{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:E37Q5R4GKP64JUXUPZTP6BPDKM","short_pith_number":"pith:E37Q5R4G","schema_version":"1.0","canonical_sha256":"26ff0ec78653fdc4d2f47e66ff05e353233c345260d3f43866c87f5187279b3c","source":{"kind":"arxiv","id":"1211.3575","version":2},"attestation_state":"computed","paper":{"title":"Local-global principle for congruence subgroups of Chevalley groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Stepanov, Himanee Apte","submitted_at":"2012-11-15T11:19:09Z","abstract_excerpt":"We prove Suslin's local-global principle for principal congruence subgroups of Chevalley groups. Let $G$ be a Chevalley--Demazure group scheme with a root system $\\Phi\\ne A_1$ and $E$ its elementary subgroup. Let $R$ be a ring and $I$ an ideal of $R$. Assume additionally that $R$ has no residue fields of 2 elements if $\\Phi=C_2$ or $G_2$.\n  Theorem. Let $g\\in G(R[X],XR[X])$. Suppose that for every maximal ideal $\\m$ of $R$ the image of $g$ under the localization homomorphism at $\\m$ belongs to $E(R_\\m[X],IR_\\m[X])$. Then, $g\\in E(R[X],IR[X])$.\n  The theorem is a common generalization of the re"},"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":"1211.3575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-15T11:19:09Z","cross_cats_sorted":[],"title_canon_sha256":"8d7078c7f416e69c97474d1b10657efc68c2c766c22b07a3b952575049dbdf71","abstract_canon_sha256":"1ceaf70d415e6f412ce7b60e68d8008e0d17b3aee786cef8274ef040a5d6e824"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:19.241104Z","signature_b64":"f/15A3wryGy7nu6hZNz0zNxxqueO6hu0byTdeHYH79yu7Fn3r8g/MFbh0/yXMNL0rI+Gwr4/XuB8CUFthqCCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26ff0ec78653fdc4d2f47e66ff05e353233c345260d3f43866c87f5187279b3c","last_reissued_at":"2026-05-18T01:26:19.240412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:19.240412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local-global principle for congruence subgroups of Chevalley groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Stepanov, Himanee Apte","submitted_at":"2012-11-15T11:19:09Z","abstract_excerpt":"We prove Suslin's local-global principle for principal congruence subgroups of Chevalley groups. Let $G$ be a Chevalley--Demazure group scheme with a root system $\\Phi\\ne A_1$ and $E$ its elementary subgroup. Let $R$ be a ring and $I$ an ideal of $R$. Assume additionally that $R$ has no residue fields of 2 elements if $\\Phi=C_2$ or $G_2$.\n  Theorem. Let $g\\in G(R[X],XR[X])$. Suppose that for every maximal ideal $\\m$ of $R$ the image of $g$ under the localization homomorphism at $\\m$ belongs to $E(R_\\m[X],IR_\\m[X])$. Then, $g\\in E(R[X],IR[X])$.\n  The theorem is a common generalization of the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3575","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":"1211.3575","created_at":"2026-05-18T01:26:19.240525+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.3575v2","created_at":"2026-05-18T01:26:19.240525+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3575","created_at":"2026-05-18T01:26:19.240525+00:00"},{"alias_kind":"pith_short_12","alias_value":"E37Q5R4GKP64","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"E37Q5R4GKP64JUXU","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"E37Q5R4G","created_at":"2026-05-18T12:27:04.183437+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/E37Q5R4GKP64JUXUPZTP6BPDKM","json":"https://pith.science/pith/E37Q5R4GKP64JUXUPZTP6BPDKM.json","graph_json":"https://pith.science/api/pith-number/E37Q5R4GKP64JUXUPZTP6BPDKM/graph.json","events_json":"https://pith.science/api/pith-number/E37Q5R4GKP64JUXUPZTP6BPDKM/events.json","paper":"https://pith.science/paper/E37Q5R4G"},"agent_actions":{"view_html":"https://pith.science/pith/E37Q5R4GKP64JUXUPZTP6BPDKM","download_json":"https://pith.science/pith/E37Q5R4GKP64JUXUPZTP6BPDKM.json","view_paper":"https://pith.science/paper/E37Q5R4G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.3575&json=true","fetch_graph":"https://pith.science/api/pith-number/E37Q5R4GKP64JUXUPZTP6BPDKM/graph.json","fetch_events":"https://pith.science/api/pith-number/E37Q5R4GKP64JUXUPZTP6BPDKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E37Q5R4GKP64JUXUPZTP6BPDKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E37Q5R4GKP64JUXUPZTP6BPDKM/action/storage_attestation","attest_author":"https://pith.science/pith/E37Q5R4GKP64JUXUPZTP6BPDKM/action/author_attestation","sign_citation":"https://pith.science/pith/E37Q5R4GKP64JUXUPZTP6BPDKM/action/citation_signature","submit_replication":"https://pith.science/pith/E37Q5R4GKP64JUXUPZTP6BPDKM/action/replication_record"}},"created_at":"2026-05-18T01:26:19.240525+00:00","updated_at":"2026-05-18T01:26:19.240525+00:00"}