Hardwood loose, has gap over radiant floor

Just bought a new place with white oak hardwood and radiant heating.

The hardwood is 3/4" (verified). Floor has developed gaps in certain areas. One area in particular is loose when I walk on it, so the gap is more pronounced. Looks like the gap had been puttied in the past and now the putty is coming out.

You can see gaps and putty coming out in the photo below. The floor board moves up and down slightly if I step on either side of the gap.

What's the best way to fix address this?

p.s. I'm not sure what kind of radiant heating installation I have either. It was done in 2009 on a new construction in SF if at all helpful.

edit: here is one part that's exposed in the closet, wood is 3/4" thick