MyUncle: a compact maintenance-lattice framework for order-persistence simulations across disciplines

Overview MyUncle is a compact (~450-line, single-file) Python framework for maintenance-lattice simulations: a directionally ordered medium is eroded by a state-dependent damage flux and restored by repair, and the framework answers when — and how much — order persists. The same skeleton underlies XY magnets under site dilution, polymer photodegradation, liquid-crystal ordering, chiral molecular scaffolds in origin-of-life chemistry, magnetic storage decay, and pair-breaking in superconducting order. Key features Closed-form analytics: a von Mises order–entropy bridge with the exact identity dS/dU = −κ (monotonicity via a Turán-type inequality for modified Bessel functions). Mean-field reduction dI/dτ = μ(I)(1−I) − ρI with universal collapse I* = 1/(1+ρ) in the linear case and a saddle-node bistable window (ρ ≈ 3.92–11.30) under Hill feedback. Site-diluted XY kinetic Monte Carlo with disorder-dependent kill rates and stochastic repair; non-equilibrium steady states carry strictly positive Schnakenberg entropy production, and the field-free limit recovers Berezinskii–Kosterlitz–Thouless behaviour via the helicity-modulus crossing 2T/π. Six discipline presets sharing one engine; a 6,000-point reference grid for landscape and optimization studies (~0.07 s per configuration at screening fidelity on one desktop CPU). One-call reproduce_paper() entry point that regenerates the complete figure suite plus a manuscript skeleton; dependencies are only numpy, scipy, and matplotlib. Repository contents MyUncle_core.py (framework), README.md (usage, including driving it with AI assistants), paper.md/paper.bib (JOSS manuscript source), tests/test_myuncle.py (validation suite), LICENSE (MIT), CONTRIBUTING.md. Links Development repository: https://github.com/sandlerleon/MyUncle The companion physics preprint "Information Preservation in Non-Equilibrium Spin Networks Under Rotating Magnetic Fields" (Zenodo, 2026) uses this framework for its supporting simulations.