{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J4F2OCGUC35VBY5SHZTOU5IXQU","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":"f91dc89d4af4aff8fb06c6827d161f191cd859c3ae5bc9f69f0223f9b24e5567","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-08-04T09:20:50Z","title_canon_sha256":"c7de8bf14bf360b688badfdc16bf8dc45f20850de8f290f4803ffc85bdd7c4f5"},"schema_version":"1.0","source":{"id":"2608.03371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03371","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03371v1","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03371","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"pith_short_12","alias_value":"J4F2OCGUC35V","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"pith_short_16","alias_value":"J4F2OCGUC35VBY5S","created_at":"2026-08-05T01:35:37Z"},{"alias_kind":"pith_short_8","alias_value":"J4F2OCGU","created_at":"2026-08-05T01:35:37Z"}],"graph_snapshots":[{"event_id":"sha256:a576971cc364f41f32d5346ef68e1fe46851f7c630c09edc0fbe1e0dcce7c150","target":"graph","created_at":"2026-08-05T01:35:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.03371/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a method to compute the primitive central idempotents of a semi-simple finite group algebra associated with an irreducible character $\\chi$ such that for every $g\\in G$, either $\\chi(g) = 0$ or all eigenvalues of $\\rho(g)$ have the same order. We then show several consequences which highlight the significance and possible applications of our approach.","authors_text":"Jagmohan Tanti, Satyam Shukla","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-08-04T09:20:50Z","title":"Primitive central idempotents of a finite group over a field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03371","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:f439be522d25ec29c912721dfb0c040791b25eee9c8f5caa3969db8ee9ff7add","target":"record","created_at":"2026-08-05T01:35:37Z","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":"f91dc89d4af4aff8fb06c6827d161f191cd859c3ae5bc9f69f0223f9b24e5567","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-08-04T09:20:50Z","title_canon_sha256":"c7de8bf14bf360b688badfdc16bf8dc45f20850de8f290f4803ffc85bdd7c4f5"},"schema_version":"1.0","source":{"id":"2608.03371","kind":"arxiv","version":1}},"canonical_sha256":"4f0ba708d416fb50e3b23e66ea7517852e75aac83dcdb6f011563c8a97b06dc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f0ba708d416fb50e3b23e66ea7517852e75aac83dcdb6f011563c8a97b06dc7","first_computed_at":"2026-08-05T01:35:37.907188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-05T01:35:37.907188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6HB+c+BIktmOqeLl6w/HHBzawouTAjgAOQG03wr1D9+mO6uCoezFv6JJmjWSx5n6tcLyj7hoez7mWRhl9RzgCw==","signature_status":"signed_v1","signed_at":"2026-08-05T01:35:37.908716Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.03371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f439be522d25ec29c912721dfb0c040791b25eee9c8f5caa3969db8ee9ff7add","sha256:a576971cc364f41f32d5346ef68e1fe46851f7c630c09edc0fbe1e0dcce7c150"],"state_sha256":"afe355065ffa29244c7c1660cb3dd7a382f01dd6988085553fa81fd5fb8e3b6a"}