierarchies of D-type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5360","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":"sha256:3ddcc78922bd627548673b6df05595cc12e32258560a56a4c7e91b4bf4dfb1ec","target":"record","created_at":"2026-05-18T02:13:11Z","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":"7588e4117c66daab8a57daa682d21a4fbc89658bca1b29c8742b57b499056355","cross_cats_sorted":["math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2009-06-29T20:06:10Z","title_canon_sha256":"72f0344d5848e8fe73d46370b9ada998d19c2439dd3f788969ec1539dd4441ad"},"schema_version":"1.0","source":{"id":"0906.5360","kind":"arxiv","version":2}},"canonical_sha256":"396dbf4bd39d113c116953aa6cb6e022aba459b846f1906d8aadbc0c3b78ce88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"396dbf4bd39d113c116953aa6cb6e022aba459b846f1906d8aadbc0c3b78ce88","first_computed_at":"2026-05-18T02:13:11.929838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:11.929838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L0ILoTF04nL9Rx3/SKYNY50o9bU0fhWSRNmXdXw8A/wHW5DaBX2Me+2q+Bp1jiUg5+lUG7J4cI1XFBIYrpucCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:11.930376Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.5360","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ddcc78922bd627548673b6df05595cc12e32258560a56a4c7e91b4bf4dfb1ec","sha256:a8ca35c43ce1e22d6c303de7e2aad19d06d9a04c9d1ba61ac49de0868ce67c23"],"state_sha256":"e028512e4a5ca85d74ee3ccfd9f28cb0c0e05f0ec5647d1e7ee4bee35c5df6b6"}