{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3QE46Q23NPLXRLCHKJRT5W4KJI","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":"2a1c4b66e3703693e243f34f798cca0ef186333fac718a116d242a4c847c1077","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-04T03:11:14Z","title_canon_sha256":"b8cb01d97efd88b7303c17c53c2360b7eb3605cf5fe34ef5ac454da30c08d85f"},"schema_version":"1.0","source":{"id":"1511.01197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01197","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01197v2","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01197","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"pith_short_12","alias_value":"3QE46Q23NPLX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3QE46Q23NPLXRLCH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3QE46Q23","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:1f7ff42e6ce6c9a8faef196087936765112cffa9458f77cb5d459f8eb2ffd51e","target":"graph","created_at":"2026-05-18T01:19:40Z","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":"The Okounkov body is a construction which, to an effective divisor D on an n-dimensional algebraic variety X, associates a convex body in the n-dimensional Euclidean space R^n. It may be seen as a generalization of the moment polytope of an ample divisor on a toric variety, and it encodes rich numerical information about the divisor D. When constructing the Okounkov body, an intermediate product is a lattice semigroup, which we will call the Okounkov semigroup. Recently it was discovered that finite generation of the Okounkov semigroup has interesting geometric implication for X regarding tori","authors_text":"Shin-Yao Jow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-04T03:11:14Z","title":"Fano varieties with finitely generated semigroups in the Okounkov body construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01197","kind":"arxiv","version":2},"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":"sha256:08fddf6e317ebec4f01e745d6bb6744a531b30f2b96c30633e6ee48026ccee79","target":"record","created_at":"2026-05-18T01:19:40Z","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":"2a1c4b66e3703693e243f34f798cca0ef186333fac718a116d242a4c847c1077","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-04T03:11:14Z","title_canon_sha256":"b8cb01d97efd88b7303c17c53c2360b7eb3605cf5fe34ef5ac454da30c08d85f"},"schema_version":"1.0","source":{"id":"1511.01197","kind":"arxiv","version":2}},"canonical_sha256":"dc09cf435b6bd778ac4752633edb8a4a0bea2e8619784877441d1e974d173676","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc09cf435b6bd778ac4752633edb8a4a0bea2e8619784877441d1e974d173676","first_computed_at":"2026-05-18T01:19:40.499932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:40.499932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qxoZTSymUEJdxrVkbPVNxoeTm00fqnB4lqtNTtRSpweAZ4wThCdzeOQMYJTsO1Wchf8GU9OlriwB/MCVpFEKAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:40.500418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08fddf6e317ebec4f01e745d6bb6744a531b30f2b96c30633e6ee48026ccee79","sha256:1f7ff42e6ce6c9a8faef196087936765112cffa9458f77cb5d459f8eb2ffd51e"],"state_sha256":"c5297f1a70260f934bac7eaad9b3c96dad64d81793bed7c81b8f74557d87ef1d"}