@@ -256,7 +256,7 @@ We obtain the following frame-preserving update:

...

@@ -256,7 +256,7 @@ We obtain the following frame-preserving update:

\subsection{Authoritative}

\subsection{Authoritative}

\label{sec:auth-cmra}

\label{sec:auth-cmra}

Given a CMRA $M$, we construct a monoid $\authm(M)$ modeling someone owning an \emph{authoritative} element $x$ of $M$, and others potentially owning fragments $\melt\le_M x$ of $x$.

Given a CMRA $M$, we construct $\authm(M)$ modeling someone owning an \emph{authoritative} element $\melt$ of $M$, and others potentially owning fragments $\meltB\mincl\melt$ of $\melt$.

We assume that $M$ has a unit $\munit$, and hence its core is total.

We assume that $M$ has a unit $\munit$, and hence its core is total.

(If $M$ is an exclusive monoid, the construction is very similar to a half-ownership monoid with two asymmetric halves.)

(If $M$ is an exclusive monoid, the construction is very similar to a half-ownership monoid with two asymmetric halves.)