{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:M7GRTJ3ZY2GXB7MZJ2NG7YLGMT","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":"9b14122dbac55a2f7a6ef446821d33292aa4b47fb38882840859771fca7c9cf8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-04T10:24:36Z","title_canon_sha256":"7271016c9e7ec7718f7f773fcfe265115470c7a7e08b89eb6b26505b103ec1d8"},"schema_version":"1.0","source":{"id":"2607.03804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03804","created_at":"2026-07-07T02:18:08Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03804v1","created_at":"2026-07-07T02:18:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03804","created_at":"2026-07-07T02:18:08Z"},{"alias_kind":"pith_short_12","alias_value":"M7GRTJ3ZY2GX","created_at":"2026-07-07T02:18:08Z"},{"alias_kind":"pith_short_16","alias_value":"M7GRTJ3ZY2GXB7MZ","created_at":"2026-07-07T02:18:08Z"},{"alias_kind":"pith_short_8","alias_value":"M7GRTJ3Z","created_at":"2026-07-07T02:18:08Z"}],"graph_snapshots":[{"event_id":"sha256:7e531d3bb5542a4cdc971495662626166322242b56ee5a195aa1bca6f8f0dbde","target":"graph","created_at":"2026-07-07T02:18:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.03804/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let \\(\\mathrm G\\) be a complex simple algebraic group and let \\(\\mathrm G_0\\subset \\mathrm G\\) be a closed connected subgroup containing a regular unipotent element of \\(\\mathrm G\\), with semisimple rank at least \\(2\\). Using Dynkin's classification, we prove that the restriction of an irreducible finite-dimensional representation of \\(\\mathrm G\\) to \\(\\mathrm G_0\\) determines the representation up to an outer automorphism of \\(\\mathrm G\\) preserving \\(\\mathrm G_0\\).\n  We extend this method to the diagonal embedding $\\mathrm G_0\\hookrightarrow \\mathrm G\\times \\mathrm G$ for the specific pairs ","authors_text":"Santosha Pattanayak, Santosh Nadimpalli","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-04T10:24:36Z","title":"Uniqueness of Branching through regular unipotent elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03804","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:a13e9c38828ce8f692ab8fe007ff154a30819f93f48f2c036dfc3adfa2254c39","target":"record","created_at":"2026-07-07T02:18:08Z","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":"9b14122dbac55a2f7a6ef446821d33292aa4b47fb38882840859771fca7c9cf8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-04T10:24:36Z","title_canon_sha256":"7271016c9e7ec7718f7f773fcfe265115470c7a7e08b89eb6b26505b103ec1d8"},"schema_version":"1.0","source":{"id":"2607.03804","kind":"arxiv","version":1}},"canonical_sha256":"67cd19a779c68d70fd994e9a6fe16664f7978205c9c2a49a9fdbb1ce474abb77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67cd19a779c68d70fd994e9a6fe16664f7978205c9c2a49a9fdbb1ce474abb77","first_computed_at":"2026-07-07T02:18:08.462564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:18:08.462564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GV48YdoTjQ/heoVzM7BrJG5Gp/e2Gp4jeh2Zt3oGb+pkOTYsQVaidzKzGh5MTi+B3JlbxLpE1aK6qeBtQrRnBQ==","signature_status":"signed_v1","signed_at":"2026-07-07T02:18:08.463304Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.03804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a13e9c38828ce8f692ab8fe007ff154a30819f93f48f2c036dfc3adfa2254c39","sha256:7e531d3bb5542a4cdc971495662626166322242b56ee5a195aa1bca6f8f0dbde"],"state_sha256":"bd1b6f1d08d655cfd548daef4100c488bbf4f399b659521b980c2fcef3b38bcc"}