{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3XUC4U2D7IGTKLOY2M3P2ATUHR","short_pith_number":"pith:3XUC4U2D","schema_version":"1.0","canonical_sha256":"dde82e5343fa0d352dd8d336fd02743c7758fe2d5e3e859bac1f52afe1aad0a5","source":{"kind":"arxiv","id":"1612.04280","version":2},"attestation_state":"computed","paper":{"title":"Weak amenability of Lie groups made discrete","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.OA"],"primary_cat":"math.FA","authors_text":"S{\\o}ren Knudby","submitted_at":"2016-12-13T16:55:33Z","abstract_excerpt":"We completely characterize connected Lie groups all of whose countable subgroups are weakly amenable. We also provide a characterization of connected semisimple Lie groups that are weakly amenable. Finally, we show that a connected Lie group is weakly amenable if the group is weakly amenable as a discrete group."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.04280","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-13T16:55:33Z","cross_cats_sorted":["math.GR","math.OA"],"title_canon_sha256":"844ff00b512acac74bca1fc4825f4ef07beea659fdeb915f3ddd819fc8165da1","abstract_canon_sha256":"6205991c8e8804c70f7a3cbbe04edfcff5f1d7966f942a6d4bf9aee1f136dafb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:10.097881Z","signature_b64":"Pz61bsnDWGGsfnWd+FWrFSbzzxEuzqQqkApimIZIe+t4Acl+NczrPo6NMN1D/auSOajqhzIar/Hb7GDZUJS+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dde82e5343fa0d352dd8d336fd02743c7758fe2d5e3e859bac1f52afe1aad0a5","last_reissued_at":"2026-05-18T00:03:10.097175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:10.097175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak amenability of Lie groups made discrete","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.OA"],"primary_cat":"math.FA","authors_text":"S{\\o}ren Knudby","submitted_at":"2016-12-13T16:55:33Z","abstract_excerpt":"We completely characterize connected Lie groups all of whose countable subgroups are weakly amenable. We also provide a characterization of connected semisimple Lie groups that are weakly amenable. Finally, we show that a connected Lie group is weakly amenable if the group is weakly amenable as a discrete group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04280","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.04280","created_at":"2026-05-18T00:03:10.097289+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.04280v2","created_at":"2026-05-18T00:03:10.097289+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04280","created_at":"2026-05-18T00:03:10.097289+00:00"},{"alias_kind":"pith_short_12","alias_value":"3XUC4U2D7IGT","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"3XUC4U2D7IGTKLOY","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"3XUC4U2D","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3XUC4U2D7IGTKLOY2M3P2ATUHR","json":"https://pith.science/pith/3XUC4U2D7IGTKLOY2M3P2ATUHR.json","graph_json":"https://pith.science/api/pith-number/3XUC4U2D7IGTKLOY2M3P2ATUHR/graph.json","events_json":"https://pith.science/api/pith-number/3XUC4U2D7IGTKLOY2M3P2ATUHR/events.json","paper":"https://pith.science/paper/3XUC4U2D"},"agent_actions":{"view_html":"https://pith.science/pith/3XUC4U2D7IGTKLOY2M3P2ATUHR","download_json":"https://pith.science/pith/3XUC4U2D7IGTKLOY2M3P2ATUHR.json","view_paper":"https://pith.science/paper/3XUC4U2D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.04280&json=true","fetch_graph":"https://pith.science/api/pith-number/3XUC4U2D7IGTKLOY2M3P2ATUHR/graph.json","fetch_events":"https://pith.science/api/pith-number/3XUC4U2D7IGTKLOY2M3P2ATUHR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3XUC4U2D7IGTKLOY2M3P2ATUHR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3XUC4U2D7IGTKLOY2M3P2ATUHR/action/storage_attestation","attest_author":"https://pith.science/pith/3XUC4U2D7IGTKLOY2M3P2ATUHR/action/author_attestation","sign_citation":"https://pith.science/pith/3XUC4U2D7IGTKLOY2M3P2ATUHR/action/citation_signature","submit_replication":"https://pith.science/pith/3XUC4U2D7IGTKLOY2M3P2ATUHR/action/replication_record"}},"created_at":"2026-05-18T00:03:10.097289+00:00","updated_at":"2026-05-18T00:03:10.097289+00:00"}