"What is truth?" Pilate asked.
Truth is not an objective quality. That's not to say that there is not some quality, truth, that comports with some standard presumed to be unchanging, or that is experienced the same for all observers, or that conforms to reality, or is seen to function consistently. That is to say that quality can never be seen to represent the absolute end of a thing, as in this is it, period. Only God has that quality, he alone is truth, all else designated by the term is subject to his whim.
Can anything be truly independent of God? I do not think that it can; that includes gravity, the speed of light, or the existence of stuff itself. It seems to me that some philosophical schools posit a concept of truth in which there are things which even God cannot do anything about, or that are independent of the divine will. In that case, truth would be even greater than God, over him, so to speak. That, certainly, is not the case.
Truth has its foundation in God. God is not encompassed by truth, truth is encompassed by God. It's communicated by the words that proceed from his mouth. It is a derivative and dependent property. The ultimate truth is God, all other truth flows from him. The truth is that there is nothing by which God must abide, but himself.