{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:C5PSLKKLABXGCNTEGMP2IOCL2G","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":"46269909a103a897693442f848f7f862b7b734504adc5cc585915a884e558cff","cross_cats_sorted":["hep-th","math.MP","math.QA","nlin.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-08-31T09:28:09Z","title_canon_sha256":"0beb8510ff8984098ba63364f18693ca1c1fd50faf4f9d130c7c2245593fff02"},"schema_version":"1.0","source":{"id":"2308.16583","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.16583","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"2308.16583v2","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.16583","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"C5PSLKKLABXG","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"pith_short_16","alias_value":"C5PSLKKLABXGCNTE","created_at":"2026-07-05T08:36:05Z"},{"alias_kind":"pith_short_8","alias_value":"C5PSLKKL","created_at":"2026-07-05T08:36:05Z"}],"graph_snapshots":[{"event_id":"sha256:d859aca611269e1c6c0706d4d636f3483ed9f8153f5a990785fd3b372db94347","target":"graph","created_at":"2026-07-05T08:36:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2308.16583/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A $(q,t)$-deformation of the 2d Toda integrable hierarchy is introduced by enhancing the underlying symmetry algebra $\\mathfrak{gl}(\\infty)\\simeq \\text{q-W}_{1+\\infty}$ to the quantum toroidal $\\mathfrak{gl}(1)$ algebra. The difference-differential equations of the hierarchy are obtained from the expansion of $(q,t)$-bilinear identities, and two equations refining the 2d Toda equation are found in this way. The derivation of the bilinear identities follows from the isomorphism between the Fock representation of level $(2,0)$ of the quantum toroidal $\\mathfrak{gl}(1)$ algebra and the tensor pro","authors_text":"Alexandr Garbali, Jean-Emile Bourgine","cross_cats":["hep-th","math.MP","math.QA","nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-08-31T09:28:09Z","title":"A $(q,t)$-deformation of the 2d Toda integrable hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.16583","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":"sha256:9b063f649bdc01e0901419e351b00a062c33f4dd6c07f62fe3ff450fa2fbdb2d","target":"record","created_at":"2026-07-05T08:36:05Z","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":"46269909a103a897693442f848f7f862b7b734504adc5cc585915a884e558cff","cross_cats_sorted":["hep-th","math.MP","math.QA","nlin.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-08-31T09:28:09Z","title_canon_sha256":"0beb8510ff8984098ba63364f18693ca1c1fd50faf4f9d130c7c2245593fff02"},"schema_version":"1.0","source":{"id":"2308.16583","kind":"arxiv","version":2}},"canonical_sha256":"175f25a94b006e613664331fa4384bd19a227a838c856d362e880c43a3371bd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"175f25a94b006e613664331fa4384bd19a227a838c856d362e880c43a3371bd7","first_computed_at":"2026-07-05T08:36:05.169702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:36:05.169702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+G8B6tv+ww0Ge8c9BnJ3OMGtM/QMsucLvwO3mdmEe9q+TaLtNWY6bHkmyZhP6ZEfqApDe6IZ0V2m+2RfPNcPDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:36:05.170194Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.16583","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b063f649bdc01e0901419e351b00a062c33f4dd6c07f62fe3ff450fa2fbdb2d","sha256:d859aca611269e1c6c0706d4d636f3483ed9f8153f5a990785fd3b372db94347"],"state_sha256":"01e40db284f2d3493d45d746d351ffd2ad8fb9d4a60d093ae2c04761f713e10d"}