{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:S6EMOQCITYCDONKKPZ75PNFKQV","short_pith_number":"pith:S6EMOQCI","canonical_record":{"source":{"id":"math/0604412","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"2006-04-19T19:13:39Z","cross_cats_sorted":[],"title_canon_sha256":"e96f9b3229e17d23130b5bc0c393e125c7a9b2c5d178843ad9545b4e06f6e277","abstract_canon_sha256":"5f00bc8f4e050e6104eee666a4308a270d8637898d4b938e799243489bf7f1c1"},"schema_version":"1.0"},"canonical_sha256":"9788c740489e0437354a7e7fd7b4aa855885cfd7769b44ed6f2690ca30e071da","source":{"kind":"arxiv","id":"math/0604412","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604412","created_at":"2026-05-18T04:38:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604412v3","created_at":"2026-05-18T04:38:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604412","created_at":"2026-05-18T04:38:05Z"},{"alias_kind":"pith_short_12","alias_value":"S6EMOQCITYCD","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"S6EMOQCITYCDONKK","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"S6EMOQCI","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:S6EMOQCITYCDONKKPZ75PNFKQV","target":"record","payload":{"canonical_record":{"source":{"id":"math/0604412","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"2006-04-19T19:13:39Z","cross_cats_sorted":[],"title_canon_sha256":"e96f9b3229e17d23130b5bc0c393e125c7a9b2c5d178843ad9545b4e06f6e277","abstract_canon_sha256":"5f00bc8f4e050e6104eee666a4308a270d8637898d4b938e799243489bf7f1c1"},"schema_version":"1.0"},"canonical_sha256":"9788c740489e0437354a7e7fd7b4aa855885cfd7769b44ed6f2690ca30e071da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:05.153962Z","signature_b64":"/ATc22lIIssSydjzTob9tBPW/qIkHpZ6pkfl5dlPJ+0+1/H5Ch3MhcYfi43T8cFTpeJxVArkqLwwzeP35LuYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9788c740489e0437354a7e7fd7b4aa855885cfd7769b44ed6f2690ca30e071da","last_reissued_at":"2026-05-18T04:38:05.153243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:05.153243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0604412","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:38:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BL0s9LiYHfDly+dUn+7+oeWZd8oNpNBmB2ewODRGtsIPujDGEzDSMKCmLwcJDNRMcV/1cQyA9nF3J1K3gX+dDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:28:59.893084Z"},"content_sha256":"f2a6331a6fecba5b53612a025f06e3a9005c1af55c704d42fd75bc22367489c2","schema_version":"1.0","event_id":"sha256:f2a6331a6fecba5b53612a025f06e3a9005c1af55c704d42fd75bc22367489c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:S6EMOQCITYCDONKKPZ75PNFKQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal coefficient theorem in triangulated categories","license":"","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Maria Julia Redondo, Teimuraz Pirashvili","submitted_at":"2006-04-19T19:13:39Z","abstract_excerpt":"Let T be a triangulated category, A a graded abelian category and h: T -> A a homology theory on T with values in A. If the functor h reflects isomorphisms, is full and is such that for any object x in A there is an object X in T with an isomorphism between h(X) and x, we prove that A is a hereditary abelian category and the ideal Ker(h) is a square zero ideal which as a bifunctor on T is isomorphic to Ext^1_A(h(-)[1], h(-))."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604412","kind":"arxiv","version":3},"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":"2026-05-18T04:38:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mX6TtbOHnv48+pwPftasTykMuaJccUtxZFgezTEtoaPjsGa6Orb5fuB4Z8NEpbnX5KhZxPVPfZuDh/kJCwZ9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:28:59.893677Z"},"content_sha256":"4c0b20577de8127405a3ceb56fcbd5c7a000f62a0fb5972f7c551b32b3e107df","schema_version":"1.0","event_id":"sha256:4c0b20577de8127405a3ceb56fcbd5c7a000f62a0fb5972f7c551b32b3e107df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S6EMOQCITYCDONKKPZ75PNFKQV/bundle.json","state_url":"https://pith.science/pith/S6EMOQCITYCDONKKPZ75PNFKQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S6EMOQCITYCDONKKPZ75PNFKQV/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":"2026-05-31T13:28:59Z","links":{"resolver":"https://pith.science/pith/S6EMOQCITYCDONKKPZ75PNFKQV","bundle":"https://pith.science/pith/S6EMOQCITYCDONKKPZ75PNFKQV/bundle.json","state":"https://pith.science/pith/S6EMOQCITYCDONKKPZ75PNFKQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S6EMOQCITYCDONKKPZ75PNFKQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:S6EMOQCITYCDONKKPZ75PNFKQV","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":"5f00bc8f4e050e6104eee666a4308a270d8637898d4b938e799243489bf7f1c1","cross_cats_sorted":[],"license":"","primary_cat":"math.CT","submitted_at":"2006-04-19T19:13:39Z","title_canon_sha256":"e96f9b3229e17d23130b5bc0c393e125c7a9b2c5d178843ad9545b4e06f6e277"},"schema_version":"1.0","source":{"id":"math/0604412","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604412","created_at":"2026-05-18T04:38:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604412v3","created_at":"2026-05-18T04:38:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604412","created_at":"2026-05-18T04:38:05Z"},{"alias_kind":"pith_short_12","alias_value":"S6EMOQCITYCD","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"S6EMOQCITYCDONKK","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"S6EMOQCI","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:4c0b20577de8127405a3ceb56fcbd5c7a000f62a0fb5972f7c551b32b3e107df","target":"graph","created_at":"2026-05-18T04:38:05Z","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":"Let T be a triangulated category, A a graded abelian category and h: T -> A a homology theory on T with values in A. If the functor h reflects isomorphisms, is full and is such that for any object x in A there is an object X in T with an isomorphism between h(X) and x, we prove that A is a hereditary abelian category and the ideal Ker(h) is a square zero ideal which as a bifunctor on T is isomorphic to Ext^1_A(h(-)[1], h(-)).","authors_text":"Maria Julia Redondo, Teimuraz Pirashvili","cross_cats":[],"headline":"","license":"","primary_cat":"math.CT","submitted_at":"2006-04-19T19:13:39Z","title":"Universal coefficient theorem in triangulated categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604412","kind":"arxiv","version":3},"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:f2a6331a6fecba5b53612a025f06e3a9005c1af55c704d42fd75bc22367489c2","target":"record","created_at":"2026-05-18T04:38:05Z","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":"5f00bc8f4e050e6104eee666a4308a270d8637898d4b938e799243489bf7f1c1","cross_cats_sorted":[],"license":"","primary_cat":"math.CT","submitted_at":"2006-04-19T19:13:39Z","title_canon_sha256":"e96f9b3229e17d23130b5bc0c393e125c7a9b2c5d178843ad9545b4e06f6e277"},"schema_version":"1.0","source":{"id":"math/0604412","kind":"arxiv","version":3}},"canonical_sha256":"9788c740489e0437354a7e7fd7b4aa855885cfd7769b44ed6f2690ca30e071da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9788c740489e0437354a7e7fd7b4aa855885cfd7769b44ed6f2690ca30e071da","first_computed_at":"2026-05-18T04:38:05.153243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:05.153243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ATc22lIIssSydjzTob9tBPW/qIkHpZ6pkfl5dlPJ+0+1/H5Ch3MhcYfi43T8cFTpeJxVArkqLwwzeP35LuYBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:05.153962Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604412","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2a6331a6fecba5b53612a025f06e3a9005c1af55c704d42fd75bc22367489c2","sha256:4c0b20577de8127405a3ceb56fcbd5c7a000f62a0fb5972f7c551b32b3e107df"],"state_sha256":"04607db17b35bb27209845382a23bc44d7a514ccefe9377277e20cf17c23fec6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8VREaGrOLj0aNhC0x5HZELl01Ws+M8RBg6pADxwfvIW1LI5wZN5Cpb3PgblrbRKN41jvnKFOet8vxsgxAPxLDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:28:59.897390Z","bundle_sha256":"96db6f112cf998642b777a8c31b79db01d89df8dc6796d1f9f105fc4eb8b2828"}}