{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YVXRPSXVSXYNXTVJUFYGOXV7QZ","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":"10614e625757b90bffcd3a3a1ca75b1aef426643887360936ccc29fbe8de90ee","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-17T10:36:33Z","title_canon_sha256":"1f8c06763d3df0a580141898130d5d773ee19d7ae53061ce010f37a3879b914a"},"schema_version":"1.0","source":{"id":"1904.08173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08173","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08173v1","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08173","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"YVXRPSXVSXYN","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YVXRPSXVSXYNXTVJ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YVXRPSXV","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:657c58a0b40514a0be526a4f623f1ad7e145f605616feb592879f94c11c47fd8","target":"graph","created_at":"2026-05-17T23:48:18Z","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":"The subject of this paper is a connection between d-orthogonal polynomials and the Toda lattice hierarchy. In more details we consider some polynomial systems similar to Hermite polynomials, but satisfying $d+2$-term recurrence relation, $d >1$. Any such polynomial system defines a solution of the Toda lattice hierarchy. However we impose also the condition that the polynomials are also eigenfunctions of a differential operator, i.e. a bispectral problem. This leads to a solution of the Toda lattice hierarchy, enjoying a number of special properties. In particular the corresponding tau-functio","authors_text":"Emil Horozov","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-17T10:36:33Z","title":"d-orthogonal polynomials, Toda Lattice and Virasoro symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08173","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:f0f7908878f6310ae862815ea708e96e4b03c72914f4dc9ec02b4aad9c732074","target":"record","created_at":"2026-05-17T23:48:18Z","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":"10614e625757b90bffcd3a3a1ca75b1aef426643887360936ccc29fbe8de90ee","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-17T10:36:33Z","title_canon_sha256":"1f8c06763d3df0a580141898130d5d773ee19d7ae53061ce010f37a3879b914a"},"schema_version":"1.0","source":{"id":"1904.08173","kind":"arxiv","version":1}},"canonical_sha256":"c56f17caf595f0dbcea9a170675ebf865232354ebf5d310b314514867d86943a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c56f17caf595f0dbcea9a170675ebf865232354ebf5d310b314514867d86943a","first_computed_at":"2026-05-17T23:48:18.552489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:18.552489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rlA8KirM68KUccvFMLhr2eJv2W/pGIV4st5KmvlhfKjrvPZzx1tXSfIpJ0zedyoESHk0iUbAxBQhLOpKMHtZDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:18.553260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.08173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0f7908878f6310ae862815ea708e96e4b03c72914f4dc9ec02b4aad9c732074","sha256:657c58a0b40514a0be526a4f623f1ad7e145f605616feb592879f94c11c47fd8"],"state_sha256":"abcc8f7772de2cc934a53c5aea1c0e083debcb2d7ed2a0b13b85541be4a08d02"}