{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GLM5VAOY7FLSKXYYMIFMD4UQKY","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":"f0cc982358a563e3707b175e47cc1e5264d778439b9666562843404e32e2e89c","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-03-10T05:21:11Z","title_canon_sha256":"255ba4e818f1d84ae6b1648cdce4728422887f61d69662b91875d271b0d63994"},"schema_version":"1.0","source":{"id":"0903.1686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1686","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1686v1","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1686","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"pith_short_12","alias_value":"GLM5VAOY7FLS","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GLM5VAOY7FLSKXYY","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GLM5VAOY","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:8f3eb38ddcb011c5d1d92e9fb234a8e0894aec389260d91e9550e3aa0f5a5036","target":"graph","created_at":"2026-05-17T23:52:45Z","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 compute the Hochschild homology of the free orthogonal quantum group $A_o(n)$. We show that it satisfies Poincar\\'e duality and should be considered to be a 3-dimensional object. We then use recent results of R. Vergnioux to derive results about the $\\ell^2$-homology of $A_o(n)$ and estimates on the free entropy dimension of its set of generators. In particular, we show that the $\\ell^2$ Betti-numbers of $A_o(n)$ all vanish and that the free entropy dimension is less than 1.","authors_text":"A. Thom, B. Collins, J. H\\\"artel","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-03-10T05:21:11Z","title":"Homology of free quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1686","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":"sha256:144c6dd14eff8d22a27781a6ae25900b796bf78a6d15bcabb16783e7cc6f7ca6","target":"record","created_at":"2026-05-17T23:52:45Z","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":"f0cc982358a563e3707b175e47cc1e5264d778439b9666562843404e32e2e89c","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-03-10T05:21:11Z","title_canon_sha256":"255ba4e818f1d84ae6b1648cdce4728422887f61d69662b91875d271b0d63994"},"schema_version":"1.0","source":{"id":"0903.1686","kind":"arxiv","version":1}},"canonical_sha256":"32d9da81d8f957255f18620ac1f2905617f0621a8f99d8ae3c665512d067a67d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32d9da81d8f957255f18620ac1f2905617f0621a8f99d8ae3c665512d067a67d","first_computed_at":"2026-05-17T23:52:45.005687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:45.005687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"raWO9ooNpTsHGBYcFLBL4Hu31nHqb0zGDJOdDg04QKDIEIrNijxPT0p83Eq5P9mfMs/9AKKdYrbMpSJsUSHLDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:45.006358Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.1686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:144c6dd14eff8d22a27781a6ae25900b796bf78a6d15bcabb16783e7cc6f7ca6","sha256:8f3eb38ddcb011c5d1d92e9fb234a8e0894aec389260d91e9550e3aa0f5a5036"],"state_sha256":"5693f272131a0d173236c6f13e24ca11e40b5b12659ec50527ab395d75bf85cc"}