{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BVFZYAB25VEBVLFXTQMLKRCA24","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":"43e1182823174df4e504d260b06993e103bebb1a3befd33b79d4cd1daba702fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-08T21:22:04Z","title_canon_sha256":"b739f257848fff06de64137237010c26a93e4c1b5009ddd85e6971a966bac47d"},"schema_version":"1.0","source":{"id":"1503.02324","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02324","created_at":"2026-05-18T02:25:18Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02324v2","created_at":"2026-05-18T02:25:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02324","created_at":"2026-05-18T02:25:18Z"},{"alias_kind":"pith_short_12","alias_value":"BVFZYAB25VEB","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BVFZYAB25VEBVLFX","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BVFZYAB2","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:cb9d0313486bb46d0cee7de2b0f5e98e3a450be7c64b27fa66f57e4e8a05b2e8","target":"graph","created_at":"2026-05-18T02:25:18Z","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":"If D is a big divisor and E is an effective divisor, then vol(D-E)<=vol(D)<=vol(D+E). We discuss when each inequality is an equality. Surprisingly, the answer is that the asymptotic equality vol(D-E)=vol(D) is equivalent to the equality of the Hilbert functions of D-E and D. The analogous result holds when vol(D)=vol(D+E).","authors_text":"Brian Lehmann, J\\'anos Koll\\'ar, Mihai Fulger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-08T21:22:04Z","title":"Volume and Hilbert function of R-divisors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02324","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":"sha256:452ef37f868242719bf6f908eb62fe36380c2bb623c9cf95f16f643ac1573747","target":"record","created_at":"2026-05-18T02:25:18Z","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":"43e1182823174df4e504d260b06993e103bebb1a3befd33b79d4cd1daba702fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-08T21:22:04Z","title_canon_sha256":"b739f257848fff06de64137237010c26a93e4c1b5009ddd85e6971a966bac47d"},"schema_version":"1.0","source":{"id":"1503.02324","kind":"arxiv","version":2}},"canonical_sha256":"0d4b9c003aed481aacb79c18b54440d710185af26445c1f89f33c03d83010303","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d4b9c003aed481aacb79c18b54440d710185af26445c1f89f33c03d83010303","first_computed_at":"2026-05-18T02:25:18.025067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:18.025067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WVyIGsCj8oe1ljRuFM/wjw4tWHJgcyGvYJS6zpHh6ybNXugujjcdC+oqcriXV47IJMMh7qE0fPHyVteRkvHnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:18.025440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02324","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:452ef37f868242719bf6f908eb62fe36380c2bb623c9cf95f16f643ac1573747","sha256:cb9d0313486bb46d0cee7de2b0f5e98e3a450be7c64b27fa66f57e4e8a05b2e8"],"state_sha256":"52f8a86cf52d7d96f67e698b57ffa6311084a41b4afaf7dcf1257306933b5801"}