{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6BNOTAVJJDMD3WVJE5KA3RQRNX","short_pith_number":"pith:6BNOTAVJ","schema_version":"1.0","canonical_sha256":"f05ae982a948d83ddaa927540dc6116dffa8c706b50b1d4d0ddfe15e3d0b4491","source":{"kind":"arxiv","id":"1602.06706","version":3},"attestation_state":"computed","paper":{"title":"On parametric extensions over number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fran\\c{c}ois Legrand","submitted_at":"2016-02-22T10:07:45Z","abstract_excerpt":"Given a number field $F$, a finite group $G$ and an indeterminate $T$, {\\it{a $G$-parametric extension over $F$}} is a finite Galois extension $E/F(T)$ with Galois group $G$ and $E/F$ regular that has all the Galois extensions of $F$ with Galois group $G$ among its specializations. We are mainly interested in producing non-$G$-parametric extensions, which relates to classical questions in inverse Galois theory like the Beckmann-Black problem. Building on a strategy developed in previous papers, we show that there exists at least one non-$G$-parametric extension over $F$ for a given non-trivial"},"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":"1602.06706","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-22T10:07:45Z","cross_cats_sorted":[],"title_canon_sha256":"01621674f82ae11d1224929e0db964c79f925b12f7af3a4b7aa42be21ba5b3b7","abstract_canon_sha256":"e210168548dcc3df4c4fee4ecb71eecc6c24508edb7738c1cb5b766e3a461e65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:47.955452Z","signature_b64":"shGhV4AiJK+mk/BWPXN4+jXrn/nd1QR4rxriqaMVXbzLYdNDL/dhSvswQiBpiuvAkQs9eVg9ixW2SP+naXf2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f05ae982a948d83ddaa927540dc6116dffa8c706b50b1d4d0ddfe15e3d0b4491","last_reissued_at":"2026-05-18T00:54:47.955009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:47.955009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On parametric extensions over number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fran\\c{c}ois Legrand","submitted_at":"2016-02-22T10:07:45Z","abstract_excerpt":"Given a number field $F$, a finite group $G$ and an indeterminate $T$, {\\it{a $G$-parametric extension over $F$}} is a finite Galois extension $E/F(T)$ with Galois group $G$ and $E/F$ regular that has all the Galois extensions of $F$ with Galois group $G$ among its specializations. We are mainly interested in producing non-$G$-parametric extensions, which relates to classical questions in inverse Galois theory like the Beckmann-Black problem. Building on a strategy developed in previous papers, we show that there exists at least one non-$G$-parametric extension over $F$ for a given non-trivial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06706","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":"1602.06706","created_at":"2026-05-18T00:54:47.955072+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.06706v3","created_at":"2026-05-18T00:54:47.955072+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06706","created_at":"2026-05-18T00:54:47.955072+00:00"},{"alias_kind":"pith_short_12","alias_value":"6BNOTAVJJDMD","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6BNOTAVJJDMD3WVJ","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6BNOTAVJ","created_at":"2026-05-18T12:30:01.593930+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/6BNOTAVJJDMD3WVJE5KA3RQRNX","json":"https://pith.science/pith/6BNOTAVJJDMD3WVJE5KA3RQRNX.json","graph_json":"https://pith.science/api/pith-number/6BNOTAVJJDMD3WVJE5KA3RQRNX/graph.json","events_json":"https://pith.science/api/pith-number/6BNOTAVJJDMD3WVJE5KA3RQRNX/events.json","paper":"https://pith.science/paper/6BNOTAVJ"},"agent_actions":{"view_html":"https://pith.science/pith/6BNOTAVJJDMD3WVJE5KA3RQRNX","download_json":"https://pith.science/pith/6BNOTAVJJDMD3WVJE5KA3RQRNX.json","view_paper":"https://pith.science/paper/6BNOTAVJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.06706&json=true","fetch_graph":"https://pith.science/api/pith-number/6BNOTAVJJDMD3WVJE5KA3RQRNX/graph.json","fetch_events":"https://pith.science/api/pith-number/6BNOTAVJJDMD3WVJE5KA3RQRNX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6BNOTAVJJDMD3WVJE5KA3RQRNX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6BNOTAVJJDMD3WVJE5KA3RQRNX/action/storage_attestation","attest_author":"https://pith.science/pith/6BNOTAVJJDMD3WVJE5KA3RQRNX/action/author_attestation","sign_citation":"https://pith.science/pith/6BNOTAVJJDMD3WVJE5KA3RQRNX/action/citation_signature","submit_replication":"https://pith.science/pith/6BNOTAVJJDMD3WVJE5KA3RQRNX/action/replication_record"}},"created_at":"2026-05-18T00:54:47.955072+00:00","updated_at":"2026-05-18T00:54:47.955072+00:00"}