From Entropy-Field Response to 7-: A Parameter-Locked Dark-Sector Ratio and Boltzmann-Code Consistency Test

Description / Abstract This paper proposes a relational-structural derivation route for the dark-to-baryonic matter density ratio: Omegacdm / Omegab = 7 - phi = 5. 381966… where phi is the golden ratio. The argument begins from a nonlinear entropy-field response function, mu (u) = u / (1 + u), interpreted as the normalized scalar response coefficient fX / kappa. A quadratic perturbation expansion distinguishes this baseline scalar response from the longitudinal stiffness term fX + 2X fXX. A self-similar active/residual response partition then fixes the transition point to uₛtar = phi, giving mu (phi) = 1 / phi. Subtracting this effective scalar response from the six independent spatial metric channels yields the residual structural count: 6 - 1 / phi = 7 - phi. The paper then tests the minimal cosmological implementation, Model 0, in which the cold dark matter abundance is not independently fitted but locked by: omegacdm = (7 - phi) omegab. A CLASS Boltzmann-code audit shows that, for omegab = 0. 02237, the model gives omegacdm = 0. 1203946 and preserves the matter power spectrum, CMB spectra, DESI Lyman-alpha-style BAO distance ratios, and growth observables at sub-percent level relative to a nearby Lambda-CDM comparison model. The analysis also reports a baryon-density robustness scan over omegab = 0. 02220–0. 02255. This work is presented as a theoretical and computational consistency note, not as a completed derivation of dark matter microphysics or a full replacement for Lambda-CDM. The key remaining tasks are deriving the scalar channel occupancy from a full covariant perturbation action, implementing any structural-entropy growth modification directly in a Boltzmann solver, and testing nonlinear structure formation. Short plain-language summary This paper explores whether the observed dark-matter-to-baryon ratio can be derived from a structural response rule rather than fitted freely. It proposes the ratio 7 - phi, where phi is the golden ratio, and checks the simplest implementation with the CLASS cosmology code. The result is not a claim that dark matter is fully solved; it is a consistency test showing that fixing the dark matter abundance this way does not disrupt standard linear cosmology. The paper should be read as a proposed derivation route plus a numerical consistency audit. It does not claim to derive the full Einstein equations, identify a dark matter particle, or complete the nonlinear structure-formation programme. Its main result is that the constrained abundance relation omegacdm = (7 - phi) omegab is compatible with standard linear cosmological observables in the tested CLASS implementation. 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.