{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F63PIPWHQI6RYG2R5NRYDPGFIP","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":"697c0b7bfb60a2dbdb40aa5c560ead0b7b1a0066d21d360feaa5651766e8ef90","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-17T02:54:50Z","title_canon_sha256":"92c63bee9c2751664620c972795954a518284d525ced8f0a78ad6a1f9eb5e2bf"},"schema_version":"1.0","source":{"id":"1712.06051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06051","created_at":"2026-05-18T00:27:51Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06051v1","created_at":"2026-05-18T00:27:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06051","created_at":"2026-05-18T00:27:51Z"},{"alias_kind":"pith_short_12","alias_value":"F63PIPWHQI6R","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F63PIPWHQI6RYG2R","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F63PIPWH","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:9e5d24ac5b3117f0c46dd6d4d90a89209b2aabe4d3175bde37b560ef172e0f23","target":"graph","created_at":"2026-05-18T00:27:51Z","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":"Let $A=\\oplus_{i\\in \\mathbb{Z}}A_i$ be a finite dimensional graded symmetric cellular algebra with a homogeneous symmetrizing trace of degree $d$. We prove that $A_{-d}$ contains the Higman ideal $H(A)$ of the center of $A$ and $\\dim H(A)\\leq \\dim A_{0}$ if $d\\neq 0$, and provide a semisimplicity criterion of $A$ in terms of the centralizer of $A_0$, which is a graded version of \\cite[Theorem 3.2]{L}.","authors_text":"Deke Zhao, Yanbo Li","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-17T02:54:50Z","title":"Notes on graded symmetric cellular algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06051","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":"sha256:104e0565769a96e836880819e2b02af672ba9ebf2299323f40b664143b735ba4","target":"record","created_at":"2026-05-18T00:27:51Z","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":"697c0b7bfb60a2dbdb40aa5c560ead0b7b1a0066d21d360feaa5651766e8ef90","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-17T02:54:50Z","title_canon_sha256":"92c63bee9c2751664620c972795954a518284d525ced8f0a78ad6a1f9eb5e2bf"},"schema_version":"1.0","source":{"id":"1712.06051","kind":"arxiv","version":1}},"canonical_sha256":"2fb6f43ec7823d1c1b51eb6381bcc543f90f4b35b31597285f29305350d18f12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fb6f43ec7823d1c1b51eb6381bcc543f90f4b35b31597285f29305350d18f12","first_computed_at":"2026-05-18T00:27:51.191982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:51.191982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EDGWEvml4a5L4sPsVxJXcvLReSdCME+5rKOMY4oyUPys7w54wFbU0+oAqF9qLLVVyv3Lc7TyBevBPRVw4UqtBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:51.192582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:104e0565769a96e836880819e2b02af672ba9ebf2299323f40b664143b735ba4","sha256:9e5d24ac5b3117f0c46dd6d4d90a89209b2aabe4d3175bde37b560ef172e0f23"],"state_sha256":"dbadf508edcdaee8ff9fc5ef46335b5f5e47448a579988e0dbf7be0987e9a3f9"}