EXISTENCE OF LIFE IN LENIA

Craig Calcaterra, Axel Boldt

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves that the Lenia arc field X_t(f)(x) = [f(x) + t G((K*f)(x))]^1_0 on M = B(R^n,[0,1]) satisfies Conditions E1 and E2 and generates a unique forward flow via Euler curves, by reducing to a general theorem (Theorem 3) and carefully handling the nonlinearity of the clip-of-clip through a multi-case argument. The candidate model reproduces E1 and the speed bound correctly, but its E2 step improperly replaces X_s(f) with f + s G(K*f) inside the clip and thus drops an O(s) term; without the paper’s clip-of-clip casework, the claimed O(st) bound does not follow. Hence the model’s proof of E2 is flawed, while the paper’s argument is sound.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The work rigorously reframes Lenia within arc-field theory, overcoming the discontinuity barriers of the naive vector-field formulation and providing a clear existence/uniqueness result with Euler-curve convergence. The arguments match established results in the metric-space flow literature and are adapted carefully to Lenia’s clipped dynamics. Minor expository refinements would enhance readability.