{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5UXIE7FP6ARRE2EK4N76POVN2X","short_pith_number":"pith:5UXIE7FP","canonical_record":{"source":{"id":"1809.09485","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-25T13:46:12Z","cross_cats_sorted":[],"title_canon_sha256":"4ddc6993f30cd31b9cff26779473aac73d3d0bea39225f0b868d81bbfbd4910f","abstract_canon_sha256":"8c9f645da6809bbc462a3e77665e0f789c01db6f6322ba0e1c1b57ed26c93f79"},"schema_version":"1.0"},"canonical_sha256":"ed2e827caff02312688ae37fe7baadd5d9c9298da923f7012576f09a7f0d1680","source":{"kind":"arxiv","id":"1809.09485","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09485","created_at":"2026-05-17T23:51:25Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09485v2","created_at":"2026-05-17T23:51:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09485","created_at":"2026-05-17T23:51:25Z"},{"alias_kind":"pith_short_12","alias_value":"5UXIE7FP6ARR","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5UXIE7FP6ARRE2EK","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5UXIE7FP","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5UXIE7FP6ARRE2EK4N76POVN2X","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09485","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-25T13:46:12Z","cross_cats_sorted":[],"title_canon_sha256":"4ddc6993f30cd31b9cff26779473aac73d3d0bea39225f0b868d81bbfbd4910f","abstract_canon_sha256":"8c9f645da6809bbc462a3e77665e0f789c01db6f6322ba0e1c1b57ed26c93f79"},"schema_version":"1.0"},"canonical_sha256":"ed2e827caff02312688ae37fe7baadd5d9c9298da923f7012576f09a7f0d1680","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:25.908909Z","signature_b64":"XQpSt1Zf2ySvSfluSlBo0HtAxPSPZL7EdEYipANLUoRSfkvKly5939YCleEHgA/Y5rMS6bDg+UgaIFUNOauSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed2e827caff02312688ae37fe7baadd5d9c9298da923f7012576f09a7f0d1680","last_reissued_at":"2026-05-17T23:51:25.908211Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:25.908211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09485","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/O1BAdC2h4h+ztweOYPO4XX5bYkRmOXW0pTwGRfYrrMCyUWnM8hwBg0QqzN01YDMTOihs0l0v/e2sV4z2gKTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:07:04.811137Z"},"content_sha256":"3c44cff6538247c5696023698807223824266e4ea5be0c3a583a39c384976c11","schema_version":"1.0","event_id":"sha256:3c44cff6538247c5696023698807223824266e4ea5be0c3a583a39c384976c11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5UXIE7FP6ARRE2EK4N76POVN2X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational curves on genus one fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fabrizio Anella","submitted_at":"2018-09-25T13:46:12Z","abstract_excerpt":"In this paper we look for necessary and sufficient conditions for a genus one fibration to have rational curves. We show that a projective variety with log terminal singularities that admits a relatively minimal genus one fibration $X\\rightarrow B$ does contain vertical rational curves if and only if it not isomorphic to a finite \\'etale quotient of a product $\\tilde{B}\\times E$ over $B$. Many sufficient conditions for the existence of rational curves in a variety that admits a genus one fibration are proved in this paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09485","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w5ijMHLxx1DAMxL0prAcAKUheCcumDvWqAxj8xqgo2zbj2WIkO8t8nmdstOazjibG9PzCFfkW69A1Wz93ISWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:07:04.811498Z"},"content_sha256":"f05168e9f755ed1f306a8cb7fbff6fedf3a834455bf2f9b385ea96be4b85667b","schema_version":"1.0","event_id":"sha256:f05168e9f755ed1f306a8cb7fbff6fedf3a834455bf2f9b385ea96be4b85667b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5UXIE7FP6ARRE2EK4N76POVN2X/bundle.json","state_url":"https://pith.science/pith/5UXIE7FP6ARRE2EK4N76POVN2X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5UXIE7FP6ARRE2EK4N76POVN2X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T20:07:04Z","links":{"resolver":"https://pith.science/pith/5UXIE7FP6ARRE2EK4N76POVN2X","bundle":"https://pith.science/pith/5UXIE7FP6ARRE2EK4N76POVN2X/bundle.json","state":"https://pith.science/pith/5UXIE7FP6ARRE2EK4N76POVN2X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5UXIE7FP6ARRE2EK4N76POVN2X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5UXIE7FP6ARRE2EK4N76POVN2X","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":"8c9f645da6809bbc462a3e77665e0f789c01db6f6322ba0e1c1b57ed26c93f79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-25T13:46:12Z","title_canon_sha256":"4ddc6993f30cd31b9cff26779473aac73d3d0bea39225f0b868d81bbfbd4910f"},"schema_version":"1.0","source":{"id":"1809.09485","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09485","created_at":"2026-05-17T23:51:25Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09485v2","created_at":"2026-05-17T23:51:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09485","created_at":"2026-05-17T23:51:25Z"},{"alias_kind":"pith_short_12","alias_value":"5UXIE7FP6ARR","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5UXIE7FP6ARRE2EK","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5UXIE7FP","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:f05168e9f755ed1f306a8cb7fbff6fedf3a834455bf2f9b385ea96be4b85667b","target":"graph","created_at":"2026-05-17T23:51:25Z","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":"In this paper we look for necessary and sufficient conditions for a genus one fibration to have rational curves. We show that a projective variety with log terminal singularities that admits a relatively minimal genus one fibration $X\\rightarrow B$ does contain vertical rational curves if and only if it not isomorphic to a finite \\'etale quotient of a product $\\tilde{B}\\times E$ over $B$. Many sufficient conditions for the existence of rational curves in a variety that admits a genus one fibration are proved in this paper.","authors_text":"Fabrizio Anella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-25T13:46:12Z","title":"Rational curves on genus one fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09485","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":"sha256:3c44cff6538247c5696023698807223824266e4ea5be0c3a583a39c384976c11","target":"record","created_at":"2026-05-17T23:51:25Z","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":"8c9f645da6809bbc462a3e77665e0f789c01db6f6322ba0e1c1b57ed26c93f79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-25T13:46:12Z","title_canon_sha256":"4ddc6993f30cd31b9cff26779473aac73d3d0bea39225f0b868d81bbfbd4910f"},"schema_version":"1.0","source":{"id":"1809.09485","kind":"arxiv","version":2}},"canonical_sha256":"ed2e827caff02312688ae37fe7baadd5d9c9298da923f7012576f09a7f0d1680","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed2e827caff02312688ae37fe7baadd5d9c9298da923f7012576f09a7f0d1680","first_computed_at":"2026-05-17T23:51:25.908211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:25.908211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XQpSt1Zf2ySvSfluSlBo0HtAxPSPZL7EdEYipANLUoRSfkvKly5939YCleEHgA/Y5rMS6bDg+UgaIFUNOauSDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:25.908909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09485","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c44cff6538247c5696023698807223824266e4ea5be0c3a583a39c384976c11","sha256:f05168e9f755ed1f306a8cb7fbff6fedf3a834455bf2f9b385ea96be4b85667b"],"state_sha256":"182cd05b2177fb122baf26c5484c153026f47f4c40e2b63a47e2ab02ef964dca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pRSIf1BahhA7ZAq9DcXtNfwvL5klGwvxTFGveM3cB/CgfRxAW2dRFJ3LVSxsj51whx2J7C27jktTGZuNQAYCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:07:04.813439Z","bundle_sha256":"14ecce3ab1a9b59b4d1de4e6680f8abfaad6fb5487dda617ac545462bb3ab803"}}