Pith Number

pith:RAI6DYA2

pith:2026:RAI6DYA2CDBYFUODNR747MPIXC

not attested not anchored not stored refs resolved

Universal Design and Physical Applications of Non-Uniform Cellular Automata on Translationally Invariant Lattices

Jie-Yu Zhang, Peng Ye, Xiang-You Huang

A non-uniform cellular automata algorithm generates subsystem symmetry-protected topological states on hyperbolic lattices unattainable on Euclidean ones.

arxiv:2605.13379 v1 · 2026-05-13 · quant-ph · cond-mat.str-el · cs.FL · nlin.CG

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RAI6DYA2CDBYFUODNR747MPIXC}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

118 extracted · 118 resolved · 4 Pith anchors

[1] 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

[2] Consider a quar- terQof an infinite 2d square lattice tessellated by regular rectangles, each of which is labelled as a node

[3] ∞X k=0 ykrk(x) + ∞X k=n ykrk(x) + n−1X k=0 yk˜rk(x) # =x −iy−j

[4] For the{5,4}lattice, we use an alternative Fibonacci representation rather than the standard language of the splitting to simplify calcula- tion [88]

[5] (39) commute with all the Hamil- tonian terms Eq

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:47.859907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8811e1e01a10c382d1c36c7fcfb1e8b8aa6287f5325e3b41bb9813de111d01a8

Aliases

arxiv: 2605.13379 · arxiv_version: 2605.13379v1 · doi: 10.48550/arxiv.2605.13379 · pith_short_12: RAI6DYA2CDBY · pith_short_16: RAI6DYA2CDBYFUOD · pith_short_8: RAI6DYA2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RAI6DYA2CDBYFUODNR747MPIXC \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8811e1e01a10c382d1c36c7fcfb1e8b8aa6287f5325e3b41bb9813de111d01a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4f90b9c3dcf081f8a1f912bd763a2d287c5dd5110d6ff0182fd5b4b30156f3d",
    "cross_cats_sorted": [
      "cond-mat.str-el",
      "cs.FL",
      "nlin.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-13T11:34:41Z",
    "title_canon_sha256": "dcf2a0d02c4211c11d839f98f741096c9315595449523894f0016b5426fc2bb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13379",
    "kind": "arxiv",
    "version": 1
  }
}