{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KQRAXUPEJ3L4WTPRLP2A7QRGKR","short_pith_number":"pith:KQRAXUPE","schema_version":"1.0","canonical_sha256":"54220bd1e44ed7cb4df15bf40fc22654409adae6aaa49159d5a933996afee358","source":{"kind":"arxiv","id":"1409.6097","version":1},"attestation_state":"computed","paper":{"title":"Geometric mitosis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Valentina Kiritchenko","submitted_at":"2014-09-22T07:50:44Z","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}."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.6097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-22T07:50:44Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"318f22b6902930998344783eae881ec30a97526beb51c71bd5ca0642bcfa6360","abstract_canon_sha256":"abedbe305924983fbc414f22536ad753257e0a9b997fd87b361b222b81aa69b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:37.203251Z","signature_b64":"bpEuAl8fOvLoEL5KPT7JTmtrbsaniKzrS+36ogMTy7+p95x1IfhKts6Jyet8JH8PtIeZ5BvQf6TvVklI0NZDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54220bd1e44ed7cb4df15bf40fc22654409adae6aaa49159d5a933996afee358","last_reissued_at":"2026-05-17T23:54:37.202706Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:37.202706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric mitosis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Valentina Kiritchenko","submitted_at":"2014-09-22T07:50:44Z","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}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6097","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.6097","created_at":"2026-05-17T23:54:37.202788+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.6097v1","created_at":"2026-05-17T23:54:37.202788+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6097","created_at":"2026-05-17T23:54:37.202788+00:00"},{"alias_kind":"pith_short_12","alias_value":"KQRAXUPEJ3L4","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KQRAXUPEJ3L4WTPR","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KQRAXUPE","created_at":"2026-05-18T12:28:35.611951+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KQRAXUPEJ3L4WTPRLP2A7QRGKR","json":"https://pith.science/pith/KQRAXUPEJ3L4WTPRLP2A7QRGKR.json","graph_json":"https://pith.science/api/pith-number/KQRAXUPEJ3L4WTPRLP2A7QRGKR/graph.json","events_json":"https://pith.science/api/pith-number/KQRAXUPEJ3L4WTPRLP2A7QRGKR/events.json","paper":"https://pith.science/paper/KQRAXUPE"},"agent_actions":{"view_html":"https://pith.science/pith/KQRAXUPEJ3L4WTPRLP2A7QRGKR","download_json":"https://pith.science/pith/KQRAXUPEJ3L4WTPRLP2A7QRGKR.json","view_paper":"https://pith.science/paper/KQRAXUPE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.6097&json=true","fetch_graph":"https://pith.science/api/pith-number/KQRAXUPEJ3L4WTPRLP2A7QRGKR/graph.json","fetch_events":"https://pith.science/api/pith-number/KQRAXUPEJ3L4WTPRLP2A7QRGKR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KQRAXUPEJ3L4WTPRLP2A7QRGKR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KQRAXUPEJ3L4WTPRLP2A7QRGKR/action/storage_attestation","attest_author":"https://pith.science/pith/KQRAXUPEJ3L4WTPRLP2A7QRGKR/action/author_attestation","sign_citation":"https://pith.science/pith/KQRAXUPEJ3L4WTPRLP2A7QRGKR/action/citation_signature","submit_replication":"https://pith.science/pith/KQRAXUPEJ3L4WTPRLP2A7QRGKR/action/replication_record"}},"created_at":"2026-05-17T23:54:37.202788+00:00","updated_at":"2026-05-17T23:54:37.202788+00:00"}