Dark Matter as a Dissipative Informational Condensate: Reynolds-Number Scaling from Galaxy Rotation Curves to Cosmological Simulations

We present the Grand Unified Brane-Informational Model (GUBIM), a field-theoretic framework in which dark matter phenomenology emerges from a real scalar condensate φ whose dissipative dynamics are governed by a Reynolds-number-dependent viscosity Γₑff (Re) = Γ₀/√ (1+Re²). The kinetic-dominated regime (Re ≪ 1, galactic scales) produces ρ_φ ∝ r⁻², reproducing flat rotation curves without exotic particles. The viscous regime (Re ≫ 1, cluster scales) generates a Stokes-drag energy-exchange term that mediates the observed dark-matter–baryonic coupling in merging clusters. We validate the framework across three independent astrophysical domains. (i) Applied to the SPARC sample of 175 disc galaxies via an Echo-State Network (ESN) trained with global normalisation, GUBIM achieves an out-of-distribution score of R²OOD = 0. 857 and a model selection advantage of ΔAIC = 351 over the Radial Acceleration Relation (RAR/MOND). Principal Component Analysis reveals a bifurcation: PC1 encodes baryonic geometry (r = −0. 924 with ḡ) while PC2 encodes entropy (r = +0. 958 with ḡ·√Λcosm), selecting √Λcosm as the natural EFT scale of the coupling λ. (ii) In a sample of 12 galaxy clusters, the DM–gas centroid offset δr/R₂₀₀ correlates with effective Reynolds number at r = 0. 704 (p = 0. 011), and the Stokes exponent α = 0. 876 ≈ 1 confirms the high-Re dissipative regime. (iii) In IllustrisTNG-100 (N = 498 star-forming halos at z = 0), the partial correlation of fDM with specific star formation rate controlling for baryonic mass yields r = −0. 709 (p = 4×10⁻⁷⁷), surviving triple and quadruple control variables at > 13σ above the permutation null. All three domains are governed by a single effective coupling λdim = 7×10⁻⁹ kpc^ (1/2) Mₛun^ (−1/2) Gyr^ (−1), demonstrating the universality predicted by the EFT formulation.