{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FZ2GFWJZKKUJMUALBHVN2TLTKN","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":"a0f24fe076fc9766fe8beffbdad3d302ed401abd30c995bcb37997f479271aac","cross_cats_sorted":["math.CO","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-16T11:58:45Z","title_canon_sha256":"e07104b881fa9c00ee1eb468270efc28db1c7012eb125c6bdcc42e87ae988627"},"schema_version":"1.0","source":{"id":"1701.04257","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04257","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04257v3","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04257","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"pith_short_12","alias_value":"FZ2GFWJZKKUJ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FZ2GFWJZKKUJMUAL","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FZ2GFWJZ","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:cc25589237b148dc6947ac00ba9b5f835653fedbc64b9385b91e4d53b43a627d","target":"graph","created_at":"2026-05-18T00:02:19Z","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":"The Kechris-Pestov-Todorcevic correspondence connects extreme amenability of non-Archimedean Polish groups with Ramsey properties of classes of finite structures. The purpose of the present paper is to recast it as one of the instances of a more general construction, allowing to show that Ramsey-type statements actually appear as natural combinatorial expressions of the existence of fixed points in certain compactifications of groups, and that similar correspondences in fact exist in various dynamical contexts.","authors_text":"Lionel Nguyen Van Th\\'e","cross_cats":["math.CO","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-16T11:58:45Z","title":"Fixed points in compactifications and combinatorial counterparts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04257","kind":"arxiv","version":3},"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":"sha256:75e418c85d158b8e31e20579baaceb013cfa99c10744e4df417d60f8304da6a1","target":"record","created_at":"2026-05-18T00:02:19Z","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":"a0f24fe076fc9766fe8beffbdad3d302ed401abd30c995bcb37997f479271aac","cross_cats_sorted":["math.CO","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-16T11:58:45Z","title_canon_sha256":"e07104b881fa9c00ee1eb468270efc28db1c7012eb125c6bdcc42e87ae988627"},"schema_version":"1.0","source":{"id":"1701.04257","kind":"arxiv","version":3}},"canonical_sha256":"2e7462d93952a896500b09eadd4d735360634991e87558e7d6dbfee360b3ea89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e7462d93952a896500b09eadd4d735360634991e87558e7d6dbfee360b3ea89","first_computed_at":"2026-05-18T00:02:19.565850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:19.565850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"twr2PwDuDavWCapyLH+NFJ9CD8aFqIYsBenQF9+L0vMrKkiAV9xqMpXOGDOByDqZFCUV49zu9tM9suG3uxTNCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:19.566206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04257","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75e418c85d158b8e31e20579baaceb013cfa99c10744e4df417d60f8304da6a1","sha256:cc25589237b148dc6947ac00ba9b5f835653fedbc64b9385b91e4d53b43a627d"],"state_sha256":"4491ea016706423cb320e713d46443cc2055f5dea5c5a41bb656af4b01084c7f"}