Source preparation

A preparation instrument may use the contraction $K_{\mathrm{succ}}=e^{-\beta H_S/2}$ and the complementary operator

Its success probability on $|B_s⟩$ is $Z_s(\beta )$. The preparation occurs before the diary is supplied. The task may start after a declared successful preparation; an attempted deterministic protocol must instead retain the failure flag and include its preparation error. No input-dependent postselection is used.

No finite-$N$, fixed-realization thermal or gravitational correspondence is inferred from Proposition prop:preparation.