{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JDMSNGSGQCWYUW7727RBI6TA4G","short_pith_number":"pith:JDMSNGSG","schema_version":"1.0","canonical_sha256":"48d9269a4680ad8a5bffd7e2147a60e1a803f42f3e72b0176a6071584e3af335","source":{"kind":"arxiv","id":"1908.02438","version":2},"attestation_state":"computed","paper":{"title":"Finite group schemes of essential dimension one","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Najmuddin Fakhruddin","submitted_at":"2019-08-07T04:37:50Z","abstract_excerpt":"We prove that if a finite group scheme $G$ over a field $k$ has essential dimension one, then it embeds in $PGL_{2/k}$. We use this to give an explicit classification of all infinitesimal group schemes of essential dimension one over any field and a characterisation of all finite group schemes of essential dimension one over algebraically closed fields."},"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":"1908.02438","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2019-08-07T04:37:50Z","cross_cats_sorted":[],"title_canon_sha256":"b02d2ba9c83573a6c9575fe3e76260bcafb764a15a40a4768e218f24598c6827","abstract_canon_sha256":"9de081adc1b2e117c45f8d73942117d6d8fe0f5ba23240b3fd5ec7b433ba2c1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:08.399142Z","signature_b64":"ufZrHbBTW0Dul1hPpHuwXry8CYOvwSUPtYeBt7obmQ5aQxPrpXQuR8RTmlSUGMUPZmY642L6DvrhtjrsjgjlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48d9269a4680ad8a5bffd7e2147a60e1a803f42f3e72b0176a6071584e3af335","last_reissued_at":"2026-07-04T23:59:08.398655Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:08.398655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite group schemes of essential dimension one","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Najmuddin Fakhruddin","submitted_at":"2019-08-07T04:37:50Z","abstract_excerpt":"We prove that if a finite group scheme $G$ over a field $k$ has essential dimension one, then it embeds in $PGL_{2/k}$. We use this to give an explicit classification of all infinitesimal group schemes of essential dimension one over any field and a characterisation of all finite group schemes of essential dimension one over algebraically closed fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02438","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/1908.02438/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":"1908.02438","created_at":"2026-07-04T23:59:08.398724+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.02438v2","created_at":"2026-07-04T23:59:08.398724+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02438","created_at":"2026-07-04T23:59:08.398724+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDMSNGSGQCWY","created_at":"2026-07-04T23:59:08.398724+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDMSNGSGQCWYUW77","created_at":"2026-07-04T23:59:08.398724+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDMSNGSG","created_at":"2026-07-04T23:59:08.398724+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/JDMSNGSGQCWYUW7727RBI6TA4G","json":"https://pith.science/pith/JDMSNGSGQCWYUW7727RBI6TA4G.json","graph_json":"https://pith.science/api/pith-number/JDMSNGSGQCWYUW7727RBI6TA4G/graph.json","events_json":"https://pith.science/api/pith-number/JDMSNGSGQCWYUW7727RBI6TA4G/events.json","paper":"https://pith.science/paper/JDMSNGSG"},"agent_actions":{"view_html":"https://pith.science/pith/JDMSNGSGQCWYUW7727RBI6TA4G","download_json":"https://pith.science/pith/JDMSNGSGQCWYUW7727RBI6TA4G.json","view_paper":"https://pith.science/paper/JDMSNGSG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.02438&json=true","fetch_graph":"https://pith.science/api/pith-number/JDMSNGSGQCWYUW7727RBI6TA4G/graph.json","fetch_events":"https://pith.science/api/pith-number/JDMSNGSGQCWYUW7727RBI6TA4G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDMSNGSGQCWYUW7727RBI6TA4G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDMSNGSGQCWYUW7727RBI6TA4G/action/storage_attestation","attest_author":"https://pith.science/pith/JDMSNGSGQCWYUW7727RBI6TA4G/action/author_attestation","sign_citation":"https://pith.science/pith/JDMSNGSGQCWYUW7727RBI6TA4G/action/citation_signature","submit_replication":"https://pith.science/pith/JDMSNGSGQCWYUW7727RBI6TA4G/action/replication_record"}},"created_at":"2026-07-04T23:59:08.398724+00:00","updated_at":"2026-07-04T23:59:08.398724+00:00"}