{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:2ATF4ESE4OFP2JF6MNK75PGDXL","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":"e8bd05098fbfa23083213c86f2e79c66374f5f3d7297d8d9a689ecf954c5993f","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2021-12-29T18:02:29Z","title_canon_sha256":"da2dc65cd264cf64dd15af58ef277faa353e1e958c139beb0149cabefb3aec90"},"schema_version":"1.0","source":{"id":"2112.14687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.14687","created_at":"2026-07-05T03:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"2112.14687v1","created_at":"2026-07-05T03:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.14687","created_at":"2026-07-05T03:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"2ATF4ESE4OFP","created_at":"2026-07-05T03:44:24Z"},{"alias_kind":"pith_short_16","alias_value":"2ATF4ESE4OFP2JF6","created_at":"2026-07-05T03:44:24Z"},{"alias_kind":"pith_short_8","alias_value":"2ATF4ESE","created_at":"2026-07-05T03:44:24Z"}],"graph_snapshots":[{"event_id":"sha256:375aebb4cbaaf82560de0fdadd243e7044ab20fef3cd9cfb90e46c1afb65c4ae","target":"graph","created_at":"2026-07-05T03:44:24Z","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/2112.14687/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We notice that the famous pentagon identity for quantum dilogarithm functions and the five-term relation for certain operators related to Macdonald polynomials discovered by Garsia and Mellit can both be understood as specific cases of a general \"master pentagon identity\" for group-like elements in the Ding-Iohara-Miki (or quantum toroidal, or elliptic Hall) algebra. We perform some checks of this remarkable identity and discuss its implications.","authors_text":"Yegor Zenkevich","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2021-12-29T18:02:29Z","title":"On pentagon identity in Ding-Iohara-Miki algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.14687","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":"sha256:9d58ecbe517295cd89f2c3c31afa0dd4a8eb9c24c9e6296159458a7131f97f4d","target":"record","created_at":"2026-07-05T03:44:24Z","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":"e8bd05098fbfa23083213c86f2e79c66374f5f3d7297d8d9a689ecf954c5993f","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2021-12-29T18:02:29Z","title_canon_sha256":"da2dc65cd264cf64dd15af58ef277faa353e1e958c139beb0149cabefb3aec90"},"schema_version":"1.0","source":{"id":"2112.14687","kind":"arxiv","version":1}},"canonical_sha256":"d0265e1244e38afd24be6355febcc3baf103f60a4f3cebf8959e3fe36bfca705","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0265e1244e38afd24be6355febcc3baf103f60a4f3cebf8959e3fe36bfca705","first_computed_at":"2026-07-05T03:44:24.450434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:44:24.450434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZFmYYArEJG3SMpiUoWyZOKbKb5yTLlMSeeYrVrIFeJnpM/D4X8aI7DyasjFD2GMwG1Bu3QGif99nUfGy710Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:44:24.450839Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.14687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d58ecbe517295cd89f2c3c31afa0dd4a8eb9c24c9e6296159458a7131f97f4d","sha256:375aebb4cbaaf82560de0fdadd243e7044ab20fef3cd9cfb90e46c1afb65c4ae"],"state_sha256":"d2104e635740cb3756b7bdd820b8a01a199dde42911f5f948bdaf2475feb34ed"}