Clarifying State Dependence in CHSH: Optimal Angular Configurations for the Four Bell States

We identify and correct a common pedagogical omission in the presentation of the CHSH inequality. The angular configuration {0, π/2, π/4, -π/4}, historically optimal for the singlet state |Ψ⁻⟩, yields S=0 when incorrectly applied to other Bell states such as |Φ⁺⟩ using the standard CHSH form. We demonstrate that each Bell state requires specific angular configurations and reveal the duality between two canonical forms of CHSH. We provide a complete table of optimal configurations for all four Bell states, Python verification code, and specific educational protocols. This work, developed under the Kaelion Project v3.0, emphasizes that entanglement certification requires state-specific geometric alignment.