{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:UHBGDGFAA2F42KR3ZJQ3WATZYW","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":"6eef5b97bbf1978d2e4bbaf066f8e0bd7d171777c8e0e898777bc5692879c506","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.RT","submitted_at":"2006-06-20T13:11:45Z","title_canon_sha256":"bc97599685fa45c710ab04b4b74aa15708a45010e1faa2d278092e387857a4df"},"schema_version":"1.0","source":{"id":"math/0606501","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606501","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606501v6","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606501","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"UHBGDGFAA2F4","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"UHBGDGFAA2F42KR3","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"UHBGDGFA","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:829bce02e3a873c9f1c4bdfed93f360af7bec5a760c4c8e4e180aa4ee8f0a5e5","target":"graph","created_at":"2026-05-18T04:08:53Z","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 radical of the Brauer algebra B_f^x is known to be non-trivial when the parameter x is an integer subject to certain conditions (with respect to f). In these cases, we display a wide family of elements in the radical, which are explicitly described by means of the diagrams of the usual basis of B_f^x . The proof is by direct approach for x=0, and via classical Invariant Theory in the other cases, exploiting then the well-known representation of Brauer algebras as centralizer algebras of orthogonal or symplectic groups acting on tensor powers of their standard representation. This also give","authors_text":"Fabio Gavarini","cross_cats":["math.RA"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2006-06-20T13:11:45Z","title":"On the radical of Brauer algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606501","kind":"arxiv","version":6},"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:d057f838581cf3d4b549f55c898e267949e80b1e526448ec4cfc3f91ddcfae80","target":"record","created_at":"2026-05-18T04:08:53Z","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":"6eef5b97bbf1978d2e4bbaf066f8e0bd7d171777c8e0e898777bc5692879c506","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.RT","submitted_at":"2006-06-20T13:11:45Z","title_canon_sha256":"bc97599685fa45c710ab04b4b74aa15708a45010e1faa2d278092e387857a4df"},"schema_version":"1.0","source":{"id":"math/0606501","kind":"arxiv","version":6}},"canonical_sha256":"a1c26198a0068bcd2a3bca61bb0279c5a527296ef3c0f12d82cb269e1af1e754","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1c26198a0068bcd2a3bca61bb0279c5a527296ef3c0f12d82cb269e1af1e754","first_computed_at":"2026-05-18T04:08:53.401260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:53.401260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yI8fYTTiM8/lHY+mV5e5hAkTwR/JOOq1VR6bXPgxed/BBceF1eNiuoe9q/kPXgtQ0af3LDgcPaOKkm8SnbYjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:53.401709Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606501","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d057f838581cf3d4b549f55c898e267949e80b1e526448ec4cfc3f91ddcfae80","sha256:829bce02e3a873c9f1c4bdfed93f360af7bec5a760c4c8e4e180aa4ee8f0a5e5"],"state_sha256":"1240ee2a77d098c6f10f1d3be9c31d3d47699f57eae428d903d03e9eb5f8eef8"}