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This is incredibly incorrect. While many colors that are additive are combinations, those combinations are simply approximations of the single wavelength true color. All colors are on a spectrum of hue, luminance (brightness) and intensity (saturation).
Pink is red with high luminance and high intensity, and brown is orange with low luminance and mid-high intensity
Nope. A whole bunch of colors do not correspond to any wavelength of light. This includes purple.
https://en.wikipedia.org/wiki/Spectral_color#Extra-spectral_colors
Pink can also be described as a reddish hue with high brightness and low saturation. But saturation is a matter of how strongly one frequency is emphasized compared to other frequencies. So colors with low saturation contain mixtures of frequencies, but each point in the rainbow, when there's no other source of light present, is only a single frequency. This is why the rainbow doesn't contain any desaturated colors like pink. Brown, I admit, can be just dark orange.