{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UOAF6BT3MSQZ26Y4E4E7R4H54O","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":"671eeb528d562768f45380ee5d05936c6e2185af96245a0323df9da09de38299","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-01T19:01:24Z","title_canon_sha256":"3973bf6711e03d38d12ff314a110641b0f479696df2920c12cd3579d5a04f6d4"},"schema_version":"1.0","source":{"id":"1506.00609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00609","created_at":"2026-05-18T01:59:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00609v1","created_at":"2026-05-18T01:59:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00609","created_at":"2026-05-18T01:59:54Z"},{"alias_kind":"pith_short_12","alias_value":"UOAF6BT3MSQZ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UOAF6BT3MSQZ26Y4","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UOAF6BT3","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:dfdc9e7cf3eccb8fa20a06cb00656ee638165ad08df3d28bc3a3813cfb5882fe","target":"graph","created_at":"2026-05-18T01:59:54Z","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":"In this note we determine the irreducible square integrable representations of a simple group which admits an admissible restriction to a subgroup $H$ locally isomorphic to $SL_2(\\mathbb R).$ We show such representation is holomorphic and we determine the essentially unique $H$ with this property as well as multiplicity formulae.","authors_text":"Esther Galina, Jorge A. Vargas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-01T19:01:24Z","title":"Discrete series of simple Lie groups with admissible restriction to a $SL_2(\\mathbb R)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00609","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:a4b3eb44650c439bcf027324b3076a2b0b0ac8e03060670e40ae960562f1bfb9","target":"record","created_at":"2026-05-18T01:59:54Z","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":"671eeb528d562768f45380ee5d05936c6e2185af96245a0323df9da09de38299","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-01T19:01:24Z","title_canon_sha256":"3973bf6711e03d38d12ff314a110641b0f479696df2920c12cd3579d5a04f6d4"},"schema_version":"1.0","source":{"id":"1506.00609","kind":"arxiv","version":1}},"canonical_sha256":"a3805f067b64a19d7b1c2709f8f0fde3943f44b1778519d17ae5736e0ab9c1a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3805f067b64a19d7b1c2709f8f0fde3943f44b1778519d17ae5736e0ab9c1a8","first_computed_at":"2026-05-18T01:59:54.117288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:54.117288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l7QJwiK+Gtwvg/pElj2ItKorrBW/Zz30d37X7i54sUqa1Nu7Zosi8HCrxvfD+DKrjESZJHkp5XjbJuoo7FhfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:54.117907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4b3eb44650c439bcf027324b3076a2b0b0ac8e03060670e40ae960562f1bfb9","sha256:dfdc9e7cf3eccb8fa20a06cb00656ee638165ad08df3d28bc3a3813cfb5882fe"],"state_sha256":"484487cd20122084cb395b522f891f7683f842dd6154456a11cb688eeeeb65c8"}