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This skill provides specialized guidance for building encoders that function as the exact mathematical inverse of a given decoder. It is particularly useful for complex tasks involving arithmetic coding, entropy encoding, or custom compression algorithms where even a single bit divergence can cause failure. The skill emphasizes a derivation-first approach, moving from state machine documentation to side-by-side verification harnesses, ensuring that developers avoid common pitfalls like renormalization errors or off-by-one offsets while maintaining strict output compatibility.