A Corrected Entropy-Gravity Test in the Minimum Relational Universe FieldFormation, Attraction, and Selection for Gradient Sensitivity

A child’s equation, 𝐸𝑚 =𝐹𝑐2/𝑟2,proposed as a toy model of the universe, is examined within the Relational-Structural Framework. The child defined 𝐹 as the first distinction, 𝑟 as a resistant plasma (the void’spushback), 𝑐 as the speed limit of causal dependency propagation, and 𝐸𝑚 as the product of Energy and Mass constituting the content of reality. We show that this equation maps directly onto the central structural equation 𝑅=𝑂·Ψ·Δ𝐸 and onto the resource allocation principle that yields the MOND interpolation function 𝜇(𝑥)=𝑥/(1 +𝑥) derived in earlier work. The child’s 𝐹 corresponds to the minimal distinction primitive of the framework; 𝑟 corresponds to the cosmological processing floor 𝑎0 and the configuration space constraint; 𝑐2 corresponds to the propagation bound on ordered dependency; and 𝐸𝑚 corresponds to realised local reality 𝑅. The golden ratio 𝜑emerges in both the child’s equation (at the balance point 𝐹=𝜑𝑟) and the 𝜇-function (at the transition point 𝑥2 =𝑥+1). The cosmological dark matter ratio Ωcdm/Ω𝑏 = 7−𝜑= 5.382 is shown to be the integral of the distinction-resistance struggle over cosmic history. We argue that the child’s equation is the global, ontological expression of the same structural law that the resource allocation principle expresses locally and differentially. A three-scale picture of cosmic structure - galaxy, cluster, and cosmological horizon-is recovered within the unified language of distinction, resistance,and causal propagation. The paper closes with reflections on the role of intuitive cosmological reasoning in theoretical physics and the continuity between metaphysical first principles and empirically testable dynamics. DISCLAIMER Generative AI was used to assist with [literature screening / coding support / draft language revision]. All AI-assisted outputs were independently checked by the author, and the author takes full responsibility for the final analysis and text. This is encompassing all the work that has been done and will be done. All code is under MIT licensing. All research papers are under Creative Commons License. All code, outputs and notes are included in the reproducibility bundle zip file.