{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VFPXRNMYEL3KSTU5KR54SGAQJR","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":"ea2d8249107084741f98717c5a7bec53fa8f7694be7bc2fba6b1ada75b2dadb8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-07-10T15:53:05Z","title_canon_sha256":"c622f10dd6fea2beedca20838d597e09e0477ba83a0cd361041cfb8210d2085f"},"schema_version":"1.0","source":{"id":"1907.04804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04804","created_at":"2026-05-17T23:40:56Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04804v1","created_at":"2026-05-17T23:40:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04804","created_at":"2026-05-17T23:40:56Z"},{"alias_kind":"pith_short_12","alias_value":"VFPXRNMYEL3K","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VFPXRNMYEL3KSTU5","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VFPXRNMY","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:d71a0163117ddcf2c60caaa45cdcb1d10e31d9c06c3a848abf0466112d875f7e","target":"graph","created_at":"2026-05-17T23:40:56Z","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":"In a $(1:b)$ biased Maker-Breaker game, how good a strategy is for a player can be measured by the bias range for which its rival can win, choosing an appropriate counterstrategy. Bednarska and {\\L}uczak proved that, in the $H$-subgraph game, the uniformly random strategy for Maker is essentially optimal with high probability. Here we prove an analogous result for the $H$-graph minor game, and we study for which choices of $H$ the random strategy is within a factor of $1+o(1)$ of being optimal.","authors_text":"Ander Lamaison","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-07-10T15:53:05Z","title":"The random strategy in Maker-Breaker graph minor games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04804","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":"sha256:23c6dc415beed2d8c2fa556dfef20cd7e7e24645d1851ff521f4b1fb76f04326","target":"record","created_at":"2026-05-17T23:40:56Z","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":"ea2d8249107084741f98717c5a7bec53fa8f7694be7bc2fba6b1ada75b2dadb8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-07-10T15:53:05Z","title_canon_sha256":"c622f10dd6fea2beedca20838d597e09e0477ba83a0cd361041cfb8210d2085f"},"schema_version":"1.0","source":{"id":"1907.04804","kind":"arxiv","version":1}},"canonical_sha256":"a95f78b59822f6a94e9d547bc918104c5824fbb8dae2e6fd110c919b626ccaef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a95f78b59822f6a94e9d547bc918104c5824fbb8dae2e6fd110c919b626ccaef","first_computed_at":"2026-05-17T23:40:56.683910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:56.683910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hg5M97jWkxBOfYra7fCVjoFGpER8ISoSsZQFD2It2nKQgzy9PttTj5SxsrPx13Wp6BHE5JyINyXDR1Gih1a0Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:56.684612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.04804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23c6dc415beed2d8c2fa556dfef20cd7e7e24645d1851ff521f4b1fb76f04326","sha256:d71a0163117ddcf2c60caaa45cdcb1d10e31d9c06c3a848abf0466112d875f7e"],"state_sha256":"cd5f2d94a1d794519d9fc35f91f3cf1b2ff290f37eec54f66c02b2244488059c"}