{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AWZR5YAPWHULXVGU6467FX3RDK","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":"c8fd0ddc92bbab6fc0820b2c655b609ebbf87e7f1353ba19c8730e1e7595ea01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-25T09:54:43Z","title_canon_sha256":"76b23c7d439ea1b42cf5fcd456f8998d311b2ee9020852fc8358bd6f78af8dfe"},"schema_version":"1.0","source":{"id":"1107.4878","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4878","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4878v2","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4878","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"AWZR5YAPWHUL","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AWZR5YAPWHULXVGU","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AWZR5YAP","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:12f5a708bd1535f61c6d20e215d10fd9f69bf06838b2ee5c3d8aea25efdede7c","target":"graph","created_at":"2026-05-18T03:38:23Z","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":"Let (X,L) be a quasi polarized pairs, i.e. X is a normal complex projective variety and L is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness) of the adjoint bundles K_X + rL for high rational number r. For this we run a Minimal Model Program with scaling relative to the divisor K_X +rL. We give some applications, namely the classification up to birational equivalence of quasi polarized pairs with sectional genus 0,1 and of embedded projective varieties X < P^N with degree smaller than 2codim(X) +2.","authors_text":"Marco Andreatta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-25T09:54:43Z","title":"Minimal Model Program with scaling and adjunction theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4878","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":"sha256:660a1d79520addeab9f2c028375b3ba68c4d6b7e581eaea75c33758a7ce566fa","target":"record","created_at":"2026-05-18T03:38:23Z","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":"c8fd0ddc92bbab6fc0820b2c655b609ebbf87e7f1353ba19c8730e1e7595ea01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-25T09:54:43Z","title_canon_sha256":"76b23c7d439ea1b42cf5fcd456f8998d311b2ee9020852fc8358bd6f78af8dfe"},"schema_version":"1.0","source":{"id":"1107.4878","kind":"arxiv","version":2}},"canonical_sha256":"05b31ee00fb1e8bbd4d4f73df2df711aa7ba58b86d884b4d7eb8ffcbf7219a0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05b31ee00fb1e8bbd4d4f73df2df711aa7ba58b86d884b4d7eb8ffcbf7219a0d","first_computed_at":"2026-05-18T03:38:23.901411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:23.901411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KqQEMVNFsKPsFqLlmPZXtBReOjHRYH0YHmjHq1GeW+eHrMzhVu/LNt/YulP1WO0H/j4kNfL8twKzkkjxlkKBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:23.902012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4878","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:660a1d79520addeab9f2c028375b3ba68c4d6b7e581eaea75c33758a7ce566fa","sha256:12f5a708bd1535f61c6d20e215d10fd9f69bf06838b2ee5c3d8aea25efdede7c"],"state_sha256":"99341b25e605c1ffc2a9d4694de102d650b90179dfdf522c3eec6f803cc3b20a"}