But how does CIE 1931 answer the question on the last page? How does it give the actual spectrum?

The math details: https://en.wikipedia.org/wiki/CIE_1931_color_space#Computing_XYZ_from_spectral_data

CIE 1931 uses specially calibrated curves to extract numbers from the spectral data.

But how does CIE 1931 answer the question on the last page? How does it give the actual spectrum?

The math details: https://en.wikipedia.org/wiki/CIE_1931_color_space#Computing_XYZ_from_spectral_data

CIE 1931 uses specially calibrated curves to extract numbers from the spectral data.