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Sorry if I misunderstand your desired setup, but try something like this and let me know if it works for you - It "works" the way I think it should, but I'm not sure that matches what you have in mind. The sky (image) is Nikita. The Cube is default white, the sphere is pure reflective (metallic 1, roughness 0) - the sphere reflects the Nikita sky, except for a bit at the bottom which is picking up a bit of the HDRI texture from the transmission in the "water". And as you can see, the water is picking up the transmission from the HDRI (which has several "reddish" sections).

If this is no good, I'll delete the answer:

Sorry if I misunderstand your desired setup, but try something like this and let me know if it works for you - It "works" the way I think it should, but I'm not sure that matches what you have in mind. The sky (image) is Nishita. The Cube is default white, the sphere is pure reflective (metallic 1, roughness 0) - the sphere reflects the Nishita sky, except for a bit at the bottom which is picking up a bit of the HDRI texture from the transmission in the "water". And as you can see, the water is picking up the transmission from the HDRI (which has several "reddish" sections).

If this is no good, I'll delete the answer:

Sorry if I misunderstand your desired setup (including your use of the math node), but try something like this and let me know if it works for you - It "works" the way I think it should, but I'm not sure that matches what you have in mind. If it's no good, I'll delete:

Sorry if I misunderstand your desired setup, but try something like this and let me know if it works for you - It "works" the way I think it should, but I'm not sure that matches what you have in mind. The sky (image) is Nikita. The Cube is default white, the sphere is pure reflective (metallic 1, roughness 0) - the sphere reflects the Nikita sky, except for a bit at the bottom which is picking up a bit of the HDRI texture from the transmission in the "water". And as you can see, the water is picking up the transmission from the HDRI (which has several "reddish" sections). 

If this is no good, I'll delete the answer:

Sorry if I misunderstand your desired setup (including your use of the math node), but try something like this and let me know if it works for you - It "works" the way I think it should, but I'm not sure that matches what you have in mind. If it's no good, I'll delete:

Sorry if I misunderstand your desired setup (including your use of the math node), but try something like this and let me know if it works for you - It "works" the way I think it should, but I'm not sure that matches what you have in mind. If it's no good, I'll delete: