Logarithmic BTT source route and local reconstruction

Felten–Petracci Theorem 1.1 reports the full logarithmic BTT interface: for any characteristic-zero field $k$, sharp toric monoid $Q$, and proper saturated log-smooth $X_0\to \mathrm{Spec}(Q\to k)$ with trivial relative log-canonical line, the full functor on ${\mathbf{A}\mathbf{r}\mathbf{t}}_{k\mathrm{⟦}Q\mathrm{⟧}}$ is smooth. The source separates a $Q=0$ Thom–Whitney/Cartan-homotopy argument and a $Q\mathrm{\ne }0$ tower-lifting argument; its Theorem 3.7 defers the algebraization of the Chan–Leung–Ma method.

Under AC, the local reconstruction now supplies the missing arguments directly: Curved finite-cover calculus controlling all log-smooth deformations constructs the full curved geometric control, Proper log Hodge degeneration and pregluing total class lifting proves central E1 and all-Artin pregluing total-class lifting for proper central fibres, and All-class Artin lifting for a curved BV calculus proves lifting of every given classical class. The resulting theorem consumes this explicit chain rather than this source-report remark or a deferred source proof. This correction does not assert that a source citation alone proves its conclusion, nor change the SNC qualification $K_X(D)\cong {\mathcal{O}}_X$ into $K_X\cong {\mathcal{O}}_X$.

Log Calabi–Yau pair, toric degeneration and scattering data

Log-smooth deformation functor over a toric Artin base

Curved finite-cover calculus controlling all log-smooth deformations

Proper log Hodge degeneration and pregluing total class lifting

All-class Artin lifting for a curved BV calculus