{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:22NKFANK6QCOUUCQFLRH5UGLMH","short_pith_number":"pith:22NKFANK","schema_version":"1.0","canonical_sha256":"d69aa281aaf404ea50502ae27ed0cb61d4b465bbaa985376c0800f20fa0ddd8d","source":{"kind":"arxiv","id":"1008.3644","version":4},"attestation_state":"computed","paper":{"title":"Higher rho-invariants and the surgery structure set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.DG","authors_text":"Charlotte Wahl","submitted_at":"2010-08-21T16:36:10Z","abstract_excerpt":"We study noncommutative eta- and rho-forms for homotopy equivalences. We prove a product formula for them and show that the rho-forms are well-defined on the structure set. We also define an index theoretic map from L-theory to C*-algebraic K-theory and show that it is compatible with the rho-forms. Our approach, which is based on methods of Hilsum-Skandalis and Piazza-Schick, also yields a unified analytic proof of the homotopy invariance of the higher signature class and of the L^2-signature for manifolds with boundary."},"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":"1008.3644","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-21T16:36:10Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"5ad640d4f1e2450f3a31539b71623c62284bda5d4b9e98b4d78f3d7a08286aef","abstract_canon_sha256":"386016b8aeeaf5952661154790c6b67a7852578b4189f687a312c8f5e8e38395"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:01.891832Z","signature_b64":"5Er2QKHlxwT1GFbw/qUnOU+PKr3e/BbyqLwm8dpg2QZr/lahCcZx689nvWJpSP30MSxDDB+cnbKiIC5dZ0+7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d69aa281aaf404ea50502ae27ed0cb61d4b465bbaa985376c0800f20fa0ddd8d","last_reissued_at":"2026-05-18T02:58:01.891276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:01.891276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher rho-invariants and the surgery structure set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.DG","authors_text":"Charlotte Wahl","submitted_at":"2010-08-21T16:36:10Z","abstract_excerpt":"We study noncommutative eta- and rho-forms for homotopy equivalences. We prove a product formula for them and show that the rho-forms are well-defined on the structure set. We also define an index theoretic map from L-theory to C*-algebraic K-theory and show that it is compatible with the rho-forms. Our approach, which is based on methods of Hilsum-Skandalis and Piazza-Schick, also yields a unified analytic proof of the homotopy invariance of the higher signature class and of the L^2-signature for manifolds with boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3644","kind":"arxiv","version":4},"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":"1008.3644","created_at":"2026-05-18T02:58:01.891371+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.3644v4","created_at":"2026-05-18T02:58:01.891371+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3644","created_at":"2026-05-18T02:58:01.891371+00:00"},{"alias_kind":"pith_short_12","alias_value":"22NKFANK6QCO","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"22NKFANK6QCOUUCQ","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"22NKFANK","created_at":"2026-05-18T12:26:03.138858+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/22NKFANK6QCOUUCQFLRH5UGLMH","json":"https://pith.science/pith/22NKFANK6QCOUUCQFLRH5UGLMH.json","graph_json":"https://pith.science/api/pith-number/22NKFANK6QCOUUCQFLRH5UGLMH/graph.json","events_json":"https://pith.science/api/pith-number/22NKFANK6QCOUUCQFLRH5UGLMH/events.json","paper":"https://pith.science/paper/22NKFANK"},"agent_actions":{"view_html":"https://pith.science/pith/22NKFANK6QCOUUCQFLRH5UGLMH","download_json":"https://pith.science/pith/22NKFANK6QCOUUCQFLRH5UGLMH.json","view_paper":"https://pith.science/paper/22NKFANK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.3644&json=true","fetch_graph":"https://pith.science/api/pith-number/22NKFANK6QCOUUCQFLRH5UGLMH/graph.json","fetch_events":"https://pith.science/api/pith-number/22NKFANK6QCOUUCQFLRH5UGLMH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/22NKFANK6QCOUUCQFLRH5UGLMH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/22NKFANK6QCOUUCQFLRH5UGLMH/action/storage_attestation","attest_author":"https://pith.science/pith/22NKFANK6QCOUUCQFLRH5UGLMH/action/author_attestation","sign_citation":"https://pith.science/pith/22NKFANK6QCOUUCQFLRH5UGLMH/action/citation_signature","submit_replication":"https://pith.science/pith/22NKFANK6QCOUUCQFLRH5UGLMH/action/replication_record"}},"created_at":"2026-05-18T02:58:01.891371+00:00","updated_at":"2026-05-18T02:58:01.891371+00:00"}