{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7HEKE36QZ7HDACG3WSMT7MAUA6","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":"774042184566c37baa2743f81837c397352ed4e1938e7f18b2672c551dd91f9b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-24T14:33:42Z","title_canon_sha256":"e5a45fc39a31345ea0a55a2fee2ea53792faa6037589adb9a369916c32f48c25"},"schema_version":"1.0","source":{"id":"1509.07387","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07387","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07387v3","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07387","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"7HEKE36QZ7HD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7HEKE36QZ7HDACG3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7HEKE36Q","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:65f9015b58484da8540a79f126a9c5aee434b911d6ada576605b7ec13a48ab63","target":"graph","created_at":"2026-05-18T00:21:00Z","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 tilting complexes over preprojective algebras of Dynkin type. We classify all tilting complexes by giving a bijection between tilting complexes and the braid group of the corresponding folded graph. In particular, we determine the derived equivalence class of the algebra. For the results, we develop the theory of silting-discrete triangulated categories and give a criterion of silting-discreteness.","authors_text":"Takuma Aihara, Yuya Mizuno","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-24T14:33:42Z","title":"Classifying tilting complexes over preprojective algebras of Dynkin type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07387","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:ac78c110e538b703ea4a706b9181de4f5dace77183890abb608bdb12932d9731","target":"record","created_at":"2026-05-18T00:21:00Z","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":"774042184566c37baa2743f81837c397352ed4e1938e7f18b2672c551dd91f9b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-24T14:33:42Z","title_canon_sha256":"e5a45fc39a31345ea0a55a2fee2ea53792faa6037589adb9a369916c32f48c25"},"schema_version":"1.0","source":{"id":"1509.07387","kind":"arxiv","version":3}},"canonical_sha256":"f9c8a26fd0cfce3008dbb4993fb0140783a5d64294ff753e3cd1b085d6a37045","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9c8a26fd0cfce3008dbb4993fb0140783a5d64294ff753e3cd1b085d6a37045","first_computed_at":"2026-05-18T00:21:00.206288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:00.206288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BZjy6w+MI+wnj3lti96BlH48RGLk9y1WC2wvMenzl1U/wNWlbs/jm4a86cAdfvRCd3iJpmC6kii9EcyP0DDuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:00.206792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07387","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac78c110e538b703ea4a706b9181de4f5dace77183890abb608bdb12932d9731","sha256:65f9015b58484da8540a79f126a9c5aee434b911d6ada576605b7ec13a48ab63"],"state_sha256":"c8601a41eb17e178b61010ba5ae12154a5960a85760105447db580caa1fd652e"}