{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OAPNARYP6W7QND7DM5A5KVATDJ","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":"43facb42669ab2fad3d721e98b087c58ab5cab54659c0b593133c0062398d388","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-09T17:55:34Z","title_canon_sha256":"392069a6e745e2efa92af166960a8ba26bffd066379d9b983c4ac76be7462481"},"schema_version":"1.0","source":{"id":"1405.2299","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2299","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2299v1","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2299","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"OAPNARYP6W7Q","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OAPNARYP6W7QND7D","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OAPNARYP","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:e210ef599ce5d9450a38672828b08418b30a648afe41776e79964ad1da2d39cc","target":"graph","created_at":"2026-05-18T02:52:13Z","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":"The maximal subgroup of unipotent upper-triangular matrices of the finite general linear groups are a fundamental family of $p$-groups. Their representation theory is well-known to be wild, but there is a standard supercharacter theory, replacing irreducible representations by super-representations, that gives us some control over its representation theory. While this theory has a beautiful underlying combinatorics built on set partitions, the structure constants of restricted super-representations remain mysterious. This paper proposes a new approach to solving the restriction problem by cons","authors_text":"Daniel Bragg, Nathaniel Thiem","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-09T17:55:34Z","title":"Restrictions of rainbow supercharacters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2299","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":"sha256:75e45304a1472bb7aa4c27aa773a8a0aaedeb29b61ef8a682babedb2765bf1bf","target":"record","created_at":"2026-05-18T02:52:13Z","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":"43facb42669ab2fad3d721e98b087c58ab5cab54659c0b593133c0062398d388","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-09T17:55:34Z","title_canon_sha256":"392069a6e745e2efa92af166960a8ba26bffd066379d9b983c4ac76be7462481"},"schema_version":"1.0","source":{"id":"1405.2299","kind":"arxiv","version":1}},"canonical_sha256":"701ed0470ff5bf068fe36741d554131a7096372fef28905728b86ac69e33b508","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"701ed0470ff5bf068fe36741d554131a7096372fef28905728b86ac69e33b508","first_computed_at":"2026-05-18T02:52:13.175939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:13.175939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zHVwB3UJ8G3kU+1bQg++4oCb+jUI+Bu2s/jde44Wox1daAT3LyNetvqkK4kcF1U6aNaurWibn4eCaCQ1RiDhAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:13.176507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75e45304a1472bb7aa4c27aa773a8a0aaedeb29b61ef8a682babedb2765bf1bf","sha256:e210ef599ce5d9450a38672828b08418b30a648afe41776e79964ad1da2d39cc"],"state_sha256":"750910317c104fdfbd128b5a40be8dd57aa832233daafcbb759e972412248865"}