{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UJPDW7CTFELVIZHAHTLVOLQYOX","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":"d828958b242701b0a34624fb747f6c21404e4038ea8b986d08bfba68f27f7578","cross_cats_sorted":["math.AT","math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-02-16T05:19:00Z","title_canon_sha256":"ceefad9fa73843ce2543af1f92cb70af372a487eda9d816331d0eb230e0e16ef"},"schema_version":"1.0","source":{"id":"1102.3240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3240","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3240v1","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3240","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"UJPDW7CTFELV","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UJPDW7CTFELVIZHA","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UJPDW7CT","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:ed88658ed86fb9e1fe76b59d2d003cde5355f4d1db4fe4f336dca561f2fc6417","target":"graph","created_at":"2026-05-17T23:53:36Z","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 prove for a large family of rings R that their lambda-pure global dimension is greater than one for each infinite regular cardinal lambda. This answers in negative a problem posed by Rosicky. The derived categories of such rings then do not satisfy the Adams lambda-representability for morphisms for any lambda. Equivalently, they are examples of well generated triangulated categories whose lambda-abelianization in the sense of Neeman is not a full functor for any lambda. In particular we show that given a compactly generated triangulated category, one may not be able to find a Rosicky funct","authors_text":"Jan Stovicek, Silvana Bazzoni","cross_cats":["math.AT","math.KT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-02-16T05:19:00Z","title":"On the abelianization of derived categories and a negative solution to Rosicky's problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3240","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:ce28760dd3b50649b328c7cfa466fde9be3c6754bfb5416a80d2bfc2e6c19535","target":"record","created_at":"2026-05-17T23:53:36Z","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":"d828958b242701b0a34624fb747f6c21404e4038ea8b986d08bfba68f27f7578","cross_cats_sorted":["math.AT","math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-02-16T05:19:00Z","title_canon_sha256":"ceefad9fa73843ce2543af1f92cb70af372a487eda9d816331d0eb230e0e16ef"},"schema_version":"1.0","source":{"id":"1102.3240","kind":"arxiv","version":1}},"canonical_sha256":"a25e3b7c5329175464e03cd7572e1875f3fe8b15e5837ed7bdfc7af6811cbe3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a25e3b7c5329175464e03cd7572e1875f3fe8b15e5837ed7bdfc7af6811cbe3e","first_computed_at":"2026-05-17T23:53:36.744405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.744405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dzgsy75/6y6oXg3uArXR9uELLyUAf57sYqMi/82xWSr3Uo5VUTb8m/1wwmmv/vfvRmv/eEgEdfkPHLXnjeagCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.745222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce28760dd3b50649b328c7cfa466fde9be3c6754bfb5416a80d2bfc2e6c19535","sha256:ed88658ed86fb9e1fe76b59d2d003cde5355f4d1db4fe4f336dca561f2fc6417"],"state_sha256":"b85f4107757cf1db2588365a3c99bcc5acab44363f38748f9ea714475a73d412"}