in stone, cast/carved/written

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carved in stone

Permanently fixed or firmly established; incapable of being changed. Often used in the negative. The deal isn't yet carved in stone, but we're confident it will go ahead as hoped.

cast in stone

Permanently fixed or firmly established; not subject to any amendment or alteration. Often used in the negative. The deal isn't yet cast in stone, but we're confident it will go ahead as hoped.

written in stone

Permanently fixed or firmly established; incapable of being changed. Often used in the negative. The deal isn't yet written in stone, but we're confident it will go ahead as hoped.

carved in stone

and engraved in stone; written in stone

Fig. permanent or not subject to change. (Often in the negative.) Now, this isn't carved in stone yet, but this looks like the way it's going to be. Is this policy carved in stone, or can it still be modified?

cast in stone

Also, etched in stone. Definite, fixed, as in We may choose to stay longer-our plans aren't cast in stone, or When Carl sets an agenda you can safely assume it's etched in stone. Both expressions allude to sculpture, with the first, from the early 1500s, using the verb cast in the sense of pouring and hardening some material into a final form, and the second cutting or corroding a permanent design.

in stone, cast/carved/written

Completely set, unchangeable. This phrase is often put in the negative—something is not cast in stone. It alludes to sculpture, where to cast means to pour and harden a material into a final form, and possibly also to the epitaphs engraved on gravestones. The first usage dates from the early 1500s. Most often it appears in such statements as, “Of course we can change it; this proposal is not cast in stone.”