57 observables derived from 2 axioms — zero free parameters. Weighted mean deviation: $\langle n_\sigma \rangle = 0.63$.
Gauge couplings, mass ratios, mixing angles, and the Higgs sector.
| Observable | Formula | SDGFT | Observed | Tension | Status |
|---|---|---|---|---|---|
| $\alpha_{\rm em}^{-1}$ | $2\pi(D^*)^3 + \delta D^*$ | 136.96 | 137.036 | 0.06% | <1σ |
| $\alpha_s(M_Z)$ | $\sqrt{2}/12$ | 0.11785 | $0.1179 \pm 0.0009$ | 0.05σ | Excellent |
| $\sin^2\theta_W$ | $1/9 + \gamma_{\rm EW}$ | 0.23122 | $0.23122 \pm 0.00003$ | 0.04σ | Excellent |
| $m_\mu / m_e$ | $3/(2\alpha) + 1 + \Delta$ | 206.77 | 206.768 | 0.001% | Excellent |
| $m_\tau / m_\mu$ | $6D^*$ | 16.75 | 16.817 | 0.4% | <1σ |
| $m_H$ | $\sqrt{2\Delta/\varphi} \cdot v$ | 124.95 GeV | $125.25 \pm 0.17$ GeV | 1.79σ | Good |
| $\lambda_H$ | $\Delta / \varphi$ | 0.1288 | $0.129 \pm 0.005$ | 0.05σ | Excellent |
| $N_{\rm gen}$ | $\max\{n:\varphi^n < 5\}$ | 3 | 3 | — | Exact |
| $\theta_{12}$ (PMNS) | $\arctan(1/\sqrt{2}) \times 23/24$ | 33.80° | $33.41° \pm 0.75°$ | 0.51σ | <1σ |
| $\theta_{23}$ (PMNS) | $45°(1+\Delta/\sqrt{6})$ | 48.83° | $49.0° \pm 1.4°$ | 0.12σ | Excellent |
| $\theta_{13}$ (PMNS) | $\arcsin(\Delta/\sqrt{2})$ | 8.47° | $8.54° \pm 0.15°$ | 0.46σ | <1σ |
| $|V_{us}|$ | $\sqrt{\Omega_B}$ | 0.2234 | $0.2243 \pm 0.0008$ | 1.11σ | Good |
| $|V_{cb}|$ | $\Delta^2$ | 0.0434 | $0.0408 \pm 0.0014$ | 1.86σ | Fair |
| $|V_{ub}|$ | $\Delta^\varphi \cdot \delta \cdot e^{(\ldots)}$ | 0.00375 | $0.00382 \pm 0.0002$ | 0.36σ | <1σ |
| $\sum m_\nu$ | Geometric see-saw | ≈ 0.058 eV | $< 0.12$ eV | — | Compatible |
Density parameters, inflation, dark energy, and structure formation.
| Observable | Formula | SDGFT | Observed | Tension | Status |
|---|---|---|---|---|---|
| $\Omega_b$ | $115/2304$ | 0.04993 | $0.0493 \pm 0.0003$ | 2.07σ | Fair |
| $\Omega_c$ | $600/2304$ | 0.2604 | $0.265 \pm 0.007$ | 0.66σ | <1σ |
| $\Omega_{\rm DE}$ | $1589/2304$ | 0.6897 | $0.685 \pm 0.007$ | 0.66σ | <1σ |
| $\Omega_{\rm tot}$ | $2304/2304$ | 1.000 | $1.000 \pm 0.004$ | — | Exact |
| $w_{\rm DE}$ | $-67/72$ | −0.931 | $-1.03 \pm 0.03$ | 3.32σ ⚡ | Tension |
| $\eta_B$ | $\delta^6(1-\delta)/8$ | $6.27 \times 10^{-10}$ | $(6.14 \pm 0.19) \times 10^{-10}$ | 0.67σ | <1σ |
| $n_s$ | From $f(R) = R^n$ | 0.9671 | $0.9649 \pm 0.0042$ | 0.53σ | <1σ |
| $r$ | From $f(R) = R^n$ | 0.013 | $< 0.036$ | — | Compatible |
| $N_e$ (e-folds) | Dim. flow integral | ≈ 60 | 50–60 | — | Compatible |
| $\sigma_8$ | $\Delta \cdot \pi$ | 0.775 | $0.776 \pm 0.017$ | 0.07σ | Excellent |
| $S_8$ | $\sigma_8\sqrt{\Omega_m/0.3}$ | 0.788 | $0.776 \pm 0.017$ | 0.67σ | <1σ |
| $\beta_{\rm iso}$ | $(1/6)^2$ | 0.028 | $< 0.038$ | — | Compatible |
Modified gravity, galactic dynamics, and quantum gravity predictions.
| Observable | Formula | SDGFT | Observed / Bound | Tension | Status |
|---|---|---|---|---|---|
| $D^*$ | $67/24$ | 2.7917 | — | — | Axiomatic |
| $D^*_{\rm UV}$ | UV fixed point | 2.0 | ≈ 2 (CDT, AS) | — | Compatible |
| $n = D^*/2$ | $67/48$ | 1.3958 | — | — | Derived |
| $\alpha_T$ | $0$ (exact) | 0 | $|c_T - c| < 10^{-15}$ | — | Exact |
| $\alpha_M$ | $19/86$ | 0.221 | — | — | Pending |
| $b_{\rm TF}$ | $D^* + 1$ | 3.792 | $3.85 \pm 0.09$ | 0.65σ | <1σ |
| $r_{\rm trans}$ | Geometric | ≈ 1 kpc | O(1 kpc) | — | Compatible |
| $\eta_{\rm LV}$ | $\Delta^2$ | 0.043 | $< 0.1$ (Fermi-LAT) | — | Compatible |
| $\dot{G}/G$ | $\neq 0$ | Predicted nonzero | ILR / MICROSCOPE | — | Pending |
SDGFT makes rigid predictions with zero free parameters. If any of these are violated beyond the stated bounds, the theory is falsified.
| # | Observable | Prediction ± Bound | Falsified if | Experiment | Timeline |
|---|---|---|---|---|---|
| 1 | $w_0$ (dark energy EoS) | $-0.931 \pm 0.010$ | $w_0 < -0.96$ or $w_0 > -0.90$ | Euclid, DESI | 2029 |
| 2 | $r$ (tensor-to-scalar) | $0.013 \pm 0.003$ | $r < 0.007$ or $r > 0.019$ | LiteBIRD, CMB-S4 | 2033 |
| 3 | $\beta_{\rm iso}$ (isocurvature) | $0.028 \pm 0.008$ | $\beta_{\rm iso} < 0.012$ or $> 0.044$ | CMB-S4 | 2035 |
| 4 | $\sigma_8$ | $0.775 \pm 0.010$ | $\sigma_8 < 0.755$ or $> 0.795$ | Euclid, DESI | 2030 |
| 5 | $\sum m_\nu$ | $0.05 - 0.10$ eV | $\sum m_\nu > 0.12$ eV | KATRIN + cosmo | 2028 |
The dark energy equation-of-state parameter is the leading tension at 3.32σ. SDGFT predicts $w = -0.931$, while current data favor $w \approx -1.03$. This will be definitively resolved by Euclid and DESI data releases by ~2029. If confirmed at $w < -0.96$, SDGFT is falsified. If $w$ shifts toward $-0.93$, it would be strong evidence for the theory.
All predictions are computed analytically from the two axioms $\delta = 1/24$ and $\Delta = 5/24$. There are zero free parameters — no fitting, no tuning, no adjustable constants.
Sigma tensions are computed as $n_\sigma = |x_{\rm pred} - x_{\rm obs}| / \sigma_{\rm obs}$, where $\sigma_{\rm obs}$ is the published experimental uncertainty. The weighted mean $\langle n_\sigma \rangle = 0.63$ is computed over the 25 observables with precise experimental uncertainties.
The complete derivation of every observable, including all intermediate steps, is available in the foundational paper.
The computational implementation is available as the open-source Python package
sdgft, which independently reproduces all numerical values on this scorecard.