  The forward Compton scattering off the proton is determined by substituting
the empirical total photoabsorption cross sections into dispersive sum rules.
In addition to the spin-independent amplitude evaluated previously [Phys. Rev.
D 92, 074031 (2015)], we obtain the spin-dependent amplitude over a broad
energy range. The two amplitudes contain all the information about this
process, and we, hence, can reconstruct the nonvanishing observables of the
proton Compton scattering in the forward kinematics. The results are compared
with predictions of chiral perturbation theory where available. The low-energy
expansion of the spin-dependent Compton scattering amplitude yields the
Gerasimov-Drell-Hearn (GDH) sum rule and relations for the forward spin
polarizabilities (FSPs) of the proton. Our evaluation provides an empirical
verification of the GDH sum rule for the proton, and yields empirical values of
the proton FSPs. For the GDH integral, we obtain $204.5(21.4)$ $\mu$b, in
agreement with the sum rule prediction: $204.784481(4)$ $\mu$b. For the FSPs,
we obtain: $\gamma_0=-92.9(10.5) \times 10^{-6}$ fm$^4$, and
$\bar{\gamma_0}=48.4(8.2) \times 10^{-6}$ fm$^6$, improving on the accuracy of
previous evaluations.
