{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QTI24XI3TNBHYEPR5XU4NBBKJ3","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":"8363953169e97001d58baa93b21ddd6d4f4f2bb240ead30cbe93df08c8058e22","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-09-12T08:17:53Z","title_canon_sha256":"45fad08cd510b157c480034ac89d310bc87d2f120e2132bcf3c3f52d65f422de"},"schema_version":"1.0","source":{"id":"1109.2395","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2395","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2395v4","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2395","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"pith_short_12","alias_value":"QTI24XI3TNBH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QTI24XI3TNBHYEPR","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QTI24XI3","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:3b045075f6290b84de6d28acc69cb362f5caf01d6b801bfdd458c2dbd5195360","target":"graph","created_at":"2026-05-18T02:26:45Z","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 paper, we discuss O-basis of symmetry classes of polynomials associated with the Brauer character of the Dicyclic group. Also, necessary and sufficient conditions are given for the existence of an orthogonal basis consisting of standard (decomposable) symmetrized tensors for the class of tensors symmetrized using a Brauer character of the Dicyclic group.","authors_text":"Mahdi Hormozi","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-09-12T08:17:53Z","title":"Orthogonal bases of Brauer relative symmetric polynomials for the the Dicyclic group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2395","kind":"arxiv","version":4},"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:b8915d5065cb6138fb4aa14d6ac46969fc17fc74f3e9d5894ddb665ef83b7568","target":"record","created_at":"2026-05-18T02:26:45Z","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":"8363953169e97001d58baa93b21ddd6d4f4f2bb240ead30cbe93df08c8058e22","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-09-12T08:17:53Z","title_canon_sha256":"45fad08cd510b157c480034ac89d310bc87d2f120e2132bcf3c3f52d65f422de"},"schema_version":"1.0","source":{"id":"1109.2395","kind":"arxiv","version":4}},"canonical_sha256":"84d1ae5d1b9b427c11f1ede9c6842a4ee1e2dd7e9bb2c6abcc5c1e318204599a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84d1ae5d1b9b427c11f1ede9c6842a4ee1e2dd7e9bb2c6abcc5c1e318204599a","first_computed_at":"2026-05-18T02:26:45.735760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:45.735760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+XeCAF82VDpSmYA0k6T3RjfQIEEKxWOfHEHQjXt1dx2rZRtIA4v9rqcxs7mR/ommMcO+epgwO3Ll0n+GnkFIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:45.736182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2395","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8915d5065cb6138fb4aa14d6ac46969fc17fc74f3e9d5894ddb665ef83b7568","sha256:3b045075f6290b84de6d28acc69cb362f5caf01d6b801bfdd458c2dbd5195360"],"state_sha256":"a97f4f10eedbb7db187e92b20066d87ee2130ebd97ed987a45414e834a6927ab"}