{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P3ZVCQI3BREEYFIZ5ECY3HC66R","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":"1555b13f934168982ba0523cdd2f254be63edbe2289150ff2e8a81457b67ff24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-24T19:06:51Z","title_canon_sha256":"e2eaf57040242aadc7c19561636bc20ba2e6bae38dc4503b7931654afd62cd7d"},"schema_version":"1.0","source":{"id":"1306.5710","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5710","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5710v1","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5710","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"P3ZVCQI3BREE","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P3ZVCQI3BREEYFIZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P3ZVCQI3","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:ef39dfc11e2fa8abccf2b6402ef32cb0ec9c7baf48234b4ebe58e564c081cb26","target":"graph","created_at":"2026-05-18T01:36:21Z","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 investigate projective covers of cyclically presented modules, characterizing the rings over which every cyclically presented module has a projective cover as the rings $R$ that are Von Neumann regular modulo their Jacobson radical $J(R)$ and in which idempotents can be lifted modulo $J(R)$. Cyclically presented modules naturally appear in the study of factorizations of elements in non-necessarily commutative integral domains. One of the possible applications is to the modules $M_R$ whose endomorphism ring $E:=(M_R)$ is Von Neumann regular modulo $J(E)$ and in which idempotents lift modulo ","authors_text":"Alberto Facchini, Daniel Smertnig, Nguyen Khanh Tung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-24T19:06:51Z","title":"Cyclically presented modules, projective covers and factorizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5710","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:a32beee4ca55c6d4368af87cad9a09d14fb8f5e238549ab689b51e35f6b6d8b5","target":"record","created_at":"2026-05-18T01:36:21Z","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":"1555b13f934168982ba0523cdd2f254be63edbe2289150ff2e8a81457b67ff24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-24T19:06:51Z","title_canon_sha256":"e2eaf57040242aadc7c19561636bc20ba2e6bae38dc4503b7931654afd62cd7d"},"schema_version":"1.0","source":{"id":"1306.5710","kind":"arxiv","version":1}},"canonical_sha256":"7ef351411b0c484c1519e9058d9c5ef453d2fef743cdad6f26720f8f444aaf75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ef351411b0c484c1519e9058d9c5ef453d2fef743cdad6f26720f8f444aaf75","first_computed_at":"2026-05-18T01:36:21.084233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:21.084233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7x1HqWaPxPIQsJOU0kSdpGOpz283jrToEZZllnhS8V88asbCGAjS0/PiVqWGKzbbELXYIM53m0xlSPL2aIBhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:21.084857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5710","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a32beee4ca55c6d4368af87cad9a09d14fb8f5e238549ab689b51e35f6b6d8b5","sha256:ef39dfc11e2fa8abccf2b6402ef32cb0ec9c7baf48234b4ebe58e564c081cb26"],"state_sha256":"fbce680c4e978c3a7c830f7f284d5fcb42f7deb436568d339a44a20643304349"}