Amenable C-sequences and ineffability in L

We give a relative consistency counterexample to the conjecture of Inamdar and Rinot that every regular uncountable cardinal carrying no amenable C-sequence is ineffable in the constructible universe L. The existence of a ${\mathrm{\Pi }}_1^2$-indescribable cardinal is equiconsistent with the existence of a ${\mathrm{\Pi }}_1^2$-indescribable cardinal carrying no amenable C-sequence and not ineffable in L. For every ground-model C-sequence on a weakly compact cardinal $\kappa$, generalized Hechler forcing adds a club D with $D\cap \beta \subseteq C_{\beta }$ at stationarily many inaccessible indices. We use this capture theorem in an iteration of length ${\kappa }^{+}$ after Johnstone’s local lottery preparation.