{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:O5SK2AQLE4IJPAWDVI4EKX7EYV","short_pith_number":"pith:O5SK2AQL","schema_version":"1.0","canonical_sha256":"7764ad020b27109782c3aa38455fe4c57e2c45e897ba3d6d85b707134c0022ed","source":{"kind":"arxiv","id":"2411.07857","version":4},"attestation_state":"computed","paper":{"title":"The constructive inverse Galois problem via Hilbert modular forms: realizing the transitive group 17T7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Edgar Costa, John Voight, Noam D. Elkies, Raymond van Bommel, Sam Schiavone, Timo Keller","submitted_at":"2024-11-12T15:15:11Z","abstract_excerpt":"We show how Hilbert modular forms can be used in the constructive inverse Galois problem over the rationals. In particular, we prove that the transitive permutation group 17T7, isomorphic to a split extension of C_2 by PSL_2(FF_16), is a Galois group over the rationals and exhibit an explicit degree 17 polynomial with this Galois group. The group arises from the field of definition of the 2-torsion on an abelian fourfold with real multiplication defined over a real quadratic field; we find such a fourfold attached to a Hilbert modular form. Building upon work of Dembele, we describe a method f"},"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":"2411.07857","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-11-12T15:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"77e0fa4a8713d1274a6f5165b569be2f794fe6cc3a12dd52caf2db3dcbd1a9f7","abstract_canon_sha256":"b409e7eaed08f17997e1c7fdaaf4426ea25af7163cc087c52c2d922d374edaa2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:04.492202Z","signature_b64":"dRHfkkCrtI47ZPB7oVzHuRsMeUwkkn1R742MDWv9VLjfjHt4xRCLJXZ04bVUUsXU8YIxbjStoQ1demUEdsS9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7764ad020b27109782c3aa38455fe4c57e2c45e897ba3d6d85b707134c0022ed","last_reissued_at":"2026-06-02T02:04:04.491739Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:04.491739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The constructive inverse Galois problem via Hilbert modular forms: realizing the transitive group 17T7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Edgar Costa, John Voight, Noam D. Elkies, Raymond van Bommel, Sam Schiavone, Timo Keller","submitted_at":"2024-11-12T15:15:11Z","abstract_excerpt":"We show how Hilbert modular forms can be used in the constructive inverse Galois problem over the rationals. In particular, we prove that the transitive permutation group 17T7, isomorphic to a split extension of C_2 by PSL_2(FF_16), is a Galois group over the rationals and exhibit an explicit degree 17 polynomial with this Galois group. The group arises from the field of definition of the 2-torsion on an abelian fourfold with real multiplication defined over a real quadratic field; we find such a fourfold attached to a Hilbert modular form. Building upon work of Dembele, we describe a method f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07857","kind":"arxiv","version":4},"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/2411.07857/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":"2411.07857","created_at":"2026-06-02T02:04:04.491811+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.07857v4","created_at":"2026-06-02T02:04:04.491811+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.07857","created_at":"2026-06-02T02:04:04.491811+00:00"},{"alias_kind":"pith_short_12","alias_value":"O5SK2AQLE4IJ","created_at":"2026-06-02T02:04:04.491811+00:00"},{"alias_kind":"pith_short_16","alias_value":"O5SK2AQLE4IJPAWD","created_at":"2026-06-02T02:04:04.491811+00:00"},{"alias_kind":"pith_short_8","alias_value":"O5SK2AQL","created_at":"2026-06-02T02:04:04.491811+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/O5SK2AQLE4IJPAWDVI4EKX7EYV","json":"https://pith.science/pith/O5SK2AQLE4IJPAWDVI4EKX7EYV.json","graph_json":"https://pith.science/api/pith-number/O5SK2AQLE4IJPAWDVI4EKX7EYV/graph.json","events_json":"https://pith.science/api/pith-number/O5SK2AQLE4IJPAWDVI4EKX7EYV/events.json","paper":"https://pith.science/paper/O5SK2AQL"},"agent_actions":{"view_html":"https://pith.science/pith/O5SK2AQLE4IJPAWDVI4EKX7EYV","download_json":"https://pith.science/pith/O5SK2AQLE4IJPAWDVI4EKX7EYV.json","view_paper":"https://pith.science/paper/O5SK2AQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.07857&json=true","fetch_graph":"https://pith.science/api/pith-number/O5SK2AQLE4IJPAWDVI4EKX7EYV/graph.json","fetch_events":"https://pith.science/api/pith-number/O5SK2AQLE4IJPAWDVI4EKX7EYV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O5SK2AQLE4IJPAWDVI4EKX7EYV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O5SK2AQLE4IJPAWDVI4EKX7EYV/action/storage_attestation","attest_author":"https://pith.science/pith/O5SK2AQLE4IJPAWDVI4EKX7EYV/action/author_attestation","sign_citation":"https://pith.science/pith/O5SK2AQLE4IJPAWDVI4EKX7EYV/action/citation_signature","submit_replication":"https://pith.science/pith/O5SK2AQLE4IJPAWDVI4EKX7EYV/action/replication_record"}},"created_at":"2026-06-02T02:04:04.491811+00:00","updated_at":"2026-06-02T02:04:04.491811+00:00"}