{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5E3OJ55IOXM4OYVVVAM7UKF4LQ","short_pith_number":"pith:5E3OJ55I","schema_version":"1.0","canonical_sha256":"e936e4f7a875d9c762b5a819fa28bc5c192b557c49d3950e47b7d3254352e91b","source":{"kind":"arxiv","id":"2606.08882","version":1},"attestation_state":"computed","paper":{"title":"Algebraic Hodge generic points are dense","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.AG","authors_text":"David Urbanik, Gal Binyamini, Gregorio Baldi","submitted_at":"2026-06-07T23:47:47Z","abstract_excerpt":"Let $f: X \\to S$ be a quasi-projective family of varieties defined over $\\overline{\\mathbb{Q}} \\subset \\mathbb{C}$. We show that the points of $S(\\overline{\\mathbb{Q}})$ that are Hodge generic for the variation of Hodge structures associated to $f$ are analytically dense in $S(\\mathbb{C})$. In fact, in the spirit of the Grothendieck period conjecture and under a large monodromy assumption, we prove the density of the points of $S(\\overline{\\mathbb{Q}})$ where the periods of the fibre do not satisfy extra relations 'up to degree $\\delta$'. As a by-product, we also establish new instances of the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.08882","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-07T23:47:47Z","cross_cats_sorted":["math.CA","math.NT"],"title_canon_sha256":"b36ae40e6aced9fd37129484af4b1a555e00909c2d637c9517f4b2eb45797200","abstract_canon_sha256":"937327e153b853ed70b45641a6178339fc0922358bce6de940c2486c130d096e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:45.160536Z","signature_b64":"pSeUKJegEjWcAFZ1x7Yofj4ABR2WM/8jsOKX4iZHRIDMldL6fH6Li7MpOAn7woPn5K1jJypr5mmE/4vp+LGnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e936e4f7a875d9c762b5a819fa28bc5c192b557c49d3950e47b7d3254352e91b","last_reissued_at":"2026-06-09T02:07:45.159673Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:45.159673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic Hodge generic points are dense","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.AG","authors_text":"David Urbanik, Gal Binyamini, Gregorio Baldi","submitted_at":"2026-06-07T23:47:47Z","abstract_excerpt":"Let $f: X \\to S$ be a quasi-projective family of varieties defined over $\\overline{\\mathbb{Q}} \\subset \\mathbb{C}$. We show that the points of $S(\\overline{\\mathbb{Q}})$ that are Hodge generic for the variation of Hodge structures associated to $f$ are analytically dense in $S(\\mathbb{C})$. In fact, in the spirit of the Grothendieck period conjecture and under a large monodromy assumption, we prove the density of the points of $S(\\overline{\\mathbb{Q}})$ where the periods of the fibre do not satisfy extra relations 'up to degree $\\delta$'. As a by-product, we also establish new instances of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08882","kind":"arxiv","version":1},"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/2606.08882/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.08882","created_at":"2026-06-09T02:07:45.159805+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.08882v1","created_at":"2026-06-09T02:07:45.159805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08882","created_at":"2026-06-09T02:07:45.159805+00:00"},{"alias_kind":"pith_short_12","alias_value":"5E3OJ55IOXM4","created_at":"2026-06-09T02:07:45.159805+00:00"},{"alias_kind":"pith_short_16","alias_value":"5E3OJ55IOXM4OYVV","created_at":"2026-06-09T02:07:45.159805+00:00"},{"alias_kind":"pith_short_8","alias_value":"5E3OJ55I","created_at":"2026-06-09T02:07:45.159805+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5E3OJ55IOXM4OYVVVAM7UKF4LQ","json":"https://pith.science/pith/5E3OJ55IOXM4OYVVVAM7UKF4LQ.json","graph_json":"https://pith.science/api/pith-number/5E3OJ55IOXM4OYVVVAM7UKF4LQ/graph.json","events_json":"https://pith.science/api/pith-number/5E3OJ55IOXM4OYVVVAM7UKF4LQ/events.json","paper":"https://pith.science/paper/5E3OJ55I"},"agent_actions":{"view_html":"https://pith.science/pith/5E3OJ55IOXM4OYVVVAM7UKF4LQ","download_json":"https://pith.science/pith/5E3OJ55IOXM4OYVVVAM7UKF4LQ.json","view_paper":"https://pith.science/paper/5E3OJ55I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.08882&json=true","fetch_graph":"https://pith.science/api/pith-number/5E3OJ55IOXM4OYVVVAM7UKF4LQ/graph.json","fetch_events":"https://pith.science/api/pith-number/5E3OJ55IOXM4OYVVVAM7UKF4LQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5E3OJ55IOXM4OYVVVAM7UKF4LQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5E3OJ55IOXM4OYVVVAM7UKF4LQ/action/storage_attestation","attest_author":"https://pith.science/pith/5E3OJ55IOXM4OYVVVAM7UKF4LQ/action/author_attestation","sign_citation":"https://pith.science/pith/5E3OJ55IOXM4OYVVVAM7UKF4LQ/action/citation_signature","submit_replication":"https://pith.science/pith/5E3OJ55IOXM4OYVVVAM7UKF4LQ/action/replication_record"}},"created_at":"2026-06-09T02:07:45.159805+00:00","updated_at":"2026-06-09T02:07:45.159805+00:00"}