N9 — Tensor-to-scalar ratio $r = _^4 0.0136$
N9: Tensor-to-scalar ratio $r = _^4 0.0136$. BICEP Array, CMB-S4, LiteBIRD.
Falsification Details
r = iota-tau-4 approx 0.014. tensor-to-scalar ratio!prediction pred:n9 Fiber dimensional suppression (V.P136): $r = _^2(T^2) = _^4$. Not slow-roll: $r 8/N_e$. The 156$$ gap between $_^4$ and $8/57$ is the sharpest inflation discriminant. Decisive at $14$ by CMB-S4.
BICEP Array, CMB-S4, LiteBIRD
2027–2030.
$14$ by CMB-S4
Context
N9: Prediction
r = iota-tau-4 approx 0.014.
Fiber dimensional suppression (V.P136): $r = ι_τ^2(T^2) = ι_τ^4$. Not slow-roll: $r ≠ 8/N_e$. The 156$×$ gap between $ι_τ^4$ and $8/57$ is the sharpest inflation discriminant. Decisive at $14σ$ by CMB-S4. Experiment: BICEP Array, CMB-S4, LiteBIRD. Timeline: 2027–2030.
Derivation Context
dimensional suppression!theorem The tensor-to-scalar ratio $r = P_t/P_s$ is determined by the fibration structure $τ^3 = τ^1 ×_f T^2$:
r \;=\; ι_τ^\,2 · (T^2) \;=\; ι_τ^2 × 2 \;=\; ι_τ^4 \;≈\; 0.01357.
- Tensor perturbations (gravitational waves) are D-sector frame-holonomy fluctuations propagating on the base $τ^1$. They are insensitive to the fiber structure.
- Scalar perturbations (curvature/density fluctuations) are boundary-character fluctuations of the full arena $τ^3$, coupling to both fiber circles of $T^2$.
- Each fiber dimension contributes a breathing-fraction suppression $ι_τ$ to the scalar amplitude relative to the tensor amplitude.
- The power spectrum is quadratic in amplitude ($P |δ|^2$).
with the first factor equal to the number of lemniscate lobes and the second factor arising from $P |δ|^2$. (Registry: V.P136, $τ$-effective, Wave 13.)