Gravitational Flux Area and the Self-Reinforcing Feedback Principle: A Framework Beyond Newtonian Gravity and General Relativity (v4)

This paper proposes two complementary principles to explain flat galactic 
rotation curves without dark matter.

Principle I (Gravitational Flux Area): The effective area A_eff(r) through 
which gravitational flux propagates is determined by the geometry of the 
matter distribution, not universally equal to 4πr². For a thin galactic 
disk of scale height H, flux propagates cylindrically with A_eff = 4πHr, 
yielding g ∝ 1/r and flat circular velocity without invoking dark matter.

Principle II (Self-Reinforcing Feedback): Gravitational flux concentrates 
toward mass overdensities, drawing more matter in, which deepens the 
overdensity and further concentrates the flux. This feedback — analogous 
to water carving a river channel — drives matter into disk configurations 
that produce cylindrical flux geometry, and self-consistently maintains 
those configurations.

Together, these principles explain: (1) flat rotation curves without dark 
matter; (2) the universal transition radius r₀ ~ √M_bulge separating 
Newtonian and flat-rotation regimes; (3) the Tully-Fisher relation v⁴ ∝ M 
as a geometric consequence; (4) the absence of dark matter signatures in 
globular clusters and the solar system; (5) galaxy alignment along cosmic 
filaments; (6) precocious massive galaxies observed by JWST.

Newtonian gravity and General Relativity remain valid as local descriptions 
of gravitational intensity. The new framework constitutes a non-local layer 
describing the propagation structure within which those local laws operate. 
Dark matter is identified as the artifact of applying spherical flux 
propagation to systems governed by cylindrical flux geometry.

This paper is an independent contribution and also represents a development 
of the author's earlier work on Bowl geometry (see related Zenodo deposits).