Gravity · 2026

The Dual-Balance S³(R) Vacuum Container: Resolving Galactic Kinematics and Weak Lensing Shear Without Dark Matter

R. G. Measey

Abstract

Synthesizing the dual response on S³(R): massive particles soften inertially (m_eff ∝ a), while photons trace 4D bulk dielectric potential deformation (Φ ∝ ln r) through refractive index n = e²ᵁ. Introduces the Clifford torus leaf symmetric scale a_sym = (2-√2) c²/R ≈ 1.603 × 10⁻¹⁰ m/s² from unit-pair projection excess. Proves optical deflection α_yield = 2π√(GM a_sym)/c² ≈ 0.470 arcsec yields an acceleration boost of 71.46x at 300 kpc, landing directly within the empirical KiDS/SDSS stacked shear band (24–104x) and resolving the photon weak-lensing kill (PASS_FT_MA_LONE_KILL_PHOTON_PHI). Finite bulk compressibility K = c⁴/G maintains center regularity, while fast face p ≥ 2 satisfies the Saturn perihelion gate and Cassini quadrupole bound (Q₂ ~ 10⁻³¹ s⁻²).

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