{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QVYOGCPWANRPUYIQYITZP4S7LX","short_pith_number":"pith:QVYOGCPW","canonical_record":{"source":{"id":"1210.6424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-24T02:53:07Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"6e61d46587b9e5828ff3a85db82931dda10e32f6e7869fa3cc9325d0faea1c58","abstract_canon_sha256":"2d99b77ff8bb7b45d8dd88efae94d75f02fe355258f7033dcfa4cc778ec4bb70"},"schema_version":"1.0"},"canonical_sha256":"8570e309f60362fa6110c22797f25f5de885fa2ed092e407ea952d4487ceef73","source":{"kind":"arxiv","id":"1210.6424","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6424","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6424v2","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6424","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"QVYOGCPWANRP","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QVYOGCPWANRPUYIQ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QVYOGCPW","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QVYOGCPWANRPUYIQYITZP4S7LX","target":"record","payload":{"canonical_record":{"source":{"id":"1210.6424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-24T02:53:07Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"6e61d46587b9e5828ff3a85db82931dda10e32f6e7869fa3cc9325d0faea1c58","abstract_canon_sha256":"2d99b77ff8bb7b45d8dd88efae94d75f02fe355258f7033dcfa4cc778ec4bb70"},"schema_version":"1.0"},"canonical_sha256":"8570e309f60362fa6110c22797f25f5de885fa2ed092e407ea952d4487ceef73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:22.175617Z","signature_b64":"cUZErqmSpNQFRfoLdw81nK7CgxHqR8wiPvLFO4NVi6AFct/N/qiygJgcObKckndE5BNPIQNxSXR4oSe9AELhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8570e309f60362fa6110c22797f25f5de885fa2ed092e407ea952d4487ceef73","last_reissued_at":"2026-05-18T03:42:22.174557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:22.174557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.6424","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGHShA1LIBoXgeAVy/O54//Wy/cdtvk81XxZumD7APMlMjf0gl1HWLlcNRuicuTD+prVpdGyRttI4709bOPOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:48:31.267654Z"},"content_sha256":"86bfdfdd5ba88a067c0b639eeadc5574593417c728b13727f8c4fbb75da8658c","schema_version":"1.0","event_id":"sha256:86bfdfdd5ba88a067c0b639eeadc5574593417c728b13727f8c4fbb75da8658c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QVYOGCPWANRPUYIQYITZP4S7LX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cotorsion pairs and t-structures in a $2-$Calabi-Yau triangulated category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Bin Zhu, Yu Zhou","submitted_at":"2012-10-24T02:53:07Z","abstract_excerpt":"For a Calabi-Yau triangulated category $\\mathcal{C}$ of Calabi-Yau dimension $d$ with a $d-$cluster tilting subcategory $\\mathcal{T}$, it is proved that the decomposition of $\\mathcal{C}$ is determined by the special decomposition of $\\mathcal{T}$, namely, $\\mathcal{C}=\\oplus_{i\\in I}\\mathcal{C}_i$, where $\\mathcal{C}_i, i\\in I$ are triangulated subcategories, if and only if $\\mathcal{T}=\\oplus_{i\\in I}\\mathcal{T}_i,$ where $\\mathcal{T}_i, i\\in I$ are subcategories with $Hom_{\\mathcal{C}}(\\mathcal{T}_i[t],\\mathcal{T}_j)=0, \\forall 1\\leq t\\leq d-2$ and $i\\not= j.$ This induces that the Gabriel "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6424","kind":"arxiv","version":2},"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":"2026-05-18T03:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZpnzOAr5VgWrnunK9xtSjJzg+ud2d0pLKDqaLEzdh9nJIsTKMBxJVYrAaLHfueqVRvDIT++3YrRTKibj9H5LDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:48:31.268001Z"},"content_sha256":"392e8a85ce9ec3f88eb9a13e90a8598c7433a2639072d7bb3ababcfd8bc56abd","schema_version":"1.0","event_id":"sha256:392e8a85ce9ec3f88eb9a13e90a8598c7433a2639072d7bb3ababcfd8bc56abd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVYOGCPWANRPUYIQYITZP4S7LX/bundle.json","state_url":"https://pith.science/pith/QVYOGCPWANRPUYIQYITZP4S7LX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVYOGCPWANRPUYIQYITZP4S7LX/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":"2026-06-04T14:48:31Z","links":{"resolver":"https://pith.science/pith/QVYOGCPWANRPUYIQYITZP4S7LX","bundle":"https://pith.science/pith/QVYOGCPWANRPUYIQYITZP4S7LX/bundle.json","state":"https://pith.science/pith/QVYOGCPWANRPUYIQYITZP4S7LX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVYOGCPWANRPUYIQYITZP4S7LX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QVYOGCPWANRPUYIQYITZP4S7LX","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":"2d99b77ff8bb7b45d8dd88efae94d75f02fe355258f7033dcfa4cc778ec4bb70","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-24T02:53:07Z","title_canon_sha256":"6e61d46587b9e5828ff3a85db82931dda10e32f6e7869fa3cc9325d0faea1c58"},"schema_version":"1.0","source":{"id":"1210.6424","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6424","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6424v2","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6424","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"QVYOGCPWANRP","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QVYOGCPWANRPUYIQ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QVYOGCPW","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:392e8a85ce9ec3f88eb9a13e90a8598c7433a2639072d7bb3ababcfd8bc56abd","target":"graph","created_at":"2026-05-18T03:42:22Z","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":"For a Calabi-Yau triangulated category $\\mathcal{C}$ of Calabi-Yau dimension $d$ with a $d-$cluster tilting subcategory $\\mathcal{T}$, it is proved that the decomposition of $\\mathcal{C}$ is determined by the special decomposition of $\\mathcal{T}$, namely, $\\mathcal{C}=\\oplus_{i\\in I}\\mathcal{C}_i$, where $\\mathcal{C}_i, i\\in I$ are triangulated subcategories, if and only if $\\mathcal{T}=\\oplus_{i\\in I}\\mathcal{T}_i,$ where $\\mathcal{T}_i, i\\in I$ are subcategories with $Hom_{\\mathcal{C}}(\\mathcal{T}_i[t],\\mathcal{T}_j)=0, \\forall 1\\leq t\\leq d-2$ and $i\\not= j.$ This induces that the Gabriel ","authors_text":"Bin Zhu, Yu Zhou","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-24T02:53:07Z","title":"Cotorsion pairs and t-structures in a $2-$Calabi-Yau triangulated category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6424","kind":"arxiv","version":2},"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":"sha256:86bfdfdd5ba88a067c0b639eeadc5574593417c728b13727f8c4fbb75da8658c","target":"record","created_at":"2026-05-18T03:42:22Z","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":"2d99b77ff8bb7b45d8dd88efae94d75f02fe355258f7033dcfa4cc778ec4bb70","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-24T02:53:07Z","title_canon_sha256":"6e61d46587b9e5828ff3a85db82931dda10e32f6e7869fa3cc9325d0faea1c58"},"schema_version":"1.0","source":{"id":"1210.6424","kind":"arxiv","version":2}},"canonical_sha256":"8570e309f60362fa6110c22797f25f5de885fa2ed092e407ea952d4487ceef73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8570e309f60362fa6110c22797f25f5de885fa2ed092e407ea952d4487ceef73","first_computed_at":"2026-05-18T03:42:22.174557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:22.174557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cUZErqmSpNQFRfoLdw81nK7CgxHqR8wiPvLFO4NVi6AFct/N/qiygJgcObKckndE5BNPIQNxSXR4oSe9AELhCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:22.175617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6424","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86bfdfdd5ba88a067c0b639eeadc5574593417c728b13727f8c4fbb75da8658c","sha256:392e8a85ce9ec3f88eb9a13e90a8598c7433a2639072d7bb3ababcfd8bc56abd"],"state_sha256":"522bc70318170a25573d27f72770de19dc0bc885b3ed08896f1446b325420689"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zYctP7wEZ1u6354eX8aaECnEcUQOX3wU2fHZR0M5cvkioVWcJJHbjG3CeoMvZSxWY6aEZ14NxmOETVwUfGOWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T14:48:31.269960Z","bundle_sha256":"fb7368fee92da2b4fbce75cc3a191163fff1e71ebd7b981bfe801613e7d8b73b"}}