Future–Mass Projection with a Constant Dark-to-Baryon Background: A Renormalized FMP Variant Preserving ΩDM/Ωb = 5.4

We develop a renormalized variant of Future–Mass Projection (FMP) in which the cosmological dark-to-baryon matter ratio is held fixed at all redshifts, \( R(z)≡Ω_F/Ω_b=R_0=5.4 \), thereby preserving the ΛCDM background inferred from precision probes. The key step removes the spatial zero mode of the FMP response and reinstates a fixed homogeneous term \( R_0\,ρ_b(a) \); only inhomogeneous fluctuations δF contribute to structure. We formulate the model, derive its linear response, prove that the background expansion H(a) and CMB/BAO/SNe distance relations remain unchanged, and place phenomenological priors on the fluctuation transfer TF (k, a) using weak lensing and redshift-space distortions. The resulting constant-R FMP (cFMP) acts as a scale-localized, baryon-tethered enhancement to clustering without introducing new particles or altering gravitational-wave propagation. We outline decisive tests: (i) baryon–mass co-variations in galaxies and groups (dynamics and lensing with the same kernel), (ii) the rarity of truly baryon-free subhalos in strong lenses, (iii) null signals in non-gravitational dark-matter searches, and (iv) merger chronologies in Bullet-like clusters. All references cited are peer reviewed.