{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IUIELU7ZZZTNBJEJPNN3GFALL2","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":"8bdcc9cfec7872fe06ca450668cf5b68d927c6c79a67843ef738f0b796f95bdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-23T06:05:15Z","title_canon_sha256":"1bb60bdc1d7c4939ac0b889289e11017c91352cd72ab1e2cb56e79d4bc435cb0"},"schema_version":"1.0","source":{"id":"1507.06391","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06391","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06391v3","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06391","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"pith_short_12","alias_value":"IUIELU7ZZZTN","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IUIELU7ZZZTNBJEJ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IUIELU7Z","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:cf284ae83e5ded7a97d01913c9367c02123424f3ffd3dc065035e611286f0546","target":"graph","created_at":"2026-05-18T01:01:52Z","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 $X$ be the blow up of $\\mathbb{P}^2$ at $r$ general points $p_1,\\ldots,p_r \\in \\mathbb{P}^2$. We study line bundles on $X$ given by plane curves of degree $d$ passing through $p_i$ with multiplicity $m_i$. We establish conditions for ampleness, very ampleness and global generation of such line bundles.","authors_text":"Krishna Hanumanthu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-23T06:05:15Z","title":"Positivity of line bundles on general blow ups of $\\mathbb{P}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06391","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":"sha256:4c46a046819e15b219122fec4cc9b7e709f093e58c529ccf5b9a8e38a69c6b64","target":"record","created_at":"2026-05-18T01:01:52Z","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":"8bdcc9cfec7872fe06ca450668cf5b68d927c6c79a67843ef738f0b796f95bdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-23T06:05:15Z","title_canon_sha256":"1bb60bdc1d7c4939ac0b889289e11017c91352cd72ab1e2cb56e79d4bc435cb0"},"schema_version":"1.0","source":{"id":"1507.06391","kind":"arxiv","version":3}},"canonical_sha256":"451045d3f9ce66d0a4897b5bb3140b5e942b89951c433d1d41a6e5b97045dc21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"451045d3f9ce66d0a4897b5bb3140b5e942b89951c433d1d41a6e5b97045dc21","first_computed_at":"2026-05-18T01:01:52.230015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:52.230015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dr9e9WBYcJlbvbiuoqAoBEu3KF/aAKTtfE/JIq9kcUSZbxQFfBgS415BQrF4hgqupEMbDBy9KG+6xGgejdrIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:52.230602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06391","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c46a046819e15b219122fec4cc9b7e709f093e58c529ccf5b9a8e38a69c6b64","sha256:cf284ae83e5ded7a97d01913c9367c02123424f3ffd3dc065035e611286f0546"],"state_sha256":"8299783451257b8a00647142f48de651aea6a98049bd550a657362403d5751c7"}