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Watermarking is a promising approach, but most existing methods either provide only binary signals or achieve multi-bit embedding by distorting the generation distribution. We propose MirrorMark, a generalizable mapping-centric approach for multi-bit LLM watermarking. MirrorMark separates the symbol mapping rule from the base watermarking sampler and maps each symbol to a mod-1 mirroring transformation of a detector-reproducible pseudorandom object, such as sampling values or permutation ranks. A binary-tokenizer analysis shows that complementary mappings yield larger matched--mismatched score gaps than independent-key or shift-based mappings. 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