{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:65XIFCP7CZMQ3N2F43V3SXDTO3","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":"65f550565ae39c25300159c96e250c14f8bdf0e7368b640d6de0c2eb30567318","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T15:59:32Z","title_canon_sha256":"a4902876bafd0563e9a60e878bf5d4b8de1420a58155ab671a0096321c40574d"},"schema_version":"1.0","source":{"id":"2606.23513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23513","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23513v1","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23513","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"65XIFCP7CZMQ","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"65XIFCP7CZMQ3N2F","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"65XIFCP7","created_at":"2026-06-23T03:14:21Z"}],"graph_snapshots":[{"event_id":"sha256:72c4daa24aadbaa3c020c52ec5f2417430b3bb0755c2723ebeca40ecd4a2436b","target":"graph","created_at":"2026-06-23T03:14:21Z","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/2606.23513/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Baker asked, as recorded by Poonen, whether a fixed smooth quasiprojective variety over a finite field must have a smooth rational hyperplane section after every sufficiently high-dimensional linearly nondegenerate embedding. Poonen predicted a negative answer for every positive-dimensional variety. We prove this predicted negative answer for each prescribed variety: if $X$ is nonempty, smooth, quasiprojective, and of pure positive dimension over $\\F_q$, then for every sufficiently large $N$ there is a locally closed embedding $X\\hookrightarrow\\PP^N_{\\F_q}$ whose components remain linearly non","authors_text":"Yaoran Yang, Yutong Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T15:59:32Z","title":"Hyperplane anti-Bertini embeddings over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23513","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:b603427256f4dc98e6c6705e9e8fa1d6a769f1f86e11ce29d233de71d76faa6c","target":"record","created_at":"2026-06-23T03:14:21Z","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":"65f550565ae39c25300159c96e250c14f8bdf0e7368b640d6de0c2eb30567318","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T15:59:32Z","title_canon_sha256":"a4902876bafd0563e9a60e878bf5d4b8de1420a58155ab671a0096321c40574d"},"schema_version":"1.0","source":{"id":"2606.23513","kind":"arxiv","version":1}},"canonical_sha256":"f76e8289ff16590db745e6ebb95c7376c31f9a0f450eb179d315c87648ed72ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f76e8289ff16590db745e6ebb95c7376c31f9a0f450eb179d315c87648ed72ea","first_computed_at":"2026-06-23T03:14:21.949951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:21.949951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F4SywRVd5cAXMX1E/1e1PIJWG3exKS2AplOMh9VYAoXzP5ssWJ/vdAkBpeG5mbGSvU4ib+3Z0iTbwbyTPCVlDQ==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:21.950312Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b603427256f4dc98e6c6705e9e8fa1d6a769f1f86e11ce29d233de71d76faa6c","sha256:72c4daa24aadbaa3c020c52ec5f2417430b3bb0755c2723ebeca40ecd4a2436b"],"state_sha256":"c1c7abcc720e6479e537ee41c8f5bd106aba55b0178e8caf10ecd3e259afa4f5"}