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The old quip about the only things certain in life are death and taxes could be added to: and concrete will crack!
Concrete cracks for a variety of reasons, but the most common one is normal and not a durability or structural problem: shrinkage. Water is necessary for concrete to cure (it does NOT dry, it is a chemical reaction called hydration), but we will add more water than is necessary for hydration just to get the concrete to flow so we can work it into the shape needed. As the concrete is curing, excess water is evaporating, and the volume of the concrete in your driveway shrinks. This causes it to pull apart from itself, and that is why you see the small cracks develop shortly after pouring. Under certain conditions they even begin the day of the pour!
Sawing control joints in the slab is an attempt to control where the cracking takes place, so it is not unsightly.
There are other reasons for cracking, but an explanation takes much more time; and from your description I think you are witnessing shrinkage cracking.
What can you do? Nothing at all. It is a normal part of a concrete slab.
Check the frequency and depths of the control joints/sawcuts they installed for your driveway. They all are subject to industry standards. A driveway that is 4" thick should have control joint/sawcut depths of 1" deep (24% of the total thickness) and not more than 12 feet apart. Check these out and if he has installed the concrete within these limits then it is difficult to warrant random cracks that appear.
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