{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DOXDTP6MZDD2WQSPRD3ZEBX2O6","short_pith_number":"pith:DOXDTP6M","schema_version":"1.0","canonical_sha256":"1bae39bfccc8c7ab424f88f79206fa77af7a823b1fad9712a92c10427d48ec79","source":{"kind":"arxiv","id":"1503.05614","version":3},"attestation_state":"computed","paper":{"title":"Percolation games, probabilistic cellular automata, and the hard-core model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander E. Holroyd, Ir\\`ene Marcovici, James B. Martin","submitted_at":"2015-03-18T23:30:31Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.05614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T23:30:31Z","cross_cats_sorted":[],"title_canon_sha256":"a46fe297a11f35f2d2099429c150a9358a933c2c3f7c2afe5a5d1ac651aae25b","abstract_canon_sha256":"522afcaaf6bf3367f5d8e0fd601e04345a50b3ee548ee16523d0b365678cbaac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:14.732611Z","signature_b64":"n1AtwrxKifxpNtt99RIPQHZ/cEcdzSO71+Qh13EL4Cbpc4MCCqiakKViNw6VoFaKinSQPCS0maSAr6xE6Y2NAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bae39bfccc8c7ab424f88f79206fa77af7a823b1fad9712a92c10427d48ec79","last_reissued_at":"2026-05-18T00:23:14.731922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:14.731922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Percolation games, probabilistic cellular automata, and the hard-core model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander E. Holroyd, Ir\\`ene Marcovici, James B. Martin","submitted_at":"2015-03-18T23:30:31Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05614","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.05614","created_at":"2026-05-18T00:23:14.732028+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.05614v3","created_at":"2026-05-18T00:23:14.732028+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05614","created_at":"2026-05-18T00:23:14.732028+00:00"},{"alias_kind":"pith_short_12","alias_value":"DOXDTP6MZDD2","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DOXDTP6MZDD2WQSP","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DOXDTP6M","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DOXDTP6MZDD2WQSPRD3ZEBX2O6","json":"https://pith.science/pith/DOXDTP6MZDD2WQSPRD3ZEBX2O6.json","graph_json":"https://pith.science/api/pith-number/DOXDTP6MZDD2WQSPRD3ZEBX2O6/graph.json","events_json":"https://pith.science/api/pith-number/DOXDTP6MZDD2WQSPRD3ZEBX2O6/events.json","paper":"https://pith.science/paper/DOXDTP6M"},"agent_actions":{"view_html":"https://pith.science/pith/DOXDTP6MZDD2WQSPRD3ZEBX2O6","download_json":"https://pith.science/pith/DOXDTP6MZDD2WQSPRD3ZEBX2O6.json","view_paper":"https://pith.science/paper/DOXDTP6M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.05614&json=true","fetch_graph":"https://pith.science/api/pith-number/DOXDTP6MZDD2WQSPRD3ZEBX2O6/graph.json","fetch_events":"https://pith.science/api/pith-number/DOXDTP6MZDD2WQSPRD3ZEBX2O6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DOXDTP6MZDD2WQSPRD3ZEBX2O6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DOXDTP6MZDD2WQSPRD3ZEBX2O6/action/storage_attestation","attest_author":"https://pith.science/pith/DOXDTP6MZDD2WQSPRD3ZEBX2O6/action/author_attestation","sign_citation":"https://pith.science/pith/DOXDTP6MZDD2WQSPRD3ZEBX2O6/action/citation_signature","submit_replication":"https://pith.science/pith/DOXDTP6MZDD2WQSPRD3ZEBX2O6/action/replication_record"}},"created_at":"2026-05-18T00:23:14.732028+00:00","updated_at":"2026-05-18T00:23:14.732028+00:00"}