{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AZZGCOTYJVTROVIAGOKXF4J2IY","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":"05ace71230243ec5a233c9db2e73da3e3f929b30a7d4541795297d5c92e3ad77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-27T17:39:33Z","title_canon_sha256":"5105d920986aadcf72c054bc0c63c033fb9389ff4a9e8bab1e86a6b102010871"},"schema_version":"1.0","source":{"id":"1804.10604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10604","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10604v1","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10604","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"pith_short_12","alias_value":"AZZGCOTYJVTR","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AZZGCOTYJVTROVIA","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AZZGCOTY","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:e813081b5ae290acefb75ec64e0d0c79e4f336076f2c5fa17efa907f080267c6","target":"graph","created_at":"2026-05-18T00:17:20Z","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 note we refine examples by Aka from arithmetic to S-arithmetic groups to show that the vanishing of the $i$-th $\\ell^2$-Betti number is not a profinite invariant for all $i \\ge 2$.","authors_text":"Holger Kammeyer, Roman Sauer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-27T17:39:33Z","title":"S-arithmetic spinor groups with the same finite quotients and distinct $\\ell^2$-cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10604","kind":"arxiv","version":1},"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:abad85bfcf01a6fd94810df02422fd2c5b70f81a87035d8ad03181061aa12d74","target":"record","created_at":"2026-05-18T00:17:20Z","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":"05ace71230243ec5a233c9db2e73da3e3f929b30a7d4541795297d5c92e3ad77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-27T17:39:33Z","title_canon_sha256":"5105d920986aadcf72c054bc0c63c033fb9389ff4a9e8bab1e86a6b102010871"},"schema_version":"1.0","source":{"id":"1804.10604","kind":"arxiv","version":1}},"canonical_sha256":"0672613a784d67175500339572f13a460b91b7992bc61a18f408e0344b240d97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0672613a784d67175500339572f13a460b91b7992bc61a18f408e0344b240d97","first_computed_at":"2026-05-18T00:17:20.373504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:20.373504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QkW1NQUtcbtwdMa3l8NihI2WFznZXz/uZLzHQgN5tz9thoB64jKQYPemouukjvTjYnaLhyEQYLg+BPqYq8Q7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:20.374143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abad85bfcf01a6fd94810df02422fd2c5b70f81a87035d8ad03181061aa12d74","sha256:e813081b5ae290acefb75ec64e0d0c79e4f336076f2c5fa17efa907f080267c6"],"state_sha256":"ed5a39c874e76b2dce86dc4d68f6fb3eef1986f5f84b1a45e30c6204025566ab"}