{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7DGMDOV22F6W4OHMNP3FGD3O7R","short_pith_number":"pith:7DGMDOV2","schema_version":"1.0","canonical_sha256":"f8ccc1babad17d6e38ec6bf6530f6efc7e66c31a34353f082b0d972056b58b82","source":{"kind":"arxiv","id":"1802.06973","version":1},"attestation_state":"computed","paper":{"title":"Bases of quasisimple linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Martin W. Liebeck, Melissa Lee","submitted_at":"2018-02-20T05:47:29Z","abstract_excerpt":"Let $V$ be a vector space of dimension $d$ over $F_q$, a finite field of $q$ elements, and let $G \\le GL(V) \\cong GL_d(q)$ be a linear group. A base of $G$ is a set of vectors whose pointwise stabiliser in $G$ is trivial. We prove that if $G$ is a quasisimple group (i.e. $G$ is perfect and $G/Z(G)$ is simple) acting irreducibly on $V$, then excluding two natural families, $G$ has a base of size at most 6. The two families consist of alternating groups ${\\rm Alt}_m$ acting on the natural module of dimension $d = m-1$ or $m-2$, and classical groups with natural module of dimension $d$ over subfi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.06973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-20T05:47:29Z","cross_cats_sorted":[],"title_canon_sha256":"bd9809b2144fb9af006f5d7701ce42e8f082fe071652db466bc725db793c92ec","abstract_canon_sha256":"f10601224847f43ce616534b998c6dcb2b77a0c10afded0fc9b710e020f3ba77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:06.689937Z","signature_b64":"NRu8EdjUu4NuA1kQZrlcoj2fuqOhUcZL/arNcRSVxMfUtQL0/dr2bi1oYrVNjM0dsSTbmoCEKnwoxCFElptxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8ccc1babad17d6e38ec6bf6530f6efc7e66c31a34353f082b0d972056b58b82","last_reissued_at":"2026-05-18T00:03:06.689441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:06.689441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bases of quasisimple linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Martin W. Liebeck, Melissa Lee","submitted_at":"2018-02-20T05:47:29Z","abstract_excerpt":"Let $V$ be a vector space of dimension $d$ over $F_q$, a finite field of $q$ elements, and let $G \\le GL(V) \\cong GL_d(q)$ be a linear group. A base of $G$ is a set of vectors whose pointwise stabiliser in $G$ is trivial. We prove that if $G$ is a quasisimple group (i.e. $G$ is perfect and $G/Z(G)$ is simple) acting irreducibly on $V$, then excluding two natural families, $G$ has a base of size at most 6. The two families consist of alternating groups ${\\rm Alt}_m$ acting on the natural module of dimension $d = m-1$ or $m-2$, and classical groups with natural module of dimension $d$ over subfi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06973","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.06973","created_at":"2026-05-18T00:03:06.689524+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.06973v1","created_at":"2026-05-18T00:03:06.689524+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06973","created_at":"2026-05-18T00:03:06.689524+00:00"},{"alias_kind":"pith_short_12","alias_value":"7DGMDOV22F6W","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7DGMDOV22F6W4OHM","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7DGMDOV2","created_at":"2026-05-18T12:32:11.075285+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7DGMDOV22F6W4OHMNP3FGD3O7R","json":"https://pith.science/pith/7DGMDOV22F6W4OHMNP3FGD3O7R.json","graph_json":"https://pith.science/api/pith-number/7DGMDOV22F6W4OHMNP3FGD3O7R/graph.json","events_json":"https://pith.science/api/pith-number/7DGMDOV22F6W4OHMNP3FGD3O7R/events.json","paper":"https://pith.science/paper/7DGMDOV2"},"agent_actions":{"view_html":"https://pith.science/pith/7DGMDOV22F6W4OHMNP3FGD3O7R","download_json":"https://pith.science/pith/7DGMDOV22F6W4OHMNP3FGD3O7R.json","view_paper":"https://pith.science/paper/7DGMDOV2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.06973&json=true","fetch_graph":"https://pith.science/api/pith-number/7DGMDOV22F6W4OHMNP3FGD3O7R/graph.json","fetch_events":"https://pith.science/api/pith-number/7DGMDOV22F6W4OHMNP3FGD3O7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7DGMDOV22F6W4OHMNP3FGD3O7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7DGMDOV22F6W4OHMNP3FGD3O7R/action/storage_attestation","attest_author":"https://pith.science/pith/7DGMDOV22F6W4OHMNP3FGD3O7R/action/author_attestation","sign_citation":"https://pith.science/pith/7DGMDOV22F6W4OHMNP3FGD3O7R/action/citation_signature","submit_replication":"https://pith.science/pith/7DGMDOV22F6W4OHMNP3FGD3O7R/action/replication_record"}},"created_at":"2026-05-18T00:03:06.689524+00:00","updated_at":"2026-05-18T00:03:06.689524+00:00"}