{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AAHFCFDVYH66GNJHAMFHLU5LEN","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":"a1092f636aa779bf438df51886837c98c3787beedaa58d24d36ea971f08bfe90","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-06-27T13:53:17Z","title_canon_sha256":"1767fad88484f0cf433e4d2a9098985dbb5d011c3de6d33d9727b64363d6b801"},"schema_version":"1.0","source":{"id":"1606.08279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08279","created_at":"2026-05-17T23:53:52Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08279v1","created_at":"2026-05-17T23:53:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08279","created_at":"2026-05-17T23:53:52Z"},{"alias_kind":"pith_short_12","alias_value":"AAHFCFDVYH66","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"AAHFCFDVYH66GNJH","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"AAHFCFDV","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:54d92a4d06e77d4158be53e2eee3718f6e971c5eb28aec8fbc19f83dffcf71ac","target":"graph","created_at":"2026-05-17T23:53:52Z","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 call a triangulated category \\emph{hereditary} provided that it is equivalent to the bounded derived category of a hereditary abelian category, where the equivalence is required to commute with the translation functors. If the triangulated category is algebraical, we may replace the equivalence by a triangle equivalence. We give two intrinsic characterizations of hereditary triangulated categories using a certain full subcategory and the non-existence of certain paths. We apply them to piecewise hereditary algebras.","authors_text":"Claus Michael Ringel, Xiao-Wu Chen","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-06-27T13:53:17Z","title":"Hereditary triangulated categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08279","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:dd352b5ad88ab5110a1a6f7ebb2cc5f554082c0928fdfc7dada47e23d6fcf6d9","target":"record","created_at":"2026-05-17T23:53:52Z","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":"a1092f636aa779bf438df51886837c98c3787beedaa58d24d36ea971f08bfe90","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-06-27T13:53:17Z","title_canon_sha256":"1767fad88484f0cf433e4d2a9098985dbb5d011c3de6d33d9727b64363d6b801"},"schema_version":"1.0","source":{"id":"1606.08279","kind":"arxiv","version":1}},"canonical_sha256":"000e511475c1fde33527030a75d3ab23610e380d4cb9a8ec437ca4de7a1b8be4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"000e511475c1fde33527030a75d3ab23610e380d4cb9a8ec437ca4de7a1b8be4","first_computed_at":"2026-05-17T23:53:52.538740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:52.538740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LFGgCiUd3N3aABiQeGqpx2aYCOlwjRlHLaAhaeQsj8o1c7w4lBReKQ2qvL0g/CdOkweHCTy0XO44g1kHN586Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:52.539282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd352b5ad88ab5110a1a6f7ebb2cc5f554082c0928fdfc7dada47e23d6fcf6d9","sha256:54d92a4d06e77d4158be53e2eee3718f6e971c5eb28aec8fbc19f83dffcf71ac"],"state_sha256":"7c43f016b075445095ca7b4e4601ede784b4d6b0c06a58d06f25708c47e05a4b"}