{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NODAV4DNKXOLJTFD7VYQUQPEYN","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":"ad14002fea6aef32247e1d11f756ea38d31c316625ede590303e3794607cb133","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-19T04:52:26Z","title_canon_sha256":"69e0082e84fbc135c4b58b9aa33c383af516fb401f5f0f4041aeff0cf0c6ff3a"},"schema_version":"1.0","source":{"id":"1608.05490","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05490","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05490v3","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05490","created_at":"2026-05-18T00:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"NODAV4DNKXOL","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NODAV4DNKXOLJTFD","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NODAV4DN","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:861cbcf357d30222de3a29b0a570bf24086d338a13ce166d1ec1ef99c34359cd","target":"graph","created_at":"2026-05-18T00:53:17Z","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 $C \\subset \\mathbb{P}^2$ be an irreducible and reduced curve of degree $e > 0$. Let $X$ be the blow up of $\\mathbb{P}^2$ at $r$ distinct smooth points $p_1,\\ldots,p_r \\in C$. We study line bundles on $X$ and establish conditions for ampleness and $k$-very ampleness.","authors_text":"Krishna Hanumanthu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-19T04:52:26Z","title":"Positivity of line bundles on special blow ups of $\\mathbb{P}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05490","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:a77703832b21a9e186b2b2f504ff4488dd62438ed5afaf193d1c3088827d9df7","target":"record","created_at":"2026-05-18T00:53:17Z","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":"ad14002fea6aef32247e1d11f756ea38d31c316625ede590303e3794607cb133","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-19T04:52:26Z","title_canon_sha256":"69e0082e84fbc135c4b58b9aa33c383af516fb401f5f0f4041aeff0cf0c6ff3a"},"schema_version":"1.0","source":{"id":"1608.05490","kind":"arxiv","version":3}},"canonical_sha256":"6b860af06d55dcb4cca3fd710a41e4c37efe119b0828dc1f4fad331b57da7013","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b860af06d55dcb4cca3fd710a41e4c37efe119b0828dc1f4fad331b57da7013","first_computed_at":"2026-05-18T00:53:17.350436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:17.350436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RWaL4Dwla4YKtgTVlDjRHBdEnUr5sMVWmu6M09KqLs6DvgwrEWOvInD9wGKUCbg9nOxkZhwqRzCCc1FJyYFLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:17.351129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05490","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a77703832b21a9e186b2b2f504ff4488dd62438ed5afaf193d1c3088827d9df7","sha256:861cbcf357d30222de3a29b0a570bf24086d338a13ce166d1ec1ef99c34359cd"],"state_sha256":"5bc69341328c29164d632aa7a361944832c2ad2bd0b1bb93962aec88da52a1d2"}