{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7LXYOJIB4TZ6MR4ZERPHTYAS37","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":"6aaf6a70c185a2914ec77043045ea46f81ab0f7657174318bbea3af735145430","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-05-18T16:58:34Z","title_canon_sha256":"cc2acf3f41b08119a38df67c744c6f5147b17c0df2695fdcb987baafcc6fa88b"},"schema_version":"1.0","source":{"id":"1905.07612","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07612","created_at":"2026-07-05T03:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07612v5","created_at":"2026-07-05T03:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07612","created_at":"2026-07-05T03:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"7LXYOJIB4TZ6","created_at":"2026-07-05T03:48:35Z"},{"alias_kind":"pith_short_16","alias_value":"7LXYOJIB4TZ6MR4Z","created_at":"2026-07-05T03:48:35Z"},{"alias_kind":"pith_short_8","alias_value":"7LXYOJIB","created_at":"2026-07-05T03:48:35Z"}],"graph_snapshots":[{"event_id":"sha256:4d2d561940d3b21d0f73591b6f2e0edf51e61839bb268be2ce6d4e34a9fed2d4","target":"graph","created_at":"2026-07-05T03:48:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1905.07612/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce several classes of localizations (idempotent monads) on the category of groups and study their properties and relations. The most interesting class for us is the class of localizations which coincide with their zero derived functors. We call them right exact (in the sense of Keune). We prove that a right exact localization $L$ preserves the class of nilpotent groups and that for a finite $p$-group $G$ the map $G\\to LG$ is an epimorphism. We also prove that some examples of localizations (Baumslag's $P$-localization with respect to a set of primes $P,$ Bousfield's $HR$-localization","authors_text":"Danil Akhtiamov, Fedor Pavutnitskiy, Sergei O. Ivanov","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-05-18T16:58:34Z","title":"Right exact localizations of groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07612","kind":"arxiv","version":5},"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":"sha256:0f95c3f135b10fe4ee7a33a5f19812f8657003001a2d3d75db682e0c8dc984ec","target":"record","created_at":"2026-07-05T03:48:35Z","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":"6aaf6a70c185a2914ec77043045ea46f81ab0f7657174318bbea3af735145430","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-05-18T16:58:34Z","title_canon_sha256":"cc2acf3f41b08119a38df67c744c6f5147b17c0df2695fdcb987baafcc6fa88b"},"schema_version":"1.0","source":{"id":"1905.07612","kind":"arxiv","version":5}},"canonical_sha256":"faef872501e4f3e64799245e79e012dfe21a7ee05a28855c5abb3f4213c1d13c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faef872501e4f3e64799245e79e012dfe21a7ee05a28855c5abb3f4213c1d13c","first_computed_at":"2026-07-05T03:48:35.145690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:48:35.145690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5o1JBupOS7DS4mA15+JvauiSv+bbjqrFhteqzYKQeL4P2vyv/3YZQXZVuEhroW2GukqQG1OHbt4DJASnUkjfBw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:48:35.146081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07612","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f95c3f135b10fe4ee7a33a5f19812f8657003001a2d3d75db682e0c8dc984ec","sha256:4d2d561940d3b21d0f73591b6f2e0edf51e61839bb268be2ce6d4e34a9fed2d4"],"state_sha256":"e24085189540dd331f2d711ac477364eb23bb6ff830294917fd3bb60d04db966"}