{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YE25C7SWWEKZXMPAFSDSER23CZ","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":"c9291ed672da89c416cd0911a1b41a797d19ce480cdac2349db1b99d7eddb83c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-09-27T22:19:40Z","title_canon_sha256":"5ae18f77f4e0984b79aa9795767b868a839cbc7cbee56e299368414ba8deaf85"},"schema_version":"1.0","source":{"id":"1809.10783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10783","created_at":"2026-05-18T00:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10783v1","created_at":"2026-05-18T00:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10783","created_at":"2026-05-18T00:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"YE25C7SWWEKZ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YE25C7SWWEKZXMPA","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YE25C7SW","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:3500feb477f3c038c78fa7d4825294cf3628ae6be64f199881fd1b9efbc93cb6","target":"graph","created_at":"2026-05-18T00:04:35Z","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":"Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger selection game involving open covers is dual to the point-open game. This extends to a general theorem: if $\\{\\operatorname{ran}{f}:f\\in\\mathbf C(\\mathcal R)\\}$ is coinitial in $\\mathcal A$ with respect to $\\subseteq$, where $\\mathbf C(\\mathcal R)=\\{f\\in(\\bigcup\\mathcal R)^{\\mathcal R}:R\\in\\mathcal R\\Rightarrow f(R)\\in R\\}$ collects the choice functions on t","authors_text":"Steven Clontz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-09-27T22:19:40Z","title":"Dual Selection Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10783","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:a2c9dba89dab800ab9496655e0cf971cbaae1c17a7278236bd272ceb09730e3e","target":"record","created_at":"2026-05-18T00:04:35Z","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":"c9291ed672da89c416cd0911a1b41a797d19ce480cdac2349db1b99d7eddb83c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-09-27T22:19:40Z","title_canon_sha256":"5ae18f77f4e0984b79aa9795767b868a839cbc7cbee56e299368414ba8deaf85"},"schema_version":"1.0","source":{"id":"1809.10783","kind":"arxiv","version":1}},"canonical_sha256":"c135d17e56b1159bb1e02c8722475b165d6191463e2babeff6dc345969076f58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c135d17e56b1159bb1e02c8722475b165d6191463e2babeff6dc345969076f58","first_computed_at":"2026-05-18T00:04:35.110125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:35.110125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wgHbsd1+PvmnZtRzXG+tNhWExYkpWxRiDBdeYV8PpJqBQJ8vQw+6UvdcrNwIUW4JKQR6CNNAbWrvgfhoROw2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:35.110585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2c9dba89dab800ab9496655e0cf971cbaae1c17a7278236bd272ceb09730e3e","sha256:3500feb477f3c038c78fa7d4825294cf3628ae6be64f199881fd1b9efbc93cb6"],"state_sha256":"4a829ee4053055c333d550cc9c22f6163dbb68fdd1a22d0da0a76957705178da"}