{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZIBLGQ5FINWGX6755AN2K5RUGT","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":"c6c8d436ea96fc1d0aa0a5e23d2db66b3d2778023330efc1dbc28719a50e32ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-17T09:52:44Z","title_canon_sha256":"de011640f455260e6c05cc93685dbace2f485ade5e5b06a841c70238e74666a9"},"schema_version":"1.0","source":{"id":"1104.3294","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3294","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3294v3","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3294","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZIBLGQ5FINWG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZIBLGQ5FINWGX675","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZIBLGQ5F","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:1a1b7cda0d0277f2ff66e01a087c696698749979bd3136e7230b86ed605eae75","target":"graph","created_at":"2026-05-18T03:32:45Z","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 introduce a notion of $L^2$-Betti numbers for locally compact, second countable, unimodular groups. We study the relation to the standard notion of $L^2$-Betti numbers of countable discrete groups for lattices. In this way, several new computations are obtained for countable groups, including lattices in algebraic groups over local fields, and Kac-Moody lattices.\n  We also extend the vanishing of reduced $L^2$-cohomology for countable amenable groups, a well known theorem due to Cheeger and Gromov, to cover all amenable, second countable, unimodular locally compact groups.","authors_text":"Henrik Densing Petersen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-17T09:52:44Z","title":"L^2-Betti Numbers of Locally Compact Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3294","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":"sha256:35773ad0f08bea27d9e5f6ccf08b4db74cb4d68601e22abcddccfa12ec927503","target":"record","created_at":"2026-05-18T03:32:45Z","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":"c6c8d436ea96fc1d0aa0a5e23d2db66b3d2778023330efc1dbc28719a50e32ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-17T09:52:44Z","title_canon_sha256":"de011640f455260e6c05cc93685dbace2f485ade5e5b06a841c70238e74666a9"},"schema_version":"1.0","source":{"id":"1104.3294","kind":"arxiv","version":3}},"canonical_sha256":"ca02b343a5436c6bfbfde81ba5763434cdd9d120e6018752ef41f916cc7a3946","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca02b343a5436c6bfbfde81ba5763434cdd9d120e6018752ef41f916cc7a3946","first_computed_at":"2026-05-18T03:32:45.641647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:45.641647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5+99KvozPdThb/0PowJSl/qf5+6jcszFwnTz0qbgcgE1tjDbjFccBBI9sR0i19w/xJHZE041tdivvIrs8cTMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:45.642324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3294","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35773ad0f08bea27d9e5f6ccf08b4db74cb4d68601e22abcddccfa12ec927503","sha256:1a1b7cda0d0277f2ff66e01a087c696698749979bd3136e7230b86ed605eae75"],"state_sha256":"54b715ddcf888408682c92084fe142a776c2f967dabdd8a1b1a8a12b1d9fe897"}