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Let $\\overline{G}$ and $\\overline{H}$ denote their closures in the topology of pointwise convergence. Assume the Polish group $\\overline{H}$ has relative Property (T) in $\\overline{G}$. Then the simplex $\\mathcal{M}_\\mathrm{inv}(2^\\mathcal{S})$ of invariant probability measures for the induced action $G\\curvearrowright 2^\\math"},"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":"2608.07649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-08-07T17:23:42Z","cross_cats_sorted":["math.FA","math.GR"],"title_canon_sha256":"892d1c5f0e10e8532fc16bae3d2f9fd7b75ee1b9857011dd7318e3f9f8f0748d","abstract_canon_sha256":"f4e54a8d5490a4de75128bf238dcb07e2dd1a9669e158e67c25d29033f229dd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T00:15:34.430148Z","signature_b64":"7j+kAcc66jxvc36dhywUk9+HvOYUu58nE0/zVt5AZd2bnmM4INWBaTEy9Xe3QLoU066MpJ5E3uQqF7FftbKPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"570a08877267d827083c47afba5abbfce666d4cbababea5f5cc74a143ebacf53","last_reissued_at":"2026-08-11T00:15:34.427952Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T00:15:34.427952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative Property (T), simplices of invariant measures, and existentially closed models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GR"],"primary_cat":"math.LO","authors_text":"Tom\\'as Ibarluc\\'ia","submitted_at":"2026-08-07T17:23:42Z","abstract_excerpt":"We prove a Bauer-Poulsen dichotomy theorem for simplices of invariant measures associated with permutation groups.\n  More precisely, let $G$ be a transitive group of permutations of a countable set $\\mathcal{S}$, and let $H$ be the stabilizer of a point of $\\mathcal{S}$. Let $\\overline{G}$ and $\\overline{H}$ denote their closures in the topology of pointwise convergence. Assume the Polish group $\\overline{H}$ has relative Property (T) in $\\overline{G}$. Then the simplex $\\mathcal{M}_\\mathrm{inv}(2^\\mathcal{S})$ of invariant probability measures for the induced action $G\\curvearrowright 2^\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07649","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.07649/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2608.07649","created_at":"2026-08-11T00:15:34.428356+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.07649v1","created_at":"2026-08-11T00:15:34.428356+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07649","created_at":"2026-08-11T00:15:34.428356+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4FARB3SM7MC","created_at":"2026-08-11T00:15:34.428356+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4FARB3SM7MCOCB4","created_at":"2026-08-11T00:15:34.428356+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4FARB3S","created_at":"2026-08-11T00:15:34.428356+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/K4FARB3SM7MCOCB4I6X3UWV37T","json":"https://pith.science/pith/K4FARB3SM7MCOCB4I6X3UWV37T.json","graph_json":"https://pith.science/api/pith-number/K4FARB3SM7MCOCB4I6X3UWV37T/graph.json","events_json":"https://pith.science/api/pith-number/K4FARB3SM7MCOCB4I6X3UWV37T/events.json","paper":"https://pith.science/paper/K4FARB3S"},"agent_actions":{"view_html":"https://pith.science/pith/K4FARB3SM7MCOCB4I6X3UWV37T","download_json":"https://pith.science/pith/K4FARB3SM7MCOCB4I6X3UWV37T.json","view_paper":"https://pith.science/paper/K4FARB3S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.07649&json=true","fetch_graph":"https://pith.science/api/pith-number/K4FARB3SM7MCOCB4I6X3UWV37T/graph.json","fetch_events":"https://pith.science/api/pith-number/K4FARB3SM7MCOCB4I6X3UWV37T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4FARB3SM7MCOCB4I6X3UWV37T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4FARB3SM7MCOCB4I6X3UWV37T/action/storage_attestation","attest_author":"https://pith.science/pith/K4FARB3SM7MCOCB4I6X3UWV37T/action/author_attestation","sign_citation":"https://pith.science/pith/K4FARB3SM7MCOCB4I6X3UWV37T/action/citation_signature","submit_replication":"https://pith.science/pith/K4FARB3SM7MCOCB4I6X3UWV37T/action/replication_record"}},"created_at":"2026-08-11T00:15:34.428356+00:00","updated_at":"2026-08-11T00:15:34.428356+00:00"}