{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RZTJ7V2IZGYLTWYCZYDDOALNUC","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":"77f97527cd8a698992a4b7d1567b6ad93aabfd7e9c3436bc321c145c1e9160d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-30T15:17:49Z","title_canon_sha256":"19003f40d7720e55dd032a99d4a000a4eabda40856c3c18b3d06f16f53cfc818"},"schema_version":"1.0","source":{"id":"0909.5630","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5630","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5630v2","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5630","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"RZTJ7V2IZGYL","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RZTJ7V2IZGYLTWYC","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RZTJ7V2I","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:ae828df1eb4d2e8f7ae3d0602b8cad2532622a7c96a41495c2aa16c940460bc5","target":"graph","created_at":"2026-05-18T04:16:32Z","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 prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free regular idempotent generated semigroup arising from a finite regular semigroup.","authors_text":"Nik Ruskuc, Robert Gray","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-30T15:17:49Z","title":"On Maximal Subgroups of Free Idempotent Generated Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5630","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":"sha256:004b5a767b9738d55b5945ee43e9cbfb1f83ee4f67fc30b3f4bc90d5c4b62a8d","target":"record","created_at":"2026-05-18T04:16:32Z","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":"77f97527cd8a698992a4b7d1567b6ad93aabfd7e9c3436bc321c145c1e9160d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-30T15:17:49Z","title_canon_sha256":"19003f40d7720e55dd032a99d4a000a4eabda40856c3c18b3d06f16f53cfc818"},"schema_version":"1.0","source":{"id":"0909.5630","kind":"arxiv","version":2}},"canonical_sha256":"8e669fd748c9b0b9db02ce0637016da0889ebd4eaa6f9c6c683c012cd45623e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e669fd748c9b0b9db02ce0637016da0889ebd4eaa6f9c6c683c012cd45623e4","first_computed_at":"2026-05-18T04:16:32.336964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:32.336964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"48fWn9BnQRA+VhAGyINOwONWDBw72Mp/zWMluCe8EFJzDa7d4R6KpIJb6ZWpShi+UCeiOkzDujzndFG1pIZ9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:32.337400Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.5630","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:004b5a767b9738d55b5945ee43e9cbfb1f83ee4f67fc30b3f4bc90d5c4b62a8d","sha256:ae828df1eb4d2e8f7ae3d0602b8cad2532622a7c96a41495c2aa16c940460bc5"],"state_sha256":"7d4789fc4604a33105b5a88313d201f58894a619d0a9179d689a46003708466b"}