{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RXYXE62ADTKIMLTLWUSGZU4W3R","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":"c47286028da606d120fd97e26150db6858c2ce29055dab00689b355da680ca26","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-11T09:58:02Z","title_canon_sha256":"690d61bf2284f1ac756ea49cddbb956aa2aa7d2efd117bee6dcc372b998e1399"},"schema_version":"1.0","source":{"id":"1303.2466","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2466","created_at":"2026-05-18T02:29:23Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2466v3","created_at":"2026-05-18T02:29:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2466","created_at":"2026-05-18T02:29:23Z"},{"alias_kind":"pith_short_12","alias_value":"RXYXE62ADTKI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RXYXE62ADTKIMLTL","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RXYXE62A","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:55df5269540ee4b1f25320c321d503e48ded282622407c3fd6bbddc2a9738478","target":"graph","created_at":"2026-05-18T02:29:23Z","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":"Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this fundamental theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer's classification of spherical rank-1-varieties.","authors_text":"Friedrich Knop","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-11T09:58:02Z","title":"Spherical roots of spherical varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2466","kind":"arxiv","version":3},"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":"sha256:8a4582d790f026360eedf58d63d85396f039f5859f4c1a61925b9e036a11d750","target":"record","created_at":"2026-05-18T02:29:23Z","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":"c47286028da606d120fd97e26150db6858c2ce29055dab00689b355da680ca26","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-11T09:58:02Z","title_canon_sha256":"690d61bf2284f1ac756ea49cddbb956aa2aa7d2efd117bee6dcc372b998e1399"},"schema_version":"1.0","source":{"id":"1303.2466","kind":"arxiv","version":3}},"canonical_sha256":"8df1727b401cd4862e6bb5246cd396dc715278e94b580d3ae11dda2135cb08ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8df1727b401cd4862e6bb5246cd396dc715278e94b580d3ae11dda2135cb08ea","first_computed_at":"2026-05-18T02:29:23.711707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:23.711707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ptPnpx092TB8VTbXildG5ZbNVdOoctdciZMW5GT2ukd8Le0yqn0C/wgu+dh3jc3Nm3FTa4/lWkk5ZcDtixtfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:23.712332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.2466","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a4582d790f026360eedf58d63d85396f039f5859f4c1a61925b9e036a11d750","sha256:55df5269540ee4b1f25320c321d503e48ded282622407c3fd6bbddc2a9738478"],"state_sha256":"16a50c9d9e5cfca2f89ad9bb74a6ca2e89e9dd1082317ecbeadcc080a9263c33"}