{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RXW7HJH34HLMNDSS36NWOUPVT7","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":"8f104354cf45d4f4e2bf50dd194c1e26bbdbf92c53202b1c4eab60fedd5622f0","cross_cats_sorted":["math.GR","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-16T20:52:23Z","title_canon_sha256":"41d09adb33353590ec7c64e681bf3fbac46f559ac4c68fe4b27c72a11777b524"},"schema_version":"1.0","source":{"id":"1706.05425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05425","created_at":"2026-05-18T00:42:11Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05425v1","created_at":"2026-05-18T00:42:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05425","created_at":"2026-05-18T00:42:11Z"},{"alias_kind":"pith_short_12","alias_value":"RXW7HJH34HLM","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RXW7HJH34HLMNDSS","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RXW7HJH3","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:80e35df1822ae9b178c2109600e9fdb7a323faa2d2c333470ce52423fb23c309","target":"graph","created_at":"2026-05-18T00:42:11Z","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 give a construction of the projective indecomposable modules and a description of the quiver for a large class of monoid algebras including the algebra of any finite monoid whose principal right ideals have at most one idempotent generator. Our results include essentially all families of finite monoids for which this has been done previously, for example, left regular bands, $\\mathscr J$-trivial and $\\mathscr R$-trivial monoids and left regular bands of groups.","authors_text":"Benjamin Steinberg, Stuart Margolis","cross_cats":["math.GR","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-16T20:52:23Z","title":"Projective indecomposable modules and quivers for monoid algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05425","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":"sha256:8c3f57d98ef287fed9d716292255feb1feb34bc923e5d7da0529b019fd75c194","target":"record","created_at":"2026-05-18T00:42:11Z","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":"8f104354cf45d4f4e2bf50dd194c1e26bbdbf92c53202b1c4eab60fedd5622f0","cross_cats_sorted":["math.GR","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-16T20:52:23Z","title_canon_sha256":"41d09adb33353590ec7c64e681bf3fbac46f559ac4c68fe4b27c72a11777b524"},"schema_version":"1.0","source":{"id":"1706.05425","kind":"arxiv","version":1}},"canonical_sha256":"8dedf3a4fbe1d6c68e52df9b6751f59fd009f461cb1e07dfebdd9ec6893bae46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dedf3a4fbe1d6c68e52df9b6751f59fd009f461cb1e07dfebdd9ec6893bae46","first_computed_at":"2026-05-18T00:42:11.666220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:11.666220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qirUyYbwE5wME9H+N4uCR1JA/LyJ4e3OJWKU4ZzI2sAqchuv7+fsL+aPFYEmDev3AQjlpcd+RhRdGHvR0k4SAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:11.666771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c3f57d98ef287fed9d716292255feb1feb34bc923e5d7da0529b019fd75c194","sha256:80e35df1822ae9b178c2109600e9fdb7a323faa2d2c333470ce52423fb23c309"],"state_sha256":"49b312fbe8f69c8b68323d7cccc12a66e96aebd159985bd1657ed8f4a84f2bbc"}