{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BV3JJ54TIZU5ODLKJFWEEN7YRJ","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":"12d9e65d1fc03a52192543d92a1633ce2cde71e76f42b71b51c1b62ec54b0c8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-11T23:58:35Z","title_canon_sha256":"2476705b186287c6dc08ba1f6472e2dc06d34af695dabfbb6c64fff935e82c44"},"schema_version":"1.0","source":{"id":"1409.3617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3617","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3617v1","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3617","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"pith_short_12","alias_value":"BV3JJ54TIZU5","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BV3JJ54TIZU5ODLK","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BV3JJ54T","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:12da3c69847708337c46266f59ad982f3c02c80f5f625bb87a4ffba6ac82af90","target":"graph","created_at":"2026-05-18T02:43:00Z","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":"We determine the decomposition of the restriction of a length-one toral supercuspidal representation of a connected reductive group to the algebraic derived subgroup, in terms of parametrizing data, and show this restriction has multiplicity one. As an application, we determine the smooth dual of the unit group of the integers $\\mathcal{O}_D^\\times$ of a quaternion algebra $D$ over a $p$-adic field $F$, for $p\\neq 2$, as a consequence of determining the branching rules for the restriction of representations $D^\\times \\supset \\mathcal{O}_D^\\times \\supset D^1$.","authors_text":"Monica Nevins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-11T23:58:35Z","title":"Restricting Toral Supercuspidal Representations to the Derived Group, and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3617","kind":"arxiv","version":1},"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:f5a5ac5dcac8ac2251ca638054e267b32913a51c3fe4c327ae15665622d91bee","target":"record","created_at":"2026-05-18T02:43:00Z","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":"12d9e65d1fc03a52192543d92a1633ce2cde71e76f42b71b51c1b62ec54b0c8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-11T23:58:35Z","title_canon_sha256":"2476705b186287c6dc08ba1f6472e2dc06d34af695dabfbb6c64fff935e82c44"},"schema_version":"1.0","source":{"id":"1409.3617","kind":"arxiv","version":1}},"canonical_sha256":"0d7694f7934669d70d6a496c4237f88a7233b2e20de1ef144f60e098390418c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d7694f7934669d70d6a496c4237f88a7233b2e20de1ef144f60e098390418c3","first_computed_at":"2026-05-18T02:43:00.108342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:00.108342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f8NgPsiEMaNEtrNpldK00Lq5GilUybh+7St+RjDL5qe3hSl/WNiryUTHR/p+i8+hSpncI7xZOJNLUviyUmDJAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:00.109062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5a5ac5dcac8ac2251ca638054e267b32913a51c3fe4c327ae15665622d91bee","sha256:12da3c69847708337c46266f59ad982f3c02c80f5f625bb87a4ffba6ac82af90"],"state_sha256":"bf0ba3aa41d79c3c4ef75b5241b40d3582df67d921d14f0c9e5743ffb1c5a4e9"}