{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QJWUKPJ7XKLDDNAZAFAZJD2GI3","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":"bccfeee9874e668d707e5a7bcc3a685970daeda2aae6adef1c3d91171481c9f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-07-08T12:53:44Z","title_canon_sha256":"030a1de51c6b5499c25b38b510070bf6ccbaab1d340caa0b014915dc0fbdc811"},"schema_version":"1.0","source":{"id":"1507.02134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02134","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02134v1","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02134","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"QJWUKPJ7XKLD","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QJWUKPJ7XKLDDNAZ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QJWUKPJ7","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:0c951cf15b6aea9e8c95b87ce55ff0c5d26ce542519e1bb2f5cf5fe44e13cde2","target":"graph","created_at":"2026-05-18T01:37:08Z","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":"We apply the theory of infinite two-person games to two well-known problems in topology: Suslin's Problem and Arhangel'skii's problem on $G_\\delta$ covers of compact spaces. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable and 2) in every compact space satisfying the game-theoretic version of the weak Lindel\\\"of property, every cover by $G_\\delta$ sets has a continuum-sized subcollection whose union is $G_\\delta$-dense.","authors_text":"Santi Spadaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-07-08T12:53:44Z","title":"Infinite games and chain conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02134","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":"sha256:3cc089db4bc1fda2744581e6ebabc9fa65e41c09426ca6cc301e9a62cc51e672","target":"record","created_at":"2026-05-18T01:37:08Z","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":"bccfeee9874e668d707e5a7bcc3a685970daeda2aae6adef1c3d91171481c9f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-07-08T12:53:44Z","title_canon_sha256":"030a1de51c6b5499c25b38b510070bf6ccbaab1d340caa0b014915dc0fbdc811"},"schema_version":"1.0","source":{"id":"1507.02134","kind":"arxiv","version":1}},"canonical_sha256":"826d453d3fba9631b4190141948f4646ea0aef9006901810b1e058983f9cd13a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"826d453d3fba9631b4190141948f4646ea0aef9006901810b1e058983f9cd13a","first_computed_at":"2026-05-18T01:37:08.553470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:08.553470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J7Ow/3wMp68n1sj6as2vaZG3vjkspn8SmxAnQIZ86qrMngDdvf9b/KM3WJHTbTRwbwENLdIe8isrYopA1RuvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:08.554070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cc089db4bc1fda2744581e6ebabc9fa65e41c09426ca6cc301e9a62cc51e672","sha256:0c951cf15b6aea9e8c95b87ce55ff0c5d26ce542519e1bb2f5cf5fe44e13cde2"],"state_sha256":"351364c67f991527b51955e67540cde7c80f3ab45eb900fddf73262a9d34b01c"}