{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:KEUFPW6OYEQHNT3FDQGJYLRZLF","short_pith_number":"pith:KEUFPW6O","schema_version":"1.0","canonical_sha256":"512857dbcec12076cf651c0c9c2e39595f205181ebbe0579086155108d1bbfaf","source":{"kind":"arxiv","id":"0911.3792","version":2},"attestation_state":"computed","paper":{"title":"Realizability and admissibility under extension of p-adic and number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RA","authors_text":"Danny Neftin, Uzi Vishne","submitted_at":"2009-11-19T13:27:07Z","abstract_excerpt":"A finite group G is K-admissible if there exists a G-crossed product K-division algebra. In this manuscript we study the behavior of admissibility under extensions of number fields M/K. We show that in many cases, including Sylow metacyclic and nilpotent groups whose order is prime to the number of roots of unity in M, a K-admissible group G is M-admissible if and only if G satisfies the easily verifiable Liedahl condition over M."},"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":"0911.3792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-11-19T13:27:07Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"381aefadbecf9e2074b376e23a8ae379693908e9cf5931b70d73b925b1b9ccff","abstract_canon_sha256":"ee2fdec83182502b42263a77ef84b55588902b4d680f0c34081b8af1cf4b69e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:54.373124Z","signature_b64":"VfyH2M/rLZCVgMRayyn2Afr8YA1J4jqMu1qn4Nc+/XVh3rTFiiQEJ9o9OH1RvV/TWpWd1CpxLYTDM1o9GyahCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"512857dbcec12076cf651c0c9c2e39595f205181ebbe0579086155108d1bbfaf","last_reissued_at":"2026-05-18T04:07:54.372545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:54.372545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Realizability and admissibility under extension of p-adic and number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RA","authors_text":"Danny Neftin, Uzi Vishne","submitted_at":"2009-11-19T13:27:07Z","abstract_excerpt":"A finite group G is K-admissible if there exists a G-crossed product K-division algebra. In this manuscript we study the behavior of admissibility under extensions of number fields M/K. We show that in many cases, including Sylow metacyclic and nilpotent groups whose order is prime to the number of roots of unity in M, a K-admissible group G is M-admissible if and only if G satisfies the easily verifiable Liedahl condition over M."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3792","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":""},"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":"0911.3792","created_at":"2026-05-18T04:07:54.372615+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.3792v2","created_at":"2026-05-18T04:07:54.372615+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3792","created_at":"2026-05-18T04:07:54.372615+00:00"},{"alias_kind":"pith_short_12","alias_value":"KEUFPW6OYEQH","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"KEUFPW6OYEQHNT3F","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"KEUFPW6O","created_at":"2026-05-18T12:26:00.592388+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/KEUFPW6OYEQHNT3FDQGJYLRZLF","json":"https://pith.science/pith/KEUFPW6OYEQHNT3FDQGJYLRZLF.json","graph_json":"https://pith.science/api/pith-number/KEUFPW6OYEQHNT3FDQGJYLRZLF/graph.json","events_json":"https://pith.science/api/pith-number/KEUFPW6OYEQHNT3FDQGJYLRZLF/events.json","paper":"https://pith.science/paper/KEUFPW6O"},"agent_actions":{"view_html":"https://pith.science/pith/KEUFPW6OYEQHNT3FDQGJYLRZLF","download_json":"https://pith.science/pith/KEUFPW6OYEQHNT3FDQGJYLRZLF.json","view_paper":"https://pith.science/paper/KEUFPW6O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.3792&json=true","fetch_graph":"https://pith.science/api/pith-number/KEUFPW6OYEQHNT3FDQGJYLRZLF/graph.json","fetch_events":"https://pith.science/api/pith-number/KEUFPW6OYEQHNT3FDQGJYLRZLF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KEUFPW6OYEQHNT3FDQGJYLRZLF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KEUFPW6OYEQHNT3FDQGJYLRZLF/action/storage_attestation","attest_author":"https://pith.science/pith/KEUFPW6OYEQHNT3FDQGJYLRZLF/action/author_attestation","sign_citation":"https://pith.science/pith/KEUFPW6OYEQHNT3FDQGJYLRZLF/action/citation_signature","submit_replication":"https://pith.science/pith/KEUFPW6OYEQHNT3FDQGJYLRZLF/action/replication_record"}},"created_at":"2026-05-18T04:07:54.372615+00:00","updated_at":"2026-05-18T04:07:54.372615+00:00"}