Numbers Already Carry Their Own Embeddings

We introduce Adelic operation-preserved embeddings (AOE), a training-free representation that captures both a number’s real value and its modular ($p$-adic) signatures. This construction preserves additive and multiplicative structure by design, turning numerical input into embeddings that “speak in the language of mathematics.” Unlike prior approaches that rely on task-specific retraining, AOE is plug-and-play and drop seamlessly into existing architectures. On algebraic combinatorics benchmarks, it delivers consistent gains—including the first-ever perfect accuracy on the Weaving Pattern task—while suggesting a principled path forward for overcoming the long-standing “number problem” in AI.