Ten-sector validation

The equilibrium density ρ_s = 7.3 × 10⁻²⁷ kg/m³ is derived from the condensation functional. The ten sectors below are the domains in which that density, and quantities derived from it, are used or tested. This is not a fit of ρ_s to the cosmological constant.

1. Cosmology and large-scale structure
   ρₛ; substrate energy density uₛ = ρₛc²; gravitational domain scale derived from ρₛ
   Cosmological vacuum-energy relationship; finite substrate gravitational domain; large-scale structure and related cosmological consequences addressed through the BFUT substrate framework.
   P14, P18, P23, P25, P26, P27
2. Gravitation and gravitational field
   ρₛ; carrier mass scale μₛ; Lₛ; acceleration scale aₛ; substrate deformation
   Covariant carrier equation, finite deformation-domain radius, DME gravitational response, and a unified gravitational description across quantum, classical, galactic, and rapid-transition regimes.
   P17, P18, P25, P26
3. Galactic dynamics and dark-matter effects
   ρₛ; aₛ = 1.208 × 10⁻¹⁰ m/s²; DME equation; DDR domain
   SPARC validation across 175 galaxies: 92.0% shape agreement, 98.8% flat classification, 14.3% non-flat classification, and median outer relative residual 0.096. DME accounts for the observed extra gravitational support without introducing a dark-matter particle.
   P18, P25, P26, P78
4. Weak gravitational lensing
   ρₛ; aₛ; DME domain response
   KiDS-1000 validation using the same DME relation and the same density-derived acceleration scale. The four stacked stellar-mass bins provide an independent weak-lensing test of the gravitational response.
   P18, P25, P27, P78
5. Particle physics and fundamental constants
   R₀; ħ_vss; m_e_vss; α_vss; αₛ_vss; M; m_W_vss; m_Z_vss; sin²θ_W_vss; λ_H_vss; v_vss; m_H_vss; m_Shankar; m_BFUT
   The P16 condensation geometry supplies the common particle-sector origin. P19 gives the independent resonances m_Z_vss = π⁴mₚ = 91.396 GeV/c² and m_W_vss = 256M = (256/3)mₚ = 80.066 GeV/c²; their ratio gives sin²θ_W_vss = 0.23257. The radial mode gives λ_H_vss = 2AR₀/π² and m_H_vss = 124.75 GeV/c². P16A gives the higher four-unit configuration excitations m_Shankar c² = 776.5 MeV (2+2) and m_BFUT c² = 1403.7 MeV (4+0).
   P16, P16A, P17, P19, P19A, P25, P27
6. Quantum mechanics
   ρₛ; condensation structure; ℏ; particle mass relations
   BFUT P19A connects the substrate-based particle structure with quantum phenomena including half-integer spin, the Born rule, wave-function collapse, and Higgs physics, within the unified quantum-gravity framework.
   P16, P19A, P25, P27
7. Atomic physics and matter stability
   ρₛ; ħ_vss; m_e_vss; α_vss; a₀_vss; E_H_vss
   Hydrogen ground-state and Bohr-radius results follow from ħ_vss, m_e_vss and α_vss. Matter stability follows from the corresponding atomic-scale and bond-energy relations.
   P16, P19, P25, P27
8. Light, photons, and gravitational-wave propagation
   ρₛ; substrate stiffness Kₛ; c
   Photon and gravitational-wave propagation arise from the same substrate propagation mechanism. The universal speed limit is written mechanically as c_vss = √(Kₛ/ρₛ), with an independent numerical reconstruction of c_vss from the BFUT quantity chain.
   P17, P18, P19, P23, P25
9. Time and relativity
   ρₛ; c; substrate propagation efficiency η; carrier response structure
   Time is treated as accumulated substrate evolution. Kinematic and gravitational time dilation arise from the allocation of finite substrate propagation capability between spatial motion, internal evolution, and gravitational deformation.
   P18, P19, P22, P23
10. Extreme gravity, singularity limits, and black holes
    ρₛ; substrate deformation and finite-density dynamics; gravitational-vortex structure
    Physical substrate dynamics impose a finite-density causal bound and remove the need to interpret infinite density as a physical state. Black holes are treated as gravitational vortices, with the Universal Centrality Rule providing an observational structural test.
    P6, P26, P28