{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DEUQAGDADNUIRY3PLAQJN5654X","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":"20345cc5fa712f512cebd518b66f44ef85978071e7fbeb47bb26bbc80c376c0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-12-03T19:43:32Z","title_canon_sha256":"932a097d07fcbdd561b58b6778ad677a39f623314ff113fad0199d8dba92e5d0"},"schema_version":"1.0","source":{"id":"1812.01055","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01055","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01055v2","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01055","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"pith_short_12","alias_value":"DEUQAGDADNUI","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DEUQAGDADNUIRY3P","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DEUQAGDA","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:9bd37439048507e8189c9227f57248b03779b663390287df603196953dbee551","target":"graph","created_at":"2026-05-17T23:47:07Z","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 show that a rank reduction technique for string C-group representations first used for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on $d$-dimensional modules over fields of even order greater than 2 possess string C-group representations of all ranks $3\\leq r\\leq d$. The broad applicability of the rank reduction technique provides fresh impetus to construct, for suitable families of groups, string C-groups of highest possible rank. It also suggests that the alternating group ${\\rm Alt}(11)$---t","authors_text":"Dimitri Leemans, Peter A. Brooksbank","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-12-03T19:43:32Z","title":"Rank reduction of string C-group representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01055","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":"sha256:2b9de47c9135dd22ea0e2c027e4836f810b051cd053f348c231e0c81e08168f0","target":"record","created_at":"2026-05-17T23:47:07Z","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":"20345cc5fa712f512cebd518b66f44ef85978071e7fbeb47bb26bbc80c376c0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-12-03T19:43:32Z","title_canon_sha256":"932a097d07fcbdd561b58b6778ad677a39f623314ff113fad0199d8dba92e5d0"},"schema_version":"1.0","source":{"id":"1812.01055","kind":"arxiv","version":2}},"canonical_sha256":"19290018601b6888e36f582096f7dde5d349072df09ea39abf767aaec8e51a0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19290018601b6888e36f582096f7dde5d349072df09ea39abf767aaec8e51a0f","first_computed_at":"2026-05-17T23:47:07.178374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:07.178374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Umh2y+UTnQAs82k3sg3Bues75vrksk8OB8YW9wFjO5kpr4jLP8EQdVhtuUxdb1fG3F281ZraYCxkrt0bbYFbBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:07.179017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.01055","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b9de47c9135dd22ea0e2c027e4836f810b051cd053f348c231e0c81e08168f0","sha256:9bd37439048507e8189c9227f57248b03779b663390287df603196953dbee551"],"state_sha256":"369c054b2783b2ac236cce51e7adc6d2757fe84652f7525f5367de6baee94d6c"}