{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XCH7QNEUVGSHT4MTPWRCANU4JV","short_pith_number":"pith:XCH7QNEU","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"},"canonical_sha256":"b88ff83494a9a479f1937da220369c4d7779bd48f996534edaa7339f38127947","source":{"kind":"arxiv","id":"1111.4003","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4003","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4003v3","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4003","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"XCH7QNEUVGSH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XCH7QNEUVGSHT4MT","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XCH7QNEU","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XCH7QNEUVGSHT4MTPWRCANU4JV","target":"record","payload":{"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"},"canonical_sha256":"b88ff83494a9a479f1937da220369c4d7779bd48f996534edaa7339f38127947","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"},"source_kind":"arxiv","source_id":"1111.4003","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBczjqPGC2/53nrYmY2LXHnb6k3WpdwNAl+S3LMjTfMItZpLhScA+y0rcNSMoPQ1S0Ku5clfe6boJyYDgmoFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:59:11.661053Z"},"content_sha256":"621804345917e6e7a0c44e6900f98a5daf4248b28dc3b5dff2c4bea890098d7a","schema_version":"1.0","event_id":"sha256:621804345917e6e7a0c44e6900f98a5daf4248b28dc3b5dff2c4bea890098d7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XCH7QNEUVGSHT4MTPWRCANU4JV","target":"graph","payload":{"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. Blumberg, Michael A. Mandell","submitted_at":"2011-11-17T01:39:35Z","abstract_excerpt":"We prove a conjecture of Hesselholt and Ausoni-Rognes, establishing localization cofiber sequences of spectra for THH(ku) and TC(ku). 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4003","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rHxh2g8923c9bRhelCBoBRfIIp41aTyLFjRbvKyvExvk/vC0w8ufSWNNr12idZCB9edk7Qs9dRnoTImWrMHXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:59:11.661414Z"},"content_sha256":"8f0c888ce7763f1d1f7b7ba2ca2d12069f45c47b6954b5729125e6eb015aa414","schema_version":"1.0","event_id":"sha256:8f0c888ce7763f1d1f7b7ba2ca2d12069f45c47b6954b5729125e6eb015aa414"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCH7QNEUVGSHT4MTPWRCANU4JV/bundle.json","state_url":"https://pith.science/pith/XCH7QNEUVGSHT4MTPWRCANU4JV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCH7QNEUVGSHT4MTPWRCANU4JV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T10:59:11Z","links":{"resolver":"https://pith.science/pith/XCH7QNEUVGSHT4MTPWRCANU4JV","bundle":"https://pith.science/pith/XCH7QNEUVGSHT4MTPWRCANU4JV/bundle.json","state":"https://pith.science/pith/XCH7QNEUVGSHT4MTPWRCANU4JV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCH7QNEUVGSHT4MTPWRCANU4JV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XCH7QNEUVGSHT4MTPWRCANU4JV","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":"32dd6d5e89396328bb4cda0cef32cba4d349e449b987a773181823fd0d474aea","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-11-17T01:39:35Z","title_canon_sha256":"3273d2ef02f200980ba16cb60cbc6c92af4ea952df2173a737535119f4e28bee"},"schema_version":"1.0","source":{"id":"1111.4003","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4003","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4003v3","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4003","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"XCH7QNEUVGSH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XCH7QNEUVGSHT4MT","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XCH7QNEU","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:8f0c888ce7763f1d1f7b7ba2ca2d12069f45c47b6954b5729125e6eb015aa414","target":"graph","created_at":"2026-05-18T02:56:11Z","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"},"paper":{"abstract_excerpt":"We prove a conjecture of Hesselholt and Ausoni-Rognes, establishing localization cofiber sequences of spectra for THH(ku) and TC(ku). 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","authors_text":"Andrew J. Blumberg, Michael A. Mandell","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-11-17T01:39:35Z","title":"Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4003","kind":"arxiv","version":3},"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":"sha256:621804345917e6e7a0c44e6900f98a5daf4248b28dc3b5dff2c4bea890098d7a","target":"record","created_at":"2026-05-18T02:56:11Z","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":"32dd6d5e89396328bb4cda0cef32cba4d349e449b987a773181823fd0d474aea","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-11-17T01:39:35Z","title_canon_sha256":"3273d2ef02f200980ba16cb60cbc6c92af4ea952df2173a737535119f4e28bee"},"schema_version":"1.0","source":{"id":"1111.4003","kind":"arxiv","version":3}},"canonical_sha256":"b88ff83494a9a479f1937da220369c4d7779bd48f996534edaa7339f38127947","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b88ff83494a9a479f1937da220369c4d7779bd48f996534edaa7339f38127947","first_computed_at":"2026-05-18T02:56:11.865486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:11.865486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W9vjl9Wed72QFfx9wAdgtNAoTofSTPhwOvq5wVSHUsad5ZQhQTqwx7UDwqiJHlIC8JceaTmHMj7vs8ViiJ9VDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:11.865954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4003","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:621804345917e6e7a0c44e6900f98a5daf4248b28dc3b5dff2c4bea890098d7a","sha256:8f0c888ce7763f1d1f7b7ba2ca2d12069f45c47b6954b5729125e6eb015aa414"],"state_sha256":"73b8ca44d97318dd7d2cdb0a0c1d8ffe6083873ca02bdada5108bae59c31eca1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V7bgCONYyH32X61N3zqA9lYW4v/scdaD8ZrI9MeU+c52KAD3Dwou//P3p/Agr30zo0VFe/ou5Vv6bwS6yNv8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:59:11.663497Z","bundle_sha256":"f7bcb905067ace3b271efef5dda42c5c32e31c9b587a39d7ff5b6fb24fc2d33d"}}