{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:SECLJLZZQ4IAD55KZVVGUIWLCY","short_pith_number":"pith:SECLJLZZ","schema_version":"1.0","canonical_sha256":"9104b4af39871001f7aacd6a6a22cb16207ae5b754fce94bdeb899294e0cfeba","source":{"kind":"arxiv","id":"0909.4340","version":3},"attestation_state":"computed","paper":{"title":"An invitation to model-theoretic Galois theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.HO"],"primary_cat":"math.LO","authors_text":"Alice Medvedev, Ramin Takloo-Bighash","submitted_at":"2009-09-24T00:35:37Z","abstract_excerpt":"We carry out some of Galois's work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite sets, and obtain the fundamental duality of Galois theory matching subgroups of the Galois group of L over F with intermediate extensions. This exposition of a special case of Poizat's \"Une th\\'eorie de Galois imaginaire.\" (1983) has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorp"},"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":"0909.4340","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-09-24T00:35:37Z","cross_cats_sorted":["math.AC","math.HO"],"title_canon_sha256":"7064b6a2c67fe21898b37a4342637c3e4a7dbbbb21f764431670cfb8abd5cbf5","abstract_canon_sha256":"6821591d7a7d3cd4bf9fe75f47a68b5dea2d7487207d0539d4b7d86e79f6707f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:01.950865Z","signature_b64":"qY5C5Boq+pUrPoQn0iwAXPEz2wOqxtc34qIhy0JP4/qKBOZcimkbqcx3msFp/aUXK+0UiaC5yqSOoWj/O9+XCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9104b4af39871001f7aacd6a6a22cb16207ae5b754fce94bdeb899294e0cfeba","last_reissued_at":"2026-05-18T04:42:01.950476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:01.950476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An invitation to model-theoretic Galois theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.HO"],"primary_cat":"math.LO","authors_text":"Alice Medvedev, Ramin Takloo-Bighash","submitted_at":"2009-09-24T00:35:37Z","abstract_excerpt":"We carry out some of Galois's work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite sets, and obtain the fundamental duality of Galois theory matching subgroups of the Galois group of L over F with intermediate extensions. This exposition of a special case of Poizat's \"Une th\\'eorie de Galois imaginaire.\" (1983) has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4340","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"0909.4340","created_at":"2026-05-18T04:42:01.950532+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.4340v3","created_at":"2026-05-18T04:42:01.950532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4340","created_at":"2026-05-18T04:42:01.950532+00:00"},{"alias_kind":"pith_short_12","alias_value":"SECLJLZZQ4IA","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"SECLJLZZQ4IAD55K","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"SECLJLZZ","created_at":"2026-05-18T12:26:01.383474+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/SECLJLZZQ4IAD55KZVVGUIWLCY","json":"https://pith.science/pith/SECLJLZZQ4IAD55KZVVGUIWLCY.json","graph_json":"https://pith.science/api/pith-number/SECLJLZZQ4IAD55KZVVGUIWLCY/graph.json","events_json":"https://pith.science/api/pith-number/SECLJLZZQ4IAD55KZVVGUIWLCY/events.json","paper":"https://pith.science/paper/SECLJLZZ"},"agent_actions":{"view_html":"https://pith.science/pith/SECLJLZZQ4IAD55KZVVGUIWLCY","download_json":"https://pith.science/pith/SECLJLZZQ4IAD55KZVVGUIWLCY.json","view_paper":"https://pith.science/paper/SECLJLZZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.4340&json=true","fetch_graph":"https://pith.science/api/pith-number/SECLJLZZQ4IAD55KZVVGUIWLCY/graph.json","fetch_events":"https://pith.science/api/pith-number/SECLJLZZQ4IAD55KZVVGUIWLCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SECLJLZZQ4IAD55KZVVGUIWLCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SECLJLZZQ4IAD55KZVVGUIWLCY/action/storage_attestation","attest_author":"https://pith.science/pith/SECLJLZZQ4IAD55KZVVGUIWLCY/action/author_attestation","sign_citation":"https://pith.science/pith/SECLJLZZQ4IAD55KZVVGUIWLCY/action/citation_signature","submit_replication":"https://pith.science/pith/SECLJLZZQ4IAD55KZVVGUIWLCY/action/replication_record"}},"created_at":"2026-05-18T04:42:01.950532+00:00","updated_at":"2026-05-18T04:42:01.950532+00:00"}