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Then it would just display a page with those links. Pretty simple? ABSOLUTELY NOT! It took me two days to get everything right, and it still makes mistakes on some browsers. Also the DIV with links isn't hidden but instead it's absolute positioned to the top of the page and has an opacity of 0.00001. It's almost 0, but it's close enough to 1 that Chrome still does render it. If I had moved it off screen, or set the width to something small, or even used transform: scale(0.00001) it wouldn't work. Chrome doesn't render things that it doesn't think are visible.
Note that this does work in Firefox but Firefox doesn't have any problems with the visibility so I didn't have to test it as much.
If you want to try it out, click here. Trust me, it won't transmit any data it collected.