Mutation that codes for a new protein would be a close assumption of new specified complexity, but not all genes code for proteins (eg Hox genes). Suppose a mutation produced a longer chain of a gene. A pile of sand is also complex, but doesn't contain a lot of information, because it specifies nothing.
Mutation that causes a loss of information may also produce a new traits (has been observed). So in the end, to make it worse for evolutionists (fr), an information-gaining mutation is a mutation that gains specified-complexity.

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