{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NRHNKRXACEJOSNOTW7YZAN64EZ","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":"4e66621cdeb276bec02b5e962b642dffb5eccc52f64c83bd92cedbfc02dc9bb6","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-06-07T01:47:44Z","title_canon_sha256":"b769a4f002606fd0144db21ee0d75607bc8166a7a0283dcb84065e4930482a4c"},"schema_version":"1.0","source":{"id":"1906.02857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.02857","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"arxiv_version","alias_value":"1906.02857v1","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.02857","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"pith_short_12","alias_value":"NRHNKRXACEJO","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NRHNKRXACEJOSNOT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NRHNKRXA","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:fbfa7bc9012337dbe5533930127f25b50e8fb6dc5211865202ebbebcb491c932","target":"graph","created_at":"2026-05-17T23:43:57Z","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":"Let S be a topological property of sequences (such as, for example, \"to contain a convergent subsequence\" or \"to have an accumulation point\"). We introduce the following open-point game OP(X,S) on a topological space X. In the n'th move, Player A chooses a non-empty open subet U_n of X, and Player B responds by selecting a point x_n in U_n. Player B wins the game if the sequence (x_n) satisfies property S in X; otherwise, Player A wins. The (non-)existence of regular or stationary winning strategies in OP(X,S) for both players defines new compactness properties of the underlying space X. We th","authors_text":"Alejandro Dorantes-Aldama, Dmitri Shakhmatov","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-06-07T01:47:44Z","title":"Compactness properties defined by open-point games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02857","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:a397e6b211fdf6b945c99cff98a4f769e75a5acabc8da2b4140cd095d81a08c8","target":"record","created_at":"2026-05-17T23:43:57Z","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":"4e66621cdeb276bec02b5e962b642dffb5eccc52f64c83bd92cedbfc02dc9bb6","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-06-07T01:47:44Z","title_canon_sha256":"b769a4f002606fd0144db21ee0d75607bc8166a7a0283dcb84065e4930482a4c"},"schema_version":"1.0","source":{"id":"1906.02857","kind":"arxiv","version":1}},"canonical_sha256":"6c4ed546e01112e935d3b7f19037dc2648de74ee827bf5c870de1bf00933f6fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c4ed546e01112e935d3b7f19037dc2648de74ee827bf5c870de1bf00933f6fc","first_computed_at":"2026-05-17T23:43:57.261769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:57.261769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yqNy6r50pc5VxSQ+eXLtx8wLMwFfCb9RTJ6fv5zTW2o3VcPwz5v/se/JwEHdsku0/Sf1WYrIm05wqt/aotwfCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:57.262570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.02857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a397e6b211fdf6b945c99cff98a4f769e75a5acabc8da2b4140cd095d81a08c8","sha256:fbfa7bc9012337dbe5533930127f25b50e8fb6dc5211865202ebbebcb491c932"],"state_sha256":"85f6837eb868304fa1958d889b1b23d3828524c8dbc4cdf35ee3187be4494172"}