{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:F3JMBNYJJICC7D4F4DCBF5BYLU","short_pith_number":"pith:F3JMBNYJ","schema_version":"1.0","canonical_sha256":"2ed2c0b7094a042f8f85e0c412f4385d239469d649057b8aa0ca10226c771308","source":{"kind":"arxiv","id":"1310.5454","version":3},"attestation_state":"computed","paper":{"title":"The minimal base size for a p-solvable linear group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Attila Mar\\'oti, Zolt\\'an Halasi","submitted_at":"2013-10-21T08:12:04Z","abstract_excerpt":"Let $V$ be a finite vector space over a finite field of order $q$ and of characteristic $p$. Let $G\\leq GL(V)$ be a $p$-solvable completely reducible linear group. Then there exists a base for $G$ on $V$ of size at most $2$ unless $q \\leq 4$ in which case there exists a base of size at most $3$. The first statement extends a recent result of Halasi and Podoski and the second statement generalizes a theorem of Seress. An extension of a theorem of P\\'alfy and Wolf is also given."},"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":"1310.5454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-21T08:12:04Z","cross_cats_sorted":[],"title_canon_sha256":"496d4d26c767da202258852cce5a8c95d65cabe72c77f9c025b9a44f39b003fe","abstract_canon_sha256":"7bc1f254ea7d3ff0c881826902a1945472a74ab930f91fb6329bde82de0ba41a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:19.458233Z","signature_b64":"V/WMom0fOg+rY3lAFj/LCv/kRp+k5gmBtB29fg2sl9pb3pt6U9owJy60zCG81kx9EI22CE4ncf29KWDhWWoEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ed2c0b7094a042f8f85e0c412f4385d239469d649057b8aa0ca10226c771308","last_reissued_at":"2026-05-17T23:52:19.457532Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:19.457532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The minimal base size for a p-solvable linear group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Attila Mar\\'oti, Zolt\\'an Halasi","submitted_at":"2013-10-21T08:12:04Z","abstract_excerpt":"Let $V$ be a finite vector space over a finite field of order $q$ and of characteristic $p$. Let $G\\leq GL(V)$ be a $p$-solvable completely reducible linear group. Then there exists a base for $G$ on $V$ of size at most $2$ unless $q \\leq 4$ in which case there exists a base of size at most $3$. The first statement extends a recent result of Halasi and Podoski and the second statement generalizes a theorem of Seress. An extension of a theorem of P\\'alfy and Wolf is also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5454","kind":"arxiv","version":3},"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":"1310.5454","created_at":"2026-05-17T23:52:19.457643+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.5454v3","created_at":"2026-05-17T23:52:19.457643+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5454","created_at":"2026-05-17T23:52:19.457643+00:00"},{"alias_kind":"pith_short_12","alias_value":"F3JMBNYJJICC","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"F3JMBNYJJICC7D4F","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"F3JMBNYJ","created_at":"2026-05-18T12:27:43.054852+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/F3JMBNYJJICC7D4F4DCBF5BYLU","json":"https://pith.science/pith/F3JMBNYJJICC7D4F4DCBF5BYLU.json","graph_json":"https://pith.science/api/pith-number/F3JMBNYJJICC7D4F4DCBF5BYLU/graph.json","events_json":"https://pith.science/api/pith-number/F3JMBNYJJICC7D4F4DCBF5BYLU/events.json","paper":"https://pith.science/paper/F3JMBNYJ"},"agent_actions":{"view_html":"https://pith.science/pith/F3JMBNYJJICC7D4F4DCBF5BYLU","download_json":"https://pith.science/pith/F3JMBNYJJICC7D4F4DCBF5BYLU.json","view_paper":"https://pith.science/paper/F3JMBNYJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.5454&json=true","fetch_graph":"https://pith.science/api/pith-number/F3JMBNYJJICC7D4F4DCBF5BYLU/graph.json","fetch_events":"https://pith.science/api/pith-number/F3JMBNYJJICC7D4F4DCBF5BYLU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F3JMBNYJJICC7D4F4DCBF5BYLU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F3JMBNYJJICC7D4F4DCBF5BYLU/action/storage_attestation","attest_author":"https://pith.science/pith/F3JMBNYJJICC7D4F4DCBF5BYLU/action/author_attestation","sign_citation":"https://pith.science/pith/F3JMBNYJJICC7D4F4DCBF5BYLU/action/citation_signature","submit_replication":"https://pith.science/pith/F3JMBNYJJICC7D4F4DCBF5BYLU/action/replication_record"}},"created_at":"2026-05-17T23:52:19.457643+00:00","updated_at":"2026-05-17T23:52:19.457643+00:00"}