I was testing a bit with different cores and layers of carbon under the core and one of my friends asked me what causes the core to print through to the carbon. And I honestly don't know the cause. This was Lantor Soric core in the example below.

I know and expect that it happens when using only a single layer... but the why is a mystery to me. Is it just that the core compresses more than the carbon under vacuum and moves the weave a little bit?
Pic for an example:

Looks like you have a precise core which is X shaped.  What happens on the edge of the foam creates a void as the fibres lay over the edge rather than conform to the 90 degree edge. Then during the infusion, the fibres lift on the surface creating that effect. Basically its the same as bridging you might have on a corner as the core is creating a corner.  You can minimise it by tapering the core edges (not so easy on Soric but easy on more rigid cores to sand it) or use carbon tape or offcuts cut in strips around the edge of the foam to taper it down so it can't bridge like that. 

That won't stop the slight hexagon pattern you get which is down to the tiny amount of shrinkage during the cure.  Thicker laminate reduces that effect.

Warren Penalver
Easy Composites / Carbon Mods - Technical Support Assistant

It is resin shrinkage. Areas of excess resin shrink more. Due to the reasons Warren explained, at the edges of a core with an unchamfered edge, you get bridging. That bridging creates a void that gets filled with resin. The resin then shrinks ever so slightly more than the resin around it. After demoulding, the resin on the surface is no longer supported by the mould surface, so that shrinkage creates a distortion.

That's why it is often the case that immediately after demoulding a part, it can appear perfect. Then if the part hasn't been post cured (and sometimes even if it has), in the hours and days afterwards as the resin continues to fully cure, you can watch the surface slowly distort and any surface print become more and more obvious.

With epoxy, thicker skins on either side of the core are sufficient to block that tiny degree of print through. With vinyl ester and polyester the shrinkage is so much higher that I have seen cores and backing structures print through 25mm+ thick skins to distort the gelcoat enough that you can easily feel it by hand.

Great info as usual both of you! Thanks!

Good thought about using slightly thick material. This was just 3k but I will add that I did in fact chamfer the edges of the core (I used a razor blade to get about a 45 degree angle). I have some 12k at home that I'll try another test panel with to see if I can reduce the print through. I like the idea of using just carbon tape at the edges of the core, I know the last panel I made I used 2 layers of 3k and then the core material and there was no print through with that.

Thanks again!

The most effective way to reduce print through would probably be to infuse the first layer individually, let it cure, super carefully rip off the peel ply and then continue with the rest of the layup. It's just a big waste of consumables and you still need to be careful about the rest of the stack.