{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NLTCNDAHNMVATFKBCCBK3WMDT6","short_pith_number":"pith:NLTCNDAH","schema_version":"1.0","canonical_sha256":"6ae6268c076b2a0995411082add9839fa4ca4730a426e3bd263b04fc597c8b65","source":{"kind":"arxiv","id":"1512.04978","version":1},"attestation_state":"computed","paper":{"title":"Real Classes of Finite Special Unitary Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Amanda Schaeffer Fry, C. Ryan Vinroot","submitted_at":"2015-12-15T21:37:49Z","abstract_excerpt":"We classify all real and strongly real classes of the finite special unitary group $SU_n(q)$. Unless $q \\equiv 3 (mod 4)$ and $n |4$, the classification of real classes is similar to that of the finite special linear group $SL_n(q)$. We relate strong reality in $SU_n(q)$ to strong reality in the finite special orthogonal groups $SO^\\pm_n(q)$, and we classify real and strongly real classes in the last case for the group $SO^\\pm_n(q)$, when q is odd and $n \\equiv 2 (mod 4)$."},"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":"1512.04978","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-15T21:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"aae704e43b9ff54e2779eb40e5969cd876fadef1654f96869c32f31d57ad3db0","abstract_canon_sha256":"1f9a16ea8b40b9abd0b5a5019112eacb882e404edf589b9d96160b72e0361a36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:13.843851Z","signature_b64":"pFVG9aVzxdrT918dxrRnNjqmmHk5vTwhkOcT7chnCqfAn3zM3k/2oo4nf9O94IsPFkSdYe+7JIvZPU2zQstHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ae6268c076b2a0995411082add9839fa4ca4730a426e3bd263b04fc597c8b65","last_reissued_at":"2026-05-18T01:24:13.843439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:13.843439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real Classes of Finite Special Unitary Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Amanda Schaeffer Fry, C. Ryan Vinroot","submitted_at":"2015-12-15T21:37:49Z","abstract_excerpt":"We classify all real and strongly real classes of the finite special unitary group $SU_n(q)$. Unless $q \\equiv 3 (mod 4)$ and $n |4$, the classification of real classes is similar to that of the finite special linear group $SL_n(q)$. We relate strong reality in $SU_n(q)$ to strong reality in the finite special orthogonal groups $SO^\\pm_n(q)$, and we classify real and strongly real classes in the last case for the group $SO^\\pm_n(q)$, when q is odd and $n \\equiv 2 (mod 4)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04978","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":""},"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":"1512.04978","created_at":"2026-05-18T01:24:13.843501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.04978v1","created_at":"2026-05-18T01:24:13.843501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04978","created_at":"2026-05-18T01:24:13.843501+00:00"},{"alias_kind":"pith_short_12","alias_value":"NLTCNDAHNMVA","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"NLTCNDAHNMVATFKB","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"NLTCNDAH","created_at":"2026-05-18T12:29:32.376354+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/NLTCNDAHNMVATFKBCCBK3WMDT6","json":"https://pith.science/pith/NLTCNDAHNMVATFKBCCBK3WMDT6.json","graph_json":"https://pith.science/api/pith-number/NLTCNDAHNMVATFKBCCBK3WMDT6/graph.json","events_json":"https://pith.science/api/pith-number/NLTCNDAHNMVATFKBCCBK3WMDT6/events.json","paper":"https://pith.science/paper/NLTCNDAH"},"agent_actions":{"view_html":"https://pith.science/pith/NLTCNDAHNMVATFKBCCBK3WMDT6","download_json":"https://pith.science/pith/NLTCNDAHNMVATFKBCCBK3WMDT6.json","view_paper":"https://pith.science/paper/NLTCNDAH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.04978&json=true","fetch_graph":"https://pith.science/api/pith-number/NLTCNDAHNMVATFKBCCBK3WMDT6/graph.json","fetch_events":"https://pith.science/api/pith-number/NLTCNDAHNMVATFKBCCBK3WMDT6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NLTCNDAHNMVATFKBCCBK3WMDT6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NLTCNDAHNMVATFKBCCBK3WMDT6/action/storage_attestation","attest_author":"https://pith.science/pith/NLTCNDAHNMVATFKBCCBK3WMDT6/action/author_attestation","sign_citation":"https://pith.science/pith/NLTCNDAHNMVATFKBCCBK3WMDT6/action/citation_signature","submit_replication":"https://pith.science/pith/NLTCNDAHNMVATFKBCCBK3WMDT6/action/replication_record"}},"created_at":"2026-05-18T01:24:13.843501+00:00","updated_at":"2026-05-18T01:24:13.843501+00:00"}