{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:URY3ECTDNWADNLT6UCXZB3ROR4","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":"fdc2d8e6df3357a23a1c2e3d94f726d9152d9eeba749ad018f3569ac731129a8","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-03T22:05:11Z","title_canon_sha256":"6f94eace927cdd3eceb738964d9ec327b408009446891601992c7bc0dbb19b23"},"schema_version":"1.0","source":{"id":"2507.03195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.03195","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"arxiv_version","alias_value":"2507.03195v1","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.03195","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"pith_short_12","alias_value":"URY3ECTDNWAD","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"pith_short_16","alias_value":"URY3ECTDNWADNLT6","created_at":"2026-07-05T11:31:54Z"},{"alias_kind":"pith_short_8","alias_value":"URY3ECTD","created_at":"2026-07-05T11:31:54Z"}],"graph_snapshots":[{"event_id":"sha256:466318bc4e9536b3a214c0039e2d72ef8e5b5646f78e8c7c9ec08ad0690f2cdd","target":"graph","created_at":"2026-07-05T11:31:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.03195/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a countable group $\\Gamma$, letting $\\mathcal{K}_\\Gamma$ denote the class of {\\pmp} actions of $\\Gamma$, we study the question of when the model companion of $\\mathcal{K}_\\Gamma$ exists. Berenstein, Henson, and Ibarluc\\'ia showed that the model companion of $\\mathcal{K}_\\Gamma$ exists when $\\Gamma$ is a nonabelian free group on a countable number of generators. We significantly generalize their result by showing that the model companion of $\\cal K_\\Gamma$ exists whenever $\\Gamma$ is an approximately treeable group. The class of approximately treeable groups contain the class of treeable ","authors_text":"Brandon Seward, Isaac Goldbring, Robin Tucker-Drob","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-03T22:05:11Z","title":"Existentially closed measure-preserving actions of approximately treeable groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.03195","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":"sha256:6342b4c8a3bcb1adc04fdf15e5bbc66ac1d67ef952dacb086d73d3f28213190c","target":"record","created_at":"2026-07-05T11:31:54Z","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":"fdc2d8e6df3357a23a1c2e3d94f726d9152d9eeba749ad018f3569ac731129a8","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-03T22:05:11Z","title_canon_sha256":"6f94eace927cdd3eceb738964d9ec327b408009446891601992c7bc0dbb19b23"},"schema_version":"1.0","source":{"id":"2507.03195","kind":"arxiv","version":1}},"canonical_sha256":"a471b20a636d8036ae7ea0af90ee2e8f0f38579d22500fd9388c308cd9d98637","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a471b20a636d8036ae7ea0af90ee2e8f0f38579d22500fd9388c308cd9d98637","first_computed_at":"2026-07-05T11:31:54.569556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:54.569556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"75lNgvBCkRyiLG+7ICS6yURDzDFJR9cY4GZMQhRUSKSD2d7GbGmbeNzQBCVbNoZdAmjfbq1tMeTQ3UZg1dZdCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:54.570074Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.03195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6342b4c8a3bcb1adc04fdf15e5bbc66ac1d67ef952dacb086d73d3f28213190c","sha256:466318bc4e9536b3a214c0039e2d72ef8e5b5646f78e8c7c9ec08ad0690f2cdd"],"state_sha256":"1f2cfa415423994f2e4485a766dde7ef067c9cd2c869d8a44a78e29b7b1849ad"}