{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:DMBKBKJWCRWCUMRXTW5Z3P4KNP","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":"8c8e192b656ab1bfe2b532e7f6475354dd69a94ddad788f723028c1f6b682b63","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1996-01-30T16:37:22Z","title_canon_sha256":"47f9fed742b2fa7ef15a6a16c0e75cd9ac10b33a094504406758e4d3838b130a"},"schema_version":"1.0","source":{"id":"hep-th/9601161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9601161","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9601161v1","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9601161","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"DMBKBKJWCRWC","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"DMBKBKJWCRWCUMRX","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"DMBKBKJW","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:0c792812e334fd35de3c3c10ba49122b2395b268ac47a6290d93a04e3e913725","target":"graph","created_at":"2026-05-18T01:38:38Z","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":"In the series of papers we represent the ``Whittaker'' wave functional of $d+1$-dimensional Liouville model as a correlator in $d+0$-dimensional theory of the sine-Gordon type (for $d=0$ and $1$). Asypmtotics of this wave function is characterized by the Harish-Chandra function, which is shown to be a product of simple $\\Gamma$-function factors over all positive roots of the corresponding algebras (finite-dimensional for $d=0$ and affine for $d=1$). This is in nice correspondence with the recent results on 2- and 3-point correlators in $1+1$ Liouville model, where emergence of peculiar double-","authors_text":"A.Gerasimov, A.Marshakov, A.Mironov, A.Morozov, Lebedev Physical Institute), M.Olshanetsky (ITEP, S.Kharchev","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1996-01-30T16:37:22Z","title":"Liouville Type Models in Group Theory Framework. I. Finite-Dimensional Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9601161","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:d00d1654465d60b7ba1553b9c66c0c54334a4738c54ef4a8545f0578cbb4e8d2","target":"record","created_at":"2026-05-18T01:38:38Z","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":"8c8e192b656ab1bfe2b532e7f6475354dd69a94ddad788f723028c1f6b682b63","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1996-01-30T16:37:22Z","title_canon_sha256":"47f9fed742b2fa7ef15a6a16c0e75cd9ac10b33a094504406758e4d3838b130a"},"schema_version":"1.0","source":{"id":"hep-th/9601161","kind":"arxiv","version":1}},"canonical_sha256":"1b02a0a936146c2a32379dbb9dbf8a6bfbd726bf81297851264aeff6a9d8ffdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b02a0a936146c2a32379dbb9dbf8a6bfbd726bf81297851264aeff6a9d8ffdb","first_computed_at":"2026-05-18T01:38:38.333376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:38.333376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z9DxdZjNRxTXMr8ydDVV0aebWxTQneSSF2pEi8b0pIikD3sGxEc6ZjznqhiEjOti74YBtRWHyyX3QPy9geD5Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:38.333812Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9601161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d00d1654465d60b7ba1553b9c66c0c54334a4738c54ef4a8545f0578cbb4e8d2","sha256:0c792812e334fd35de3c3c10ba49122b2395b268ac47a6290d93a04e3e913725"],"state_sha256":"838fc7258949c3c10f0d0cde0f784002b2954af0f427f18de741e229a2574a37"}