{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MG7ZSU3PWCJTUPKQY7A6M6SAA3","short_pith_number":"pith:MG7ZSU3P","canonical_record":{"source":{"id":"1803.09280","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-25T15:49:29Z","cross_cats_sorted":[],"title_canon_sha256":"72eee10e02f0312c1984369d4ca664d5ed921cc3a4080b159f3768b2f26fc59a","abstract_canon_sha256":"7b074f4e8ec7bc62a9fdc43ca874112c46166f09c5bd597194d2e11ce8d7ae4a"},"schema_version":"1.0"},"canonical_sha256":"61bf99536fb0933a3d50c7c1e67a4006d86bff72badf5fee96b06082bf6feea8","source":{"kind":"arxiv","id":"1803.09280","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.09280","created_at":"2026-05-18T00:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1803.09280v1","created_at":"2026-05-18T00:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09280","created_at":"2026-05-18T00:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"MG7ZSU3PWCJT","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MG7ZSU3PWCJTUPKQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MG7ZSU3P","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MG7ZSU3PWCJTUPKQY7A6M6SAA3","target":"record","payload":{"canonical_record":{"source":{"id":"1803.09280","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-25T15:49:29Z","cross_cats_sorted":[],"title_canon_sha256":"72eee10e02f0312c1984369d4ca664d5ed921cc3a4080b159f3768b2f26fc59a","abstract_canon_sha256":"7b074f4e8ec7bc62a9fdc43ca874112c46166f09c5bd597194d2e11ce8d7ae4a"},"schema_version":"1.0"},"canonical_sha256":"61bf99536fb0933a3d50c7c1e67a4006d86bff72badf5fee96b06082bf6feea8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:12.118836Z","signature_b64":"BX74oBOAjp8G+iRwsMDJ6pDNTr+SglBZrVeXu9WlDQizfjwaDYSA85Yh+xtMCUoAf4zNLDmxjqNwyBS5YXHaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61bf99536fb0933a3d50c7c1e67a4006d86bff72badf5fee96b06082bf6feea8","last_reissued_at":"2026-05-18T00:20:12.118239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:12.118239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.09280","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iKO3vXmbRW1xhapiNkbJD8/YKyfnP298SXM5tVWrLqZKYU+OFB+i9JVgzjXEY9StovhOLRJRRt9eTFimDOzgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:47:34.546543Z"},"content_sha256":"db9106b476bee5dbd05a31029c557570990ae3a90b54a4176b6b968596815cec","schema_version":"1.0","event_id":"sha256:db9106b476bee5dbd05a31029c557570990ae3a90b54a4176b6b968596815cec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MG7ZSU3PWCJTUPKQY7A6M6SAA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generically nef vector bundles on ruled surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Zucconi, Valentina Beorchia","submitted_at":"2018-03-25T15:49:29Z","abstract_excerpt":"The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta - Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be considered as a weak form of semistability. We establish a Bogomolov type inequality for generically nef vector bundles with nef general fiber restriction on ruled surfaces with no negative section. This gives an affermative answer in this case to a problem posed by Th. Peternell.\n  Concerning ruled surfaces with a negative section, we prove a a similar result "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09280","kind":"arxiv","version":1},"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":"2026-05-18T00:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rpwSPyLg8zhUx4AFPbZQ6DyRIe0hFqTkGBMsOSi5YjMFrPhEvwjwaRH0iiU/GEOaz+BV6VJafLLJjQOqzyekCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:47:34.546892Z"},"content_sha256":"9234a7e285a4310a38fb50f814b6c30fc6fc86014303dfe8286258294084329d","schema_version":"1.0","event_id":"sha256:9234a7e285a4310a38fb50f814b6c30fc6fc86014303dfe8286258294084329d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MG7ZSU3PWCJTUPKQY7A6M6SAA3/bundle.json","state_url":"https://pith.science/pith/MG7ZSU3PWCJTUPKQY7A6M6SAA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MG7ZSU3PWCJTUPKQY7A6M6SAA3/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":"2026-06-24T08:47:34Z","links":{"resolver":"https://pith.science/pith/MG7ZSU3PWCJTUPKQY7A6M6SAA3","bundle":"https://pith.science/pith/MG7ZSU3PWCJTUPKQY7A6M6SAA3/bundle.json","state":"https://pith.science/pith/MG7ZSU3PWCJTUPKQY7A6M6SAA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MG7ZSU3PWCJTUPKQY7A6M6SAA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MG7ZSU3PWCJTUPKQY7A6M6SAA3","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":"7b074f4e8ec7bc62a9fdc43ca874112c46166f09c5bd597194d2e11ce8d7ae4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-25T15:49:29Z","title_canon_sha256":"72eee10e02f0312c1984369d4ca664d5ed921cc3a4080b159f3768b2f26fc59a"},"schema_version":"1.0","source":{"id":"1803.09280","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.09280","created_at":"2026-05-18T00:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1803.09280v1","created_at":"2026-05-18T00:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09280","created_at":"2026-05-18T00:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"MG7ZSU3PWCJT","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MG7ZSU3PWCJTUPKQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MG7ZSU3P","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:9234a7e285a4310a38fb50f814b6c30fc6fc86014303dfe8286258294084329d","target":"graph","created_at":"2026-05-18T00:20:12Z","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 present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta - Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be considered as a weak form of semistability. We establish a Bogomolov type inequality for generically nef vector bundles with nef general fiber restriction on ruled surfaces with no negative section. This gives an affermative answer in this case to a problem posed by Th. Peternell.\n  Concerning ruled surfaces with a negative section, we prove a a similar result ","authors_text":"Francesco Zucconi, Valentina Beorchia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-25T15:49:29Z","title":"Generically nef vector bundles on ruled surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09280","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:db9106b476bee5dbd05a31029c557570990ae3a90b54a4176b6b968596815cec","target":"record","created_at":"2026-05-18T00:20:12Z","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":"7b074f4e8ec7bc62a9fdc43ca874112c46166f09c5bd597194d2e11ce8d7ae4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-25T15:49:29Z","title_canon_sha256":"72eee10e02f0312c1984369d4ca664d5ed921cc3a4080b159f3768b2f26fc59a"},"schema_version":"1.0","source":{"id":"1803.09280","kind":"arxiv","version":1}},"canonical_sha256":"61bf99536fb0933a3d50c7c1e67a4006d86bff72badf5fee96b06082bf6feea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61bf99536fb0933a3d50c7c1e67a4006d86bff72badf5fee96b06082bf6feea8","first_computed_at":"2026-05-18T00:20:12.118239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:12.118239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BX74oBOAjp8G+iRwsMDJ6pDNTr+SglBZrVeXu9WlDQizfjwaDYSA85Yh+xtMCUoAf4zNLDmxjqNwyBS5YXHaAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:12.118836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.09280","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db9106b476bee5dbd05a31029c557570990ae3a90b54a4176b6b968596815cec","sha256:9234a7e285a4310a38fb50f814b6c30fc6fc86014303dfe8286258294084329d"],"state_sha256":"8e1b5121d134dcd97cdd881c534154559b8f84ffd5271d7c734dd2e55ca5e0ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkGyTfhOauB20o2LFwglCGYiyt5EjwFOAoQJhxBXMqMnO8/NHAEnJnIJ2rSkm7cw/S06vlBNNwEo24OfrFufCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:47:34.548850Z","bundle_sha256":"5fd27f728595caebd6a1dfa233683e5286301c5bfdea130eaa1a3b8b6d8f7f2a"}}