{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:Y5KYSIVDFFFSHHOK4T6XDM4PYX","short_pith_number":"pith:Y5KYSIVD","schema_version":"1.0","canonical_sha256":"c7558922a3294b239dcae4fd71b38fc5d6dfd7ba7d439a29a55ad4958d3c2962","source":{"kind":"arxiv","id":"1704.07811","version":1},"attestation_state":"computed","paper":{"title":"$R$-triviality of some exceptional groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Maneesh Thakur","submitted_at":"2017-04-25T17:41:45Z","abstract_excerpt":"The main aim of this paper is to prove $R$-triviality for simple, simply connected algebraic groups with Tits index $E_{8,2}^{78}$ or $E_{7,1}^{78}$, defined over a field $k$ of arbitrary characteristic. Let $G$ be such a group. We prove that there exists a quadratic extension $K$ of $k$ such that $G$ is $R$-trivial over $K$, i.e., for any extension $F$ of $K$, $G(F)/R=\\{1\\}$, where $G(F)/R$ denotes the group of $R$-equivalence classes in $G(F)$, in the sense of Manin (see \\cite{M}). As a consequence, it follows that the variety $G$ is retract $K$-rational and that the Kneser-Tits conjecture h"},"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":"1704.07811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-25T17:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"fc58b1a07e5d9113da21ad81a793fdb3189d1cec74955d655ceacc6dd275de8e","abstract_canon_sha256":"07c8c45c1ec39b6d1eefc3d8632d5fde96aad4669440dc377d61de9664df73de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:36.818655Z","signature_b64":"nP/O8cd+RYO1hPpzA8/bAMYrTm0BDDx9fD0ZhVXo9Fp4XW+LfKFo4GLErCguEb2dWeD80y5yMUpxtyogErc8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7558922a3294b239dcae4fd71b38fc5d6dfd7ba7d439a29a55ad4958d3c2962","last_reissued_at":"2026-05-18T00:45:36.817626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:36.817626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$R$-triviality of some exceptional groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Maneesh Thakur","submitted_at":"2017-04-25T17:41:45Z","abstract_excerpt":"The main aim of this paper is to prove $R$-triviality for simple, simply connected algebraic groups with Tits index $E_{8,2}^{78}$ or $E_{7,1}^{78}$, defined over a field $k$ of arbitrary characteristic. Let $G$ be such a group. We prove that there exists a quadratic extension $K$ of $k$ such that $G$ is $R$-trivial over $K$, i.e., for any extension $F$ of $K$, $G(F)/R=\\{1\\}$, where $G(F)/R$ denotes the group of $R$-equivalence classes in $G(F)$, in the sense of Manin (see \\cite{M}). As a consequence, it follows that the variety $G$ is retract $K$-rational and that the Kneser-Tits conjecture h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07811","kind":"arxiv","version":1},"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":"1704.07811","created_at":"2026-05-18T00:45:36.818057+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.07811v1","created_at":"2026-05-18T00:45:36.818057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07811","created_at":"2026-05-18T00:45:36.818057+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y5KYSIVDFFFS","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y5KYSIVDFFFSHHOK","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y5KYSIVD","created_at":"2026-05-18T12:31:56.362134+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/Y5KYSIVDFFFSHHOK4T6XDM4PYX","json":"https://pith.science/pith/Y5KYSIVDFFFSHHOK4T6XDM4PYX.json","graph_json":"https://pith.science/api/pith-number/Y5KYSIVDFFFSHHOK4T6XDM4PYX/graph.json","events_json":"https://pith.science/api/pith-number/Y5KYSIVDFFFSHHOK4T6XDM4PYX/events.json","paper":"https://pith.science/paper/Y5KYSIVD"},"agent_actions":{"view_html":"https://pith.science/pith/Y5KYSIVDFFFSHHOK4T6XDM4PYX","download_json":"https://pith.science/pith/Y5KYSIVDFFFSHHOK4T6XDM4PYX.json","view_paper":"https://pith.science/paper/Y5KYSIVD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.07811&json=true","fetch_graph":"https://pith.science/api/pith-number/Y5KYSIVDFFFSHHOK4T6XDM4PYX/graph.json","fetch_events":"https://pith.science/api/pith-number/Y5KYSIVDFFFSHHOK4T6XDM4PYX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y5KYSIVDFFFSHHOK4T6XDM4PYX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y5KYSIVDFFFSHHOK4T6XDM4PYX/action/storage_attestation","attest_author":"https://pith.science/pith/Y5KYSIVDFFFSHHOK4T6XDM4PYX/action/author_attestation","sign_citation":"https://pith.science/pith/Y5KYSIVDFFFSHHOK4T6XDM4PYX/action/citation_signature","submit_replication":"https://pith.science/pith/Y5KYSIVDFFFSHHOK4T6XDM4PYX/action/replication_record"}},"created_at":"2026-05-18T00:45:36.818057+00:00","updated_at":"2026-05-18T00:45:36.818057+00:00"}