{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SILX7MJ36YNDPQSCCUPBR4Y4JX","short_pith_number":"pith:SILX7MJ3","schema_version":"1.0","canonical_sha256":"92177fb13bf61a37c242151e18f31c4df3e514f07dff6d128d25ca0b33fbc2f2","source":{"kind":"arxiv","id":"1410.8070","version":1},"attestation_state":"computed","paper":{"title":"Deformed Cohomology of Flag Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Dominic Searles, Oliver Pechenik","submitted_at":"2014-10-29T17:46:17Z","abstract_excerpt":"This paper introduces a two-parameter deformation of the cohomology of generalized flag varieties. One special case is the Belkale-Kumar deformation (used to study eigencones of Lie groups). Another picks out intersections of Schubert varieties that behave nicely under projections. Our construction yields a new proof that the Belkale-Kumar product is well-defined. This proof is shorter and more elementary than earlier proofs."},"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":"1410.8070","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-29T17:46:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"981b16b866ab7b40d1f1a945df5f5145ec339e0c97ed3ed1684cc0c4046d6e41","abstract_canon_sha256":"140dd5ccd7e2a6253627e8ebf502efbd7de19a9c4726b38c03798d8e1cd08560"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:00.837685Z","signature_b64":"VJiWWsih+UCMZCwjgLkDDjMtvGieuSeNkyO8etZWMfxqO8xAefjRQLpF0mELPrdgbqlE3tyi5QF1xZesTivYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92177fb13bf61a37c242151e18f31c4df3e514f07dff6d128d25ca0b33fbc2f2","last_reissued_at":"2026-05-18T00:11:00.836887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:00.836887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformed Cohomology of Flag Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Dominic Searles, Oliver Pechenik","submitted_at":"2014-10-29T17:46:17Z","abstract_excerpt":"This paper introduces a two-parameter deformation of the cohomology of generalized flag varieties. One special case is the Belkale-Kumar deformation (used to study eigencones of Lie groups). Another picks out intersections of Schubert varieties that behave nicely under projections. Our construction yields a new proof that the Belkale-Kumar product is well-defined. This proof is shorter and more elementary than earlier proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8070","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":"1410.8070","created_at":"2026-05-18T00:11:00.837007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.8070v1","created_at":"2026-05-18T00:11:00.837007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8070","created_at":"2026-05-18T00:11:00.837007+00:00"},{"alias_kind":"pith_short_12","alias_value":"SILX7MJ36YND","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SILX7MJ36YNDPQSC","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SILX7MJ3","created_at":"2026-05-18T12:28:49.207871+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/SILX7MJ36YNDPQSCCUPBR4Y4JX","json":"https://pith.science/pith/SILX7MJ36YNDPQSCCUPBR4Y4JX.json","graph_json":"https://pith.science/api/pith-number/SILX7MJ36YNDPQSCCUPBR4Y4JX/graph.json","events_json":"https://pith.science/api/pith-number/SILX7MJ36YNDPQSCCUPBR4Y4JX/events.json","paper":"https://pith.science/paper/SILX7MJ3"},"agent_actions":{"view_html":"https://pith.science/pith/SILX7MJ36YNDPQSCCUPBR4Y4JX","download_json":"https://pith.science/pith/SILX7MJ36YNDPQSCCUPBR4Y4JX.json","view_paper":"https://pith.science/paper/SILX7MJ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.8070&json=true","fetch_graph":"https://pith.science/api/pith-number/SILX7MJ36YNDPQSCCUPBR4Y4JX/graph.json","fetch_events":"https://pith.science/api/pith-number/SILX7MJ36YNDPQSCCUPBR4Y4JX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SILX7MJ36YNDPQSCCUPBR4Y4JX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SILX7MJ36YNDPQSCCUPBR4Y4JX/action/storage_attestation","attest_author":"https://pith.science/pith/SILX7MJ36YNDPQSCCUPBR4Y4JX/action/author_attestation","sign_citation":"https://pith.science/pith/SILX7MJ36YNDPQSCCUPBR4Y4JX/action/citation_signature","submit_replication":"https://pith.science/pith/SILX7MJ36YNDPQSCCUPBR4Y4JX/action/replication_record"}},"created_at":"2026-05-18T00:11:00.837007+00:00","updated_at":"2026-05-18T00:11:00.837007+00:00"}