The shot-budget split is not special (any ratio works). The golden-section search in the optimizer is provably optimal for a unimodal slice (Kiefer 1953): on H₂, whose slice is unimodal, it reaches chemical accuracy on every restart while momentum lags; on the non-unimodal LiH active-space landscape that edge does not hold, so the advantage is real exactly where the theorem applies. The E8 critical-Ising mass spectrum is golden to the core: its eight masses form four exact φ pairs.

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measured in CoNb₂O₆ (Coldea et al., 2010)