{"paper":{"title":"Analysis of the asymptotic density of endogamous diploid cellular automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CG","authors_text":"Henryk Fuk{\\'s}, LORIA), Nazim Fat\\`es (MOCQUA","submitted_at":"2026-07-02T09:16:11Z","abstract_excerpt":"We investigate the asymptotic behaviour of diploid Elementary Cellular Automata (ECA), that is, the stochastic mixtures between two ECAs. In this model, each cell independently applies one rule with probability $\\lambda$ and the other rule with probability $ 1 - \\lambda$. Focusing on the endogamous diploids where the two ECAs are related by the reflection or conjugation symmetry, we analyse how the density varies as function of $\\lambda$, the ``degree of mixing'' of these two rules. We propose a classification into six distinct classes depending on the profile of the density vs. $\\lambda$ curv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01917","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01917/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}