The SNC index specialization conjecture

Let $K$ be a Henselian discrete valuation field with perfect residue field $k$, and let $R$ be its valuation ring. For a smooth, projective, geometrically integral finite-type $K$-scheme $V_{/K}$, suppose that $V$ admits a regular $R$-model whose special fiber is $V_{/k}$. Let $I(V_{/K})$ denote the index of the generic fiber and let $I'(V_{/k})$ denote the greatest common divisor of the component indices weighted by their residue degrees and multiplicities.

SNC index specialization conjecture. Under these assumptions,

$$I(V_{/K})=I'(V_{/k}).$$

This extends the known index formula for semistable reduction to regular models with simple normal-crossings special fiber. The source notes evidence over finite residue fields and indicates that the argument should extend to perfect residue fields, while a general index specialization theorem remains open.