{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4TQ2X4ZC3GYBZ6QPXOITVPB6YO","short_pith_number":"pith:4TQ2X4ZC","canonical_record":{"source":{"id":"1005.5354","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-28T18:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"e51c2971652c4c821536fbffb80ab6833aefbb3c9c3edd28b8a2e40430f67d47","abstract_canon_sha256":"0b07acc079d850347d8e2984f57666c2688b52263141e62c2eee39b4b11dfed8"},"schema_version":"1.0"},"canonical_sha256":"e4e1abf322d9b01cfa0fbb913abc3ec3908f6d78a3afe343eb5ba5aa6157d7b5","source":{"kind":"arxiv","id":"1005.5354","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5354","created_at":"2026-05-18T03:10:12Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5354v2","created_at":"2026-05-18T03:10:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5354","created_at":"2026-05-18T03:10:12Z"},{"alias_kind":"pith_short_12","alias_value":"4TQ2X4ZC3GYB","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4TQ2X4ZC3GYBZ6QP","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4TQ2X4ZC","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4TQ2X4ZC3GYBZ6QPXOITVPB6YO","target":"record","payload":{"canonical_record":{"source":{"id":"1005.5354","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-28T18:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"e51c2971652c4c821536fbffb80ab6833aefbb3c9c3edd28b8a2e40430f67d47","abstract_canon_sha256":"0b07acc079d850347d8e2984f57666c2688b52263141e62c2eee39b4b11dfed8"},"schema_version":"1.0"},"canonical_sha256":"e4e1abf322d9b01cfa0fbb913abc3ec3908f6d78a3afe343eb5ba5aa6157d7b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:12.510714Z","signature_b64":"aEjwQxtkdp5rFNQDLrM09wwf3unFQTKk6MWRI5B2ipWTj8+8iQ/PR5dwtv8wpKoMDSaKhLIEDtTiiPxc/ztyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4e1abf322d9b01cfa0fbb913abc3ec3908f6d78a3afe343eb5ba5aa6157d7b5","last_reissued_at":"2026-05-18T03:10:12.510110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:12.510110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.5354","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":"2026-05-18T03:10:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+fyLr+PwYuDJfBFUNqsppHswLVkv8AisuJsszkJ9vj9jbDiZ1P+SiU6ovo3IDZZyT1KXUYgfI+doYAeSWdEgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:56:26.380156Z"},"content_sha256":"6ff77cac9a26c696607646830cbd82e446a9b6e17e471628eaca510ace4abe13","schema_version":"1.0","event_id":"sha256:6ff77cac9a26c696607646830cbd82e446a9b6e17e471628eaca510ace4abe13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4TQ2X4ZC3GYBZ6QPXOITVPB6YO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The classification of universal Jacobians over the moduli space of curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Verra, Gavril Farkas","submitted_at":"2010-05-28T18:17:33Z","abstract_excerpt":"We carry out a complete birational classification of the degree g universal Jacobian P_g over the moduli space of curves, highlighting the transition cases g=10, 11. The universal Jacobian is unirational when g<10, has Kodaira dimension zero for g=10 and Kodaira dimension 19 for g=11. For g>11, the variety P_g has Kodaira dimension 3g-3, that is, the maximum allowed by Iitaka's easy addition formula for fibre spaces. In particular, we disprove the expectation that P_g and M_g have the same Kodaira dimension for all genera."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5354","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":"2026-05-18T03:10:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wG1UqxRirGQWE3j3UZYX1N3tzYhMu/EKkkByc8tqyCywJiFSIschNY0HYD0JKEkzgN1DXxTWcBKX0yEyLjzmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:56:26.380528Z"},"content_sha256":"7b76b3c6963bae70d2636b63d89943f80908065edceb86372f917b07cc8f52c0","schema_version":"1.0","event_id":"sha256:7b76b3c6963bae70d2636b63d89943f80908065edceb86372f917b07cc8f52c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TQ2X4ZC3GYBZ6QPXOITVPB6YO/bundle.json","state_url":"https://pith.science/pith/4TQ2X4ZC3GYBZ6QPXOITVPB6YO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TQ2X4ZC3GYBZ6QPXOITVPB6YO/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":"2026-06-02T18:56:26Z","links":{"resolver":"https://pith.science/pith/4TQ2X4ZC3GYBZ6QPXOITVPB6YO","bundle":"https://pith.science/pith/4TQ2X4ZC3GYBZ6QPXOITVPB6YO/bundle.json","state":"https://pith.science/pith/4TQ2X4ZC3GYBZ6QPXOITVPB6YO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TQ2X4ZC3GYBZ6QPXOITVPB6YO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4TQ2X4ZC3GYBZ6QPXOITVPB6YO","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":"0b07acc079d850347d8e2984f57666c2688b52263141e62c2eee39b4b11dfed8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-28T18:17:33Z","title_canon_sha256":"e51c2971652c4c821536fbffb80ab6833aefbb3c9c3edd28b8a2e40430f67d47"},"schema_version":"1.0","source":{"id":"1005.5354","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5354","created_at":"2026-05-18T03:10:12Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5354v2","created_at":"2026-05-18T03:10:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5354","created_at":"2026-05-18T03:10:12Z"},{"alias_kind":"pith_short_12","alias_value":"4TQ2X4ZC3GYB","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4TQ2X4ZC3GYBZ6QP","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4TQ2X4ZC","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:7b76b3c6963bae70d2636b63d89943f80908065edceb86372f917b07cc8f52c0","target":"graph","created_at":"2026-05-18T03:10:12Z","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":"We carry out a complete birational classification of the degree g universal Jacobian P_g over the moduli space of curves, highlighting the transition cases g=10, 11. The universal Jacobian is unirational when g<10, has Kodaira dimension zero for g=10 and Kodaira dimension 19 for g=11. For g>11, the variety P_g has Kodaira dimension 3g-3, that is, the maximum allowed by Iitaka's easy addition formula for fibre spaces. In particular, we disprove the expectation that P_g and M_g have the same Kodaira dimension for all genera.","authors_text":"Alessandro Verra, Gavril Farkas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-28T18:17:33Z","title":"The classification of universal Jacobians over the moduli space of curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5354","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":"sha256:6ff77cac9a26c696607646830cbd82e446a9b6e17e471628eaca510ace4abe13","target":"record","created_at":"2026-05-18T03:10:12Z","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":"0b07acc079d850347d8e2984f57666c2688b52263141e62c2eee39b4b11dfed8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-28T18:17:33Z","title_canon_sha256":"e51c2971652c4c821536fbffb80ab6833aefbb3c9c3edd28b8a2e40430f67d47"},"schema_version":"1.0","source":{"id":"1005.5354","kind":"arxiv","version":2}},"canonical_sha256":"e4e1abf322d9b01cfa0fbb913abc3ec3908f6d78a3afe343eb5ba5aa6157d7b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4e1abf322d9b01cfa0fbb913abc3ec3908f6d78a3afe343eb5ba5aa6157d7b5","first_computed_at":"2026-05-18T03:10:12.510110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:12.510110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aEjwQxtkdp5rFNQDLrM09wwf3unFQTKk6MWRI5B2ipWTj8+8iQ/PR5dwtv8wpKoMDSaKhLIEDtTiiPxc/ztyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:12.510714Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5354","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ff77cac9a26c696607646830cbd82e446a9b6e17e471628eaca510ace4abe13","sha256:7b76b3c6963bae70d2636b63d89943f80908065edceb86372f917b07cc8f52c0"],"state_sha256":"d56554ce5a33734c853dc532128b53463ce55a95db52854eae45be60a481994a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4hnlRCM1s6Y74wjkLZE13GwYmpQRCexhe7xVQRdljXboTtaRQH9UBXG34btrHqq+tRqV2ECuvy4uMaX5WJYDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:56:26.382753Z","bundle_sha256":"aa7e84a46241d93e5f9fffa5695a5a9d12e5c4570604ebac45a6163a4947627d"}}