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For any $\\ell\\in\\mathbb{N}$ let $G^\\ell$ denote the $\\ell$-th principal congruence subgroup of $\\mathbf{G}(\\mathfrak{o})$. An irreducible character of the group $\\mathbf{G}(\\mathfrak{o})$ is said to be regular if it is trivial on a subgroup $G^{\\ell+1}$ for some $\\ell$, and if its restriction to $G^\\ell/G^{\\ell+1}\\simeq \\mathrm{Lie}(\\mathbf{G})(\\mathsf{k})$ consists of characters of mi"},"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":"1709.01685","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-06T06:20:30Z","cross_cats_sorted":[],"title_canon_sha256":"84c0a1e0413002d32d3b5e16a3d1bab9babf70d2bba4466ad38a64cee3fdbccc","abstract_canon_sha256":"60c54df16003857786817539a883cdf403b33ac0ecc306df8fcc1d34219008e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:39.533948Z","signature_b64":"RQB9owgi8JHHjZm4sRTdJnVaiah4ExWyXyV1sbf9UYrtjZ9zUSjBkya61nNyzSde4LUXLP0//AYMvGethOEsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b74973a38aff00b1cd671a68772d1f6ed439894abe9acb0eb89875d1d33ca0c8","last_reissued_at":"2026-05-17T23:59:39.533223Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:39.533223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regular characters of classical groups over complete discrete valuation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Shai Shechter","submitted_at":"2017-09-06T06:20:30Z","abstract_excerpt":"Let $\\mathfrak{o}$ be a complete discrete valuation ring with finide residue field $\\mathsf{k}$ of odd characteristic, and let $\\mathbf{G}$ be a symplectic or special orthogonal group scheme over $\\mathfrak{o}$. For any $\\ell\\in\\mathbb{N}$ let $G^\\ell$ denote the $\\ell$-th principal congruence subgroup of $\\mathbf{G}(\\mathfrak{o})$. An irreducible character of the group $\\mathbf{G}(\\mathfrak{o})$ is said to be regular if it is trivial on a subgroup $G^{\\ell+1}$ for some $\\ell$, and if its restriction to $G^\\ell/G^{\\ell+1}\\simeq \\mathrm{Lie}(\\mathbf{G})(\\mathsf{k})$ consists of characters of mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01685","kind":"arxiv","version":4},"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":"1709.01685","created_at":"2026-05-17T23:59:39.533344+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.01685v4","created_at":"2026-05-17T23:59:39.533344+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01685","created_at":"2026-05-17T23:59:39.533344+00:00"},{"alias_kind":"pith_short_12","alias_value":"W5EXHI4K74AL","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"W5EXHI4K74ALDTLH","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"W5EXHI4K","created_at":"2026-05-18T12:31:53.515858+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/W5EXHI4K74ALDTLHDJUHOLI7N3","json":"https://pith.science/pith/W5EXHI4K74ALDTLHDJUHOLI7N3.json","graph_json":"https://pith.science/api/pith-number/W5EXHI4K74ALDTLHDJUHOLI7N3/graph.json","events_json":"https://pith.science/api/pith-number/W5EXHI4K74ALDTLHDJUHOLI7N3/events.json","paper":"https://pith.science/paper/W5EXHI4K"},"agent_actions":{"view_html":"https://pith.science/pith/W5EXHI4K74ALDTLHDJUHOLI7N3","download_json":"https://pith.science/pith/W5EXHI4K74ALDTLHDJUHOLI7N3.json","view_paper":"https://pith.science/paper/W5EXHI4K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.01685&json=true","fetch_graph":"https://pith.science/api/pith-number/W5EXHI4K74ALDTLHDJUHOLI7N3/graph.json","fetch_events":"https://pith.science/api/pith-number/W5EXHI4K74ALDTLHDJUHOLI7N3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W5EXHI4K74ALDTLHDJUHOLI7N3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W5EXHI4K74ALDTLHDJUHOLI7N3/action/storage_attestation","attest_author":"https://pith.science/pith/W5EXHI4K74ALDTLHDJUHOLI7N3/action/author_attestation","sign_citation":"https://pith.science/pith/W5EXHI4K74ALDTLHDJUHOLI7N3/action/citation_signature","submit_replication":"https://pith.science/pith/W5EXHI4K74ALDTLHDJUHOLI7N3/action/replication_record"}},"created_at":"2026-05-17T23:59:39.533344+00:00","updated_at":"2026-05-17T23:59:39.533344+00:00"}