You should wait until they fall, otherwise they're not likely to be fully ripe. Also, are you soaking them in or out of the husks?

yes, if you havent already, you will need to remove the husk. if your still not sure, crack a few open and see what the inside is like. good nuts will be full of kernel. bad ones will have shriveled or rotten kernel.

They've already fallen and are out of their husks. But 99% float! Does that seem right? They are definitely mature nuts.

Have you had a particularly dry growing season where you are?

Maybe it's already considered fall in zone 4?

If a hickory nut floats, it's no good. Hickory nuts are heavy by nature, and sometimes even bad ones will sink.

Could you be picking up nuts from last year?

OK. Let me lay it all out. The nuts are from this year. We have not had a frost or freeze yet. The trees still have all/most of their leaves. The nuts are still falling from the trees. I have opened sinkers and floaters and they both have beautiful nut meats inside. Still, 90%+ float.

I want to plant these shagbark hickory. Could it be possible that the sink or swim theory doesn't always work?

Kay

If they have good kernels, go ahead and plant them. Forget the float test, since it is obviously not working here!

Resin

OK, this is why I usually try to remember to recommend that when 'float testing' nuts, you should crack a few of the floaters to make certain that they are, indeed, 'blanks' or have incompletely-filled kernels. Some nuts - particularly hickory and black walnut selections with really thin shells will float, particularly if they've been off the tree for a few days and have had an opportunity to cure/dry a bit. Even some well-filled pecans float, albeit not as high in the water as those that are empty.
Sometimes, especially if I'm dealing with seednuts that are in short supply, I'll let 'em soak for a day or so before I make the 'cut'. If they sink, or are at least mostly underwater after 24 hours - and a sample cracking suggests the nutmeats are well-filled - I'll take a chance on planting them. They may not all germinate, but what have you got to lose?

Thank you Lucky. That's what I wanted/needed to hear. I'll plant several nuts in a hole and hope for the best.

"I'll plant several nuts in a hole and hope for the best"

Give them one hole each! And cover with chicken wire to stop squirrels and mice from digging them all up.

Resin

resin is correct about protecting against pilfering - squirrels, chipmunks, mice, and even raccoons are bad about digging up acorns/hickory nuts/pecans, and it may be imperative to provide some protection, whether it be chicken wire, a polyethylene tree shelter, or a metal soup can with an 'X' cut in the bottom and peeled back partially, shoved down over the nut - the shoot can come up through the peeled-back portions, and you can remove it later, or allow it to rust away - you just have to make sure it has done so before it girdles the seedling.
A word of caution - I've known the bushy-tailed tree rats to dig up 2-yr old seedlings to get at the remaining nutmeat in an acorn or hickory.

I am now, I think, the expert on shagbark hickory nuts and viability for their planting. This does not necessarily apply to other nuts.

I took about 20 hickory nuts and put them in a pail of water. They all floated! So......I left them over night and they all sank. Thus, the sink or swim theory needs about 24 hours to be effective.

I cracked several open and they all have beautiful nut meats.

I am fortunate in where I am going to plant them. There are currently only saplings and thus, no squirrels!! I've picked the nuts from the back of the house where many squirrels enjoy them. I'm planting them several acres away in the front of the house. My new nut trees will be able to mature with no fear of being dug up from bushy tails. Of course some will be lost to mother nature and some to other rodents but the potential is stupendous.

I have @ 8 acres that i'm trying to turn into a semi-woods. I'll never see it come to fruition but someone will enjoy the paths I have cut in the meadow and lined with trees. There are elm, oak, maple, cedar, black walnut, pine, and now even hickory! I've got about 100 trees so far that have made it but that's only in 2 years and they are all from saplings or nuts!

Thank you all for your advice.

Sometimes curious dogs will dig them up too.