You might give a better description of your specimen
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In a sound, on a small beach. It is very hard as you can see there is almost no wear(from water movement), not rounded as all the other rocks were. And the formation of it is very unique, the curves, the round segment at the bottom.
Looks like it might have been liquid (molten) at some point in the not too distant past. Any volcanic activity in your area? I also like the concretion theory. However I am still behind the rock theory 75% and do rule out the petrified elephant theory completely. I would like to add this theory though; oil or asphalt that has rolled around in the ocean for a wicked long time (; see if it burns
Its a metamorphic rock, where over millions of years sort of time the minerals hardened due to extreme pressure and heat. Then over time, a long time, the softer minerals exfoliated from natural erosion resulting in the line pattern you now see.