{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:352OU5BTT5GYFK7S3ZB3FBY2WZ","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":"4ed25a5c95b05b080b9121ccaf3a141cc3f3d1ac05d271f72ddbca2eaa6b8d3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-29T15:29:06Z","title_canon_sha256":"57d09bcef8ee24440608ab0890bf2697043f5165e332a3a65c6fa118c0551acb"},"schema_version":"1.0","source":{"id":"1109.6559","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6559","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6559v2","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6559","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"352OU5BTT5GY","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"352OU5BTT5GYFK7S","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"352OU5BT","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:b5c285bd27f5839b92e4f5bab222bfb98c227551cc31e4a1bd55fe38288c97e0","target":"graph","created_at":"2026-05-18T04:05:57Z","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":"In this paper we answer a question of Gabriel Navarro about orbit sizes of a finite linear group H acting completely reducibly on a vector space V: if the orbits containing the vectors a and b have coprime lengths m and n, we prove that the orbit containing a+b has length mn. Such groups H are always reducible if n and m are greater than 1. In fact, if H is an irreducible linear group, we show that, for every pair of non-zero vectors, their orbit lengths have a non-trivial common factor.\n  In the more general context of finite primitive permutation groups G, we show that coprime non-identity s","authors_text":"Cheryl Praeger, Pablo Spiga, Robert Guralnick, Silvio Dolfi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-29T15:29:06Z","title":"Coprime subdegrees for primitive permutation groups and completely reducible linear groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6559","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:a1f8a05a1c76e8ae839610a244e59ed9c3b6c69c1683f037cd354af3708512ce","target":"record","created_at":"2026-05-18T04:05:57Z","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":"4ed25a5c95b05b080b9121ccaf3a141cc3f3d1ac05d271f72ddbca2eaa6b8d3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-29T15:29:06Z","title_canon_sha256":"57d09bcef8ee24440608ab0890bf2697043f5165e332a3a65c6fa118c0551acb"},"schema_version":"1.0","source":{"id":"1109.6559","kind":"arxiv","version":2}},"canonical_sha256":"df74ea74339f4d82abf2de43b2871ab650f763f294710c905dc84aa8b0733b53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df74ea74339f4d82abf2de43b2871ab650f763f294710c905dc84aa8b0733b53","first_computed_at":"2026-05-18T04:05:57.383637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:57.383637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IFRxCTgsOsAATzQ6cz0980MBGetFCZghkQHDLrMyRznSY6RBtuqVOgw1Oee6YPZY0XZ+CDDwJ3K6sJLN6HbICA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:57.384226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6559","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1f8a05a1c76e8ae839610a244e59ed9c3b6c69c1683f037cd354af3708512ce","sha256:b5c285bd27f5839b92e4f5bab222bfb98c227551cc31e4a1bd55fe38288c97e0"],"state_sha256":"b8ca67f5e43189de0caad945d697d2b741b8cd9264d2944950806053bf449be6"}