{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NP4IMXHNPXJ7JFKF67AT42ESSA","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":"c3180687c68c718060e06f3095883b233a59103c5c170ffa4b07b266e9e10026","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-02T16:12:27Z","title_canon_sha256":"a5d3636f5f6f20b69e9c5b9e16360ebef6531702cb06266a5454760a1f0f3d28"},"schema_version":"1.0","source":{"id":"1602.00992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00992","created_at":"2026-05-18T00:54:40Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00992v1","created_at":"2026-05-18T00:54:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00992","created_at":"2026-05-18T00:54:40Z"},{"alias_kind":"pith_short_12","alias_value":"NP4IMXHNPXJ7","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NP4IMXHNPXJ7JFKF","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NP4IMXHN","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:89ec76c8fa0484f281de969411de5e0c9e16f3125e169fa5cf747c513213df88","target":"graph","created_at":"2026-05-18T00:54:40Z","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 investigate the structure of representations of the (positive half of the) Virasoro algebra and situations in which they decompose as a tensor product of Lie algebra representations. As an illustration, we apply these results to the differential operators defined by the Virasoro conjecture and obtain some factorization properties of the solutions as well as a link to the multicomponent KP hierarchy.","authors_text":"Carlos Tejero Prieto, Francisco J. Plaza Mart\\'in","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-02T16:12:27Z","title":"Virasoro and KdV"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00992","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:f576828d281643d4fe20a8ca3f494944b2986b023cb18204ed59fb11b39c1423","target":"record","created_at":"2026-05-18T00:54:40Z","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":"c3180687c68c718060e06f3095883b233a59103c5c170ffa4b07b266e9e10026","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-02T16:12:27Z","title_canon_sha256":"a5d3636f5f6f20b69e9c5b9e16360ebef6531702cb06266a5454760a1f0f3d28"},"schema_version":"1.0","source":{"id":"1602.00992","kind":"arxiv","version":1}},"canonical_sha256":"6bf8865ced7dd3f49545f7c13e6892901cccf7854fe59af1e4a25c4d95dcf0f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bf8865ced7dd3f49545f7c13e6892901cccf7854fe59af1e4a25c4d95dcf0f1","first_computed_at":"2026-05-18T00:54:40.857669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:40.857669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0DQWjw/nBH5tdSHypnVw1ScnMsw08llWSLtfLgewWwfPk9JYfGl0Lr6Eh5KdfJMQBd3a5giBrqLA6fx+ckRuBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:40.858274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f576828d281643d4fe20a8ca3f494944b2986b023cb18204ed59fb11b39c1423","sha256:89ec76c8fa0484f281de969411de5e0c9e16f3125e169fa5cf747c513213df88"],"state_sha256":"16e8a593fcea403fea93ed71664da30e165412d0f4399c19cae0ce351279aad6"}