Formal Verification

We prove that for any $N \geq 3$ bodies with positive masses in $\mathbb{R}^d$ ($d \geq 2$), the number of central configurations modulo similarity is finite, resolving Smale's 6th Problem in **every spatial dimension $d \geq 2$ simultaneously**.

The Z₃ Ansatz $\sqrt{m_r} = a(1 + b\cos(\theta_0 + 2\pi r/3))$ with $b^2 = 2$ is a parametrization — not a dynamical model — that encodes the Koide mass relation $Q = 2/3$.

**Theorem A (Main result, conditional).** Conditional on the 20 named Tier A–D hypotheses of §7.1 — in particular the three Tier-D perturbative-QFT inputs (`tomboulis_formula`, `b_zero_from_feynman`, `beta_1_rge_def`) — we establish that Yang-Mills t

We introduce a grade decomposition of the Gevrey energy balance for the incompressible Navier-Stokes equations. The physically correct model uses $\mathbb{C}$-valued Fourier coefficients with a factor of $i$ in the advection; the real-coefficient model trivializes all grade-3 terms.