{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HGJRWUPYN3OJ7D27ZDPOPDWMBX","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":"5d7d18760880a543edd3bbd52117a794c7c51d2a607246b8e1cbe2027f2b6cac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-07T16:15:59Z","title_canon_sha256":"4231d7821404a44a8b434f06ec129707fd96a7e631979ee414920fc39a019647"},"schema_version":"1.0","source":{"id":"1703.02452","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02452","created_at":"2026-05-18T00:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02452v1","created_at":"2026-05-18T00:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02452","created_at":"2026-05-18T00:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"HGJRWUPYN3OJ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HGJRWUPYN3OJ7D27","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HGJRWUPY","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:8e111899d829230ae508d25eebc6dd100e5647db9adc64b676fb468e8322aef5","target":"graph","created_at":"2026-05-18T00:49:19Z","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":"Let $G$ be a finite solvable group, and let $p$ be a prime. In this note, we prove that $p$ does not divide $\\varphi(1)$ for every irreducible monomial $p$-Brauer character $\\varphi$ of $G$ if and only if $G$ has a normal Sylow $p$-subgroup.","authors_text":"Mark L. Lewis, Xiaoyou Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-07T16:15:59Z","title":"It\\^{o}'s theorem and monomial Brauer characters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02452","kind":"arxiv","version":1},"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:b31fe5f749d8e5feb4c43355e8294f7cef380f37ccb5d4acc6090a613fd20c57","target":"record","created_at":"2026-05-18T00:49:19Z","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":"5d7d18760880a543edd3bbd52117a794c7c51d2a607246b8e1cbe2027f2b6cac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-07T16:15:59Z","title_canon_sha256":"4231d7821404a44a8b434f06ec129707fd96a7e631979ee414920fc39a019647"},"schema_version":"1.0","source":{"id":"1703.02452","kind":"arxiv","version":1}},"canonical_sha256":"39931b51f86edc9f8f5fc8dee78ecc0df5ce759c4376a4004821aa3315230859","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39931b51f86edc9f8f5fc8dee78ecc0df5ce759c4376a4004821aa3315230859","first_computed_at":"2026-05-18T00:49:19.898551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:19.898551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"08g1P9gZJrF4QXLNx1aXf6e7IFvypRTsgxSlPjylXpZRnYNxb2SeV7+zqK4NyA7kJKs+BXbbl+720O2MUjCjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:19.898973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02452","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b31fe5f749d8e5feb4c43355e8294f7cef380f37ccb5d4acc6090a613fd20c57","sha256:8e111899d829230ae508d25eebc6dd100e5647db9adc64b676fb468e8322aef5"],"state_sha256":"df15f569e2db1e281125278445c3ba4fd7a7ff936749bf6560766f497dd00695"}