{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CB5BCOFX4O672LAEUCC2UJETZ2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9c0e1041e7ddceb37bc66ab2cdb373f5fda7997ea0ce96a947d93a1d7c34f0ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-16T11:16:10Z","title_canon_sha256":"b1895bf0af49efba43f8360d1ceb624a38a953761fa17b593f2be4e95d10a7cd"},"schema_version":"1.0","source":{"id":"1308.3604","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3604","created_at":"2026-05-18T00:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3604v4","created_at":"2026-05-18T00:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3604","created_at":"2026-05-18T00:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"CB5BCOFX4O67","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CB5BCOFX4O672LAE","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CB5BCOFX","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:842f1b37353850eab061c949127e38ec0eb3e3668e7873e2bbaceec8bbca7306","target":"graph","created_at":"2026-05-18T00:05:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The motivating question of this paper is roughly the following: given a group scheme $G$ over $\\mathbb{Z}_p$, $p$ prime, with semisimple generic fiber $G_{\\mathbb{Q}_p}$, how far are open subgroups of $G(\\mathbb{Z}_p)$ from subgroups of the form $X(\\mathbb{Z}_p)\\mathbf{K}_p(p^n)$, where $X$ is a subgroup scheme of $G$ and $\\mathbf{K}_p(p^n)$ is the principal congruence subgroup $\\operatorname{Ker} (G(\\mathbb{Z}_p)\\rightarrow G(\\mathbb{Z}/p^n\\mathbb{Z}))$? More precisely, we will show that for $G_{\\mathbb{Q}_p}$ simply connected there exist constants $J\\ge1$ and $\\varepsilon>0$, depending only ","authors_text":"Erez Lapid, Tobias Finis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-16T11:16:10Z","title":"An approximation principle for congruence subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3604","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4a41300b840a9205a13aadf4eb3b9107dec3f31ad00cb3aeda59f780da28704f","target":"record","created_at":"2026-05-18T00:05:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9c0e1041e7ddceb37bc66ab2cdb373f5fda7997ea0ce96a947d93a1d7c34f0ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-16T11:16:10Z","title_canon_sha256":"b1895bf0af49efba43f8360d1ceb624a38a953761fa17b593f2be4e95d10a7cd"},"schema_version":"1.0","source":{"id":"1308.3604","kind":"arxiv","version":4}},"canonical_sha256":"107a1138b7e3bdfd2c04a085aa2493ce9fbd263d9b6699a6e50c308e3cac890c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"107a1138b7e3bdfd2c04a085aa2493ce9fbd263d9b6699a6e50c308e3cac890c","first_computed_at":"2026-05-18T00:05:08.246769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:08.246769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JoJueb9jH7lF7QGfpsXhdfu3rJmVnjc6ZpYE9FyFDLShPNgOhVR/YtJEVfwQZku9Ded4qmG/plOzdEA6Hj7IDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:08.247376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3604","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a41300b840a9205a13aadf4eb3b9107dec3f31ad00cb3aeda59f780da28704f","sha256:842f1b37353850eab061c949127e38ec0eb3e3668e7873e2bbaceec8bbca7306"],"state_sha256":"134f411de01dc23f598850363b5655946b3c1d9a739bcd1bb8da761c85c182b2"}