{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FMOFZ4IPCIQXD6N37RBSX2RHPZ","short_pith_number":"pith:FMOFZ4IP","canonical_record":{"source":{"id":"1811.03502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-08T15:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"b45b1375f5ebf99bc43ab04d74a1a260730c580c376f47f4b47a4caaf40afffa","abstract_canon_sha256":"4352b32fc29a5418df8aa0dd6aec7f9a1edc5484688e4dad743d96d8713dd11b"},"schema_version":"1.0"},"canonical_sha256":"2b1c5cf10f122171f9bbfc432bea277e62275fcd86df7141cc303a28838569cd","source":{"kind":"arxiv","id":"1811.03502","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03502","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03502v2","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03502","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"pith_short_12","alias_value":"FMOFZ4IPCIQX","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"pith_short_16","alias_value":"FMOFZ4IPCIQXD6N3","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"pith_short_8","alias_value":"FMOFZ4IP","created_at":"2026-07-05T00:00:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FMOFZ4IPCIQXD6N37RBSX2RHPZ","target":"record","payload":{"canonical_record":{"source":{"id":"1811.03502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-08T15:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"b45b1375f5ebf99bc43ab04d74a1a260730c580c376f47f4b47a4caaf40afffa","abstract_canon_sha256":"4352b32fc29a5418df8aa0dd6aec7f9a1edc5484688e4dad743d96d8713dd11b"},"schema_version":"1.0"},"canonical_sha256":"2b1c5cf10f122171f9bbfc432bea277e62275fcd86df7141cc303a28838569cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:00:53.111694Z","signature_b64":"7dV2511Fa4osrS79Vlvw1CRhd02XyFF0QOxdFmRCEUdVGaHtNYvoDkwN4BqUJrZB5nC23uFfDyE+VXN+mWpqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b1c5cf10f122171f9bbfc432bea277e62275fcd86df7141cc303a28838569cd","last_reissued_at":"2026-07-05T00:00:53.111303Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:00:53.111303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.03502","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":"2026-07-05T00:00:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7wGHjrwgPiCwmFUcVwWkVmzHwg7gfQIF5gTqfyxt66zPdgJdeWYqMb31188EbVY2/7s75Wl4TMr01sIv05vxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T03:34:29.778265Z"},"content_sha256":"27bd2bd7d5d1fd33381f486be7ed08e152a37b6a77db66297b9dec975a60e746","schema_version":"1.0","event_id":"sha256:27bd2bd7d5d1fd33381f486be7ed08e152a37b6a77db66297b9dec975a60e746"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FMOFZ4IPCIQXD6N37RBSX2RHPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit rationality of some cubic fourfolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Russo, Giovanni Staglian\\`o","submitted_at":"2018-11-08T15:44:39Z","abstract_excerpt":"Recent results of Hassett, Kuznetsov and others pointed out countably many divisors $C_d$ in the open subset of $\\mathbb{P}^{55}=\\mathbb{P}(H^0(\\mathcal{O}_{\\mathbb{P}^5}(3)))$ parametrizing all cubic 4-folds and lead to the conjecture that the cubics corresponding to these divisors should be precisely the rational ones. Rationality has been proved by Fano for the first divisor $C_{14}$ and in [arXiv:1707.00999] for the divisors $C_{26}$ and $C_{38}$. In this note we describe explicit birational maps from a general cubic fourfold in $C_{14}$, in $C_{26}$ and in $C_{38}$ to $\\mathbb{P}^4$, prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03502","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/1811.03502/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":"2026-07-05T00:00:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rzvnaW9nyYpHqeV3k6tl0VQMLVY26Yj+kKgsmq68oV3I071mf9isOi4ZAsMtREO9KpsXdOjtjxq7Rf/MbLY4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T03:34:29.778929Z"},"content_sha256":"fa22a5e158be44b0277ac29aa6bfce13c6f0ed5a26c159b387088e71115a66c7","schema_version":"1.0","event_id":"sha256:fa22a5e158be44b0277ac29aa6bfce13c6f0ed5a26c159b387088e71115a66c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/bundle.json","state_url":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/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":"2026-08-15T03:34:29Z","links":{"resolver":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ","bundle":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/bundle.json","state":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FMOFZ4IPCIQXD6N37RBSX2RHPZ","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":"4352b32fc29a5418df8aa0dd6aec7f9a1edc5484688e4dad743d96d8713dd11b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-08T15:44:39Z","title_canon_sha256":"b45b1375f5ebf99bc43ab04d74a1a260730c580c376f47f4b47a4caaf40afffa"},"schema_version":"1.0","source":{"id":"1811.03502","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03502","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03502v2","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03502","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"pith_short_12","alias_value":"FMOFZ4IPCIQX","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"pith_short_16","alias_value":"FMOFZ4IPCIQXD6N3","created_at":"2026-07-05T00:00:53Z"},{"alias_kind":"pith_short_8","alias_value":"FMOFZ4IP","created_at":"2026-07-05T00:00:53Z"}],"graph_snapshots":[{"event_id":"sha256:fa22a5e158be44b0277ac29aa6bfce13c6f0ed5a26c159b387088e71115a66c7","target":"graph","created_at":"2026-07-05T00:00:53Z","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/1811.03502/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent results of Hassett, Kuznetsov and others pointed out countably many divisors $C_d$ in the open subset of $\\mathbb{P}^{55}=\\mathbb{P}(H^0(\\mathcal{O}_{\\mathbb{P}^5}(3)))$ parametrizing all cubic 4-folds and lead to the conjecture that the cubics corresponding to these divisors should be precisely the rational ones. Rationality has been proved by Fano for the first divisor $C_{14}$ and in [arXiv:1707.00999] for the divisors $C_{26}$ and $C_{38}$. In this note we describe explicit birational maps from a general cubic fourfold in $C_{14}$, in $C_{26}$ and in $C_{38}$ to $\\mathbb{P}^4$, prov","authors_text":"Francesco Russo, Giovanni Staglian\\`o","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-08T15:44:39Z","title":"Explicit rationality of some cubic fourfolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03502","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":"sha256:27bd2bd7d5d1fd33381f486be7ed08e152a37b6a77db66297b9dec975a60e746","target":"record","created_at":"2026-07-05T00:00:53Z","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":"4352b32fc29a5418df8aa0dd6aec7f9a1edc5484688e4dad743d96d8713dd11b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-08T15:44:39Z","title_canon_sha256":"b45b1375f5ebf99bc43ab04d74a1a260730c580c376f47f4b47a4caaf40afffa"},"schema_version":"1.0","source":{"id":"1811.03502","kind":"arxiv","version":2}},"canonical_sha256":"2b1c5cf10f122171f9bbfc432bea277e62275fcd86df7141cc303a28838569cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b1c5cf10f122171f9bbfc432bea277e62275fcd86df7141cc303a28838569cd","first_computed_at":"2026-07-05T00:00:53.111303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:00:53.111303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7dV2511Fa4osrS79Vlvw1CRhd02XyFF0QOxdFmRCEUdVGaHtNYvoDkwN4BqUJrZB5nC23uFfDyE+VXN+mWpqAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:00:53.111694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03502","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27bd2bd7d5d1fd33381f486be7ed08e152a37b6a77db66297b9dec975a60e746","sha256:fa22a5e158be44b0277ac29aa6bfce13c6f0ed5a26c159b387088e71115a66c7"],"state_sha256":"0fb0201d92d159d94f0a4f610f034e240e2f4ad0a4d07fb5a7f5001722458acb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQDQJj4yBgViANtkXzCx3K9eI1k6fnOoFM7y9+bzD6tkDPSEblFtC7rSSxmhiI1FU8ChwCDejKYzMN4ulzzcDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T03:34:29.785206Z","bundle_sha256":"ad673a21c46a549b8a570b763e3fc59cf343f110f8f2771d1ab268860aa9f48c"}}