{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LRQB3ICR7RTEL2RHWQO5DH35GB","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":"4e7851bf78017421225f5773d3009ab85b85bfec7b75d339ac2b9b60091e60aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-08T20:33:35Z","title_canon_sha256":"793b83a2d7f74571f7194219f0e6b9c28f7359cbbef39118671918cb90cec137"},"schema_version":"1.0","source":{"id":"1009.1645","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1645","created_at":"2026-05-18T04:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1645v1","created_at":"2026-05-18T04:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1645","created_at":"2026-05-18T04:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"LRQB3ICR7RTE","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LRQB3ICR7RTEL2RH","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LRQB3ICR","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:4f4eef0adc2a0fc7f54c09ffbbca9caa7c1149c4f8372570ea55aeaa9f30ec1b","target":"graph","created_at":"2026-05-18T04:41:13Z","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 construct the RR varieties as the fiber products of Bott-Samelson varieties over Richardson varieties. We study their homogeneous coordinate rings and standard monomial theory.","authors_text":"Philip Foth, Sangjib Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-08T20:33:35Z","title":"Standard Monomial Theory of RR varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1645","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":"sha256:9edddea6813fc9330f19b2977e685682db28d49869ea92c4926c3c7b547b1545","target":"record","created_at":"2026-05-18T04:41:13Z","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":"4e7851bf78017421225f5773d3009ab85b85bfec7b75d339ac2b9b60091e60aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-08T20:33:35Z","title_canon_sha256":"793b83a2d7f74571f7194219f0e6b9c28f7359cbbef39118671918cb90cec137"},"schema_version":"1.0","source":{"id":"1009.1645","kind":"arxiv","version":1}},"canonical_sha256":"5c601da051fc6645ea27b41dd19f7d3065322504e8158c797ac0ca754287f55d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c601da051fc6645ea27b41dd19f7d3065322504e8158c797ac0ca754287f55d","first_computed_at":"2026-05-18T04:41:13.818319Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:13.818319Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W7iHiB62pAp7/aweta98r67rE068o+/7/gSZnslK8Hk612v/Vkg5Sp1ObgmxYecTS9sXfRZ/iB9kdC+AwWmVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:13.818777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1645","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9edddea6813fc9330f19b2977e685682db28d49869ea92c4926c3c7b547b1545","sha256:4f4eef0adc2a0fc7f54c09ffbbca9caa7c1149c4f8372570ea55aeaa9f30ec1b"],"state_sha256":"626bba736dcded25c36dbd664f9f2bd44690a1803d0cddf5a874c31ee5e62a54"}