{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:QYPJJFWF5F5WNIKBVWLULDPQP4","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":"1bed813d4dfeef2b3826bc9a49cb2f48f3fb468da84417fa0d4fc952850b791b","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.AG","submitted_at":"1999-08-31T22:12:37Z","title_canon_sha256":"87a80a59ebfad69f29c6dbfc5cc06056abab1e4244fbea9634cc9c15a5bb2a3c"},"schema_version":"1.0","source":{"id":"math/9908172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9908172","created_at":"2026-07-04T14:41:17Z"},{"alias_kind":"arxiv_version","alias_value":"math/9908172v1","created_at":"2026-07-04T14:41:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9908172","created_at":"2026-07-04T14:41:17Z"},{"alias_kind":"pith_short_12","alias_value":"QYPJJFWF5F5W","created_at":"2026-07-04T14:41:17Z"},{"alias_kind":"pith_short_16","alias_value":"QYPJJFWF5F5WNIKB","created_at":"2026-07-04T14:41:17Z"},{"alias_kind":"pith_short_8","alias_value":"QYPJJFWF","created_at":"2026-07-04T14:41:17Z"}],"graph_snapshots":[{"event_id":"sha256:0f87f8593cd4fcb1d2c921477f1357176384e56b1325478ff4195e34cd68daaa","target":"graph","created_at":"2026-07-04T14:41:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/9908172/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a conjecture of Dale Peterson on positivity in the multiplication in the T-equivariant cohomology of the flag variety. The theorem follows from a more general positivity result about the equivariant cohomology of varieties with actions of a solvable group with finitely many orbits. This more general result is an equivariant version of a theorem of Kumar and Nori.","authors_text":"William Graham","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1999-08-31T22:12:37Z","title":"Positivity in equivariant Schubert calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9908172","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":"sha256:127c7803d68195e312bcd47e9c0e519f23e39f685309fa5dd0de088c88961c91","target":"record","created_at":"2026-07-04T14:41:17Z","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":"1bed813d4dfeef2b3826bc9a49cb2f48f3fb468da84417fa0d4fc952850b791b","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.AG","submitted_at":"1999-08-31T22:12:37Z","title_canon_sha256":"87a80a59ebfad69f29c6dbfc5cc06056abab1e4244fbea9634cc9c15a5bb2a3c"},"schema_version":"1.0","source":{"id":"math/9908172","kind":"arxiv","version":1}},"canonical_sha256":"861e9496c5e97b66a141ad97458df07f1785b07ec7194f2544d4f7715e83dd4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"861e9496c5e97b66a141ad97458df07f1785b07ec7194f2544d4f7715e83dd4e","first_computed_at":"2026-07-04T14:41:17.649674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:41:17.649674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BQPUfzkCw2t95HvS0OVk5HjhIwKM6rpWqMp050Ku0fquRUxrzilp6tuKO6VzVrqGVvMbNW5ZI9VnvipwuoopDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:41:17.650063Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9908172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:127c7803d68195e312bcd47e9c0e519f23e39f685309fa5dd0de088c88961c91","sha256:0f87f8593cd4fcb1d2c921477f1357176384e56b1325478ff4195e34cd68daaa"],"state_sha256":"e1eea74d8a57c5c6d8c2e8faa68a04ffac8e2ca342303ee2694c695e7d1d6cc2"}