{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:HSGZFEUBJU3G2XQ5WCVAWTABXA","short_pith_number":"pith:HSGZFEUB","schema_version":"1.0","canonical_sha256":"3c8d9292814d366d5e1db0aa0b4c01b812f6bee3842d7c3e11e8099a15726587","source":{"kind":"arxiv","id":"2502.09462","version":1},"attestation_state":"computed","paper":{"title":"Thomason's completion for K-theory and cyclic homology of quotient stacks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Amalendu Krishna, Ritankar Nath","submitted_at":"2025-02-13T16:28:19Z","abstract_excerpt":"We prove several completion theorems for equivariant K-theory\n  and cyclic homology of schemes with group action over a field. One of these\n  shows that for an algebraic space over a field acted upon by a linear algebraic\n  group, the derived completion of equivariant K'-theory at the\n  augmentation ideal of the representation ring of the group coincides with the\n  ordinary K'-theory of the bar construction associated to the group action.\n  This provides a solution to Thomason's completion problem. For action with finite\n  stabilizers, we show that the equivariant K-theory and cyclic homology "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2502.09462","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-02-13T16:28:19Z","cross_cats_sorted":[],"title_canon_sha256":"58839df88b96b46176e0c36b561967634b9515cb8f3d20e90f7bda419f01301a","abstract_canon_sha256":"f9f0660b5ea6dc74e1e21e6a11979afab4afa214e3f2e84766698bf8cdd68446"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:13:58.123041Z","signature_b64":"7UKTlxWbcuJQFXuFH/jdl2Qf6kaB6iq6LCrTXVHqZIWQ0yiRWxFlSBf1wa8fxDGLI48kYqyC1uMB8NEosz/pDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c8d9292814d366d5e1db0aa0b4c01b812f6bee3842d7c3e11e8099a15726587","last_reissued_at":"2026-07-05T10:13:58.122591Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:13:58.122591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thomason's completion for K-theory and cyclic homology of quotient stacks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Amalendu Krishna, Ritankar Nath","submitted_at":"2025-02-13T16:28:19Z","abstract_excerpt":"We prove several completion theorems for equivariant K-theory\n  and cyclic homology of schemes with group action over a field. One of these\n  shows that for an algebraic space over a field acted upon by a linear algebraic\n  group, the derived completion of equivariant K'-theory at the\n  augmentation ideal of the representation ring of the group coincides with the\n  ordinary K'-theory of the bar construction associated to the group action.\n  This provides a solution to Thomason's completion problem. For action with finite\n  stabilizers, we show that the equivariant K-theory and cyclic homology "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.09462","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.09462/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2502.09462","created_at":"2026-07-05T10:13:58.122647+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.09462v1","created_at":"2026-07-05T10:13:58.122647+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.09462","created_at":"2026-07-05T10:13:58.122647+00:00"},{"alias_kind":"pith_short_12","alias_value":"HSGZFEUBJU3G","created_at":"2026-07-05T10:13:58.122647+00:00"},{"alias_kind":"pith_short_16","alias_value":"HSGZFEUBJU3G2XQ5","created_at":"2026-07-05T10:13:58.122647+00:00"},{"alias_kind":"pith_short_8","alias_value":"HSGZFEUB","created_at":"2026-07-05T10:13:58.122647+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HSGZFEUBJU3G2XQ5WCVAWTABXA","json":"https://pith.science/pith/HSGZFEUBJU3G2XQ5WCVAWTABXA.json","graph_json":"https://pith.science/api/pith-number/HSGZFEUBJU3G2XQ5WCVAWTABXA/graph.json","events_json":"https://pith.science/api/pith-number/HSGZFEUBJU3G2XQ5WCVAWTABXA/events.json","paper":"https://pith.science/paper/HSGZFEUB"},"agent_actions":{"view_html":"https://pith.science/pith/HSGZFEUBJU3G2XQ5WCVAWTABXA","download_json":"https://pith.science/pith/HSGZFEUBJU3G2XQ5WCVAWTABXA.json","view_paper":"https://pith.science/paper/HSGZFEUB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.09462&json=true","fetch_graph":"https://pith.science/api/pith-number/HSGZFEUBJU3G2XQ5WCVAWTABXA/graph.json","fetch_events":"https://pith.science/api/pith-number/HSGZFEUBJU3G2XQ5WCVAWTABXA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HSGZFEUBJU3G2XQ5WCVAWTABXA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HSGZFEUBJU3G2XQ5WCVAWTABXA/action/storage_attestation","attest_author":"https://pith.science/pith/HSGZFEUBJU3G2XQ5WCVAWTABXA/action/author_attestation","sign_citation":"https://pith.science/pith/HSGZFEUBJU3G2XQ5WCVAWTABXA/action/citation_signature","submit_replication":"https://pith.science/pith/HSGZFEUBJU3G2XQ5WCVAWTABXA/action/replication_record"}},"created_at":"2026-07-05T10:13:58.122647+00:00","updated_at":"2026-07-05T10:13:58.122647+00:00"}