{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZORB57GD65L6ZO42AALESDQKHY","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":"d1200716e0177289ee0dabe9d1847ac50f0a948ff6aa140b740525bf495be029","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-06-09T20:44:38Z","title_canon_sha256":"1d0d02192c867fc01ff892ffaf14de914e7f77ea74317663f3fca250d7229aab"},"schema_version":"1.0","source":{"id":"0906.1820","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.1820","created_at":"2026-05-18T04:42:12Z"},{"alias_kind":"arxiv_version","alias_value":"0906.1820v3","created_at":"2026-05-18T04:42:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.1820","created_at":"2026-05-18T04:42:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZORB57GD65L6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZORB57GD65L6ZO42","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZORB57GD","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:c80ad4365aaf8576658e36aedfb6a11a485aa7b10a330da6bc1c4d3f805cb8b6","target":"graph","created_at":"2026-05-18T04:42:12Z","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 [7], G. Navarro proposed a refinement of the McKay conjecture involving a special class of Galois automorphisms. In [6] this new conjecture was verified by the author for the alternating groups A(n) when p=2. In this note the Navarro conjecture is verified for the p-singular characters of the principal block of the alternating groups in the case of abelian defect when p is odd.","authors_text":"Rishi Nath","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-06-09T20:44:38Z","title":"A note on the Navarro conjecture for alternating groups with abelian defect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.1820","kind":"arxiv","version":3},"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":"sha256:988be2c3628d67acce775da4a47bccd0a2ab7e733664f2ed46c757b99dd76889","target":"record","created_at":"2026-05-18T04:42:12Z","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":"d1200716e0177289ee0dabe9d1847ac50f0a948ff6aa140b740525bf495be029","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-06-09T20:44:38Z","title_canon_sha256":"1d0d02192c867fc01ff892ffaf14de914e7f77ea74317663f3fca250d7229aab"},"schema_version":"1.0","source":{"id":"0906.1820","kind":"arxiv","version":3}},"canonical_sha256":"cba21efcc3f757ecbb9a0016490e0a3e3917e6397d78c2b022c731dc4effe248","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cba21efcc3f757ecbb9a0016490e0a3e3917e6397d78c2b022c731dc4effe248","first_computed_at":"2026-05-18T04:42:12.481338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:12.481338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WPM29rilqp5AqXQKJfWqeqgVmv5UC3Mn5urnaFcNIudyRtplReBfmbwQxC3kvEE4mFfMNN9ygaIbd6AfHJJsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:12.481996Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.1820","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:988be2c3628d67acce775da4a47bccd0a2ab7e733664f2ed46c757b99dd76889","sha256:c80ad4365aaf8576658e36aedfb6a11a485aa7b10a330da6bc1c4d3f805cb8b6"],"state_sha256":"d572a278312dcc5d3dfdeedc010464ca885d47f6d747aac759e381ed62b36563"}