Spectral isometries of unital $C^*$-algebras

This paper provides a human digestion of a proof of the spectral isometry conjecture for C*-algebras found by GPT-6 Astra. We prove that every unital surjective complex-linear spectral isometry between unital $C^*$-algebras is a Jordan isomorphism. The main step is to show that an entire one-parameter group of unital spectral isometries consists of algebra automorphisms. We establish this on the bidual using tracial moments on the finite summand and square-zero preservation on the properly infinite summand. A uniform resolvent estimate extends preservation of real spectra to self-adjoint elements of the bidual. Holomorphy eliminates the off-diagonal component. Applying the group result to transported inner automorphisms reduces the proof to Nagasawa's theorem for commutative Banach algebras. Surjective spectral isometries that need not preserve the identity are central unitary multiples of Jordan isomorphisms.