{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CKR2BUJZJOXKCWPE774WW7AYEP","short_pith_number":"pith:CKR2BUJZ","canonical_record":{"source":{"id":"1202.4161","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-19T15:46:44Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"4c76491b818f756e9324c4502818479752bbe004a8a787ff4dfd2a33717f48a9","abstract_canon_sha256":"5d7094a31dc4685532109d5d12c73eeb7468644ad1d5a5d73af8ede5bba0b35a"},"schema_version":"1.0"},"canonical_sha256":"12a3a0d1394baea159e4fff96b7c1823e7e0899f8c2ed22c981062296b1437a7","source":{"kind":"arxiv","id":"1202.4161","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4161","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4161v4","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4161","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"pith_short_12","alias_value":"CKR2BUJZJOXK","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CKR2BUJZJOXKCWPE","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CKR2BUJZ","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CKR2BUJZJOXKCWPE774WW7AYEP","target":"record","payload":{"canonical_record":{"source":{"id":"1202.4161","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-19T15:46:44Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"4c76491b818f756e9324c4502818479752bbe004a8a787ff4dfd2a33717f48a9","abstract_canon_sha256":"5d7094a31dc4685532109d5d12c73eeb7468644ad1d5a5d73af8ede5bba0b35a"},"schema_version":"1.0"},"canonical_sha256":"12a3a0d1394baea159e4fff96b7c1823e7e0899f8c2ed22c981062296b1437a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:15.210856Z","signature_b64":"IT3fuwb8XTpTUClulCS9I36nVMf9pHbOqGl8P85dvgYpyuRpgGwj9wcqWD1uBtPATpaygK7rs59izxz0rPVRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12a3a0d1394baea159e4fff96b7c1823e7e0899f8c2ed22c981062296b1437a7","last_reissued_at":"2026-05-18T04:00:15.210110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:15.210110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.4161","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:00:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+5w3PFPbJGHojEjssSqoTzXprZDxEF8q4QpUt7Wy1JV0vJzn/2u6HwuDxw5URLDytKnl5aAZXZ8nTpahcFkKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:42:38.233313Z"},"content_sha256":"c626e7ef22318ab7eb0415763273c4cd77571a3f1327c4226ec7c003f87316cf","schema_version":"1.0","event_id":"sha256:c626e7ef22318ab7eb0415763273c4cd77571a3f1327c4226ec7c003f87316cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CKR2BUJZJOXKCWPE774WW7AYEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster algebras and derived categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.RT","authors_text":"Bernhard Keller","submitted_at":"2012-02-19T15:46:44Z","abstract_excerpt":"This is an introductory survey on cluster algebras and their (additive) categorification using derived categories of Ginzburg algebras. After a gentle introduction to cluster combinatorics, we review important examples of coordinate rings admitting a cluster algebra structure. We then present the general definition of a cluster algebra and describe the interplay between cluster variables, coefficients, c-vectors and g-vectors. We show how c-vectors appear in the study of quantum cluster algebras and their links to the quantum dilogarithm. We then present the framework of additive categorificat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4161","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:00:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RyrBYkymw7PtqmoBcUr2gnsRwPFmrLvLok1SoFxwh14DF1V+T4x1dHKscI1FrpZ/qM1Bi4ZmVw36bhOMt/LpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:42:38.234044Z"},"content_sha256":"83942d8681c1e8a64af54327faf599687f30970914de63ae800aab8f609f5a4a","schema_version":"1.0","event_id":"sha256:83942d8681c1e8a64af54327faf599687f30970914de63ae800aab8f609f5a4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKR2BUJZJOXKCWPE774WW7AYEP/bundle.json","state_url":"https://pith.science/pith/CKR2BUJZJOXKCWPE774WW7AYEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKR2BUJZJOXKCWPE774WW7AYEP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T19:42:38Z","links":{"resolver":"https://pith.science/pith/CKR2BUJZJOXKCWPE774WW7AYEP","bundle":"https://pith.science/pith/CKR2BUJZJOXKCWPE774WW7AYEP/bundle.json","state":"https://pith.science/pith/CKR2BUJZJOXKCWPE774WW7AYEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKR2BUJZJOXKCWPE774WW7AYEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CKR2BUJZJOXKCWPE774WW7AYEP","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":"5d7094a31dc4685532109d5d12c73eeb7468644ad1d5a5d73af8ede5bba0b35a","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-19T15:46:44Z","title_canon_sha256":"4c76491b818f756e9324c4502818479752bbe004a8a787ff4dfd2a33717f48a9"},"schema_version":"1.0","source":{"id":"1202.4161","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4161","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4161v4","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4161","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"pith_short_12","alias_value":"CKR2BUJZJOXK","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CKR2BUJZJOXKCWPE","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CKR2BUJZ","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:83942d8681c1e8a64af54327faf599687f30970914de63ae800aab8f609f5a4a","target":"graph","created_at":"2026-05-18T04:00:15Z","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":"This is an introductory survey on cluster algebras and their (additive) categorification using derived categories of Ginzburg algebras. After a gentle introduction to cluster combinatorics, we review important examples of coordinate rings admitting a cluster algebra structure. We then present the general definition of a cluster algebra and describe the interplay between cluster variables, coefficients, c-vectors and g-vectors. We show how c-vectors appear in the study of quantum cluster algebras and their links to the quantum dilogarithm. We then present the framework of additive categorificat","authors_text":"Bernhard Keller","cross_cats":["math.CO","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-19T15:46:44Z","title":"Cluster algebras and derived categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4161","kind":"arxiv","version":4},"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:c626e7ef22318ab7eb0415763273c4cd77571a3f1327c4226ec7c003f87316cf","target":"record","created_at":"2026-05-18T04:00:15Z","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":"5d7094a31dc4685532109d5d12c73eeb7468644ad1d5a5d73af8ede5bba0b35a","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-02-19T15:46:44Z","title_canon_sha256":"4c76491b818f756e9324c4502818479752bbe004a8a787ff4dfd2a33717f48a9"},"schema_version":"1.0","source":{"id":"1202.4161","kind":"arxiv","version":4}},"canonical_sha256":"12a3a0d1394baea159e4fff96b7c1823e7e0899f8c2ed22c981062296b1437a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12a3a0d1394baea159e4fff96b7c1823e7e0899f8c2ed22c981062296b1437a7","first_computed_at":"2026-05-18T04:00:15.210110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:15.210110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IT3fuwb8XTpTUClulCS9I36nVMf9pHbOqGl8P85dvgYpyuRpgGwj9wcqWD1uBtPATpaygK7rs59izxz0rPVRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:15.210856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4161","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c626e7ef22318ab7eb0415763273c4cd77571a3f1327c4226ec7c003f87316cf","sha256:83942d8681c1e8a64af54327faf599687f30970914de63ae800aab8f609f5a4a"],"state_sha256":"5cde50935dfafe6059d3f5db8fadec6dbff5fc4736b21bf1a669b4544ce93a47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dP2/3FQoIKs5ho0tkK5AnaYyuGDNbk3/Ix3aB+FLFgamA3Z3jOwMKVMQZLx07i0NlyvHzCqHUi6k49oNoakuDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T19:42:38.238475Z","bundle_sha256":"935e54e8a56a7beae376cfc757a98b4d2aa720933e4b2d9408aec5ecf4b48de9"}}