{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N2Q3EJ6REZAVMXUDKCMPSIVRTL","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":"49ee0098f1b618cf57e6c4b9b02a702388013e2a86e0d6b317a04fba129a0151","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-27T13:24:50Z","title_canon_sha256":"4e5b1eea514542cb05e5f2b99e124726f3dfab06c8c54aeb051c0afb1121ace6"},"schema_version":"1.0","source":{"id":"1504.07077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07077","created_at":"2026-05-18T02:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07077v1","created_at":"2026-05-18T02:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07077","created_at":"2026-05-18T02:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"N2Q3EJ6REZAV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N2Q3EJ6REZAVMXUD","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N2Q3EJ6R","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:855bb6115479ce3d5628de521a0f10598008b185c93d5b7d67cdb8a45fc2f3c7","target":"graph","created_at":"2026-05-18T02:17:43Z","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":"We study the growth of the central polynomials for the algebras $G$ and $M_k(F)$, the infinite dimensional Grassmann algebra and the $k\\times k$ matrices over a field $F$ of characteristic zero. In particular it follows that $M_k(F)$ satisfy many proper central polynomials.","authors_text":"Amitai Regev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-27T13:24:50Z","title":"Growth for the central polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07077","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":"sha256:7aa4adaf00d27aff003edc5ce058a8edea4d989a3c3047ebcaa1753850abb0c0","target":"record","created_at":"2026-05-18T02:17:43Z","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":"49ee0098f1b618cf57e6c4b9b02a702388013e2a86e0d6b317a04fba129a0151","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-27T13:24:50Z","title_canon_sha256":"4e5b1eea514542cb05e5f2b99e124726f3dfab06c8c54aeb051c0afb1121ace6"},"schema_version":"1.0","source":{"id":"1504.07077","kind":"arxiv","version":1}},"canonical_sha256":"6ea1b227d12641565e835098f922b19ad547374615945ba3b6c83c8db30ce962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ea1b227d12641565e835098f922b19ad547374615945ba3b6c83c8db30ce962","first_computed_at":"2026-05-18T02:17:43.758443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:43.758443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9PDHCjvJXgSv7MxoDdhld4TXPi7lcyWNsIr8IZqqztXNpd1oWe9+RTF5YiS6vpGD1flTyVBIoYGUklDEXwVeCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:43.758873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aa4adaf00d27aff003edc5ce058a8edea4d989a3c3047ebcaa1753850abb0c0","sha256:855bb6115479ce3d5628de521a0f10598008b185c93d5b7d67cdb8a45fc2f3c7"],"state_sha256":"cc3fb032f6642318ffb912d5c97982579208a07079917cd5fe42f8e1eafe50ee"}