Prime Numerators of the Triangular-Fractional Grid: A shell stratification and a lens for prime-in-progression density

We study the \emph{prime numerators} of the triangular-fractional grid $a(n,k)=n-1+k/n$. Grouping the reduced fractions by their reduced denominator (their "shell" $s=n/\gcd(k,n)$) gives a stratification of the prime numerators that we did not find in the surveyed literature as a named object. We show that within a fixed shell the numerator has the closed form $\Rs=s^2m-s+t$, so each shell is a union of $\varphi(s)$ arithmetic progressions modulo $s^2$. This reduces the per-shell prime-density question to the prime-number theorem in arithmetic progressions. The naive comparison of per-shell prime density against $1/\varphi(s)$ shows a strong, persistent upward trend (Spearman $\rho_{\mathrm{Sp}}\approx 0.96$--$0.99$); this trend \emph{vanishes} under the cellwise predictor $\widehat\rho_N(s)$, whose coprimality factor $s/\varphi(s)$ is exact because $\varphi(s^2)=s\varphi(s)$. The corrected ratio is flat with no trend, its coefficient of variation "shrinks" with $N$ ($0.138\to0.058$ across $N=250\to2000$), and at $N=1000$ a fraction $0.994$ of shells fall within two binomial standard errors of the prediction. We conclude that the shell stratification is a lens, not a new prime law: the triangular-fractional shell coordinate makes a classical prime-in-progression mechanism visible in a clean, controlled way. We prove a within-shell numerator uniqueness result, record the controls, and fence the claim explicitly. No new prime phenomenon, no Riemann-hypothesis relevance, and no higher-dimensional claim is asserted.