{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:2ATF4ESE4OFP2JF6MNK75PGDXL","short_pith_number":"pith:2ATF4ESE","canonical_record":{"source":{"id":"2112.14687","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2021-12-29T18:02:29Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"da2dc65cd264cf64dd15af58ef277faa353e1e958c139beb0149cabefb3aec90","abstract_canon_sha256":"e8bd05098fbfa23083213c86f2e79c66374f5f3d7297d8d9a689ecf954c5993f"},"schema_version":"1.0"},"canonical_sha256":"d0265e1244e38afd24be6355febcc3baf103f60a4f3cebf8959e3fe36bfca705","source":{"kind":"arxiv","id":"2112.14687","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:2ATF4ESE4OFP2JF6MNK75PGDXL","target":"record","payload":{"canonical_record":{"source":{"id":"2112.14687","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2021-12-29T18:02:29Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"da2dc65cd264cf64dd15af58ef277faa353e1e958c139beb0149cabefb3aec90","abstract_canon_sha256":"e8bd05098fbfa23083213c86f2e79c66374f5f3d7297d8d9a689ecf954c5993f"},"schema_version":"1.0"},"canonical_sha256":"d0265e1244e38afd24be6355febcc3baf103f60a4f3cebf8959e3fe36bfca705","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:44:24.450839Z","signature_b64":"TZFmYYArEJG3SMpiUoWyZOKbKb5yTLlMSeeYrVrIFeJnpM/D4X8aI7DyasjFD2GMwG1Bu3QGif99nUfGy710Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0265e1244e38afd24be6355febcc3baf103f60a4f3cebf8959e3fe36bfca705","last_reissued_at":"2026-07-05T03:44:24.450434Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:44:24.450434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.14687","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SnJoDhbhQWu6rGxFzXL3Owqqye9YcKtE43UfyQsv8nSqvxvNCnzpl5WviaTUS54TxuU4JP/Xvl+qXfDbgNuyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:58:46.281615Z"},"content_sha256":"9d58ecbe517295cd89f2c3c31afa0dd4a8eb9c24c9e6296159458a7131f97f4d","schema_version":"1.0","event_id":"sha256:9d58ecbe517295cd89f2c3c31afa0dd4a8eb9c24c9e6296159458a7131f97f4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:2ATF4ESE4OFP2JF6MNK75PGDXL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On pentagon identity in Ding-Iohara-Miki algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"Yegor Zenkevich","submitted_at":"2021-12-29T18:02:29Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.14687","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.14687/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W6wmr1VZ4UuraCQagvJGOZa4UNikgp44g+/oR2if+EYyk3Vm6IuILr+d529RZ9U7QUZu9usKNlCusqCS6MHpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:58:46.282106Z"},"content_sha256":"375aebb4cbaaf82560de0fdadd243e7044ab20fef3cd9cfb90e46c1afb65c4ae","schema_version":"1.0","event_id":"sha256:375aebb4cbaaf82560de0fdadd243e7044ab20fef3cd9cfb90e46c1afb65c4ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ATF4ESE4OFP2JF6MNK75PGDXL/bundle.json","state_url":"https://pith.science/pith/2ATF4ESE4OFP2JF6MNK75PGDXL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ATF4ESE4OFP2JF6MNK75PGDXL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T19:58:46Z","links":{"resolver":"https://pith.science/pith/2ATF4ESE4OFP2JF6MNK75PGDXL","bundle":"https://pith.science/pith/2ATF4ESE4OFP2JF6MNK75PGDXL/bundle.json","state":"https://pith.science/pith/2ATF4ESE4OFP2JF6MNK75PGDXL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ATF4ESE4OFP2JF6MNK75PGDXL/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zF1YxWJ8BIxeUxa2Yo4FtxWWWKF4oJ4w7XNFbnCBIIRu2uauMUqiPWQi7kq9edQzV4A/l0R7eryvRvTcaanaBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:58:46.285631Z","bundle_sha256":"cf58945e3d557da3160b046d5b39c0f30c636cdde36022eb96d3e7f03c0f2c96"}}