Gravitational Flux Transport Networks v4.0: Geometry Without Darkness — A Parameter-Free Alternative to Dark Matter

This paper presents a geometric resolution to the dark matter problem. The central claim is: Newton was right, the calculation was right, and the geometry was wrong. Applying spherical Gaussian surfaces (A_eff = 4πr²) to disk-shaped galaxies understates the effective flux area by a factor of r/H ≈ 20–100. Dark matter is the mathematical residual of this geometric error, not a physical substance. We develop the Gravitational Flux Transport Network framework, in which the gravitational acceleration is g = GM_enc/A_eff, where A_eff depends on the geometry of the mass distribution. Two foundational principles determine A_eff: (1) A feedback principle: gravitational flux concentrates matter, which further concentrates flux, driving disk and filament formation (A_eff = 4πHr for spirals, g ∝ 1/r, flat rotation curves). (2) A lazy propagation principle: the universe invests in efficient flux channels only when the lifetime cost of construction is less than the lifetime cost of inefficient propagation (d > d_max = √(2GMH/σ²)). Together these principles reproduce, without free parameters:- Flat galactic rotation curves- The Tully–Fisher relation (v_c⁴ ∝ M, derived)- The Faber–Jackson relation (L ∝ σ⁴, derived from lazy propagation ceiling)- The NFW profile (geometric artifact)- The M_BH–σ relation (r_s = d_max condition)- The universal M_BH/M_bulge ≈ 10⁻³ ratio- The cosmic web topology (Steiner network optimisation)- The galaxy morphology–density relation (8-strategy taxonomy S1–S8)- The dark matter distribution as a flux efficiency map (f_DM ∝ ε·d/d_max·n)- The Hubble tension (KBC void outflow 8–11%)- Apparent dark energy as void pressure Λ_eff(t)- DESI's evolving w(z) ≠ −1 Thirty-eight new observational predictions are listed, testable with JWST, DESI, Euclid, and SKA.