{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DOXDTP6MZDD2WQSPRD3ZEBX2O6","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":"522afcaaf6bf3367f5d8e0fd601e04345a50b3ee548ee16523d0b365678cbaac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T23:30:31Z","title_canon_sha256":"a46fe297a11f35f2d2099429c150a9358a933c2c3f7c2afe5a5d1ac651aae25b"},"schema_version":"1.0","source":{"id":"1503.05614","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05614","created_at":"2026-05-18T00:23:14Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05614v3","created_at":"2026-05-18T00:23:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05614","created_at":"2026-05-18T00:23:14Z"},{"alias_kind":"pith_short_12","alias_value":"DOXDTP6MZDD2","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DOXDTP6MZDD2WQSP","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DOXDTP6M","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:48c194d3edbcddf6c89c13f98ae80f90df02430d254281accc1a3584cb2d2bec","target":"graph","created_at":"2026-05-18T00:23:14Z","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 each site of the square lattice $\\mathbb{Z}^2$ be independently assigned one of three states: a \\textit{trap} with probability $p$, a \\textit{target} with probability $q$, and \\textit{open} with probability $1-p-q$, where $0<p+q<1$. Consider the following game: a token starts at the origin, and two players take turns to move, where a move consists of moving the token from its current site $x$ to either $x+(0,1)$ or $x+(1,0)$. A player who moves the token to a trap loses the game immediately, while a player who moves the token to a target wins the game immediately. Is there positive probabi","authors_text":"Alexander E. Holroyd, Ir\\`ene Marcovici, James B. Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T23:30:31Z","title":"Percolation games, probabilistic cellular automata, and the hard-core model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05614","kind":"arxiv","version":3},"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":"sha256:6fae80db9a3c1934b85d246e753601772c608fa9c8bbb826c5617ea5eaae5db9","target":"record","created_at":"2026-05-18T00:23:14Z","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":"522afcaaf6bf3367f5d8e0fd601e04345a50b3ee548ee16523d0b365678cbaac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T23:30:31Z","title_canon_sha256":"a46fe297a11f35f2d2099429c150a9358a933c2c3f7c2afe5a5d1ac651aae25b"},"schema_version":"1.0","source":{"id":"1503.05614","kind":"arxiv","version":3}},"canonical_sha256":"1bae39bfccc8c7ab424f88f79206fa77af7a823b1fad9712a92c10427d48ec79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bae39bfccc8c7ab424f88f79206fa77af7a823b1fad9712a92c10427d48ec79","first_computed_at":"2026-05-18T00:23:14.731922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:14.731922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n1AtwrxKifxpNtt99RIPQHZ/cEcdzSO71+Qh13EL4Cbpc4MCCqiakKViNw6VoFaKinSQPCS0maSAr6xE6Y2NAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:14.732611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05614","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fae80db9a3c1934b85d246e753601772c608fa9c8bbb826c5617ea5eaae5db9","sha256:48c194d3edbcddf6c89c13f98ae80f90df02430d254281accc1a3584cb2d2bec"],"state_sha256":"4c4e7333d4c087dbcedd8be732f037d6157c15363336720fee855e030d27b271"}