Upper-bound conjecture for Pomerance's constant

Let $P$ denote Pomerance's constant, the sum of the reciprocals of all amicable numbers. Based on the observed convergence of the partial sums $P_j$, where $P_j$ is the sum of the reciprocals of amicable numbers not exceeding $10^j$, one estimates the tail beyond $10^{14}$ by

$$|P-P_{14}|<P_{14}-P_{13}.$$

Pomerance's upper-bound conjecture. Pomerance's constant satisfies

$$P<0.0119841563134.$$

This is a numerical conjecture based on the apparent rapid convergence of the reciprocal sum and the available exhaustive search through $10^{14}$. The supplied text gives no proof or resolution.