{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:R6UR46V5BI2QQRQLYI2HHDWV5H","short_pith_number":"pith:R6UR46V5","schema_version":"1.0","canonical_sha256":"8fa91e7abd0a3508460bc234738ed5e9e2adb435daf5f22312d584937be1bd72","source":{"kind":"arxiv","id":"1802.05894","version":2},"attestation_state":"computed","paper":{"title":"Conjugation of semisimple subgroups over real number fields of bounded degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.GR","authors_text":"Christopher Daw, Jinbo Ren, Mikhail Borovoi","submitted_at":"2018-02-16T11:10:38Z","abstract_excerpt":"Let $G$ be a linear algebraic group over a field $k$ of characteristic 0. We show that any two connected semisimple $k$-subgroups of $G$ that are conjugate over an algebraic closure of $k$ are actually conjugate over a finite field extension of $k$ of degree bounded independently of the subgroups. Moreover, if $k$ is a real number field, we show that any two connected semisimple $k$-subgroups of $G$ that are conjugate over the field of real numbers $\\mathbb{R}$ are actually conjugate over a finite real extension of $k$ of degree bounded independently of the subgroups."},"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":"1802.05894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-16T11:10:38Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"22975cd921cdd40776a379ecb78b884983107aac7c8827a0b3969b909f21f392","abstract_canon_sha256":"dd544543b99df48c30f0a95f1b4a83d43383f9741a74f1511757b5a2783b6cd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:41.980221Z","signature_b64":"Iy9QAS7/7hagmhoOlo4ZKeDuVuTL+spbI1Y9giP4qNxnTAIa7dK5MIGPRVCokupu0cl+fuYy+34Ttg5RLlCpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fa91e7abd0a3508460bc234738ed5e9e2adb435daf5f22312d584937be1bd72","last_reissued_at":"2026-05-17T23:58:41.979568Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:41.979568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conjugation of semisimple subgroups over real number fields of bounded degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.GR","authors_text":"Christopher Daw, Jinbo Ren, Mikhail Borovoi","submitted_at":"2018-02-16T11:10:38Z","abstract_excerpt":"Let $G$ be a linear algebraic group over a field $k$ of characteristic 0. We show that any two connected semisimple $k$-subgroups of $G$ that are conjugate over an algebraic closure of $k$ are actually conjugate over a finite field extension of $k$ of degree bounded independently of the subgroups. Moreover, if $k$ is a real number field, we show that any two connected semisimple $k$-subgroups of $G$ that are conjugate over the field of real numbers $\\mathbb{R}$ are actually conjugate over a finite real extension of $k$ of degree bounded independently of the subgroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05894","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":"1802.05894","created_at":"2026-05-17T23:58:41.979673+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.05894v2","created_at":"2026-05-17T23:58:41.979673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05894","created_at":"2026-05-17T23:58:41.979673+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6UR46V5BI2Q","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6UR46V5BI2QQRQL","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6UR46V5","created_at":"2026-05-18T12:32:50.500415+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/R6UR46V5BI2QQRQLYI2HHDWV5H","json":"https://pith.science/pith/R6UR46V5BI2QQRQLYI2HHDWV5H.json","graph_json":"https://pith.science/api/pith-number/R6UR46V5BI2QQRQLYI2HHDWV5H/graph.json","events_json":"https://pith.science/api/pith-number/R6UR46V5BI2QQRQLYI2HHDWV5H/events.json","paper":"https://pith.science/paper/R6UR46V5"},"agent_actions":{"view_html":"https://pith.science/pith/R6UR46V5BI2QQRQLYI2HHDWV5H","download_json":"https://pith.science/pith/R6UR46V5BI2QQRQLYI2HHDWV5H.json","view_paper":"https://pith.science/paper/R6UR46V5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.05894&json=true","fetch_graph":"https://pith.science/api/pith-number/R6UR46V5BI2QQRQLYI2HHDWV5H/graph.json","fetch_events":"https://pith.science/api/pith-number/R6UR46V5BI2QQRQLYI2HHDWV5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6UR46V5BI2QQRQLYI2HHDWV5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6UR46V5BI2QQRQLYI2HHDWV5H/action/storage_attestation","attest_author":"https://pith.science/pith/R6UR46V5BI2QQRQLYI2HHDWV5H/action/author_attestation","sign_citation":"https://pith.science/pith/R6UR46V5BI2QQRQLYI2HHDWV5H/action/citation_signature","submit_replication":"https://pith.science/pith/R6UR46V5BI2QQRQLYI2HHDWV5H/action/replication_record"}},"created_at":"2026-05-17T23:58:41.979673+00:00","updated_at":"2026-05-17T23:58:41.979673+00:00"}