{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BPSOLKVXD567AAPUXWORODWJTJ","short_pith_number":"pith:BPSOLKVX","canonical_record":{"source":{"id":"2602.11559","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-02-12T04:26:41Z","cross_cats_sorted":["math.AG","math.QA"],"title_canon_sha256":"af70fdfeccd7ee64b88bf713fb0a7508ba21e8147d5e7b7f68e197cdb19490a8","abstract_canon_sha256":"b59ac9374d7dbdc98c9030f6f8fa9ab45abb3bf89398d5d8bf2ea400e3089ba3"},"schema_version":"1.0"},"canonical_sha256":"0be4e5aab71f7df001f4bd9d170ec99a517e4712030b497226e5e901379dcd18","source":{"kind":"arxiv","id":"2602.11559","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.11559","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"2602.11559v5","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.11559","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"BPSOLKVXD567","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"pith_short_16","alias_value":"BPSOLKVXD567AAPU","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"pith_short_8","alias_value":"BPSOLKVX","created_at":"2026-05-26T02:04:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BPSOLKVXD567AAPUXWORODWJTJ","target":"record","payload":{"canonical_record":{"source":{"id":"2602.11559","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-02-12T04:26:41Z","cross_cats_sorted":["math.AG","math.QA"],"title_canon_sha256":"af70fdfeccd7ee64b88bf713fb0a7508ba21e8147d5e7b7f68e197cdb19490a8","abstract_canon_sha256":"b59ac9374d7dbdc98c9030f6f8fa9ab45abb3bf89398d5d8bf2ea400e3089ba3"},"schema_version":"1.0"},"canonical_sha256":"0be4e5aab71f7df001f4bd9d170ec99a517e4712030b497226e5e901379dcd18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:06.062816Z","signature_b64":"k2yt7OIsTs8LkyGUkncE/8DjAdFflptoVB2awCKFW2/8vrA77cUxu7p1xO1nCAbu9hktzoSMne2WzCUHRdPLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0be4e5aab71f7df001f4bd9d170ec99a517e4712030b497226e5e901379dcd18","last_reissued_at":"2026-05-26T02:04:06.061910Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:06.061910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.11559","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T02:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"geUG1y9xXpzL6wIWQqB4iTUwAU0/yd+hLM4/ShuopLJKxDvQCF9V4FxERonh1TVS1OLoQLXd79jxsYFyuc0+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:38:37.571560Z"},"content_sha256":"784ccfdc9985fc1e6c2dec88825d26e95201eacd34dedad06ba2b28447f6e6c0","schema_version":"1.0","event_id":"sha256:784ccfdc9985fc1e6c2dec88825d26e95201eacd34dedad06ba2b28447f6e6c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BPSOLKVXD567AAPUXWORODWJTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"Yingjin Bi","submitted_at":"2026-02-12T04:26:41Z","abstract_excerpt":"Let $G$ be a simple, simply connected, simply laced algebraic group. We construct a monoidal category of representations of the quantum affine algebra $U_q(\\widehat{\\mathfrak{g}})$ whose Grothendieck ring contains a cluster algebra with initial seed given by that of the coordinate ring of twisted products of flag varieties. This class of varieties includes, in particular, braid varieties and reduced double Bruhat cells."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.11559","kind":"arxiv","version":5},"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/2602.11559/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":"2026-05-26T02:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ENTbXKOaZqfDjsarCb4x6BlkSX6QsfJOLROpYkB3aKZQkkXhRqqVJxlypqSSVHl1pihfOsXUcvjuA/aUkCe4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:38:37.572113Z"},"content_sha256":"99a549304b30bd46ada0d051c29e5e790791aa97efd4fb6d371ad2302c02b5ae","schema_version":"1.0","event_id":"sha256:99a549304b30bd46ada0d051c29e5e790791aa97efd4fb6d371ad2302c02b5ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BPSOLKVXD567AAPUXWORODWJTJ/bundle.json","state_url":"https://pith.science/pith/BPSOLKVXD567AAPUXWORODWJTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BPSOLKVXD567AAPUXWORODWJTJ/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":"2026-08-08T20:38:37Z","links":{"resolver":"https://pith.science/pith/BPSOLKVXD567AAPUXWORODWJTJ","bundle":"https://pith.science/pith/BPSOLKVXD567AAPUXWORODWJTJ/bundle.json","state":"https://pith.science/pith/BPSOLKVXD567AAPUXWORODWJTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BPSOLKVXD567AAPUXWORODWJTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BPSOLKVXD567AAPUXWORODWJTJ","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":"b59ac9374d7dbdc98c9030f6f8fa9ab45abb3bf89398d5d8bf2ea400e3089ba3","cross_cats_sorted":["math.AG","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-02-12T04:26:41Z","title_canon_sha256":"af70fdfeccd7ee64b88bf713fb0a7508ba21e8147d5e7b7f68e197cdb19490a8"},"schema_version":"1.0","source":{"id":"2602.11559","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.11559","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"2602.11559v5","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.11559","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"BPSOLKVXD567","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"pith_short_16","alias_value":"BPSOLKVXD567AAPU","created_at":"2026-05-26T02:04:06Z"},{"alias_kind":"pith_short_8","alias_value":"BPSOLKVX","created_at":"2026-05-26T02:04:06Z"}],"graph_snapshots":[{"event_id":"sha256:99a549304b30bd46ada0d051c29e5e790791aa97efd4fb6d371ad2302c02b5ae","target":"graph","created_at":"2026-05-26T02:04:06Z","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/2602.11559/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a simple, simply connected, simply laced algebraic group. We construct a monoidal category of representations of the quantum affine algebra $U_q(\\widehat{\\mathfrak{g}})$ whose Grothendieck ring contains a cluster algebra with initial seed given by that of the coordinate ring of twisted products of flag varieties. This class of varieties includes, in particular, braid varieties and reduced double Bruhat cells.","authors_text":"Yingjin Bi","cross_cats":["math.AG","math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.11559","kind":"arxiv","version":5},"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":"sha256:784ccfdc9985fc1e6c2dec88825d26e95201eacd34dedad06ba2b28447f6e6c0","target":"record","created_at":"2026-05-26T02:04:06Z","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":"b59ac9374d7dbdc98c9030f6f8fa9ab45abb3bf89398d5d8bf2ea400e3089ba3","cross_cats_sorted":["math.AG","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-02-12T04:26:41Z","title_canon_sha256":"af70fdfeccd7ee64b88bf713fb0a7508ba21e8147d5e7b7f68e197cdb19490a8"},"schema_version":"1.0","source":{"id":"2602.11559","kind":"arxiv","version":5}},"canonical_sha256":"0be4e5aab71f7df001f4bd9d170ec99a517e4712030b497226e5e901379dcd18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0be4e5aab71f7df001f4bd9d170ec99a517e4712030b497226e5e901379dcd18","first_computed_at":"2026-05-26T02:04:06.061910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:06.061910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k2yt7OIsTs8LkyGUkncE/8DjAdFflptoVB2awCKFW2/8vrA77cUxu7p1xO1nCAbu9hktzoSMne2WzCUHRdPLDg==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:06.062816Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.11559","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:784ccfdc9985fc1e6c2dec88825d26e95201eacd34dedad06ba2b28447f6e6c0","sha256:99a549304b30bd46ada0d051c29e5e790791aa97efd4fb6d371ad2302c02b5ae"],"state_sha256":"832dce5b6bdc3ed777048febe51691404e7a800322ab651f08c0c54c47cbb951"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nM5WbGfP7Egu2HvxcS3fF0uJd6rjMSDreTA9g3uYbi7lLsmUUpta+g0Ara8sPFVajbQV9GqD42iBEtSq9xyvDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T20:38:37.577168Z","bundle_sha256":"1924b6f361fa734a7de4d6e50f097c939e9329d2ce248b2d8a8e9d5a5b43a49c"}}