A unified framework deriving the Standard Model and cosmology from two topological axioms of the 24-cell polytope — the unique self-dual regular polytope in four dimensions.
Both constants emerge from the 24-cell — the unique self-dual regular polytope in 4D with 24 vertices, 96 edges, and extraordinary symmetry.
The minimal fractional perturbation a single vertex can impart on the 24-cell lattice. This encodes Planck-scale discreteness — the irreducible quantum of geometric deformation.
The same $1/24$ appears in the Dedekind η-function, bosonic string critical dimension ($d=24+2$), and partition asymptotics.
$F_5 = 5$ is the largest Fibonacci number that non-trivially divides into 24 vertex slots. This encodes matter–antimatter asymmetry at the topological level.
The ratio $\Delta/\delta = 5$ yields the golden ratio: $\varphi = (1+\sqrt{5})/2$.
This defines the half-opening angle of the six-cone geometry.
The 24-cell is the only regular polytope in any dimension that is simultaneously self-dual and whose vertices form a root lattice ($D_4$). Its 24 vertices map to the 24 generators of $SU(5)$, and its symmetry group has order 1152.
| Quantity | Formula | Value |
|---|---|---|
| Golden ratio $\varphi$ | $(1+\sqrt{\Delta/\delta})/2$ | 1.61803… |
| Effective dim $D^*$ | $3 - \sin^2 30° + 1/24$ | 67/24 ≈ 2.792 |
| $f(R)$ exponent | $D^*/2 = 67/48$ | 1.396 |
| Spin-½ | $\sin(30°)$ | 0.5 (exact) |
| Generations | $\max\{n : \varphi^n < 5\}$ | 3 (exact) |
From two rational numbers, the full landscape of particle physics and cosmology emerges — with zero tuning.
57 observables tracked — weighted mean deviation $\langle n_\sigma \rangle = 0.63$ over 25 precisely tested quantities.
| Observable | SDGFT Prediction | Observed | Status |
|---|---|---|---|
| $\alpha_s(M_Z)$ | $\sqrt{2}/12 = 0.11785$ | $0.1179 \pm 0.0009$ | 0.05σ |
| $\sin^2\theta_W$ | $0.23122$ | $0.23122 \pm 0.00003$ | 0.04σ |
| $m_H$ | $124.95$ GeV | $125.25 \pm 0.17$ GeV | 1.79σ |
| $n_s$ | $0.9671$ | $0.9649 \pm 0.0042$ | 0.53σ |
| $\sigma_8$ | $0.775$ | $0.776 \pm 0.017$ | 0.07σ |
| $w_{\rm DE}$ | $-67/72 = -0.931$ | $-1.03 \pm 0.03$ | 3.32σ ⚡ |
"The universe is not made of particles in spacetime.
The universe is spacetime — with non-trivial topology."
— David A. Besemer, Foundations of SDGFT
SDGFT is maximally falsifiable — every prediction is rigid with zero free parameters. These experiments will confirm or refute the theory.
$w_{\rm DE} = -0.931 \pm 0.010$
The leading tension with $\Lambda$CDM. A clear, falsifiable deviation from $w = -1$.
$r = 0.013 \pm 0.003$
Primordial gravitational waves from $f(R) = R^{67/48}$ inflation.
$\eta_{\rm LV} = \Delta^2 \approx 0.043$
Observable Planck-suppressed Lorentz violation from lattice discreteness.
$\dot{G}/G \neq 0$
Newton's constant runs with scale — direct consequence of dimensional flow.
$\sigma_8 = 0.775$, $S_8 = 0.788$
Structure growth predicted from $\Delta \cdot \pi$ — resolves the $S_8$ tension.
The foundational paper with all derivations, proofs, and the complete scorecard is available open-access on Zenodo.