{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WJCDJ7T4DXBHYFF534Y3F7XX5N","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":"9b5013cdbbb9ca600669f32136ad4c58cf54d2bc202d93e02e4b8907bdb26f51","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-05-10T16:39:35Z","title_canon_sha256":"90685cfb76756008206ebe3fa8e8e18ea646251b9f47d93fb2450d6d0e5ac635"},"schema_version":"1.0","source":{"id":"2405.06584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.06584","created_at":"2026-07-05T08:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"2405.06584v1","created_at":"2026-07-05T08:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.06584","created_at":"2026-07-05T08:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"WJCDJ7T4DXBH","created_at":"2026-07-05T08:17:51Z"},{"alias_kind":"pith_short_16","alias_value":"WJCDJ7T4DXBHYFF5","created_at":"2026-07-05T08:17:51Z"},{"alias_kind":"pith_short_8","alias_value":"WJCDJ7T4","created_at":"2026-07-05T08:17:51Z"}],"graph_snapshots":[{"event_id":"sha256:eb841f33245437c6ddaabb9b3d7facfb2e736841ae556fc2685eadfc57bb44da","target":"graph","created_at":"2026-07-05T08:17:51Z","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/2405.06584/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A cubic hypersurface in $\\mathbb{P}^n$ defined over $\\mathbb{Q}$ is given by the vanishing locus of a cubic form $f$ in $n+1$ variables. It is conjectured that when $n \\geq 4$, such cubic hypersurfaces satisfy the Hasse principle. This is now known to hold on average due to recent work of Browning, Le Boudec, and Sawin. Using this result, we determine the proportion of cubic hypersurfaces in $\\mathbb{P}^n$, ordered by the height of $f$, with a rational point for $n \\geq 4$ explicitly as a product over primes $p$ of rational functions in $p$. In particular, this proportion is equal to 1 for cub","authors_text":"Christopher Keyes, Lea Beneish","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-05-10T16:39:35Z","title":"How often does a cubic hypersurface have a rational point?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.06584","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":"sha256:8644198ccf5bef3fe2ab4ad87443f8f40a565b3f74247714d44c1a355c1667d4","target":"record","created_at":"2026-07-05T08:17:51Z","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":"9b5013cdbbb9ca600669f32136ad4c58cf54d2bc202d93e02e4b8907bdb26f51","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-05-10T16:39:35Z","title_canon_sha256":"90685cfb76756008206ebe3fa8e8e18ea646251b9f47d93fb2450d6d0e5ac635"},"schema_version":"1.0","source":{"id":"2405.06584","kind":"arxiv","version":1}},"canonical_sha256":"b24434fe7c1dc27c14bddf31b2fef7eb5e35dcae2680a73a8205ea8b48bc0498","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b24434fe7c1dc27c14bddf31b2fef7eb5e35dcae2680a73a8205ea8b48bc0498","first_computed_at":"2026-07-05T08:17:51.792631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:17:51.792631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m+cN4DOQ5UKRpQqjCeIq0ZtLYJhFZlyV5VYp8mVW/SrGtbn5d4GM4Ex5VWrJ4fJ2LUY70faySxsd4+al4PSVBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:17:51.793067Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.06584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8644198ccf5bef3fe2ab4ad87443f8f40a565b3f74247714d44c1a355c1667d4","sha256:eb841f33245437c6ddaabb9b3d7facfb2e736841ae556fc2685eadfc57bb44da"],"state_sha256":"471fe2ad0d42ecac6489b4a1f8777a8efbe417ec1efeb004096e4dbbea18c272"}