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Introduces Adelic operation-preserved embeddings (AOE), a training-free representation that encodes numbers by combining real value with p-adic expansions, preserving additive and multiplicative structure. Achieves perfect accuracy on the Weaving Pattern benchmark.
Thomas Bloom provides an expository blog post on recent counterexamples to the Erdős unit distance conjecture and sum-product conjecture over the reals, including an OpenAI-assisted disproof of the unit distance conjecture and a collaborative disproof of the sum-product conjecture, sketching the constructions and intuition behind them.