{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UTEEVVFQAI3W5SJ74T3V33JP2C","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":"c7cc5f454b64ae6e796d51647484ce54734fe4412ed762dd4678fdfd4b915f4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-26T19:54:18Z","title_canon_sha256":"05eca811765074c4fbd390de3211914d2451b23c70d96896453b6c5baaf31654"},"schema_version":"1.0","source":{"id":"1311.6791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6791","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6791v1","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6791","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"pith_short_12","alias_value":"UTEEVVFQAI3W","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UTEEVVFQAI3W5SJ7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UTEEVVFQ","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:6c2ee63773f369baa5f4454eae010f16be9d19216dfe854edfd3a7fe4c626011","target":"graph","created_at":"2026-05-18T03:06:05Z","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 show that nef cycle classes on smooth complete spherical varieties are effective, and the products of nef cycle classes are also nef. Let X be a smooth projective spherical variety such that its effective cycle classes of codimension k are nef, where 1<= k <= dim(X)-1. We study the properties of X. And we show that if X is a toric variety, then X is isomorphic to the product of some projective spaces; if X is toroidal, then X is isomorphic to a rational homogeneous space; if X is horospherical, dim(X)>= 3 and k=2, then effective divisors on X are nef; if X is horospherical and effective div","authors_text":"Qifeng Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-26T19:54:18Z","title":"Pseudo-effective and nef cones on spherical varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6791","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":"sha256:9963b6dfed7476dcbabae1d6b0f7c55c8cd24a8fa8e89952f4a11c52d276aa12","target":"record","created_at":"2026-05-18T03:06:05Z","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":"c7cc5f454b64ae6e796d51647484ce54734fe4412ed762dd4678fdfd4b915f4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-26T19:54:18Z","title_canon_sha256":"05eca811765074c4fbd390de3211914d2451b23c70d96896453b6c5baaf31654"},"schema_version":"1.0","source":{"id":"1311.6791","kind":"arxiv","version":1}},"canonical_sha256":"a4c84ad4b002376ec93fe4f75ded2fd0a5d2ee1708591aa71a8984a26d30f9ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4c84ad4b002376ec93fe4f75ded2fd0a5d2ee1708591aa71a8984a26d30f9ed","first_computed_at":"2026-05-18T03:06:05.800823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:05.800823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RaYvaqQtdm4CjhAimxOuu7hoIEUsobaPCbAXzaZJh18YtckYq5Yn439Gi9was4uUkGOwKB2seykVjQux1ruJDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:05.801254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9963b6dfed7476dcbabae1d6b0f7c55c8cd24a8fa8e89952f4a11c52d276aa12","sha256:6c2ee63773f369baa5f4454eae010f16be9d19216dfe854edfd3a7fe4c626011"],"state_sha256":"34f2f56b7bd8996ac639b88fe9647df1132584de0c3a7495eb6fe6a33bf4bc4e"}