{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ANQQXYKHVGCLCPWON7RLZPS5SA","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":"57087906ac8d09816764a8fcd510714d1d85a9060ae3629a93e8096332f93119","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-15T08:56:00Z","title_canon_sha256":"0cf3754034a641aa40d11420acbd27c2f481d49dbb739c1cb925f7fb92db90a8"},"schema_version":"1.0","source":{"id":"1505.03988","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03988","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03988v4","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03988","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"ANQQXYKHVGCL","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ANQQXYKHVGCLCPWO","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ANQQXYKH","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:4d1440ecf08b747aa7d97f5938305ab6b8ba1df22f40f7440303dc66d9e1133d","target":"graph","created_at":"2026-05-18T00:18:54Z","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":"We will show that for a polynomially contractible manifold of bounded geometry and of polynomial volume growth every coarse and rough cohomology class pairs continuously with the K-theory of the uniform Roe algebra. As an application we will discuss non-vanishing of rough index classes of Dirac operators over such manifolds, and we will furthermore get higher-codimensional index obstructions to metrics of positive scalar curvature on closed manifolds with virtually nilpotent fundamental groups. We will give a computation of the homology of (a dense, smooth subalgebra of) the uniform Roe algebr","authors_text":"Alexander Engel","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-15T08:56:00Z","title":"Rough index theory on spaces of polynomial growth and contractibility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03988","kind":"arxiv","version":4},"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:ae028120eaa1e2eb4301c98184b8208970af6fe3f2ddafc8a4cb54bfe8ff2d63","target":"record","created_at":"2026-05-18T00:18:54Z","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":"57087906ac8d09816764a8fcd510714d1d85a9060ae3629a93e8096332f93119","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-15T08:56:00Z","title_canon_sha256":"0cf3754034a641aa40d11420acbd27c2f481d49dbb739c1cb925f7fb92db90a8"},"schema_version":"1.0","source":{"id":"1505.03988","kind":"arxiv","version":4}},"canonical_sha256":"03610be147a984b13ece6fe2bcbe5d90287604174e102ce2d36ba51a8baffa82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03610be147a984b13ece6fe2bcbe5d90287604174e102ce2d36ba51a8baffa82","first_computed_at":"2026-05-18T00:18:54.343695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:54.343695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P+bgGcgexCPW5+VYFs32Ma17WoalaSpRXUIJDYj9gNmA4bAh4qaR56CAmBUlhBARInEklPL25eiA44+reQxNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:54.344146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03988","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae028120eaa1e2eb4301c98184b8208970af6fe3f2ddafc8a4cb54bfe8ff2d63","sha256:4d1440ecf08b747aa7d97f5938305ab6b8ba1df22f40f7440303dc66d9e1133d"],"state_sha256":"c6c42fd3e8a6fc3d4730662425ce4c8eecc565ccff33f3dce94ae0c92c709150"}