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Timaeus believes that Singular Learning Theory provides the mathematical foundation needed to rigorously understand how neural networks develop internal structure during training, including when and how they acquire capabilities, values, and potentially dangerous behaviors. By detecting and understanding phase transitions in training through measures like the Local Learning Coefficient, Timaeus aims to build scalable evaluation and interpretability tools that can identify critical developmental moments before dangerous properties emerge. This would enable alignment interventions at the training level, ensuring models develop in ways that reflect human values. Their approach bridges pure mathematics with empirical machine learning, creating a scientific framework where alignment properties can be formally stated, measured, and verified rather than merely hoped for.