{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:H2GSS4C4RCGQHRYH7JFNUHJLB7","short_pith_number":"pith:H2GSS4C4","schema_version":"1.0","canonical_sha256":"3e8d29705c888d03c707fa4ada1d2b0ff2a16680665c5b241e074be6ca4929be","source":{"kind":"arxiv","id":"1011.3987","version":2},"attestation_state":"computed","paper":{"title":"Positive scalar curvature, K-area and essentialness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.KT"],"primary_cat":"math.DG","authors_text":"Bernhard Hanke","submitted_at":"2010-11-17T16:11:49Z","abstract_excerpt":"The Lichnerowicz formula yields an index theoretic obstruction to positive scalar curvature metrics on closed spin manifolds. The most general form of this obstruction is due to Rosenberg and takes values in the $K$-theory of the group $C^*$-algebra of the fundamental group of the underlying manifold. We give an overview of recent results clarifying the relation of the Rosenberg index to notions from large scale geometry like enlargeability and essentialness. One central topic is the concept of $K$-homology classes of infinite $K$-area. This notion, which in its original form is due to Gromov,"},"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":"1011.3987","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-17T16:11:49Z","cross_cats_sorted":["math.GT","math.KT"],"title_canon_sha256":"7fa79eaf64bf65162a369cac7ca99f12d25d98408ce280697ab7d94312c75b82","abstract_canon_sha256":"25938572cf93066987cf420bf514498ac4b7231d1d99334a37148bb69753971d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:51.605188Z","signature_b64":"ldcm3zt7BNbJwMk+Ya+9vWReDdZhvguD/810YZQWq5NV5dCD4Si1rL9+xtvH4tOsqtZBEnppmbD2fa34LxJKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e8d29705c888d03c707fa4ada1d2b0ff2a16680665c5b241e074be6ca4929be","last_reissued_at":"2026-05-18T04:21:51.604478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:51.604478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive scalar curvature, K-area and essentialness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.KT"],"primary_cat":"math.DG","authors_text":"Bernhard Hanke","submitted_at":"2010-11-17T16:11:49Z","abstract_excerpt":"The Lichnerowicz formula yields an index theoretic obstruction to positive scalar curvature metrics on closed spin manifolds. The most general form of this obstruction is due to Rosenberg and takes values in the $K$-theory of the group $C^*$-algebra of the fundamental group of the underlying manifold. We give an overview of recent results clarifying the relation of the Rosenberg index to notions from large scale geometry like enlargeability and essentialness. One central topic is the concept of $K$-homology classes of infinite $K$-area. This notion, which in its original form is due to Gromov,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3987","kind":"arxiv","version":2},"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":"1011.3987","created_at":"2026-05-18T04:21:51.604608+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.3987v2","created_at":"2026-05-18T04:21:51.604608+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3987","created_at":"2026-05-18T04:21:51.604608+00:00"},{"alias_kind":"pith_short_12","alias_value":"H2GSS4C4RCGQ","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"H2GSS4C4RCGQHRYH","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"H2GSS4C4","created_at":"2026-05-18T12:26:07.630475+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/H2GSS4C4RCGQHRYH7JFNUHJLB7","json":"https://pith.science/pith/H2GSS4C4RCGQHRYH7JFNUHJLB7.json","graph_json":"https://pith.science/api/pith-number/H2GSS4C4RCGQHRYH7JFNUHJLB7/graph.json","events_json":"https://pith.science/api/pith-number/H2GSS4C4RCGQHRYH7JFNUHJLB7/events.json","paper":"https://pith.science/paper/H2GSS4C4"},"agent_actions":{"view_html":"https://pith.science/pith/H2GSS4C4RCGQHRYH7JFNUHJLB7","download_json":"https://pith.science/pith/H2GSS4C4RCGQHRYH7JFNUHJLB7.json","view_paper":"https://pith.science/paper/H2GSS4C4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.3987&json=true","fetch_graph":"https://pith.science/api/pith-number/H2GSS4C4RCGQHRYH7JFNUHJLB7/graph.json","fetch_events":"https://pith.science/api/pith-number/H2GSS4C4RCGQHRYH7JFNUHJLB7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H2GSS4C4RCGQHRYH7JFNUHJLB7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H2GSS4C4RCGQHRYH7JFNUHJLB7/action/storage_attestation","attest_author":"https://pith.science/pith/H2GSS4C4RCGQHRYH7JFNUHJLB7/action/author_attestation","sign_citation":"https://pith.science/pith/H2GSS4C4RCGQHRYH7JFNUHJLB7/action/citation_signature","submit_replication":"https://pith.science/pith/H2GSS4C4RCGQHRYH7JFNUHJLB7/action/replication_record"}},"created_at":"2026-05-18T04:21:51.604608+00:00","updated_at":"2026-05-18T04:21:51.604608+00:00"}