{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UXJ6NEXFCGAI6AVIUZWVD323JP","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":"1b3a722464a7a381fef7e3b9703170a689483bb5767ab5648ad1774413858a23","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-10-25T16:18:32Z","title_canon_sha256":"a2a25b01b896c57a2aec54996520f3d85ac20042711a5addcb91db111717f8c2"},"schema_version":"1.0","source":{"id":"1210.6892","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6892","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6892v3","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6892","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"UXJ6NEXFCGAI","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UXJ6NEXFCGAI6AVI","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UXJ6NEXF","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:bf597d40d5bfa751062392f8fcc89904afba58ba5793c4ed12c39baa973212f0","target":"graph","created_at":"2026-05-18T01:34:51Z","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":"In this paper, we study the space of metrics of positive scalar curvature using methods from coarse geometry.\n  Given a closed spin manifold M with fundamental group G, Stephan Stolz introduced the positive scalar curvature exact sequence, in analogy to the surgery exact sequence in topology. It calculates a structure group of metrics of positive scalar curvature on M (the object we want to understand) in terms of spin-bordism of BG and a somewhat mysterious group R(G).\n  Higson and Roe introduced a K-theory exact sequence in coarse geometry which contains the Baum-Connes assembly map, with on","authors_text":"Paolo Piazza (Universita La Sapienza Roma), Thomas Schick (Georg-August-Universit\\\"at G\\\"ottingen)","cross_cats":["math.DG","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-10-25T16:18:32Z","title":"Rho-classes, index theory and Stolz' positive scalar curvature sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6892","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:bbd1e4074a588435ee2c4930271fc7db080e368117571ba71b11727bb1d843d8","target":"record","created_at":"2026-05-18T01:34:51Z","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":"1b3a722464a7a381fef7e3b9703170a689483bb5767ab5648ad1774413858a23","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-10-25T16:18:32Z","title_canon_sha256":"a2a25b01b896c57a2aec54996520f3d85ac20042711a5addcb91db111717f8c2"},"schema_version":"1.0","source":{"id":"1210.6892","kind":"arxiv","version":3}},"canonical_sha256":"a5d3e692e511808f02a8a66d51ef5b4bc56c20e7a508ffd7334ed52e5cac8659","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5d3e692e511808f02a8a66d51ef5b4bc56c20e7a508ffd7334ed52e5cac8659","first_computed_at":"2026-05-18T01:34:51.293463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:51.293463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MsBdqmEZGJl7DQz5cGxK6VB1m8oasXuNrNX933vdLjPSrSv8qEJucO18vR9hptbmePdD50Lg3J0ONn+HSfJNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:51.293872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6892","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbd1e4074a588435ee2c4930271fc7db080e368117571ba71b11727bb1d843d8","sha256:bf597d40d5bfa751062392f8fcc89904afba58ba5793c4ed12c39baa973212f0"],"state_sha256":"cb0bbf847d89d4ff865a284f07fa7af73a2738cc93438b070aeae4732dbce423"}