{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:TFRT2ZE2ZNDB66PG4E7PI4OE2B","short_pith_number":"pith:TFRT2ZE2","schema_version":"1.0","canonical_sha256":"99633d649acb461f79e6e13ef471c4d062c1aad61e9e799f9d3e4faaebc342d6","source":{"kind":"arxiv","id":"2412.15988","version":1},"attestation_state":"computed","paper":{"title":"Continuity of heights in families and complete intersections in toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO"],"primary_cat":"math.NT","authors_text":"Micha{\\l} Szachniewicz, Nuno Hultberg, Pablo Destic","submitted_at":"2024-12-20T15:32:52Z","abstract_excerpt":"We study the variation of heights of cycles in flat families over number fields or, more generally, globally valued fields. To a finite type scheme over a GVF we associate a locally compact Hausdorff space which we refer to as its GVF analytification. For a flat projective family, we prove that the height of fibres is a continuous function on the GVF analytification of the base. As an application, we prove Roberto Gualdi's conjecture on limit heights of complete intersections in toric varieties."},"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":"2412.15988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-12-20T15:32:52Z","cross_cats_sorted":["math.AG","math.LO"],"title_canon_sha256":"c18146f143631f04c7ad84fa23564e0587d583f750065c06b249f01b490cf02a","abstract_canon_sha256":"d5426695086c5e29ee88b576e01c0f08bf15ead657baca40170e05348cc8aaa4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:33.133581Z","signature_b64":"spVn0LTcrgtVvSbLLL+9Eik9y5a38REm4t7cqmR184zffpx5x45r3OHxiRUzDP3XNTZudxnTth1mqsEu0/yPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99633d649acb461f79e6e13ef471c4d062c1aad61e9e799f9d3e4faaebc342d6","last_reissued_at":"2026-07-05T09:52:33.133140Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:33.133140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuity of heights in families and complete intersections in toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO"],"primary_cat":"math.NT","authors_text":"Micha{\\l} Szachniewicz, Nuno Hultberg, Pablo Destic","submitted_at":"2024-12-20T15:32:52Z","abstract_excerpt":"We study the variation of heights of cycles in flat families over number fields or, more generally, globally valued fields. To a finite type scheme over a GVF we associate a locally compact Hausdorff space which we refer to as its GVF analytification. For a flat projective family, we prove that the height of fibres is a continuous function on the GVF analytification of the base. As an application, we prove Roberto Gualdi's conjecture on limit heights of complete intersections in toric varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15988","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/2412.15988/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":"2412.15988","created_at":"2026-07-05T09:52:33.133204+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.15988v1","created_at":"2026-07-05T09:52:33.133204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15988","created_at":"2026-07-05T09:52:33.133204+00:00"},{"alias_kind":"pith_short_12","alias_value":"TFRT2ZE2ZNDB","created_at":"2026-07-05T09:52:33.133204+00:00"},{"alias_kind":"pith_short_16","alias_value":"TFRT2ZE2ZNDB66PG","created_at":"2026-07-05T09:52:33.133204+00:00"},{"alias_kind":"pith_short_8","alias_value":"TFRT2ZE2","created_at":"2026-07-05T09:52:33.133204+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/TFRT2ZE2ZNDB66PG4E7PI4OE2B","json":"https://pith.science/pith/TFRT2ZE2ZNDB66PG4E7PI4OE2B.json","graph_json":"https://pith.science/api/pith-number/TFRT2ZE2ZNDB66PG4E7PI4OE2B/graph.json","events_json":"https://pith.science/api/pith-number/TFRT2ZE2ZNDB66PG4E7PI4OE2B/events.json","paper":"https://pith.science/paper/TFRT2ZE2"},"agent_actions":{"view_html":"https://pith.science/pith/TFRT2ZE2ZNDB66PG4E7PI4OE2B","download_json":"https://pith.science/pith/TFRT2ZE2ZNDB66PG4E7PI4OE2B.json","view_paper":"https://pith.science/paper/TFRT2ZE2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.15988&json=true","fetch_graph":"https://pith.science/api/pith-number/TFRT2ZE2ZNDB66PG4E7PI4OE2B/graph.json","fetch_events":"https://pith.science/api/pith-number/TFRT2ZE2ZNDB66PG4E7PI4OE2B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TFRT2ZE2ZNDB66PG4E7PI4OE2B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TFRT2ZE2ZNDB66PG4E7PI4OE2B/action/storage_attestation","attest_author":"https://pith.science/pith/TFRT2ZE2ZNDB66PG4E7PI4OE2B/action/author_attestation","sign_citation":"https://pith.science/pith/TFRT2ZE2ZNDB66PG4E7PI4OE2B/action/citation_signature","submit_replication":"https://pith.science/pith/TFRT2ZE2ZNDB66PG4E7PI4OE2B/action/replication_record"}},"created_at":"2026-07-05T09:52:33.133204+00:00","updated_at":"2026-07-05T09:52:33.133204+00:00"}