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These sequences support Hesselholt's view of the map l to ku as a \"tamely ramified\" extension of ring spectra, and validate the hypotheses necessary for Ausoni's simplified computation of V(1)_* K(KU).\n  In order to make sense of the relative term THH(ku|KU) in the cofiber sequence and prove these results, we develop a theory of THH and TC of Waldhausen categories and prove the analogues of Waldhausen's theorems for K-theory. We resolve the longstanding confusio"},"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":"1111.4003","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-11-17T01:39:35Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"3273d2ef02f200980ba16cb60cbc6c92af4ea952df2173a737535119f4e28bee","abstract_canon_sha256":"32dd6d5e89396328bb4cda0cef32cba4d349e449b987a773181823fd0d474aea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:11.865954Z","signature_b64":"W9vjl9Wed72QFfx9wAdgtNAoTofSTPhwOvq5wVSHUsad5ZQhQTqwx7UDwqiJHlIC8JceaTmHMj7vs8ViiJ9VDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b88ff83494a9a479f1937da220369c4d7779bd48f996534edaa7339f38127947","last_reissued_at":"2026-05-18T02:56:11.865486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:11.865486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.KT","authors_text":"Andrew J. 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