{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:U56BNDB3MYEUAZSNPP2JPEY5ZZ","short_pith_number":"pith:U56BNDB3","canonical_record":{"source":{"id":"2203.07072","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-03-14T13:04:32Z","cross_cats_sorted":["math-ph","math.AG","math.MP","math.RT"],"title_canon_sha256":"e0883afcbe0fb81b2cc872ad13f51f998e11b5a4839a0cbe1666767fd673b5ca","abstract_canon_sha256":"dd0b7c7119f4b566c9d2ce8de2a24d3483e5a2c89f25648d98c562a57ca331ad"},"schema_version":"1.0"},"canonical_sha256":"a77c168c3b660940664d7bf497931dce6f469afd7c54674303a0208661bc597b","source":{"kind":"arxiv","id":"2203.07072","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.07072","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"2203.07072v2","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.07072","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"U56BNDB3MYEU","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"pith_short_16","alias_value":"U56BNDB3MYEUAZSN","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"pith_short_8","alias_value":"U56BNDB3","created_at":"2026-07-05T05:19:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:U56BNDB3MYEUAZSNPP2JPEY5ZZ","target":"record","payload":{"canonical_record":{"source":{"id":"2203.07072","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-03-14T13:04:32Z","cross_cats_sorted":["math-ph","math.AG","math.MP","math.RT"],"title_canon_sha256":"e0883afcbe0fb81b2cc872ad13f51f998e11b5a4839a0cbe1666767fd673b5ca","abstract_canon_sha256":"dd0b7c7119f4b566c9d2ce8de2a24d3483e5a2c89f25648d98c562a57ca331ad"},"schema_version":"1.0"},"canonical_sha256":"a77c168c3b660940664d7bf497931dce6f469afd7c54674303a0208661bc597b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:19:14.313899Z","signature_b64":"BILqxn8TrS8JSQivGMC71+aTZtszzMaBASa/lsl77QWxBfD0UlHXlhvi+mpmjdD+55q5R5ilB8MPxQDASjS+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a77c168c3b660940664d7bf497931dce6f469afd7c54674303a0208661bc597b","last_reissued_at":"2026-07-05T05:19:14.313523Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:19:14.313523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.07072","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dftio1oG0EHQ4oaP8goAbmkDWeYPPcwJj9DG+3xjqBXPbrFMeKCV3R1ilQB75eXxmqGGxWtSsoouurgPr2JGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T06:13:58.854000Z"},"content_sha256":"166955cd9407b3dda7a522230d239655ae959f80d55b5563df81a6147d73dc5e","schema_version":"1.0","event_id":"sha256:166955cd9407b3dda7a522230d239655ae959f80d55b5563df81a6147d73dc5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:U56BNDB3MYEUAZSNPP2JPEY5ZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Representation-Theoretic Approach to $qq$-Characters","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Henry Liu","submitted_at":"2022-03-14T13:04:32Z","abstract_excerpt":"We raise the question of whether (a slightly generalized notion of) $qq$-characters can be constructed purely representation-theoretically. In the main example of the quantum toroidal $\\mathfrak{gl}_1$ algebra, geometric engineering of adjoint matter produces an explicit vertex operator $\\mathsf{RR}$ which computes certain $qq$-characters, namely Hirzebruch $\\chi_y$-genera, completely analogously to how the R-matrix $\\mathsf{R}$ computes $q$-characters. We give a geometric proof of the independence of preferred direction for the refined vertex in this and more general non-toric settings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.07072","kind":"arxiv","version":2},"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/2203.07072/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":"2026-07-05T05:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+K4CZkndW1eFuHrxDG2+dviUqObb0u8ZNdU49QEHYNxEctDbbje+K4lXBmDNXx5mDSMH8L8j65JFNtMwtsVeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T06:13:58.854326Z"},"content_sha256":"7f118f12ed1ecb45f2386a9d430f55e349115d6e2a2df1dc0c8e125d83afb7a1","schema_version":"1.0","event_id":"sha256:7f118f12ed1ecb45f2386a9d430f55e349115d6e2a2df1dc0c8e125d83afb7a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U56BNDB3MYEUAZSNPP2JPEY5ZZ/bundle.json","state_url":"https://pith.science/pith/U56BNDB3MYEUAZSNPP2JPEY5ZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U56BNDB3MYEUAZSNPP2JPEY5ZZ/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":"2026-08-21T06:13:58Z","links":{"resolver":"https://pith.science/pith/U56BNDB3MYEUAZSNPP2JPEY5ZZ","bundle":"https://pith.science/pith/U56BNDB3MYEUAZSNPP2JPEY5ZZ/bundle.json","state":"https://pith.science/pith/U56BNDB3MYEUAZSNPP2JPEY5ZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U56BNDB3MYEUAZSNPP2JPEY5ZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:U56BNDB3MYEUAZSNPP2JPEY5ZZ","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":"dd0b7c7119f4b566c9d2ce8de2a24d3483e5a2c89f25648d98c562a57ca331ad","cross_cats_sorted":["math-ph","math.AG","math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-03-14T13:04:32Z","title_canon_sha256":"e0883afcbe0fb81b2cc872ad13f51f998e11b5a4839a0cbe1666767fd673b5ca"},"schema_version":"1.0","source":{"id":"2203.07072","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.07072","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"2203.07072v2","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.07072","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"U56BNDB3MYEU","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"pith_short_16","alias_value":"U56BNDB3MYEUAZSN","created_at":"2026-07-05T05:19:14Z"},{"alias_kind":"pith_short_8","alias_value":"U56BNDB3","created_at":"2026-07-05T05:19:14Z"}],"graph_snapshots":[{"event_id":"sha256:7f118f12ed1ecb45f2386a9d430f55e349115d6e2a2df1dc0c8e125d83afb7a1","target":"graph","created_at":"2026-07-05T05:19:14Z","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/2203.07072/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We raise the question of whether (a slightly generalized notion of) $qq$-characters can be constructed purely representation-theoretically. In the main example of the quantum toroidal $\\mathfrak{gl}_1$ algebra, geometric engineering of adjoint matter produces an explicit vertex operator $\\mathsf{RR}$ which computes certain $qq$-characters, namely Hirzebruch $\\chi_y$-genera, completely analogously to how the R-matrix $\\mathsf{R}$ computes $q$-characters. We give a geometric proof of the independence of preferred direction for the refined vertex in this and more general non-toric settings.","authors_text":"Henry Liu","cross_cats":["math-ph","math.AG","math.MP","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-03-14T13:04:32Z","title":"A Representation-Theoretic Approach to $qq$-Characters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.07072","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":"sha256:166955cd9407b3dda7a522230d239655ae959f80d55b5563df81a6147d73dc5e","target":"record","created_at":"2026-07-05T05:19:14Z","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":"dd0b7c7119f4b566c9d2ce8de2a24d3483e5a2c89f25648d98c562a57ca331ad","cross_cats_sorted":["math-ph","math.AG","math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-03-14T13:04:32Z","title_canon_sha256":"e0883afcbe0fb81b2cc872ad13f51f998e11b5a4839a0cbe1666767fd673b5ca"},"schema_version":"1.0","source":{"id":"2203.07072","kind":"arxiv","version":2}},"canonical_sha256":"a77c168c3b660940664d7bf497931dce6f469afd7c54674303a0208661bc597b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a77c168c3b660940664d7bf497931dce6f469afd7c54674303a0208661bc597b","first_computed_at":"2026-07-05T05:19:14.313523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:19:14.313523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BILqxn8TrS8JSQivGMC71+aTZtszzMaBASa/lsl77QWxBfD0UlHXlhvi+mpmjdD+55q5R5ilB8MPxQDASjS+BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:19:14.313899Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.07072","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:166955cd9407b3dda7a522230d239655ae959f80d55b5563df81a6147d73dc5e","sha256:7f118f12ed1ecb45f2386a9d430f55e349115d6e2a2df1dc0c8e125d83afb7a1"],"state_sha256":"3dc5f63bec94807317f97c8953f39dac40e949922f9d79a343fbb9c44afb69f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xYJMYotAo54xSemSkKf8MbanHXTnCAvcZYngyS0hXq6Ajjae09vnchJxhXYxm6h6EK6fjVJ0m+k9fwT++dYLAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T06:13:58.857948Z","bundle_sha256":"2d61115d6694b2f85061b279ded7e104cfc9af1f22e0babe6cbb526121a42883"}}