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Using regular LPE syntax this result is basically correct, even the double reflections, but in the beauty image this secondary reflection isn't visible because of the HDRI, the balls just aren't bright enough. (However, the equivalent LPE of the mirror reflection will indeed show this secondary ball reflection not visible in the beauty.) This is not intuitive at first because you'd expect a similar response to what is seen in the beauty. But User Lobes are not energy conserving material responses, instead they are data. So we can remove this extra reflection easily by changing the LPE slightly:

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