{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:3EZZ35SOH2KDBY3DJZZ6ISULIC","short_pith_number":"pith:3EZZ35SO","schema_version":"1.0","canonical_sha256":"d9339df64e3e9430e3634e73e44a8b4080decb295b18626389205f83eb3a8b48","source":{"kind":"arxiv","id":"0708.2160","version":1},"attestation_state":"computed","paper":{"title":"Rational algebraic K-theory of topological K-theory","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.KT","authors_text":"Christian Ausoni, John Rognes","submitted_at":"2007-08-16T14:39:43Z","abstract_excerpt":"We show that after rationalization there is a homotopy fiber sequence BBU -> K(ku) -> K(Z). We interpret this as a correspondence between the virtual 2-vector bundles over a space X and their associated anomaly bundles over the free loop space LX. We also rationally compute K(KU) by using the localization sequence, and K(MU) by a method that applies to all connective S-algebras."},"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":"0708.2160","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.KT","submitted_at":"2007-08-16T14:39:43Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"5c45eadf6a9883ff36542be68df85794a8d5d4f2fb529c0f2998daea18cf8628","abstract_canon_sha256":"5cbcafb0c492b78b5263539501a1c93082ad8fff6ffa9c9af015ad2c65916da3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:19.422029Z","signature_b64":"EKKZ0F6uCvpmeJ+DIV6PNA/ZxCnasCukUMy7v79Mvut8sWnfoZLXHgeLAdoIuCsabNRYIXvUQ+uSw/menCBiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9339df64e3e9430e3634e73e44a8b4080decb295b18626389205f83eb3a8b48","last_reissued_at":"2026-05-18T02:38:19.421379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:19.421379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational algebraic K-theory of topological K-theory","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.KT","authors_text":"Christian Ausoni, John Rognes","submitted_at":"2007-08-16T14:39:43Z","abstract_excerpt":"We show that after rationalization there is a homotopy fiber sequence BBU -> K(ku) -> K(Z). We interpret this as a correspondence between the virtual 2-vector bundles over a space X and their associated anomaly bundles over the free loop space LX. We also rationally compute K(KU) by using the localization sequence, and K(MU) by a method that applies to all connective S-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2160","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":""},"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":"0708.2160","created_at":"2026-05-18T02:38:19.421483+00:00"},{"alias_kind":"arxiv_version","alias_value":"0708.2160v1","created_at":"2026-05-18T02:38:19.421483+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2160","created_at":"2026-05-18T02:38:19.421483+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EZZ35SOH2KD","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EZZ35SOH2KDBY3D","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EZZ35SO","created_at":"2026-05-18T12:25:54.717736+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/3EZZ35SOH2KDBY3DJZZ6ISULIC","json":"https://pith.science/pith/3EZZ35SOH2KDBY3DJZZ6ISULIC.json","graph_json":"https://pith.science/api/pith-number/3EZZ35SOH2KDBY3DJZZ6ISULIC/graph.json","events_json":"https://pith.science/api/pith-number/3EZZ35SOH2KDBY3DJZZ6ISULIC/events.json","paper":"https://pith.science/paper/3EZZ35SO"},"agent_actions":{"view_html":"https://pith.science/pith/3EZZ35SOH2KDBY3DJZZ6ISULIC","download_json":"https://pith.science/pith/3EZZ35SOH2KDBY3DJZZ6ISULIC.json","view_paper":"https://pith.science/paper/3EZZ35SO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0708.2160&json=true","fetch_graph":"https://pith.science/api/pith-number/3EZZ35SOH2KDBY3DJZZ6ISULIC/graph.json","fetch_events":"https://pith.science/api/pith-number/3EZZ35SOH2KDBY3DJZZ6ISULIC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EZZ35SOH2KDBY3DJZZ6ISULIC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EZZ35SOH2KDBY3DJZZ6ISULIC/action/storage_attestation","attest_author":"https://pith.science/pith/3EZZ35SOH2KDBY3DJZZ6ISULIC/action/author_attestation","sign_citation":"https://pith.science/pith/3EZZ35SOH2KDBY3DJZZ6ISULIC/action/citation_signature","submit_replication":"https://pith.science/pith/3EZZ35SOH2KDBY3DJZZ6ISULIC/action/replication_record"}},"created_at":"2026-05-18T02:38:19.421483+00:00","updated_at":"2026-05-18T02:38:19.421483+00:00"}