The missing mass anomaly in galactic rotation curves and the Hubble tension have historically been interpreted as independent phenomena requiring non-baryonic dark matter and modified expansion histories. This paper establishes a first-principles geometric framework, demonstrating that both anomalies arise as the fundamental dynamic consequence of macroscopic spacetime responding to the accelerated expansion of the universe. We first show that the conventional dark matter density parameter is a geometric projection artifact that parameterizes the ergodic volumetric resonance of the primordial cavity, thereby natively reconciling the Hubble tension. As the cosmos undergoes accelerated expansion, the underlying spatial metric resists structural divergence, generating a uniform reactionary stress defined as the Space Lattice Tension (a₀ = c H₀ / 2). Within this absolute boundary condition, baryonic mass (M) emerges as the localized topological anchor preventing linear spatial rupture, while the residual tension (Q) geometrically bifurcates into three distinct kinematic and thermodynamic usages dictated by the system's specific spatial topology. We propose that macroscopic cosmic equilibrium operates through multiplicative geometric coupling rather than linear addition. Consequently, the effective centripetal acceleration in the outer regions of a spiral galaxy is strictly governed by the geometric mean of the local Newtonian gravitational acceleration and this universal reactionary tension, yielding a = aN a₀. When this geometric mean coupling is applied to the planar topology of a rotating galactic disk, macroscopic angular momentum induces an intrinsic spatial expansion. The dynamic interaction between this rotational expansion and the Space Lattice Tension mathematically forces the complete algebraic cancellation of the radial distance variable (r²). This precise cancellation permanently locks the asymptotic orbital velocity to a flat constant (vf), preventing geometric divergence. By evaluating this dynamic equilibrium at the asymptotic locking threshold, we derive a rigorous quadratic equation. Incorporating the macroscopic angular momentum constraint of virialized systems (L M^5/3), the analytical solution demonstrates that higher-order geometric scaling mathematically dominates the classical Newtonian term. This first-principles derivation yields a precise fractional scaling exponent of 24/7 (3. 43) for the Baryonic Tully-Fisher Relation (BTFR), natively aligning with empirical observations. Furthermore, this geometric locking mechanism isolates the specific angular momentum, deductively deriving the Fall relation as a deterministic topological ratio. Ultimately, we demonstrate that flat galactic rotation curves are not the product of hidden mass, but the profound geometric manifestation of local baryonic matter dynamically anchoring itself against the macroscopic accelerated expansion of the cosmos through multiplicative space lattice coupling.
Cheol Woong Lee (Thu,) studied this question.