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.