{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EREEF3ETLZFHJZWT7TRG3NJMMR","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":"4deab6c4e0c7f22d08e65a5fe67b7c5c94463886daadeaf04a1f50ab0dff6eb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-24T20:43:14Z","title_canon_sha256":"5a6aa1d6d7612c7a41fe785677ac05fc5e9cddf6177cbf1f39ca1bc755fd6251"},"schema_version":"1.0","source":{"id":"1009.4943","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4943","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4943v3","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4943","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"EREEF3ETLZFH","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EREEF3ETLZFHJZWT","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EREEF3ET","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:179dbc7e51f39808f810cf1a76b5fc43369e63cc833dd7cfa2aeca2977419706","target":"graph","created_at":"2026-05-18T04:10:09Z","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":"We construct a recursive formula for a complete system of primitive orthogonal idempotents for any $R$-trivial monoid. This uses the newly proved equivalence between the notions of $R$-trivial monoid and weakly ordered monoid.","authors_text":"Chris Berg, Franco Saliola, Nantel Bergeron, Sandeep Bhargava","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-24T20:43:14Z","title":"Primitive orthogonal idempotents for R-trivial monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4943","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":"sha256:72e4b1036e8021b43704d8b7483282bd32141e076e30303a5cfc85cd288cd37a","target":"record","created_at":"2026-05-18T04:10:09Z","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":"4deab6c4e0c7f22d08e65a5fe67b7c5c94463886daadeaf04a1f50ab0dff6eb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-24T20:43:14Z","title_canon_sha256":"5a6aa1d6d7612c7a41fe785677ac05fc5e9cddf6177cbf1f39ca1bc755fd6251"},"schema_version":"1.0","source":{"id":"1009.4943","kind":"arxiv","version":3}},"canonical_sha256":"244842ec935e4a74e6d3fce26db52c6443842b364e074e9f726a02dc056b49d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"244842ec935e4a74e6d3fce26db52c6443842b364e074e9f726a02dc056b49d8","first_computed_at":"2026-05-18T04:10:09.005268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:09.005268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lBbMT1Yu7HLAyNySfTEHB+y9sp15NdNTxoUcDexXAuv1RSHvogAcMPj6OGJroyOUECMx39PMHXWG2ZmJMHTnCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:09.006148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4943","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72e4b1036e8021b43704d8b7483282bd32141e076e30303a5cfc85cd288cd37a","sha256:179dbc7e51f39808f810cf1a76b5fc43369e63cc833dd7cfa2aeca2977419706"],"state_sha256":"bc3c9d14016c65a6b3d720abeefadb6deb09de9a730a4cf470527fead8ab773c"}