{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:VMNW5MTWUZ42M4JAMDR5WBPGT7","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":"a0bad615260b2839a30874ddc7cdcccbd1d7c8655fc2ef5a523b4c5a9242e475","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1996-07-08T00:00:00Z","title_canon_sha256":"638056544c0267302ed62c8648cb8da4e09be30b5032a86ea61ffcb553b0545f"},"schema_version":"1.0","source":{"id":"math/9607217","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9607217","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/9607217v1","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9607217","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"VMNW5MTWUZ42","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"VMNW5MTWUZ42M4JA","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"VMNW5MTW","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:b256106741a17a8c5652091e95cc7843b5333aec5503b152f65e337b562304b7","target":"graph","created_at":"2026-05-18T01:05:47Z","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 purpose of this paper is to translate positivity properties of the tangent bundle (and the anti-canonical bundle) of an algebraic manifold into existence and movability properties of rational curves and to investigate the impact on the global geometry of the manifold $X$. Among the results we prove are these:\n  \\quad If $X$ is a projective manifold, and ${\\cal E} \\subset T_X$ is an ample locally free sheaf with $n-2\\ge rk {\\cal E}\\ge n$, then $X \\simeq \\EP_n$.\n  \\quad Let $X$ be a projective manifold. If $X$ is rationally connected, then there exists a free $T_X$-ample family of (rational)","authors_text":"Fr\\'ed\\'eric Campana, Thomas Peternell","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1996-07-08T00:00:00Z","title":"Rational curves and ampleness properties of the tangent bundle of algebraic varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9607217","kind":"arxiv","version":1},"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":"sha256:571cd83315a146ce0c856977de48a56ba5819ae3e2c0be3c380d4518fcd98708","target":"record","created_at":"2026-05-18T01:05:47Z","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":"a0bad615260b2839a30874ddc7cdcccbd1d7c8655fc2ef5a523b4c5a9242e475","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1996-07-08T00:00:00Z","title_canon_sha256":"638056544c0267302ed62c8648cb8da4e09be30b5032a86ea61ffcb553b0545f"},"schema_version":"1.0","source":{"id":"math/9607217","kind":"arxiv","version":1}},"canonical_sha256":"ab1b6eb276a679a6712060e3db05e69fdd7987479cd29c1ca92d61c14d1a062b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab1b6eb276a679a6712060e3db05e69fdd7987479cd29c1ca92d61c14d1a062b","first_computed_at":"2026-05-18T01:05:47.197395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:47.197395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rjsMRj2qiS1Ji2AmNN6/E5enNpQa0ie48knTqi8EGCNw1wiTgTfnpJnPEZ3mLhT7mIltYJD5bqVrn4CMlAoDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:47.198157Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9607217","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:571cd83315a146ce0c856977de48a56ba5819ae3e2c0be3c380d4518fcd98708","sha256:b256106741a17a8c5652091e95cc7843b5333aec5503b152f65e337b562304b7"],"state_sha256":"bba9b8f22ca6876bf3cf30e0cfb33e83c1690fefc5558a037b1c9f580c2c7699"}