{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E72CYXVDXBZ6VKFRXZ3FRAKYJ7","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":"925ce552d66179dad4df6363951135c47680262c615f8b9fc98033caf7eff62b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-21T17:36:33Z","title_canon_sha256":"c56b6e3b019543e0ec7db53ed935c0d4ebe94506760f5d6d2a2e3b4f08610a29"},"schema_version":"1.0","source":{"id":"1210.5740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5740","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5740v1","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5740","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"E72CYXVDXBZ6","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E72CYXVDXBZ6VKFR","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E72CYXVD","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:f895d1ce96ba05c896fb379f539e85c246bf72a71ad5cd1e92b6c55c73b8f4b6","target":"graph","created_at":"2026-05-18T02:40:03Z","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":"Let $G$ be a reductive complex algebraic group, $T$ a maximal torus of $G$, $B$ a Borel subgroup of $G$ containing $T$, $\\Phi$ the root system of $G$ w.r.t. $T$, $W$ the Weyl group of $\\Phi$. Denote by $\\Fo = G/B$ the flag variety, by $X_w$ the Schubert subvariety of $\\Fo$ associated with an element $w\\in W$, and by $C_w$ the tangent cone to $X_w$ at the point $p = eB$. Then $C_w$ is a subscheme of the tangent space $T_pX_w\\subseteq T_p\\Fo$. Suppose $w$, $w'$ are distinct involutions in $W$. Using the so-called Kostant--Kumar polynomials, we show that if every irreducible component of $\\Phi$ i","authors_text":"Dmitriy Y. Eliseev, Mikhail V. Ignatyev","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-21T17:36:33Z","title":"Kostant--Kumar polynomials and tangent cones to Schubert varieties for involutions in $A_n$, $F_4$ and $G_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5740","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:cb54976ff0d34eb8351b2bd60361ca083c2bbe24a3972baf92beb3ed7c40dc0a","target":"record","created_at":"2026-05-18T02:40:03Z","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":"925ce552d66179dad4df6363951135c47680262c615f8b9fc98033caf7eff62b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-21T17:36:33Z","title_canon_sha256":"c56b6e3b019543e0ec7db53ed935c0d4ebe94506760f5d6d2a2e3b4f08610a29"},"schema_version":"1.0","source":{"id":"1210.5740","kind":"arxiv","version":1}},"canonical_sha256":"27f42c5ea3b873eaa8b1be765881584fcffa724101a287e5f2c6378656820378","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27f42c5ea3b873eaa8b1be765881584fcffa724101a287e5f2c6378656820378","first_computed_at":"2026-05-18T02:40:03.527612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:03.527612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EuNF78iVVZcbp5ux1vVCUgpUIoEMZ+Y+S7UsBn9oBjIaoNqRhWHSJcZJcGDJUYAXOC7dcevVVoX8DEbQp5G0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:03.528045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb54976ff0d34eb8351b2bd60361ca083c2bbe24a3972baf92beb3ed7c40dc0a","sha256:f895d1ce96ba05c896fb379f539e85c246bf72a71ad5cd1e92b6c55c73b8f4b6"],"state_sha256":"d7381a73a95ae48bbe7a061cd405677513b8ca51516059f2064f88fd2f69fec6"}