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 Aₑff (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 Aₑff = 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 ~ √Mbulge 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). This version adds four major results not present in the previous version: Variational proof of disk stability — The flat disk is proven to be the unique stable attractor of the feedback dynamics for systems with non-zero angular momentum, via minimization of the flux concentration functional subject to fixed mass and angular momentum constraints. Derivation of the feedback threshold — The critical mass fraction fcrit=H/R (disk aspect ratio) is derived from first principles as a purely geometric, parameter-free condition separating feedback-active from feedback-inactive systems. Verified across all major system types: solar system, globular clusters, dwarf galaxies, spiral galaxies, elliptical galaxies. Numerical verification of H (r) ≈ const — The effective disk thickness H (r) is derived from the Miyamoto-Nagai potential and shown to vary by only 4. 2% across galactic radii, confirming that the constant-H approximation is a consequence of disk structure, not an assumption. Gravitational lensing predictions — Two new lensing mechanisms are proposed: (a) disk-plane lensing amplification by a factor r/H, with a viewing-angle anisotropy testable with Euclid; (b) Void-Anchored Lensing (VAL), in which cosmic voids act as boundary conditions that focus light paths toward filaments and clusters — naturally explaining the mass-centroid offset observed in merging clusters such as the Bullet Cluster without dark matter. The two core principles remain unchanged from v1: (I) gravitational flux propagates through an effective area determined by matter geometry, not universally 4πr²; (II) a self-reinforcing feedback between flux concentration and matter accumulation drives stable structures toward flat disks, filaments, and voids.