{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BVC3S7KNA2FMQ6234TLD73FECU","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":"7e486625443d56a3368267c90375766f30d9e8d5ebc7e819d26ee8d2c5c4d65b","cross_cats_sorted":["cs.IT","math.GR","math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-15T13:03:36Z","title_canon_sha256":"db93ebf15e385e3a99206fdf8dbfb929025a77184a9d676052b390a110310114"},"schema_version":"1.0","source":{"id":"1302.3747","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3747","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3747v2","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3747","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"BVC3S7KNA2FM","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BVC3S7KNA2FMQ623","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BVC3S7KN","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:995aa084236e6d4973d87c6b7bd4dfb336439f66d7604d187ff6de48bca14bcf","target":"graph","created_at":"2026-05-18T03:02:57Z","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":"Algorithms to construct minimal left group codes are provided. These are based on results describing a complete set of orthogonal primitive idempotents in each Wedderburn component of a semisimple finite group algebra FG for a large class of groups G.\n  As an illustration of our methods, alternative constructions to some best linear codes over F_2 and F_3 are given.","authors_text":"Gabriela Olteanu, Inneke Van Gelder","cross_cats":["cs.IT","math.GR","math.IT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-15T13:03:36Z","title":"Construction of minimal non-abelian left group codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3747","kind":"arxiv","version":2},"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":"sha256:283fd36f4369a009f9d19d412b3cd9389cc363f7af9c6d4a217db1e76be94ad3","target":"record","created_at":"2026-05-18T03:02:57Z","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":"7e486625443d56a3368267c90375766f30d9e8d5ebc7e819d26ee8d2c5c4d65b","cross_cats_sorted":["cs.IT","math.GR","math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-15T13:03:36Z","title_canon_sha256":"db93ebf15e385e3a99206fdf8dbfb929025a77184a9d676052b390a110310114"},"schema_version":"1.0","source":{"id":"1302.3747","kind":"arxiv","version":2}},"canonical_sha256":"0d45b97d4d068ac87b5be4d63feca41531e1494755937967486bf052ba276c90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d45b97d4d068ac87b5be4d63feca41531e1494755937967486bf052ba276c90","first_computed_at":"2026-05-18T03:02:57.363901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:57.363901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qTswxuSLG7yWyormgFzQh5wjCicLscT9O53oybk9u2fDRjsBjZhmCmoiUbHi5ew0/rDySTFK/0c+ebwIc8ziBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:57.364620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3747","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:283fd36f4369a009f9d19d412b3cd9389cc363f7af9c6d4a217db1e76be94ad3","sha256:995aa084236e6d4973d87c6b7bd4dfb336439f66d7604d187ff6de48bca14bcf"],"state_sha256":"17d74c5f2374f110ed375527fecf06d393dab7e0b8080263b11869a01cc5aec6"}