{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IPQVTEKXUKUI236YEBBWIXWHWN","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":"391fce85607b9dd15f7fb49dc621502c87708d25f7408277416a9870734a042f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-25T17:57:51Z","title_canon_sha256":"dd454cbb25bc67eb9ace556a074e207c0ce201e20ed8e30518d498bfde7ddcd4"},"schema_version":"1.0","source":{"id":"1312.6990","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6990","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6990v5","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6990","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"IPQVTEKXUKUI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IPQVTEKXUKUI236Y","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IPQVTEKX","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:6c2212e455fd7ddb71ce33d7efe1085d9ec398319fd4fe9427ec7718e5f6f0e9","target":"graph","created_at":"2026-05-18T02:07:32Z","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":"This paper considers a class of probabilistic cellular automata undergoing a phase transition with an absorbing state. Denoting by ${\\mathcal{U}}(x)$ the neighbourhood of site $x$, the transition probability is $T(\\eta_x = 1 | \\eta_{{\\mathcal{U}}(x)}) = 0$ if $\\eta_{{\\mathcal{U}}(x)}= \\mathbf{0}$ or $p$ otherwise, $\\forall x \\in \\mathbb{Z}$. For any $\\mathcal{U}$ there exists a non-trivial critical probability $p_c({\\mathcal{U}})$ that separates a phase with an absorbing state from a fluctuating phase. This paper studies how the neighbourhood affects the value of $p_c({\\mathcal{U}})$ and provi","authors_text":"Lorenzo Taggi","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-25T17:57:51Z","title":"Critical probabilities and convergence time of Percolation Probabilistic Cellular Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6990","kind":"arxiv","version":5},"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:ade8b411398a1be055d5fbb1b3c4a66bda7c6d81e8e2f4106c14dc837cf41065","target":"record","created_at":"2026-05-18T02:07:32Z","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":"391fce85607b9dd15f7fb49dc621502c87708d25f7408277416a9870734a042f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-25T17:57:51Z","title_canon_sha256":"dd454cbb25bc67eb9ace556a074e207c0ce201e20ed8e30518d498bfde7ddcd4"},"schema_version":"1.0","source":{"id":"1312.6990","kind":"arxiv","version":5}},"canonical_sha256":"43e1599157a2a88d6fd82043645ec7b3553a1b11ba15f36890ed5d893666c18b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43e1599157a2a88d6fd82043645ec7b3553a1b11ba15f36890ed5d893666c18b","first_computed_at":"2026-05-18T02:07:32.107425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:32.107425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XZj7MR0j0WAkIyR05Hcqn+q/cgB9R9cx3zNQVP7Zh7915knOllu7scVr8wi4Ch6xSxxFb7hKQ1/KYIcl560ODw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:32.108014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6990","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ade8b411398a1be055d5fbb1b3c4a66bda7c6d81e8e2f4106c14dc837cf41065","sha256:6c2212e455fd7ddb71ce33d7efe1085d9ec398319fd4fe9427ec7718e5f6f0e9"],"state_sha256":"0262bf468352680ea6e8bc0fa6757e70a8391db31a1eff56a09e0e857b67b1e7"}