{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RWLNW3GSCFUS5CBLRHRFM73R5H","short_pith_number":"pith:RWLNW3GS","schema_version":"1.0","canonical_sha256":"8d96db6cd211692e882b89e2567f71e9e467de3a1add98d7aa46ce7aef067964","source":{"kind":"arxiv","id":"1308.0218","version":1},"attestation_state":"computed","paper":{"title":"Flat bundles, von Neumann algebras and $K$-theory with $\\R/\\Z$-coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.KT"],"primary_cat":"math.OA","authors_text":"Georges Skandalis (IMJ), Paolo Antonini (IMJ), Sara Azzali (IMJ)","submitted_at":"2013-08-01T14:19:17Z","abstract_excerpt":"Let $M$ be a closed manifold and $\\alpha : \\pi_1(M)\\to U_n$ a representation. We give a purely $K$-theoretic description of the associated element $[\\alpha]$ in the $K$-theory of $M$ with $\\R/\\Z$-coefficients. To that end, it is convenient to describe the $\\R/\\Z$-$K$-theory as a relative $K$-theory with respect to the inclusion of $\\C$ in a finite von Neumann algebra $B$. We use the following fact: there is, associated with $\\alpha$, a finite von Neumann algebra $B$ together with a flat bundle $\\cE\\to M$ with fibers $B$, such that $E_\\a\\otimes \\cE$ is canonically isomorphic with $\\C^n\\otimes \\"},"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":"1308.0218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-08-01T14:19:17Z","cross_cats_sorted":["math.FA","math.KT"],"title_canon_sha256":"02096bcf3fbf06b86a4c332cf0121682559a1693c6959c958c7b6a8c93bdd797","abstract_canon_sha256":"b729e9c673fa87dc9974d383708ce96f24b3fbf04f87f1e338658e971560c230"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:59.547306Z","signature_b64":"2YeS1O3ibI7sQ/SIUfcrIO8i9CgNKQXP/or5RUnA0sn5sfuXkDGDJGhd5oPk4wcDjV/NWFE2jdZF9jR94UYiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d96db6cd211692e882b89e2567f71e9e467de3a1add98d7aa46ce7aef067964","last_reissued_at":"2026-05-18T03:16:59.546573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:59.546573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flat bundles, von Neumann algebras and $K$-theory with $\\R/\\Z$-coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.KT"],"primary_cat":"math.OA","authors_text":"Georges Skandalis (IMJ), Paolo Antonini (IMJ), Sara Azzali (IMJ)","submitted_at":"2013-08-01T14:19:17Z","abstract_excerpt":"Let $M$ be a closed manifold and $\\alpha : \\pi_1(M)\\to U_n$ a representation. We give a purely $K$-theoretic description of the associated element $[\\alpha]$ in the $K$-theory of $M$ with $\\R/\\Z$-coefficients. To that end, it is convenient to describe the $\\R/\\Z$-$K$-theory as a relative $K$-theory with respect to the inclusion of $\\C$ in a finite von Neumann algebra $B$. We use the following fact: there is, associated with $\\alpha$, a finite von Neumann algebra $B$ together with a flat bundle $\\cE\\to M$ with fibers $B$, such that $E_\\a\\otimes \\cE$ is canonically isomorphic with $\\C^n\\otimes \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0218","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":"1308.0218","created_at":"2026-05-18T03:16:59.546701+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.0218v1","created_at":"2026-05-18T03:16:59.546701+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0218","created_at":"2026-05-18T03:16:59.546701+00:00"},{"alias_kind":"pith_short_12","alias_value":"RWLNW3GSCFUS","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"RWLNW3GSCFUS5CBL","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"RWLNW3GS","created_at":"2026-05-18T12:27:59.945178+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/RWLNW3GSCFUS5CBLRHRFM73R5H","json":"https://pith.science/pith/RWLNW3GSCFUS5CBLRHRFM73R5H.json","graph_json":"https://pith.science/api/pith-number/RWLNW3GSCFUS5CBLRHRFM73R5H/graph.json","events_json":"https://pith.science/api/pith-number/RWLNW3GSCFUS5CBLRHRFM73R5H/events.json","paper":"https://pith.science/paper/RWLNW3GS"},"agent_actions":{"view_html":"https://pith.science/pith/RWLNW3GSCFUS5CBLRHRFM73R5H","download_json":"https://pith.science/pith/RWLNW3GSCFUS5CBLRHRFM73R5H.json","view_paper":"https://pith.science/paper/RWLNW3GS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.0218&json=true","fetch_graph":"https://pith.science/api/pith-number/RWLNW3GSCFUS5CBLRHRFM73R5H/graph.json","fetch_events":"https://pith.science/api/pith-number/RWLNW3GSCFUS5CBLRHRFM73R5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RWLNW3GSCFUS5CBLRHRFM73R5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RWLNW3GSCFUS5CBLRHRFM73R5H/action/storage_attestation","attest_author":"https://pith.science/pith/RWLNW3GSCFUS5CBLRHRFM73R5H/action/author_attestation","sign_citation":"https://pith.science/pith/RWLNW3GSCFUS5CBLRHRFM73R5H/action/citation_signature","submit_replication":"https://pith.science/pith/RWLNW3GSCFUS5CBLRHRFM73R5H/action/replication_record"}},"created_at":"2026-05-18T03:16:59.546701+00:00","updated_at":"2026-05-18T03:16:59.546701+00:00"}