{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TOFEXM3YSQYBFJ4DYYDJAIENK6","short_pith_number":"pith:TOFEXM3Y","canonical_record":{"source":{"id":"2407.06865","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-07-09T13:53:08Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"dfefc02065a7e8d1dbe36ea63503bc9c710360a143912d7bb1aee988721c1ed9","abstract_canon_sha256":"788805ba44109e9b0649301c3bd1ce3c669ac504e82ceb540ccb5ffd5267ed27"},"schema_version":"1.0"},"canonical_sha256":"9b8a4bb378943012a783c60690208d57ab9dd41f43cfdc3d35be14853444389b","source":{"kind":"arxiv","id":"2407.06865","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.06865","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2407.06865v3","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.06865","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"TOFEXM3YSQYB","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"TOFEXM3YSQYBFJ4D","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"TOFEXM3Y","created_at":"2026-05-29T01:04:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TOFEXM3YSQYBFJ4DYYDJAIENK6","target":"record","payload":{"canonical_record":{"source":{"id":"2407.06865","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-07-09T13:53:08Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"dfefc02065a7e8d1dbe36ea63503bc9c710360a143912d7bb1aee988721c1ed9","abstract_canon_sha256":"788805ba44109e9b0649301c3bd1ce3c669ac504e82ceb540ccb5ffd5267ed27"},"schema_version":"1.0"},"canonical_sha256":"9b8a4bb378943012a783c60690208d57ab9dd41f43cfdc3d35be14853444389b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:04:50.816456Z","signature_b64":"FddHGG9Okq+iJtWB4v+k0UmtEJ9PWslqCIEUd3+hXuEtlZhYeXgVVi97S2uzdSxA28C+KFOHN2q4vk2dsqP3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b8a4bb378943012a783c60690208d57ab9dd41f43cfdc3d35be14853444389b","last_reissued_at":"2026-05-29T01:04:50.815712Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:04:50.815712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.06865","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T01:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/CIyqyDazgsNmOWSdiapXf9EWWTjZepddXUHt4XLT1xDQrwKMj3lLw6kBOG1VEPmGwZClOvFZSEHATarDbF4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:06:24.710729Z"},"content_sha256":"5d0a3b3fddd497efaaea8b16cef87ebaf370991bf49c909d941ccc5bbb58c993","schema_version":"1.0","event_id":"sha256:5d0a3b3fddd497efaaea8b16cef87ebaf370991bf49c909d941ccc5bbb58c993"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TOFEXM3YSQYBFJ4DYYDJAIENK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Affine $\\imath$quantum groups and Steinberg varieties of type C","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Changjian Su, Weiqiang Wang","submitted_at":"2024-07-09T13:53:08Z","abstract_excerpt":"We provide a geometric realization of the quasi-split affine $\\imath$quantum group of type AIII$_{2n-1}^{(\\tau)}$ in terms of equivariant K-groups of non-connected Steinberg varieties of type C. This uses a new Drinfeld type presentation of this affine $\\imath$quantum group which admits very nontrivial Serre relations. We then construct \\`a la Springer a family of finite-dimensional standard modules and irreducible modules of this $\\imath$quantum group, and provide a composition multiplicity formula of the standard modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06865","kind":"arxiv","version":3},"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/2407.06865/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":"2026-05-29T01:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1HUFj1C3i6bSZg25j0ImGwL0oWQGvmu5JhCkbDp/WcZY2nmUm5I73KkYZIzxHP9dOsdXn4kv+MLZwwK/YXq0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:06:24.711312Z"},"content_sha256":"dc14280ceef765b36c3d89fa59580b377412daa15bb32d2c99e9e19e70d919b9","schema_version":"1.0","event_id":"sha256:dc14280ceef765b36c3d89fa59580b377412daa15bb32d2c99e9e19e70d919b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TOFEXM3YSQYBFJ4DYYDJAIENK6/bundle.json","state_url":"https://pith.science/pith/TOFEXM3YSQYBFJ4DYYDJAIENK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TOFEXM3YSQYBFJ4DYYDJAIENK6/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":"2026-08-03T18:06:24Z","links":{"resolver":"https://pith.science/pith/TOFEXM3YSQYBFJ4DYYDJAIENK6","bundle":"https://pith.science/pith/TOFEXM3YSQYBFJ4DYYDJAIENK6/bundle.json","state":"https://pith.science/pith/TOFEXM3YSQYBFJ4DYYDJAIENK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TOFEXM3YSQYBFJ4DYYDJAIENK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TOFEXM3YSQYBFJ4DYYDJAIENK6","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":"788805ba44109e9b0649301c3bd1ce3c669ac504e82ceb540ccb5ffd5267ed27","cross_cats_sorted":["math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-07-09T13:53:08Z","title_canon_sha256":"dfefc02065a7e8d1dbe36ea63503bc9c710360a143912d7bb1aee988721c1ed9"},"schema_version":"1.0","source":{"id":"2407.06865","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.06865","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2407.06865v3","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.06865","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"TOFEXM3YSQYB","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"TOFEXM3YSQYBFJ4D","created_at":"2026-05-29T01:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"TOFEXM3Y","created_at":"2026-05-29T01:04:50Z"}],"graph_snapshots":[{"event_id":"sha256:dc14280ceef765b36c3d89fa59580b377412daa15bb32d2c99e9e19e70d919b9","target":"graph","created_at":"2026-05-29T01:04:50Z","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/2407.06865/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a geometric realization of the quasi-split affine $\\imath$quantum group of type AIII$_{2n-1}^{(\\tau)}$ in terms of equivariant K-groups of non-connected Steinberg varieties of type C. This uses a new Drinfeld type presentation of this affine $\\imath$quantum group which admits very nontrivial Serre relations. We then construct \\`a la Springer a family of finite-dimensional standard modules and irreducible modules of this $\\imath$quantum group, and provide a composition multiplicity formula of the standard modules.","authors_text":"Changjian Su, Weiqiang Wang","cross_cats":["math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-07-09T13:53:08Z","title":"Affine $\\imath$quantum groups and Steinberg varieties of type C"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06865","kind":"arxiv","version":3},"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":"sha256:5d0a3b3fddd497efaaea8b16cef87ebaf370991bf49c909d941ccc5bbb58c993","target":"record","created_at":"2026-05-29T01:04:50Z","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":"788805ba44109e9b0649301c3bd1ce3c669ac504e82ceb540ccb5ffd5267ed27","cross_cats_sorted":["math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-07-09T13:53:08Z","title_canon_sha256":"dfefc02065a7e8d1dbe36ea63503bc9c710360a143912d7bb1aee988721c1ed9"},"schema_version":"1.0","source":{"id":"2407.06865","kind":"arxiv","version":3}},"canonical_sha256":"9b8a4bb378943012a783c60690208d57ab9dd41f43cfdc3d35be14853444389b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b8a4bb378943012a783c60690208d57ab9dd41f43cfdc3d35be14853444389b","first_computed_at":"2026-05-29T01:04:50.815712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:04:50.815712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FddHGG9Okq+iJtWB4v+k0UmtEJ9PWslqCIEUd3+hXuEtlZhYeXgVVi97S2uzdSxA28C+KFOHN2q4vk2dsqP3Aw==","signature_status":"signed_v1","signed_at":"2026-05-29T01:04:50.816456Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.06865","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d0a3b3fddd497efaaea8b16cef87ebaf370991bf49c909d941ccc5bbb58c993","sha256:dc14280ceef765b36c3d89fa59580b377412daa15bb32d2c99e9e19e70d919b9"],"state_sha256":"73747f347614768f282270797de707bd6d0af9fbcf55849aa30332a3eb712369"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pQbTM1PsjkoU+wu1uD0sNU/TyZMuAWgiVCa2PiXStLJ1CRzb96M6Q+8STRKyH9qEBQ7PHfs2U0Dm++8dT3iqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T18:06:24.715663Z","bundle_sha256":"cb03fadc9415adb2821d6c29a3cc208f0ae73fa679c5c310bd1683ca8d71ca12"}}