{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LP2KXNTCRSU64ZH7PNDDCZEV2F","short_pith_number":"pith:LP2KXNTC","schema_version":"1.0","canonical_sha256":"5bf4abb6628ca9ee64ff7b46316495d16a2fe8297a10407b09a281f48d044478","source":{"kind":"arxiv","id":"1312.5140","version":2},"attestation_state":"computed","paper":{"title":"Free actions of free groups on countable structures and property (T)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"David M. Evans, Todor Tsankov","submitted_at":"2013-12-18T13:56:26Z","abstract_excerpt":"We show that if $G$ is a non-archimedean, Roelcke precompact, Polish group, then $G$ has Kazhdan's property (T). Moreover, if $G$ has a smallest open subgroup of finite index, then $G$ has a finite Kazhdan set. Examples of such $G$ include automorphism groups of countable $\\omega$-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite permutation groups. The latter allows the construction of a non-abelian free subgroup "},"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":"1312.5140","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-18T13:56:26Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"03b8e917af80f3695b94f3715524d5dc28f49d0df7e2d0c26488e9d2309583fa","abstract_canon_sha256":"f0ed01ff78659dbe206505aa8d93941bd377c14475a1210673fd33196ac0fb78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:13.649032Z","signature_b64":"LdHHvmh3vznZj0Ld20FadESKfBMVfaR5FcILRFl3Y+WHbo62q9ND6ncYPx/itNeC5lKcPGuvFVcD5ts0P/CRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bf4abb6628ca9ee64ff7b46316495d16a2fe8297a10407b09a281f48d044478","last_reissued_at":"2026-05-18T01:34:13.648190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:13.648190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Free actions of free groups on countable structures and property (T)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"David M. Evans, Todor Tsankov","submitted_at":"2013-12-18T13:56:26Z","abstract_excerpt":"We show that if $G$ is a non-archimedean, Roelcke precompact, Polish group, then $G$ has Kazhdan's property (T). Moreover, if $G$ has a smallest open subgroup of finite index, then $G$ has a finite Kazhdan set. Examples of such $G$ include automorphism groups of countable $\\omega$-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite permutation groups. The latter allows the construction of a non-abelian free subgroup "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5140","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":"1312.5140","created_at":"2026-05-18T01:34:13.648348+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.5140v2","created_at":"2026-05-18T01:34:13.648348+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5140","created_at":"2026-05-18T01:34:13.648348+00:00"},{"alias_kind":"pith_short_12","alias_value":"LP2KXNTCRSU6","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LP2KXNTCRSU64ZH7","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LP2KXNTC","created_at":"2026-05-18T12:27:51.066281+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/LP2KXNTCRSU64ZH7PNDDCZEV2F","json":"https://pith.science/pith/LP2KXNTCRSU64ZH7PNDDCZEV2F.json","graph_json":"https://pith.science/api/pith-number/LP2KXNTCRSU64ZH7PNDDCZEV2F/graph.json","events_json":"https://pith.science/api/pith-number/LP2KXNTCRSU64ZH7PNDDCZEV2F/events.json","paper":"https://pith.science/paper/LP2KXNTC"},"agent_actions":{"view_html":"https://pith.science/pith/LP2KXNTCRSU64ZH7PNDDCZEV2F","download_json":"https://pith.science/pith/LP2KXNTCRSU64ZH7PNDDCZEV2F.json","view_paper":"https://pith.science/paper/LP2KXNTC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.5140&json=true","fetch_graph":"https://pith.science/api/pith-number/LP2KXNTCRSU64ZH7PNDDCZEV2F/graph.json","fetch_events":"https://pith.science/api/pith-number/LP2KXNTCRSU64ZH7PNDDCZEV2F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LP2KXNTCRSU64ZH7PNDDCZEV2F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LP2KXNTCRSU64ZH7PNDDCZEV2F/action/storage_attestation","attest_author":"https://pith.science/pith/LP2KXNTCRSU64ZH7PNDDCZEV2F/action/author_attestation","sign_citation":"https://pith.science/pith/LP2KXNTCRSU64ZH7PNDDCZEV2F/action/citation_signature","submit_replication":"https://pith.science/pith/LP2KXNTCRSU64ZH7PNDDCZEV2F/action/replication_record"}},"created_at":"2026-05-18T01:34:13.648348+00:00","updated_at":"2026-05-18T01:34:13.648348+00:00"}