{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E4N2DR4RCJF7NMDGVYFFJLNQHQ","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":"44b776905f19ac738548a8270a83343a41188b539a3c92422f040f4efe4d864a","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-31T15:19:10Z","title_canon_sha256":"444351e76631bb77248e339e0f600403ed93bacb6154aadaa8f5f474bbb0f3ee"},"schema_version":"1.0","source":{"id":"1305.7449","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7449","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7449v2","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7449","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"E4N2DR4RCJF7","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E4N2DR4RCJF7NMDG","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E4N2DR4R","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:9e9a3f02e129f11a277f853b6d030ffac6e8bfcce7a05cbc42928c90f445c543","target":"graph","created_at":"2026-05-18T01:25:47Z","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":"This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we prove analogues of this result for p-blocks of alternating groups (where the blocks must also have the same sign when p is odd), of double covers of alternating and symmetric groups (for p odd, and where we obtain crossover isometries when the blocks have opposite signs),of complex reflection groups G(d,1,n) (for d prime to p), of Weyl groups of type B and D (","authors_text":"Jean-Baptiste Gramain, Olivier Brunat","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-31T15:19:10Z","title":"Perfect isometries and Murnaghan-Nakayama rules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7449","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":"sha256:34d9fa91be556dacb8d2fd1fd30130ffa9fb859be3485c9f061c8eb057c15285","target":"record","created_at":"2026-05-18T01:25:47Z","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":"44b776905f19ac738548a8270a83343a41188b539a3c92422f040f4efe4d864a","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-31T15:19:10Z","title_canon_sha256":"444351e76631bb77248e339e0f600403ed93bacb6154aadaa8f5f474bbb0f3ee"},"schema_version":"1.0","source":{"id":"1305.7449","kind":"arxiv","version":2}},"canonical_sha256":"271ba1c791124bf6b066ae0a54adb03c139b36f77a50e6b617b868c2a4297490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"271ba1c791124bf6b066ae0a54adb03c139b36f77a50e6b617b868c2a4297490","first_computed_at":"2026-05-18T01:25:47.872154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:47.872154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9fi3A+2lTjiQvYkJ4rvdg82hhnuAjQCcAJaOIVYnpEMdKxXT7US5ZvF6mC4cxAxCEyjym5xHfdZL+zPBJlNLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:47.872604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.7449","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34d9fa91be556dacb8d2fd1fd30130ffa9fb859be3485c9f061c8eb057c15285","sha256:9e9a3f02e129f11a277f853b6d030ffac6e8bfcce7a05cbc42928c90f445c543"],"state_sha256":"48850367e1982e2580ccfeb1d79942b3275aa7a28dc223f78630f309311d60d4"}