{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:S7XUHPJWIHENRRVWK7VOHLP2AW","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":"f76a2dec92b9246fe3e6103659380b44c1caa0640a255d98128d5a285f979460","cross_cats_sorted":["math.AT","math.CT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-11-22T06:48:41Z","title_canon_sha256":"c20fe6c78df976aaa9cd2049af2daa865be626f34605396d2d2e0edcb2b8f488"},"schema_version":"1.0","source":{"id":"2411.14761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14761","created_at":"2026-07-05T09:39:11Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14761v1","created_at":"2026-07-05T09:39:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14761","created_at":"2026-07-05T09:39:11Z"},{"alias_kind":"pith_short_12","alias_value":"S7XUHPJWIHEN","created_at":"2026-07-05T09:39:11Z"},{"alias_kind":"pith_short_16","alias_value":"S7XUHPJWIHENRRVW","created_at":"2026-07-05T09:39:11Z"},{"alias_kind":"pith_short_8","alias_value":"S7XUHPJW","created_at":"2026-07-05T09:39:11Z"}],"graph_snapshots":[{"event_id":"sha256:8e1d6a9a0f3cff9dd4bed375776ae8ab5a1b4c2aed32aac47dd304b5b0098994","target":"graph","created_at":"2026-07-05T09:39:11Z","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/2411.14761/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\hat{R}$ be the $I$-adic completion of a commutative ring $R$ with respect to a finitely generated ideal $I$. We give a necessary and sufficient criterion for the category of perfect complexes over $\\hat{R}$ to be equivalent to the subcategory of dualizable objects in the derived category of $I$-complete complexes of $R$-modules. Our criterion is always satisfied when $R$ is noetherian. When specialized to $R$ local and noetherian and to $I$ the maximal ideal, our theorem recovers a recent result of Benson, Iyengar, Krause and Pevtsova.","authors_text":"Beren Sanders, Paul Balmer","cross_cats":["math.AT","math.CT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-11-22T06:48:41Z","title":"Perfect complexes and completion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14761","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":"sha256:0f50af92cf3902f38b8c221b099f22cf8d997980a2ce2ae4e1ae447f9a7ee4d0","target":"record","created_at":"2026-07-05T09:39:11Z","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":"f76a2dec92b9246fe3e6103659380b44c1caa0640a255d98128d5a285f979460","cross_cats_sorted":["math.AT","math.CT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-11-22T06:48:41Z","title_canon_sha256":"c20fe6c78df976aaa9cd2049af2daa865be626f34605396d2d2e0edcb2b8f488"},"schema_version":"1.0","source":{"id":"2411.14761","kind":"arxiv","version":1}},"canonical_sha256":"97ef43bd3641c8d8c6b657eae3adfa05822ce5aa9ee20a90bbab07017f4a465b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97ef43bd3641c8d8c6b657eae3adfa05822ce5aa9ee20a90bbab07017f4a465b","first_computed_at":"2026-07-05T09:39:11.548067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:11.548067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VijK3Bks8eISYRv6hkC7uRl7kbkJ5u8Y4ztj0xoA6q4p/iDZ3Au+XM3Py47JdwXchU08uTqiYWfbd95pE2MxBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:11.548515Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f50af92cf3902f38b8c221b099f22cf8d997980a2ce2ae4e1ae447f9a7ee4d0","sha256:8e1d6a9a0f3cff9dd4bed375776ae8ab5a1b4c2aed32aac47dd304b5b0098994"],"state_sha256":"7daa6eefe536c16ad3123182f8afd630776299a96306d36d0e8dd9bd6f384147"}