{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4PBKXNYIC5UOQ7GKQTH7HZMVII","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":"e7410c78b773e206994d376ea933693d87223591b62d8892546fef5415960473","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-06T15:00:32Z","title_canon_sha256":"82c94bb3704023825fadf8a0ac39f3093a64710c54d668af01ec59758b2cf1d2"},"schema_version":"1.0","source":{"id":"1410.1403","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1403","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1403v5","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1403","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"4PBKXNYIC5UO","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4PBKXNYIC5UOQ7GK","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4PBKXNYI","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:f3d4dabecee41fb28c48426af87a9adc2965ffd7359bebd37c98a8a82acfccb7","target":"graph","created_at":"2026-05-18T00:42:39Z","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 introduce and study a class of Iwanaga-Gorenstein algebras defined via quivers with relations associated with symmetrizable Cartan matrices. These algebras generalize the path algebras of quivers associated with symmetric Cartan matrices. We also define a corresponding class of generalized preprojective algebras. Without any assumption on the ground field, we obtain new representation-theoretic realizations of all finite root systems.","authors_text":"Bernard Leclerc, Christof Geiss, Jan Schr\\\"oer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-06T15:00:32Z","title":"Quivers with relations for symmetrizable Cartan matrices I : Foundations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1403","kind":"arxiv","version":5},"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":"sha256:77a2145d44cf5ccee1dcce7808f76cd53416bdfea46856dae52406a1b12c64cb","target":"record","created_at":"2026-05-18T00:42:39Z","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":"e7410c78b773e206994d376ea933693d87223591b62d8892546fef5415960473","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-06T15:00:32Z","title_canon_sha256":"82c94bb3704023825fadf8a0ac39f3093a64710c54d668af01ec59758b2cf1d2"},"schema_version":"1.0","source":{"id":"1410.1403","kind":"arxiv","version":5}},"canonical_sha256":"e3c2abb7081768e87cca84cff3e595420542fbe2bce4f775173da27bd9a25636","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3c2abb7081768e87cca84cff3e595420542fbe2bce4f775173da27bd9a25636","first_computed_at":"2026-05-18T00:42:39.904739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:39.904739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zXJNnMQAnN8MA4rVio4NeU6sqGAfVNC6cIj5tZ9T2DpIO2GaCawxUGP+GR1h3iMCfXO/GRhqVgyMKPb20BkDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:39.905411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1403","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77a2145d44cf5ccee1dcce7808f76cd53416bdfea46856dae52406a1b12c64cb","sha256:f3d4dabecee41fb28c48426af87a9adc2965ffd7359bebd37c98a8a82acfccb7"],"state_sha256":"0633bfd049fb6c6287d098bc50d9a19779e45e93d0aafe7de304a40f1e531823"}