{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TR4UWXJEBO7ZHIZESCLOJ2DLD3","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":"50b26b4fdd16a8ebf0745062cf0e240b930ac515d13c8ebda7557a87f5047674","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-17T05:04:35Z","title_canon_sha256":"aedd1e2d9eac8588ea54fa159ac6248c627ccd760f0154c3e98c00dfe800cbef"},"schema_version":"1.0","source":{"id":"1301.3983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3983","created_at":"2026-05-18T03:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3983v1","created_at":"2026-05-18T03:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3983","created_at":"2026-05-18T03:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"TR4UWXJEBO7Z","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TR4UWXJEBO7ZHIZE","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TR4UWXJE","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:d8a2d96ab0dce654b0d83219fec996a0c0d3a22737394489abc83708c6272553","target":"graph","created_at":"2026-05-18T03:36:14Z","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":"Let $Q$ be a finite quiver of Dynkin type and $\\Lambda=\\Lambda_Q$ be the preprojective algebra of $Q$ over an algebraically closed field $k$. Let $\\mathcal {T}_\\Lambda$ be the mutation graph of maximal rigid $\\Lambda$ modules. Geiss, Leclerc and Schr$\\ddot{\\rm o}$er conjectured that $\\mathcal {T}_\\Lambda$ is connected, see [C.Geiss, B.Leclerc, J.Schr\\\"{o}er, Rigid modules over preprojective algebras, Invent.Math., 165(2006), 589-632]. In this paper, we prove that this conjecture is true when $\\Lambda$ is of representation finite type or tame type. Moreover, we also prove that $\\mathcal {T}_\\La","authors_text":"Hongbo Yin, Shunhua Zhang","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-17T05:04:35Z","title":"Mutation graphs of maximal rigid modules over finite dimensional preprojective algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3983","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:e040d1b31af9965fa6da03920e789aec893c1c300664345ab2ee3a5b1750689d","target":"record","created_at":"2026-05-18T03:36:14Z","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":"50b26b4fdd16a8ebf0745062cf0e240b930ac515d13c8ebda7557a87f5047674","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-17T05:04:35Z","title_canon_sha256":"aedd1e2d9eac8588ea54fa159ac6248c627ccd760f0154c3e98c00dfe800cbef"},"schema_version":"1.0","source":{"id":"1301.3983","kind":"arxiv","version":1}},"canonical_sha256":"9c794b5d240bbf93a3249096e4e86b1ed27445251ec1d3f896250403b0a8dfaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c794b5d240bbf93a3249096e4e86b1ed27445251ec1d3f896250403b0a8dfaf","first_computed_at":"2026-05-18T03:36:14.718126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:14.718126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SRDehjazM7hJJXoyPuTEdSYz5xd1kayqCvmfjlnt9M+q4Ek/vTeM+GIko6tp5sHgoosfq3Z6N/jiLCySQ55jCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:14.718633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e040d1b31af9965fa6da03920e789aec893c1c300664345ab2ee3a5b1750689d","sha256:d8a2d96ab0dce654b0d83219fec996a0c0d3a22737394489abc83708c6272553"],"state_sha256":"ccaaafbe375679d83faf0c11fb6359b7ae7b9e5eabf293002f5e85ec1de5551f"}