{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JBF5QVXQRRSMOCA7U3E5VI2BYA","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":"84c2da20c69bccd6cea13e208c7f2db5581d9fc2cdf6daa9f6ff1996244e21b5","cross_cats_sorted":["cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2017-04-17T15:36:59Z","title_canon_sha256":"4da6667d0a7e7d1bbde200c55109200a2aaff8a1ccd07cddf34386101598dda6"},"schema_version":"1.0","source":{"id":"1704.05003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05003","created_at":"2026-05-18T00:46:17Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05003v1","created_at":"2026-05-18T00:46:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05003","created_at":"2026-05-18T00:46:17Z"},{"alias_kind":"pith_short_12","alias_value":"JBF5QVXQRRSM","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"JBF5QVXQRRSMOCA7","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"JBF5QVXQ","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:b5dcd8bfa55278bfd1521533f98dc2b1fdd860cca417a4c23b778be8fd6111df","target":"graph","created_at":"2026-05-18T00:46:17Z","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 study 2-player turn-based perfect-information stochastic games with countably infinite state space. The players aim at maximizing/minimizing the probability of a given event (i.e., measurable set of infinite plays), such as reachability, B\\\"uchi, omega-regular or more general objectives.\n  These games are known to be weakly determined, i.e., they have value. However, strong determinacy of threshold objectives (given by an event and a threshold $c \\in [0,1]$) was open in many cases: is it always the case that the maximizer or the minimizer has a winning strategy, i.e., one that enforces, aga","authors_text":"Dominik Wojtczak, Mahsa Shirmohammadi, Richard Mayr, Stefan Kiefer","cross_cats":["cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2017-04-17T15:36:59Z","title":"On Strong Determinacy of Countable Stochastic Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05003","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:edbe40e512fbf81356b2889fc1be389c1c8b6d996598c7974a098a3fae171591","target":"record","created_at":"2026-05-18T00:46:17Z","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":"84c2da20c69bccd6cea13e208c7f2db5581d9fc2cdf6daa9f6ff1996244e21b5","cross_cats_sorted":["cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2017-04-17T15:36:59Z","title_canon_sha256":"4da6667d0a7e7d1bbde200c55109200a2aaff8a1ccd07cddf34386101598dda6"},"schema_version":"1.0","source":{"id":"1704.05003","kind":"arxiv","version":1}},"canonical_sha256":"484bd856f08c64c7081fa6c9daa341c02757db2bc7192eb6aa1e4040feb19cb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"484bd856f08c64c7081fa6c9daa341c02757db2bc7192eb6aa1e4040feb19cb5","first_computed_at":"2026-05-18T00:46:17.268714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:17.268714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OoLYG6OTp49L4hEGwuA1SjI6Hi8p1RxpZFGZIxU35OWm5UNMeVpIIa6UN0A1+Pkekz9q5L6KCs5WghhvAJwQAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:17.269174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edbe40e512fbf81356b2889fc1be389c1c8b6d996598c7974a098a3fae171591","sha256:b5dcd8bfa55278bfd1521533f98dc2b1fdd860cca417a4c23b778be8fd6111df"],"state_sha256":"cf0fef8434dd6ea3003803ba852259960f068d84a118498d2654bf224503b6af"}