{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SRROFBU42B7WKC4AQJGOUGO2FU","short_pith_number":"pith:SRROFBU4","schema_version":"1.0","canonical_sha256":"9462e2869cd07f650b80824cea19da2d30725617460a1b675f14943ece9e6bb3","source":{"kind":"arxiv","id":"1407.3765","version":2},"attestation_state":"computed","paper":{"title":"Notes on Triangulated Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Tobias Fritz","submitted_at":"2014-07-14T18:56:07Z","abstract_excerpt":"We give an elementary introduction to the theory of triangulated categories covering their axioms, homological algebra in triangulated categories, triangulated subcategories, and Verdier localization. We try to use a minimal set of axioms for triangulated categories and derive all other statements from these, including the existence of biproducts. We conclude with a list of examples."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.3765","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-07-14T18:56:07Z","cross_cats_sorted":[],"title_canon_sha256":"0de65fbb26fac4c98447735916d8a9c2b200db4ba591897bde2155f4f0caa784","abstract_canon_sha256":"25fa853bb90a6308a092bbbaa756748fd1c38e54ac4d69eb7e5a750a36a67969"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:31.044304Z","signature_b64":"ZKP1LM2tWkUwCwLioL+6SbqmytUsBgdjPe9xzLd9ekLA4GZ+3nW/EYu19ontWG7FN/G8maw5V5K7VCBU9FXdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9462e2869cd07f650b80824cea19da2d30725617460a1b675f14943ece9e6bb3","last_reissued_at":"2026-05-18T02:47:31.043884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:31.043884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Notes on Triangulated Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Tobias Fritz","submitted_at":"2014-07-14T18:56:07Z","abstract_excerpt":"We give an elementary introduction to the theory of triangulated categories covering their axioms, homological algebra in triangulated categories, triangulated subcategories, and Verdier localization. We try to use a minimal set of axioms for triangulated categories and derive all other statements from these, including the existence of biproducts. We conclude with a list of examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3765","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.3765","created_at":"2026-05-18T02:47:31.043947+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.3765v2","created_at":"2026-05-18T02:47:31.043947+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3765","created_at":"2026-05-18T02:47:31.043947+00:00"},{"alias_kind":"pith_short_12","alias_value":"SRROFBU42B7W","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SRROFBU42B7WKC4A","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SRROFBU4","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.11235","citing_title":"Pro-$p$ Iwahori-Hecke modules in semisimple rank one and singularity categories","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SRROFBU42B7WKC4AQJGOUGO2FU","json":"https://pith.science/pith/SRROFBU42B7WKC4AQJGOUGO2FU.json","graph_json":"https://pith.science/api/pith-number/SRROFBU42B7WKC4AQJGOUGO2FU/graph.json","events_json":"https://pith.science/api/pith-number/SRROFBU42B7WKC4AQJGOUGO2FU/events.json","paper":"https://pith.science/paper/SRROFBU4"},"agent_actions":{"view_html":"https://pith.science/pith/SRROFBU42B7WKC4AQJGOUGO2FU","download_json":"https://pith.science/pith/SRROFBU42B7WKC4AQJGOUGO2FU.json","view_paper":"https://pith.science/paper/SRROFBU4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.3765&json=true","fetch_graph":"https://pith.science/api/pith-number/SRROFBU42B7WKC4AQJGOUGO2FU/graph.json","fetch_events":"https://pith.science/api/pith-number/SRROFBU42B7WKC4AQJGOUGO2FU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SRROFBU42B7WKC4AQJGOUGO2FU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SRROFBU42B7WKC4AQJGOUGO2FU/action/storage_attestation","attest_author":"https://pith.science/pith/SRROFBU42B7WKC4AQJGOUGO2FU/action/author_attestation","sign_citation":"https://pith.science/pith/SRROFBU42B7WKC4AQJGOUGO2FU/action/citation_signature","submit_replication":"https://pith.science/pith/SRROFBU42B7WKC4AQJGOUGO2FU/action/replication_record"}},"created_at":"2026-05-18T02:47:31.043947+00:00","updated_at":"2026-05-18T02:47:31.043947+00:00"}