{"paper":{"title":"Universal Design and Physical Applications of Non-Uniform Cellular Automata on Translationally Invariant Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A non-uniform cellular automata algorithm generates subsystem symmetry-protected topological states on hyperbolic lattices unattainable on Euclidean ones.","cross_cats":["cond-mat.str-el","cs.FL","nlin.CG"],"primary_cat":"quant-ph","authors_text":"Jie-Yu Zhang, Peng Ye, Xiang-You Huang","submitted_at":"2026-05-13T11:34:41Z","abstract_excerpt":"Lattice geometry profoundly shapes physical phenomena such as subsystem symmetry and directed percolation (DP). Among various lattice geometries, hyperbolic lattices are characterized by constant negative curvature and non-Abelian translation symmetry, offering a rich platform for investigating this geometry-physics interplay. However, the exponentially growing lattice size and nontrivial translation symmetry make approaches developed for Euclidean lattices incompatible, a limitation particularly evident in uniform cellular automata (CA). To resolve this, we develop a higher-order non-uniform "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We develop a higher-order non-uniform cellular automata (NUCA) algorithm applicable to both translationally invariant regular Euclidean and hyperbolic lattices... By applying a linear NUCA, we generate subsystem symmetry-protected topological (SSPT) states and spontaneous subsystem symmetry-breaking states associated with regular or irregular subsystem symmetries unattainable on Euclidean lattices.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The lattice-deforming procedure correctly folds nontrivial geometric data into the non-uniform update rules while preserving the required translation invariance and without introducing spurious correlations or breaking the intended symmetry protection.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A higher-order non-uniform cellular automata algorithm is introduced for translationally invariant Euclidean and hyperbolic lattices, demonstrated on the {5,4} lattice to generate subsystem symmetry-protected topological states and simulate directed percolation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A non-uniform cellular automata algorithm generates subsystem symmetry-protected topological states on hyperbolic lattices unattainable on Euclidean ones.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ac6c0b413b293ac8d1ad98f7d77797ebe3db08dcdc0b53214b7eea9b0e75999e"},"source":{"id":"2605.13379","kind":"arxiv","version":1},"verdict":{"id":"4e8a535b-7747-47c2-aae6-57a841313bef","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:10:15.015462Z","strongest_claim":"We develop a higher-order non-uniform cellular automata (NUCA) algorithm applicable to both translationally invariant regular Euclidean and hyperbolic lattices... By applying a linear NUCA, we generate subsystem symmetry-protected topological (SSPT) states and spontaneous subsystem symmetry-breaking states associated with regular or irregular subsystem symmetries unattainable on Euclidean lattices.","one_line_summary":"A higher-order non-uniform cellular automata algorithm is introduced for translationally invariant Euclidean and hyperbolic lattices, demonstrated on the {5,4} lattice to generate subsystem symmetry-protected topological states and simulate directed percolation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The lattice-deforming procedure correctly folds nontrivial geometric data into the non-uniform update rules while preserving the required translation invariance and without introducing spurious correlations or breaking the intended symmetry protection.","pith_extraction_headline":"A non-uniform cellular automata algorithm generates subsystem symmetry-protected topological states on hyperbolic lattices unattainable on Euclidean ones."},"references":{"count":118,"sample":[{"doi":"","year":null,"title":"III and Appendix D, we develop a lattice- deforming procedure for the hyperbolic lattice based on the splitting method and the language of splitting, to design the deformed lattice","work_id":"fda11330-e375-4c94-8512-7df6831cd404","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Consider a quar- terQof an infinite 2d square lattice tessellated by regular rectangles, each of which is labelled as a node","work_id":"48264eff-d3de-4325-bf7e-b859c5bd5a15","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"∞X k=0 ykrk(x) + ∞X k=n ykrk(x) + n−1X k=0 yk˜rk(x) # =x −iy−j","work_id":"4aa6b134-cdd4-4e2a-979b-2d7211996615","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"For the{5,4}lattice, we use an alternative Fibonacci representation rather than the standard language of the splitting to simplify calcula- tion [88]","work_id":"11edc0a1-9d08-4cfd-8fde-6f8253e33b8e","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"(39) commute with all the Hamil- tonian terms Eq","work_id":"8d29ebf2-771a-4eb1-9cc1-605143895e48","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":118,"snapshot_sha256":"e7cdadeba6edbe449b8c9e9a9874840633b3979ef12b19f8f1c385ab18d4f9d6","internal_anchors":4},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f69b80cc2d5a51de92c2f0b2ecda992f68b45242aea8a614c0ade6e22fee7539"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}