{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DSRVTMSEEJQABYEYNXQG4DPPAS","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":"617a2d6709ecd9dfab23092791e742081789a88cde6689e170b9df430cee692d","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-05-12T19:14:13Z","title_canon_sha256":"2934015102b3ceb9549200593a1f188d397815398e30709a9e19368a1084bd4d"},"schema_version":"1.0","source":{"id":"1605.03934","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03934","created_at":"2026-07-05T00:29:17Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03934v8","created_at":"2026-07-05T00:29:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03934","created_at":"2026-07-05T00:29:17Z"},{"alias_kind":"pith_short_12","alias_value":"DSRVTMSEEJQA","created_at":"2026-07-05T00:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DSRVTMSEEJQABYEY","created_at":"2026-07-05T00:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DSRVTMSE","created_at":"2026-07-05T00:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:4470e2139759fd4df56d30b75649cc523aca797b64accd0fb50657c251881de4","target":"graph","created_at":"2026-07-05T00:29:17Z","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/1605.03934/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is devoted to the more elementary aspects of the contramodule story, and can be viewed as an extended introduction to the more technically complicated arXiv:1503.05523. Reduced cotorsion abelian groups form an abelian category, which is in some sense covariantly dual to the category of torsion abelian groups. An abelian group is reduced cotorsion if and only if it is isomorphic to a product of p-contramodule abelian groups over prime numbers p. Any p-contraadjusted abelian group is p-adically complete, and any p-adically separated and complete group is a p-contramodule, but the conv","authors_text":"Leonid Positselski","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-05-12T19:14:13Z","title":"Contraadjusted modules, contramodules, and reduced cotorsion modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03934","kind":"arxiv","version":8},"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":"sha256:31d96d9ab3231e81ef271b535d30bdaf0aca979e4603a331a7cfa6a740656a40","target":"record","created_at":"2026-07-05T00:29:17Z","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":"617a2d6709ecd9dfab23092791e742081789a88cde6689e170b9df430cee692d","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-05-12T19:14:13Z","title_canon_sha256":"2934015102b3ceb9549200593a1f188d397815398e30709a9e19368a1084bd4d"},"schema_version":"1.0","source":{"id":"1605.03934","kind":"arxiv","version":8}},"canonical_sha256":"1ca359b244226000e0986de06e0def0480d35be79b74344819c9747b63488ff7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ca359b244226000e0986de06e0def0480d35be79b74344819c9747b63488ff7","first_computed_at":"2026-07-05T00:29:17.638520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:29:17.638520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+NEFuYS2PIbjmRomDIgds12pDG7f0S7neVuqll5eubpDJNYt75k7roMFeFMcidCDN4co71V9Owzi1MIuIH2hCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:29:17.639033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03934","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31d96d9ab3231e81ef271b535d30bdaf0aca979e4603a331a7cfa6a740656a40","sha256:4470e2139759fd4df56d30b75649cc523aca797b64accd0fb50657c251881de4"],"state_sha256":"2b5dc5740f5a0cf4cf3cb4967712448defc531414590f941a57ef499b52edde5"}