Perturbation-Stable Discrete Attractors in an Unbiased Recursive Clustering Model

Perturbation-Stable Discrete Attractors in an Unbiased Recursive Clustering Model This repository contains the full manuscript, source code, and analysis outputs associated with a computational study of discrete attractors in a non-equilibrium molecular clustering system. The work introduces and validates a perturbation–reformation protocol for identifying stable configurations in dynamical systems without imposing target states or equilibrium assumptions. A model consisting of 40 water molecules surrounding a hydrophobic guest was evolved over multiple independent simulations (5 runs × 1000 ps). Cluster size was tracked continuously, with no preferred or constrained target values. Stability was tested dynamically by applying repeated randomized perturbations (hydrogen-bond disruption and kinetic noise) to candidate stable states and measuring spontaneous reformation rates. Across 1,050 independent perturbation events, nine cluster sizes exhibited perfect reformation behavior, with four sizes (14, 17, 22, and 24) qualifying as primary attractors based on statistical robustness and neighbor suppression. The system displayed a hierarchical basin structure, with cluster size 24 emerging as a terminal attractor, characterized by late-time dominance, perfect perturbation recovery, and a hard upper boundary (no configurations with N > 24 observed). Notably, the terminal attractor (N = 24) coincides numerically with Z₀ ≈ 23.97, a constant derived independently in prior theoretical work from fundamental constants. No elements of that derivation were used in the construction, parameterization, or execution of the present model, making the agreement an emergent numerical correspondence rather than an imposed constraint. The repository includes: The peer-review-ready manuscript (PDF and LaTeX source) The full perturbation validation script Aggregated perturbation statistics (JSON) Visualization outputs used in the paper A README detailing methodology, reproducibility, and limitations All materials are released under CC BY-NC-ND 4.0. The code is provided for replication and methodological study; no claims are made regarding direct physical realism beyond the defined model. This work establishes perturbation–reformation testing as a general, system-agnostic method for attractor discovery in complex dynamical systems where equilibrium approaches are insufficient or misleading. For futher information about the ENSO Framework, please contact Eric Needham:ensotheory1@gmail.com