{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3MROLC5SDCJLUV2CHEWRXTOYKH","short_pith_number":"pith:3MROLC5S","schema_version":"1.0","canonical_sha256":"db22e58bb21892ba5742392d1bcdd851f2a621ea7a79d5c9d0079cc6a92f5679","source":{"kind":"arxiv","id":"1408.5398","version":3},"attestation_state":"computed","paper":{"title":"Transfers for non-stable K_1-functors of classical type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Anastasia Stavrova","submitted_at":"2014-08-22T19:43:37Z","abstract_excerpt":"Let k be a field. Let G be an absolutely almost simple simply connected k-group of type A_l, l>=2, or D_l, l>=4, containing a 2-dimensional split torus. If G is of type D_l, assume moreover that char k is different from 2. We show that the Nisnevich sheafification of the non-stable K_1-functor K_1^G, also called the Whitehead group of G, on the category of smooth k-schemes is A^1-invariant, and has oriented weak transfers for affine varieties in the sense of Panin-Yagunov-Ross. If k has characteristic 0, this implies that the Nisnevich sheafification of K_1^G is birationally invariant.\n  We al"},"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":"1408.5398","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-08-22T19:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"64af02899118fb96c662adaf8d33c7dbda9f51f100c5e4d81b26dbd9456dff5a","abstract_canon_sha256":"36a89e320e513e3311d6aae7d6b8147bcbf59ec9c104550118adc7d545cee418"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:47.587267Z","signature_b64":"WMucEGNaqs63LNvLTNZjx9H8ouyKM9wGj/IqWcF7ciKotzOKrEm2bPBpDQqySYGLePxOcqmasgF1NjtNWKGCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db22e58bb21892ba5742392d1bcdd851f2a621ea7a79d5c9d0079cc6a92f5679","last_reissued_at":"2026-05-18T01:25:47.586837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:47.586837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transfers for non-stable K_1-functors of classical type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Anastasia Stavrova","submitted_at":"2014-08-22T19:43:37Z","abstract_excerpt":"Let k be a field. Let G be an absolutely almost simple simply connected k-group of type A_l, l>=2, or D_l, l>=4, containing a 2-dimensional split torus. If G is of type D_l, assume moreover that char k is different from 2. We show that the Nisnevich sheafification of the non-stable K_1-functor K_1^G, also called the Whitehead group of G, on the category of smooth k-schemes is A^1-invariant, and has oriented weak transfers for affine varieties in the sense of Panin-Yagunov-Ross. If k has characteristic 0, this implies that the Nisnevich sheafification of K_1^G is birationally invariant.\n  We al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5398","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":"1408.5398","created_at":"2026-05-18T01:25:47.586895+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.5398v3","created_at":"2026-05-18T01:25:47.586895+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5398","created_at":"2026-05-18T01:25:47.586895+00:00"},{"alias_kind":"pith_short_12","alias_value":"3MROLC5SDCJL","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3MROLC5SDCJLUV2C","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3MROLC5S","created_at":"2026-05-18T12:28:11.866339+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/3MROLC5SDCJLUV2CHEWRXTOYKH","json":"https://pith.science/pith/3MROLC5SDCJLUV2CHEWRXTOYKH.json","graph_json":"https://pith.science/api/pith-number/3MROLC5SDCJLUV2CHEWRXTOYKH/graph.json","events_json":"https://pith.science/api/pith-number/3MROLC5SDCJLUV2CHEWRXTOYKH/events.json","paper":"https://pith.science/paper/3MROLC5S"},"agent_actions":{"view_html":"https://pith.science/pith/3MROLC5SDCJLUV2CHEWRXTOYKH","download_json":"https://pith.science/pith/3MROLC5SDCJLUV2CHEWRXTOYKH.json","view_paper":"https://pith.science/paper/3MROLC5S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.5398&json=true","fetch_graph":"https://pith.science/api/pith-number/3MROLC5SDCJLUV2CHEWRXTOYKH/graph.json","fetch_events":"https://pith.science/api/pith-number/3MROLC5SDCJLUV2CHEWRXTOYKH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3MROLC5SDCJLUV2CHEWRXTOYKH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3MROLC5SDCJLUV2CHEWRXTOYKH/action/storage_attestation","attest_author":"https://pith.science/pith/3MROLC5SDCJLUV2CHEWRXTOYKH/action/author_attestation","sign_citation":"https://pith.science/pith/3MROLC5SDCJLUV2CHEWRXTOYKH/action/citation_signature","submit_replication":"https://pith.science/pith/3MROLC5SDCJLUV2CHEWRXTOYKH/action/replication_record"}},"created_at":"2026-05-18T01:25:47.586895+00:00","updated_at":"2026-05-18T01:25:47.586895+00:00"}