The Dark Matter Ratio Seven Minus the Golden Ratio A prediction from spacetime dimensionality, the covariant entropy action, and Shannon's channel capacity theorem

This document presents a zero‑parameter prediction of the dark matter to baryon ratio in the universe: Ωcdm/Ωb=7−ϕ=5.382Ωcdm/Ωb=7−ϕ=5.382, where ϕ=(1+5)/2ϕ=(1+5)/2 is the golden ratio. The derivation proceeds from three inputs: (i) the physical metric of (3+1)‑dimensional spacetime has six independent degrees of freedom; (ii) the covariant k‑essence action for the scalar entropy field yields a coupling coefficient f′(Xϕ)=κ/ϕf′(Xϕ)=κ/ϕ at the self‑similar transition point (obtained by differentiating the Lagrangian and applying ϕ2=ϕ+1ϕ2=ϕ+1); and (iii) the information‑processing derivation: the effective number of degrees of freedom captured by the scalar field equals its processing fraction μ(ϕ)=1/ϕμ(ϕ)=1/ϕ, which follows from the resource‑allocation principle together with Shannon's channel capacity theorem. The remaining 6−1/ϕ=7−ϕ6−1/ϕ=7−ϕ degrees of freedom constitute structural entropy, which gravitates as cold dark matter. The predicted ωcdm=0.1204ωcdm=0.1204 deviates from the Planck 2018 measurement (0.1200±0.00120.1200±0.0012) by 0.3σ0.3σ. The CMB power spectrum, computed with the CLASS Boltzmann code, matches ΛΛCDM to 0.031%0.031% RMS. The prediction is consistent with the DESI DR2 neutrino mass constraint (∑mν<0.064∑mν<0.064 eV), which excludes the alternative bare‑DOF prediction (∑mν=0.76∑mν=0.76 eV) by a factor of 12. If the effective number of relativistic species NeffNeff exceeds the Standard Model value (for example due to a partially thermalised majoron), the best‑fit H0H0 shifts toward 72 km s−1 Mpc−172 kms−1Mpc−1, easing the Hubble tension. The paper is part of the Minimum Relational Universe (MRU) programme, which derives gravitational phenomenology from an entropy density field sourced by the Landauer cost of maintaining persistent structures. 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.