There are several synonyms for the phrase "are founded". One could say that something is established, created, built, formulated, or initiated. These words convey the idea that something has been put into motion or created in a deliberate and intentional way. Additionally, one could use synonyms such as grounded, rooted, or based to describe the foundation of something. These words emphasize the stability and durability of the foundation. Altogether, the use of synonyms can add depth and specificity to one's writing, helping to convey precision and clarity to the reader.