What question did this study set out to answer?

The aim is to explore how discrete nodes emerge from continuous dynamics in a noise-ballast phase model.

April 13, 2026Open Access

Critical Ridge and Emergent Discreteness in a Noise–Ballast Phase Model

Key Points

The aim is to explore how discrete nodes emerge from continuous dynamics in a noise-ballast phase model.
Developed a noise-ballast phase model to observe emergent behavior.
Analyzed the phase surface for complexity and scaling relationships.
Employed a distance-to-ridge coordinate for examining near-critical phenomena.
Identified a ridge of maximal complexity in the phase surface.
Found an approximate scaling law related to noise with alpha_crit ~ noise^-p, where p is about 1.1.
Demonstrated that the distance-to-ridge coordinate improves clarity in critical behavior analysis.

Abstract

This deposit presents a noise–ballast phase model in which discrete nodes emerge from continuous noisy dynamics through threshold retention. The main result is a ridge of maximal complexity across the phase surface, with an approximate scaling law alphacrit ~ noise^-p and p close to 1. 1. While a global one-parameter collapse fails, a distance-to-ridge coordinate organizes the near-critical behavior more clearly. The deposit includes the main text, core figures, and ridge-fit data.

Critical Ridge and Emergent Discreteness in a Noise–Ballast Phase Model

Key Points

Abstract

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