{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EOOSRT2AJHVRQPGE46MJNQPQF5","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":"8310e2776322683ff76ba709353cec4366ea018f9865ef21ce4ec066890df5e4","cross_cats_sorted":["math.CO","math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-12-30T11:01:56Z","title_canon_sha256":"a945b09485a057c4066a2b8a61600ce2b1bbfea3da3f6f3968f053dcd353574a"},"schema_version":"1.0","source":{"id":"1312.7678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7678","created_at":"2026-05-18T01:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7678v1","created_at":"2026-05-18T01:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7678","created_at":"2026-05-18T01:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"EOOSRT2AJHVR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EOOSRT2AJHVRQPGE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EOOSRT2A","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:0ffb6ad2fca1365ca4e565e78d69c3867743f2ae708d81d734f7ff379c516e71","target":"graph","created_at":"2026-05-18T01:45:35Z","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":"From the viewpoint of mutation, we will give a brief survey of tilting theory and cluster-tilting theory together with a motivation from cluster algebras. Then we will give an introdution to \\tau-tilting theory which was recently developed in [AIR].","authors_text":"Idun Reiten, Osamu Iyama","cross_cats":["math.CO","math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-12-30T11:01:56Z","title":"Introduction to $\\tau$-tilting theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7678","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:e9190d704c41d65afc85abb8d2173d4e113ec7e2780fb96e30a0afe874a0f2d9","target":"record","created_at":"2026-05-18T01:45:35Z","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":"8310e2776322683ff76ba709353cec4366ea018f9865ef21ce4ec066890df5e4","cross_cats_sorted":["math.CO","math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-12-30T11:01:56Z","title_canon_sha256":"a945b09485a057c4066a2b8a61600ce2b1bbfea3da3f6f3968f053dcd353574a"},"schema_version":"1.0","source":{"id":"1312.7678","kind":"arxiv","version":1}},"canonical_sha256":"239d28cf4049eb183cc4e79896c1f02f41c4ccf9e5f7aa5312b411224883149c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"239d28cf4049eb183cc4e79896c1f02f41c4ccf9e5f7aa5312b411224883149c","first_computed_at":"2026-05-18T01:45:35.215965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:35.215965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K8BdpHENIyT25ROluE29q34+tFRhOlWm8Oh+rWKwcJZJFJODQee4TqDMbQxn3e/m6voCI/mE2YVtvYFaZhytCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:35.216546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9190d704c41d65afc85abb8d2173d4e113ec7e2780fb96e30a0afe874a0f2d9","sha256:0ffb6ad2fca1365ca4e565e78d69c3867743f2ae708d81d734f7ff379c516e71"],"state_sha256":"ca71bc1079617fc197abaf3ec8598775b508109bc7871d263ee2ff8887aa5f12"}