N10 — Spectral index $n_s = 1 - 2/57$
N10: Spectral index $n_s = 1 - 2/57$. CMB-S4, LiteBIRD.
Status boundary
Falsification status is a program-side tracking label. It separates current internal stance from formal verification, empirical support, and external acceptance; it is not a claim that the wider scientific community has accepted the result.
Falsification Details
n-s = 1 - 2/57. spectral index!prediction pred:n10 $N_e = 57 = 3 19 = (^3) W_5(3)$ (V.D253). $n_s = 0.96491$ at $+13$~ppm from Planck.
CMB-S4, LiteBIRD
2028–2032.
Context
N10: Prediction
n-s = 1 - 2/57.
$N_e = 57 = 3 × 19 = (τ^3) × W_5(3)$ (V.D253). $n_s = 0.96491$ at $+13$ ppm from Planck. Experiment: CMB-S4, LiteBIRD. Timeline: 2028–2032.
Derivation Context
where $W_5(3) = 19$ is the Waring number—the minimum number of fifth powers of non-negative integers needed to represent any natural number as a sum of $3$-bounded summands. The number $19 = W_5(3)$ appears in the continued-fraction expansion of $ιτ^-1$ as the $[5,3]$ window: the 5th-order CF coefficient evaluated at the 3rd structural depth. (Registry: V.D253, $τ$-effective, Wave 14A.)
Structural origin. The e-fold count is not a tuned parameter. It arises from two independent quantities:
- $(τ^3) = 3$: the dimension of the fibered product, itself decomposed as $1 + 2$ (base plus fiber).
- $W_5(3) = 19$: the CF window that governs the inflationary duration, encoding the number of primorial ticks at which the boundary characters remain above the exponential-expansion threshold.
The product $3 × 19 = 57$ falls within the range $50 ≤ N_e ≤ 60$ required by CMB observations to solve the flatness and horizon problems.
Metadata
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