{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3AEE6OYOUGM7ABVQA226BQGSSD","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":"b9469ff9e3a80d2842e3f79797a18c25b7e73a9d3ed64e3a86769bf7b01f899e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-31T20:00:02Z","title_canon_sha256":"7258af11853df00fa581d5a94af5ca2c24ca78174f53de76d88b33c4d2378435"},"schema_version":"1.0","source":{"id":"1311.0010","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0010","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0010v3","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0010","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"pith_short_12","alias_value":"3AEE6OYOUGM7","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3AEE6OYOUGM7ABVQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3AEE6OYO","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:3ffd2bd529258cfda213c53f1f141ff8bc19e8b288f4dd775ee37120d9c75b60","target":"graph","created_at":"2026-05-17T23:53:14Z","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":"We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting dimensions of $\\operatorname{Ext}^1$ as intersection numbers of tagged curves and Auslander-Reiten translation as tagged rotation. An important consequence is that the cluster(-tilting) exchange graphs of such cluster categories are connected.","authors_text":"Yu Qiu, Yu Zhou","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-31T20:00:02Z","title":"Cluster categories for marked surfaces: punctured case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0010","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":"sha256:2bd95521ad49b500e197414b39dff8224280fd358d3805241e3d228f9d9326c9","target":"record","created_at":"2026-05-17T23:53:14Z","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":"b9469ff9e3a80d2842e3f79797a18c25b7e73a9d3ed64e3a86769bf7b01f899e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-31T20:00:02Z","title_canon_sha256":"7258af11853df00fa581d5a94af5ca2c24ca78174f53de76d88b33c4d2378435"},"schema_version":"1.0","source":{"id":"1311.0010","kind":"arxiv","version":3}},"canonical_sha256":"d8084f3b0ea199f006b006b5e0c0d290ddb6b00761899c561cf3be5edc52bc56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8084f3b0ea199f006b006b5e0c0d290ddb6b00761899c561cf3be5edc52bc56","first_computed_at":"2026-05-17T23:53:14.986753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:14.986753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jGi17Vf4mB6lOLPdw3cBdqL8zQlCZDD2O8RaGR9E6PNWn3hiXHxwS0+rnSMIO8B13jjmq/ZBHRx/3xzg9HMdBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:14.987254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0010","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bd95521ad49b500e197414b39dff8224280fd358d3805241e3d228f9d9326c9","sha256:3ffd2bd529258cfda213c53f1f141ff8bc19e8b288f4dd775ee37120d9c75b60"],"state_sha256":"36b778399260ecb840045b010f3c7c6f951135a1e5d8e5168c426a01953447d6"}