{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XALA2KM7HE7BJTG35YGBPAWLD6","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":"b28f25fc88719b257d896263f3138d0f9a6eb9e81661c24e2a0d9c595d9116ff","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-26T19:55:16Z","title_canon_sha256":"1e8d01b2dd7afd5d847252ea211fd4486ab97bb62e2907f32549abbcc8ee458b"},"schema_version":"1.0","source":{"id":"1601.07146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07146","created_at":"2026-05-18T01:21:57Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07146v1","created_at":"2026-05-18T01:21:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07146","created_at":"2026-05-18T01:21:57Z"},{"alias_kind":"pith_short_12","alias_value":"XALA2KM7HE7B","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XALA2KM7HE7BJTG3","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XALA2KM7","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:9cd9f449bfa435b1a7dfb829e2d5bdc69c18233690654c30c043d385a10abcf8","target":"graph","created_at":"2026-05-18T01:21:57Z","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 construct combinatorial bases of the $T$-equivariant ($T$ is the maximal torus) cohomology $H^\\bullet_T(\\Sigma,k)$ of the Bott-Samelson variety $\\Sigma$ under some mild restrictions on the field of coefficients $k$. This bases allow us to prove the surjectivity of the restrictions $H^\\bullet_T(\\Sigma,k)\\to H^\\bullet_T(\\pi^{-1}(x),k)$ and $H^\\bullet_T(\\Sigma,k)\\to H^\\bullet_T(\\Sigma\\setminus\\pi^{-1}(x),k)$, where $\\pi:\\Sigma\\to G/B$ is the canonical resolution. In fact, we also construct bases of the targets of these restrictions by picking up certain subsets of certain bases of $H^\\bullet_T","authors_text":"Vladimir Shchigolev","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-26T19:55:16Z","title":"Bases of T-equivariant cohomology of Bott-Samelson varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07146","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":"sha256:7a5e6441f8949c182e03281d1055af78755a4920470cfc732e46a282d6c92806","target":"record","created_at":"2026-05-18T01:21:57Z","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":"b28f25fc88719b257d896263f3138d0f9a6eb9e81661c24e2a0d9c595d9116ff","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-26T19:55:16Z","title_canon_sha256":"1e8d01b2dd7afd5d847252ea211fd4486ab97bb62e2907f32549abbcc8ee458b"},"schema_version":"1.0","source":{"id":"1601.07146","kind":"arxiv","version":1}},"canonical_sha256":"b8160d299f393e14ccdbee0c1782cb1fa4902a4b92547b43a72fd0af0e0f3522","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8160d299f393e14ccdbee0c1782cb1fa4902a4b92547b43a72fd0af0e0f3522","first_computed_at":"2026-05-18T01:21:57.299582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:57.299582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LwUV2sdPr9d93qwakOnpHpILGWpbhl+QsQIxDYdIHYFs2tU9vtVrODLwFxR4QJiUHZfA4L2sY/ejFwHcD4eWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:57.300132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a5e6441f8949c182e03281d1055af78755a4920470cfc732e46a282d6c92806","sha256:9cd9f449bfa435b1a7dfb829e2d5bdc69c18233690654c30c043d385a10abcf8"],"state_sha256":"9743baeca03b1ece96581a5a99cf1e898804387ea3e96698585f89b49e6c43d1"}