{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:53AIADCMOTWJXWCIDDAZH2S4D6","short_pith_number":"pith:53AIADCM","schema_version":"1.0","canonical_sha256":"eec0800c4c74ec9bd84818c193ea5c1fa73fdf67047e8fd6c77bb3e05c3183b8","source":{"kind":"arxiv","id":"2411.17308","version":1},"attestation_state":"computed","paper":{"title":"Chevalley groups over Laurent polynomial rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.GR","authors_text":"Anastasia Stavrova","submitted_at":"2024-11-26T10:53:39Z","abstract_excerpt":"Let $G$ be a simply connected Chevalley--Demazure group scheme without $SL_2$-factors. For any unital commutative ring $R$, we denote by $E(R)$ the standard elementary subgroup of $G(R)$, that is, the subgroup generated by the elementary root unipotent elements. We prove that the map $$ G(R[x_1^{\\pm 1},\\ldots,x_n^{\\pm 1}])/E(R[x_1^{\\pm 1},\\ldots,x_n^{\\pm 1}])\\to G\\bigl(R((x_1))\\ldots((x_n))\\bigr)/E\\bigl(R((x_1))\\ldots((x_n))\\bigr) $$ is injective for any $n\\ge 1$, if $R$ is either a Dedekind domain or a Noetherian ring that is geometrically regular over a Dedekind domain with perfect residue f"},"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":"2411.17308","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2024-11-26T10:53:39Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"014a67cae19fe3bf59d0898937686dffdfbfaeba3bbccb0466c048c745381f45","abstract_canon_sha256":"91bcda765af68fc1ea34ed8e5f81aefcfb1a20a2c7ee3e44e711cf9a81fdc672"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:30.313789Z","signature_b64":"pDkolgQn41nVdIzFoOB9THhhhQxAP/MQkAr//JVruLTcWI2mDHOiUuuDaDpmgF/Tojjx5mZEa6YyPem8piaOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eec0800c4c74ec9bd84818c193ea5c1fa73fdf67047e8fd6c77bb3e05c3183b8","last_reissued_at":"2026-07-05T09:40:30.313370Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:30.313370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chevalley groups over Laurent polynomial rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.GR","authors_text":"Anastasia Stavrova","submitted_at":"2024-11-26T10:53:39Z","abstract_excerpt":"Let $G$ be a simply connected Chevalley--Demazure group scheme without $SL_2$-factors. For any unital commutative ring $R$, we denote by $E(R)$ the standard elementary subgroup of $G(R)$, that is, the subgroup generated by the elementary root unipotent elements. We prove that the map $$ G(R[x_1^{\\pm 1},\\ldots,x_n^{\\pm 1}])/E(R[x_1^{\\pm 1},\\ldots,x_n^{\\pm 1}])\\to G\\bigl(R((x_1))\\ldots((x_n))\\bigr)/E\\bigl(R((x_1))\\ldots((x_n))\\bigr) $$ is injective for any $n\\ge 1$, if $R$ is either a Dedekind domain or a Noetherian ring that is geometrically regular over a Dedekind domain with perfect residue f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17308","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.17308/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.17308","created_at":"2026-07-05T09:40:30.313424+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.17308v1","created_at":"2026-07-05T09:40:30.313424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17308","created_at":"2026-07-05T09:40:30.313424+00:00"},{"alias_kind":"pith_short_12","alias_value":"53AIADCMOTWJ","created_at":"2026-07-05T09:40:30.313424+00:00"},{"alias_kind":"pith_short_16","alias_value":"53AIADCMOTWJXWCI","created_at":"2026-07-05T09:40:30.313424+00:00"},{"alias_kind":"pith_short_8","alias_value":"53AIADCM","created_at":"2026-07-05T09:40:30.313424+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/53AIADCMOTWJXWCIDDAZH2S4D6","json":"https://pith.science/pith/53AIADCMOTWJXWCIDDAZH2S4D6.json","graph_json":"https://pith.science/api/pith-number/53AIADCMOTWJXWCIDDAZH2S4D6/graph.json","events_json":"https://pith.science/api/pith-number/53AIADCMOTWJXWCIDDAZH2S4D6/events.json","paper":"https://pith.science/paper/53AIADCM"},"agent_actions":{"view_html":"https://pith.science/pith/53AIADCMOTWJXWCIDDAZH2S4D6","download_json":"https://pith.science/pith/53AIADCMOTWJXWCIDDAZH2S4D6.json","view_paper":"https://pith.science/paper/53AIADCM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.17308&json=true","fetch_graph":"https://pith.science/api/pith-number/53AIADCMOTWJXWCIDDAZH2S4D6/graph.json","fetch_events":"https://pith.science/api/pith-number/53AIADCMOTWJXWCIDDAZH2S4D6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53AIADCMOTWJXWCIDDAZH2S4D6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53AIADCMOTWJXWCIDDAZH2S4D6/action/storage_attestation","attest_author":"https://pith.science/pith/53AIADCMOTWJXWCIDDAZH2S4D6/action/author_attestation","sign_citation":"https://pith.science/pith/53AIADCMOTWJXWCIDDAZH2S4D6/action/citation_signature","submit_replication":"https://pith.science/pith/53AIADCMOTWJXWCIDDAZH2S4D6/action/replication_record"}},"created_at":"2026-07-05T09:40:30.313424+00:00","updated_at":"2026-07-05T09:40:30.313424+00:00"}