{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YIGS2PIPYWKHEZMFOHBPUZG2TQ","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":"89dea510fa3f47e20d8c2617b78425821ea2d57ee98d69a6e93907109d695e5c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-09-05T18:42:41Z","title_canon_sha256":"361846af55fda97671d337c8d514445b8df6a4e9a382f3398f4bbc2ba9fbc85e"},"schema_version":"1.0","source":{"id":"1309.1430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1430","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1430v1","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1430","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"YIGS2PIPYWKH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YIGS2PIPYWKHEZMF","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YIGS2PIP","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:0a76e061ca4eb74396281a19224564c3563e3d411dc11ad9cdc3aeaff24706f1","target":"graph","created_at":"2026-05-18T03:14:07Z","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":"Moore characterized the amenability of automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to automorphism groups of metric Fra\\\"iss\\'e structures, which encompass all Polish groups. As an application, we prove that amenability is a G_delta condition.","authors_text":"Adriane Ka\\\"ichouh (ICJ)","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-09-05T18:42:41Z","title":"Amenability and Ramsey theory in the metric setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1430","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":"sha256:80bc6e510698f64a4e71dcb9b79e97ba76c3a730f904b0b681bbd65fd2599db2","target":"record","created_at":"2026-05-18T03:14:07Z","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":"89dea510fa3f47e20d8c2617b78425821ea2d57ee98d69a6e93907109d695e5c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-09-05T18:42:41Z","title_canon_sha256":"361846af55fda97671d337c8d514445b8df6a4e9a382f3398f4bbc2ba9fbc85e"},"schema_version":"1.0","source":{"id":"1309.1430","kind":"arxiv","version":1}},"canonical_sha256":"c20d2d3d0fc59472658571c2fa64da9c208886149b289d5b6e71b534680b3b93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c20d2d3d0fc59472658571c2fa64da9c208886149b289d5b6e71b534680b3b93","first_computed_at":"2026-05-18T03:14:07.327146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:07.327146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KMpQY+M/tg96NX+e+xrmWlUEWyMu/pBWiIrlFc69qC4j7SUQC68IBGTEMSkVulHgwXo/jfjwy/PTLCFfajLTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:07.327677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80bc6e510698f64a4e71dcb9b79e97ba76c3a730f904b0b681bbd65fd2599db2","sha256:0a76e061ca4eb74396281a19224564c3563e3d411dc11ad9cdc3aeaff24706f1"],"state_sha256":"8233b7d36156d16125d96b9e3f90a929cc7bf8929271b16beefcd184fd9667f1"}