{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:G7IRU466XPVXJ6CPAUXVM5SNPL","short_pith_number":"pith:G7IRU466","canonical_record":{"source":{"id":"2002.01420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-02-04T17:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"85d459a3fee02b9b208abc878af4a9718cdcc784bc538ef320c34810b7ae798e","abstract_canon_sha256":"963749f7db3be3ca0b1bd49aef7178ccde4b082137d7ce4c22853262bc47d919"},"schema_version":"1.0"},"canonical_sha256":"37d11a73debbeb74f84f052f56764d7ae83f0574b3d4f519fa2bde8531dff5fa","source":{"kind":"arxiv","id":"2002.01420","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.01420","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"arxiv_version","alias_value":"2002.01420v2","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.01420","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"pith_short_12","alias_value":"G7IRU466XPVX","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"pith_short_16","alias_value":"G7IRU466XPVXJ6CP","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"pith_short_8","alias_value":"G7IRU466","created_at":"2026-07-05T06:22:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:G7IRU466XPVXJ6CPAUXVM5SNPL","target":"record","payload":{"canonical_record":{"source":{"id":"2002.01420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-02-04T17:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"85d459a3fee02b9b208abc878af4a9718cdcc784bc538ef320c34810b7ae798e","abstract_canon_sha256":"963749f7db3be3ca0b1bd49aef7178ccde4b082137d7ce4c22853262bc47d919"},"schema_version":"1.0"},"canonical_sha256":"37d11a73debbeb74f84f052f56764d7ae83f0574b3d4f519fa2bde8531dff5fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:22:27.531889Z","signature_b64":"b7n2rrFfXk0OP/TNkrKoT8cOuWbT88GGMhFDUVcyTj7cP9IFjtddOuewcNON4Jgse5G4f96ZRgND4KlqKX0qDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37d11a73debbeb74f84f052f56764d7ae83f0574b3d4f519fa2bde8531dff5fa","last_reissued_at":"2026-07-05T06:22:27.531407Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:22:27.531407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.01420","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":"2026-07-05T06:22:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iiYbj7uKiFDd/JhUCmfHpORNe/EP4MbN8VtFjQOZvqcwTdBPmmfAOCDx/ChR65VjT7xhRomg9b1pgK+bqHjWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:37:59.716290Z"},"content_sha256":"19156f3603ea05db278c85e0aa300389d64ba229d2ac454f7ced6e264c900bec","schema_version":"1.0","event_id":"sha256:19156f3603ea05db278c85e0aa300389d64ba229d2ac454f7ced6e264c900bec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:G7IRU466XPVXJ6CPAUXVM5SNPL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Birational geometry of the intermediate Jacobian fibration of a cubic fourfold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giulia Sacc\\`a, with an appendix by Claire Voisin","submitted_at":"2020-02-04T17:39:18Z","abstract_excerpt":"We show that the intermediate Jacobian fibration associated to any smooth cubic fourfold $X$ admits a hyper-K\\\"ahler compactification $J(X)$ with a regular Lagrangian fibration $J \\to \\mathbb P^5$. This builds upon arXiv:1602.05534, where the result is proved for general $X$, as well as on the degeneration techniques on arXiv:1704.02731 and techniques from the minimal model program. We then study some aspects of the birational geometry of $J(X)$: for very general $X$ we compute the movable and nef cones of $J(X)$, showing that $J(X)$ is not birational to the twisted version of the intermediate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.01420","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.01420/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:22:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wXoRQ6Mxu3kBWfgctYfGHZzM8Ijjd2f+q7sj6Uj2TmVGt7iy1fYIH3InljEx/PkBi5b+2bVlzLhEBhWSruvnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:37:59.716825Z"},"content_sha256":"d87304f0bed5ae34f6ec9fec9e49365de50bc7fb7ab2df1062cd1e5d630bb01b","schema_version":"1.0","event_id":"sha256:d87304f0bed5ae34f6ec9fec9e49365de50bc7fb7ab2df1062cd1e5d630bb01b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G7IRU466XPVXJ6CPAUXVM5SNPL/bundle.json","state_url":"https://pith.science/pith/G7IRU466XPVXJ6CPAUXVM5SNPL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G7IRU466XPVXJ6CPAUXVM5SNPL/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":"2026-08-08T20:37:59Z","links":{"resolver":"https://pith.science/pith/G7IRU466XPVXJ6CPAUXVM5SNPL","bundle":"https://pith.science/pith/G7IRU466XPVXJ6CPAUXVM5SNPL/bundle.json","state":"https://pith.science/pith/G7IRU466XPVXJ6CPAUXVM5SNPL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G7IRU466XPVXJ6CPAUXVM5SNPL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:G7IRU466XPVXJ6CPAUXVM5SNPL","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":"963749f7db3be3ca0b1bd49aef7178ccde4b082137d7ce4c22853262bc47d919","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-02-04T17:39:18Z","title_canon_sha256":"85d459a3fee02b9b208abc878af4a9718cdcc784bc538ef320c34810b7ae798e"},"schema_version":"1.0","source":{"id":"2002.01420","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.01420","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"arxiv_version","alias_value":"2002.01420v2","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.01420","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"pith_short_12","alias_value":"G7IRU466XPVX","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"pith_short_16","alias_value":"G7IRU466XPVXJ6CP","created_at":"2026-07-05T06:22:27Z"},{"alias_kind":"pith_short_8","alias_value":"G7IRU466","created_at":"2026-07-05T06:22:27Z"}],"graph_snapshots":[{"event_id":"sha256:d87304f0bed5ae34f6ec9fec9e49365de50bc7fb7ab2df1062cd1e5d630bb01b","target":"graph","created_at":"2026-07-05T06:22:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2002.01420/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the intermediate Jacobian fibration associated to any smooth cubic fourfold $X$ admits a hyper-K\\\"ahler compactification $J(X)$ with a regular Lagrangian fibration $J \\to \\mathbb P^5$. This builds upon arXiv:1602.05534, where the result is proved for general $X$, as well as on the degeneration techniques on arXiv:1704.02731 and techniques from the minimal model program. We then study some aspects of the birational geometry of $J(X)$: for very general $X$ we compute the movable and nef cones of $J(X)$, showing that $J(X)$ is not birational to the twisted version of the intermediate","authors_text":"Giulia Sacc\\`a, with an appendix by Claire Voisin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-02-04T17:39:18Z","title":"Birational geometry of the intermediate Jacobian fibration of a cubic fourfold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.01420","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":"sha256:19156f3603ea05db278c85e0aa300389d64ba229d2ac454f7ced6e264c900bec","target":"record","created_at":"2026-07-05T06:22:27Z","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":"963749f7db3be3ca0b1bd49aef7178ccde4b082137d7ce4c22853262bc47d919","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-02-04T17:39:18Z","title_canon_sha256":"85d459a3fee02b9b208abc878af4a9718cdcc784bc538ef320c34810b7ae798e"},"schema_version":"1.0","source":{"id":"2002.01420","kind":"arxiv","version":2}},"canonical_sha256":"37d11a73debbeb74f84f052f56764d7ae83f0574b3d4f519fa2bde8531dff5fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37d11a73debbeb74f84f052f56764d7ae83f0574b3d4f519fa2bde8531dff5fa","first_computed_at":"2026-07-05T06:22:27.531407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:22:27.531407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b7n2rrFfXk0OP/TNkrKoT8cOuWbT88GGMhFDUVcyTj7cP9IFjtddOuewcNON4Jgse5G4f96ZRgND4KlqKX0qDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:22:27.531889Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.01420","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19156f3603ea05db278c85e0aa300389d64ba229d2ac454f7ced6e264c900bec","sha256:d87304f0bed5ae34f6ec9fec9e49365de50bc7fb7ab2df1062cd1e5d630bb01b"],"state_sha256":"78992f2de14f7f43b172a099c35e49761a838275b544226cb231f4059368118c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YJOdANHuDQh9PTLfmuAeg/VfIVP4MJZv3lbPIFFThLw6C7623p+4BdPhMoHkIkxluXE8YNtESIkwMTILN+1QBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T20:37:59.722319Z","bundle_sha256":"df3931358df711a6608724eebee1c08a0d4cce59a9fbc68329353f61787935ac"}}