{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KQRAXUPEJ3L4WTPRLP2A7QRGKR","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":"abedbe305924983fbc414f22536ad753257e0a9b997fd87b361b222b81aa69b7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-22T07:50:44Z","title_canon_sha256":"318f22b6902930998344783eae881ec30a97526beb51c71bd5ca0642bcfa6360"},"schema_version":"1.0","source":{"id":"1409.6097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6097","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6097v1","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6097","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"pith_short_12","alias_value":"KQRAXUPEJ3L4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KQRAXUPEJ3L4WTPR","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KQRAXUPE","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:4cbf5a68dc95fdc1544c84d569a4666a5e9a22bb0f2d7ceabbd033e002ca9653","target":"graph","created_at":"2026-05-17T23:54:37Z","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 describe an elementary convex geometric algorithm for realizing Schubert cycles in complete flag varieties by unions of faces of polytopes. For GL_n and Gelfand--Zetlin polytopes, combinatorics of this algorithm coincides with that of the mitosis on pipe dreams introduced by Knutson and Miller. For Sp_4 and a Newton--Okounkov polytope of the symplectic flag variety, the algorithm yields a new combinatorial rule that extends to Sp_{2n}.","authors_text":"Valentina Kiritchenko","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-22T07:50:44Z","title":"Geometric mitosis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6097","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:aba3d68d0b992128e0b68b6cf205c4d16bff198094bdd219c73ecec4df84c634","target":"record","created_at":"2026-05-17T23:54:37Z","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":"abedbe305924983fbc414f22536ad753257e0a9b997fd87b361b222b81aa69b7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-22T07:50:44Z","title_canon_sha256":"318f22b6902930998344783eae881ec30a97526beb51c71bd5ca0642bcfa6360"},"schema_version":"1.0","source":{"id":"1409.6097","kind":"arxiv","version":1}},"canonical_sha256":"54220bd1e44ed7cb4df15bf40fc22654409adae6aaa49159d5a933996afee358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54220bd1e44ed7cb4df15bf40fc22654409adae6aaa49159d5a933996afee358","first_computed_at":"2026-05-17T23:54:37.202706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:37.202706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bpEuAl8fOvLoEL5KPT7JTmtrbsaniKzrS+36ogMTy7+p95x1IfhKts6Jyet8JH8PtIeZ5BvQf6TvVklI0NZDCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:37.203251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aba3d68d0b992128e0b68b6cf205c4d16bff198094bdd219c73ecec4df84c634","sha256:4cbf5a68dc95fdc1544c84d569a4666a5e9a22bb0f2d7ceabbd033e002ca9653"],"state_sha256":"22ac595909fdce6f93159d79d7458db567cad7095f34f1226eb65900860fefe8"}