{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:F4HJAZQ5MGAIUG3HYNLS5L4QUA","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":"f5404475adefc65cc5c0a6ff56bb84fb79940b0ff4ad3f0b80d20c0a461a2a8e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-09-23T06:24:01Z","title_canon_sha256":"69609b40cabb88c1e727eca31a84c04e275143dd08297e9337799d4a3bcac4df"},"schema_version":"1.0","source":{"id":"1009.4526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4526","created_at":"2026-05-18T04:40:30Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4526v1","created_at":"2026-05-18T04:40:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4526","created_at":"2026-05-18T04:40:30Z"},{"alias_kind":"pith_short_12","alias_value":"F4HJAZQ5MGAI","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F4HJAZQ5MGAIUG3H","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F4HJAZQ5","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:03172af6d6539435642bf6a61433f2072c370af56f022b832445ae85ed9fbf7c","target":"graph","created_at":"2026-05-18T04:40:30Z","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"},"paper":{"abstract_excerpt":"We give (conjectural) analogs of Berenstein-Zelevinsky data for affine type $A$. Moreover, by using these affine analogs of Berenstein-Zelevinsky data, we realize the crystal basis of the negative part of the quantized universal enveloping algebra of the (Langlands dual) Lie algebra of affine type $A$.","authors_text":"Daisuke Sagaki, Satoshi Naito, Yoshihisa Saito","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-09-23T06:24:01Z","title":"Toward Berenstein-Zelevinsky data in affine type $A$, I: Construction of affine analogs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4526","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":"sha256:1e6a6eabb6fe795146a4b0e3e74d77c2707bef692e8b0d1ad53ab13a2918191a","target":"record","created_at":"2026-05-18T04:40:30Z","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":"f5404475adefc65cc5c0a6ff56bb84fb79940b0ff4ad3f0b80d20c0a461a2a8e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-09-23T06:24:01Z","title_canon_sha256":"69609b40cabb88c1e727eca31a84c04e275143dd08297e9337799d4a3bcac4df"},"schema_version":"1.0","source":{"id":"1009.4526","kind":"arxiv","version":1}},"canonical_sha256":"2f0e90661d61808a1b67c3572eaf90a007892dd14a030487dc874cb4048e6420","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f0e90661d61808a1b67c3572eaf90a007892dd14a030487dc874cb4048e6420","first_computed_at":"2026-05-18T04:40:30.242012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:30.242012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xCurkNzJ7mcqAv/yYvvERrhNo8LPbXbGryIUqd/REX2C9AHitJhakFnP/mIm+BqhFqk8aNdl1jBpZeMMdY2aCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:30.242591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e6a6eabb6fe795146a4b0e3e74d77c2707bef692e8b0d1ad53ab13a2918191a","sha256:03172af6d6539435642bf6a61433f2072c370af56f022b832445ae85ed9fbf7c"],"state_sha256":"7518e216f6db12d959a0386f8601b7aa3cfd7573e232787b629b4f956a29bd1c"}