{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JW2CY77IMZSN2RSLR7R76LPZZC","short_pith_number":"pith:JW2CY77I","schema_version":"1.0","canonical_sha256":"4db42c7fe86664dd464b8fe3ff2df9c8a4a7290f6d05aab65c99fa2214dcb234","source":{"kind":"arxiv","id":"1304.7301","version":4},"attestation_state":"computed","paper":{"title":"Percolation and disorder-resistance in cellular automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Alexander E. Holroyd, Janko Gravner","submitted_at":"2013-04-26T22:37:42Z","abstract_excerpt":"We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random initial seed on an interval of length $L$, with probability tending to one as $L\\to\\infty$, the evolution is a replicator. That is, a region of space-time of density one is filled with a spatially and temporally periodic pattern, punctuated by a finite set of other finite patterns repeated at a fractal set of locations. On the other hand, the same rules exhibit "},"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":"1304.7301","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-26T22:37:42Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"6e1468c29f819c842a24ce7db532c572cf2c675d6a36d1290d8b30d201e084d6","abstract_canon_sha256":"bad057e9d03029b7c1f56e2d4522bdaf5625665adc3d406b8a0df5aa59925f6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:53.555652Z","signature_b64":"Qq6oLx8Pnv/pFZ2VtQGxobIqLslRDa9HHA0IF2DLmFyP65AHSbd/1BfRkP/1J3lQ4fWvI/BdNGQajnhAUNl3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4db42c7fe86664dd464b8fe3ff2df9c8a4a7290f6d05aab65c99fa2214dcb234","last_reissued_at":"2026-05-18T01:31:53.555067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:53.555067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Percolation and disorder-resistance in cellular automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Alexander E. Holroyd, Janko Gravner","submitted_at":"2013-04-26T22:37:42Z","abstract_excerpt":"We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random initial seed on an interval of length $L$, with probability tending to one as $L\\to\\infty$, the evolution is a replicator. That is, a region of space-time of density one is filled with a spatially and temporally periodic pattern, punctuated by a finite set of other finite patterns repeated at a fractal set of locations. On the other hand, the same rules exhibit "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7301","kind":"arxiv","version":4},"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":"1304.7301","created_at":"2026-05-18T01:31:53.555149+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.7301v4","created_at":"2026-05-18T01:31:53.555149+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7301","created_at":"2026-05-18T01:31:53.555149+00:00"},{"alias_kind":"pith_short_12","alias_value":"JW2CY77IMZSN","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JW2CY77IMZSN2RSL","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JW2CY77I","created_at":"2026-05-18T12:27:49.015174+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/JW2CY77IMZSN2RSLR7R76LPZZC","json":"https://pith.science/pith/JW2CY77IMZSN2RSLR7R76LPZZC.json","graph_json":"https://pith.science/api/pith-number/JW2CY77IMZSN2RSLR7R76LPZZC/graph.json","events_json":"https://pith.science/api/pith-number/JW2CY77IMZSN2RSLR7R76LPZZC/events.json","paper":"https://pith.science/paper/JW2CY77I"},"agent_actions":{"view_html":"https://pith.science/pith/JW2CY77IMZSN2RSLR7R76LPZZC","download_json":"https://pith.science/pith/JW2CY77IMZSN2RSLR7R76LPZZC.json","view_paper":"https://pith.science/paper/JW2CY77I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.7301&json=true","fetch_graph":"https://pith.science/api/pith-number/JW2CY77IMZSN2RSLR7R76LPZZC/graph.json","fetch_events":"https://pith.science/api/pith-number/JW2CY77IMZSN2RSLR7R76LPZZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JW2CY77IMZSN2RSLR7R76LPZZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JW2CY77IMZSN2RSLR7R76LPZZC/action/storage_attestation","attest_author":"https://pith.science/pith/JW2CY77IMZSN2RSLR7R76LPZZC/action/author_attestation","sign_citation":"https://pith.science/pith/JW2CY77IMZSN2RSLR7R76LPZZC/action/citation_signature","submit_replication":"https://pith.science/pith/JW2CY77IMZSN2RSLR7R76LPZZC/action/replication_record"}},"created_at":"2026-05-18T01:31:53.555149+00:00","updated_at":"2026-05-18T01:31:53.555149+00:00"}