{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2WW2JNOQSOKHDXIH2E43GS6SVJ","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":"e8eff7717c4856f0570711380b1bff04b5516a62cc49a71d7cbc2959ce170a29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-11T15:43:17Z","title_canon_sha256":"9647e3b28db787c9fa1e30c80e65fbeb7e9a7e5d75520d2d82a1c7316bbf67bf"},"schema_version":"1.0","source":{"id":"1502.03341","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03341","created_at":"2026-05-18T01:29:46Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03341v2","created_at":"2026-05-18T01:29:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03341","created_at":"2026-05-18T01:29:46Z"},{"alias_kind":"pith_short_12","alias_value":"2WW2JNOQSOKH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2WW2JNOQSOKHDXIH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2WW2JNOQ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:9beec1185a4498f6c19546d969132a78473cadd596f72200d69a0ded1899cadc","target":"graph","created_at":"2026-05-18T01:29:46Z","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 note we use a result of Kantor to prove a conjecture of Degos. Specifically we prove the following: let $\\mathbb{F}$ be a finite field of order $q$ and let $f, g\\in\\mathbb{F}[X]$ be distinct polynomials of degree $n$ such that $f$ is primitive, and the constant term of $g$ is non-zero. Then $<C_f, C_g>=\\mathrm{GL}_n(q)$.","authors_text":"Nick Gill","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-11T15:43:17Z","title":"On a conjecture of Degos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03341","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":"sha256:2eb0fb25a02970b42b78f515a2f84139c60d44f0c3b9e4b30d66d897808c6ac1","target":"record","created_at":"2026-05-18T01:29:46Z","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":"e8eff7717c4856f0570711380b1bff04b5516a62cc49a71d7cbc2959ce170a29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-11T15:43:17Z","title_canon_sha256":"9647e3b28db787c9fa1e30c80e65fbeb7e9a7e5d75520d2d82a1c7316bbf67bf"},"schema_version":"1.0","source":{"id":"1502.03341","kind":"arxiv","version":2}},"canonical_sha256":"d5ada4b5d0939471dd07d139b34bd2aa7b3b88b00ee4cfaaf1fcba329d19ecd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5ada4b5d0939471dd07d139b34bd2aa7b3b88b00ee4cfaaf1fcba329d19ecd0","first_computed_at":"2026-05-18T01:29:46.491574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:46.491574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vzT/N1Z1cH1rzQsDRhX/ralhEwgCxkAQ7zfqeQKfpFCP6xezYYwmvjwBsTES26SEXA0vX6h0OVQhC07Qx/N1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:46.492253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.03341","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2eb0fb25a02970b42b78f515a2f84139c60d44f0c3b9e4b30d66d897808c6ac1","sha256:9beec1185a4498f6c19546d969132a78473cadd596f72200d69a0ded1899cadc"],"state_sha256":"dcacf2f6e60bbc40a35eec6f9e8087fa4d878bdb3c5fea4967fb409404047c72"}