{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NMRUKBQCEBZ67D3UGANB4MD6IW","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":"0aece54931be7b26cf2d017eab3b1ee9ed8488089cbf2efa1bcef56ad9eff0bb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-27T04:44:01Z","title_canon_sha256":"2f25a10a42a3ea41c05594c05cbcdaf86667ad3f692b90a9e4f236868350d245"},"schema_version":"1.0","source":{"id":"1801.09033","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09033","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09033v6","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09033","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"NMRUKBQCEBZ6","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"NMRUKBQCEBZ67D3U","created_at":"2026-05-20T00:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"NMRUKBQC","created_at":"2026-05-20T00:01:31Z"}],"graph_snapshots":[{"event_id":"sha256:d4fa59406fa8495eb14841272bca1400ec80dbc1991f6a885cf530bf4cd4e580","target":"graph","created_at":"2026-05-20T00:01:31Z","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/1801.09033/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define an action of the double coinvariant algebra\n  $DR_n$ on the equivariant Borel-Moore homology of the affine flag variety\n  $\\widetilde{Fl}_n$ in type $A$, which has an explicit form in terms of\n  the left and right action of the (extended) affine Weyl group and multiplication by Chern classes.\n  Up to first order in the augmentation ideal, we show that it coincides with the\n  action of the Cherednik algebra on the equivariant homology of\n  the homogeneous affine Springer fiber $\\widetilde{S}_{n,n+1} \\subset \\widetilde{Fl}_n$\n  due to Yun and the second author, and therefore\n  preserve","authors_text":"Alexei Oblomkov, Erik Carlsson","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-27T04:44:01Z","title":"Affine Schubert calculus and double coinvariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09033","kind":"arxiv","version":6},"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":"sha256:7d68ea074c57de751558b85d53bfa4e2ee75540978e9b37288b166f863f929ee","target":"record","created_at":"2026-05-20T00:01:31Z","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":"0aece54931be7b26cf2d017eab3b1ee9ed8488089cbf2efa1bcef56ad9eff0bb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-27T04:44:01Z","title_canon_sha256":"2f25a10a42a3ea41c05594c05cbcdaf86667ad3f692b90a9e4f236868350d245"},"schema_version":"1.0","source":{"id":"1801.09033","kind":"arxiv","version":6}},"canonical_sha256":"6b234506022073ef8f74301a1e307e45b1af8666def38f0017b5ffb1cb9738cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b234506022073ef8f74301a1e307e45b1af8666def38f0017b5ffb1cb9738cc","first_computed_at":"2026-05-20T00:01:31.587235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:31.587235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ign8o1aMCkxv7RKyQ7r10qKlDjaycK+NLZtWJfw1jGaRUB0GJlaTLLDV3jyFlhvyp0KDHww3jd/R/bfwopkrAg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:31.588082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09033","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d68ea074c57de751558b85d53bfa4e2ee75540978e9b37288b166f863f929ee","sha256:d4fa59406fa8495eb14841272bca1400ec80dbc1991f6a885cf530bf4cd4e580"],"state_sha256":"d31f7488cbc53e1700ffe0a355738b54d5ca93d672bb295f22b0e01eea6db24d"}