diff --git a/DESCRIPTION b/DESCRIPTION
index b5c7bdf..c9135e8 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,6 +1,6 @@
 Package: ergm.userterms
 Version: 4.0.0
-Date: 2019-05-15
+Date: 2025-02-10
 Title: User-specified Terms for the statnet Suite of Packages
 Authors@R: c(
 	   person("Mark S.", "Handcock", role=c("aut"), email="handcock@stat.ucla.edu"),
diff --git a/R/InitErgmTerm.users.R b/R/InitErgmTerm.users.R
index 550edad..1ebad23 100644
--- a/R/InitErgmTerm.users.R
+++ b/R/InitErgmTerm.users.R
@@ -62,7 +62,8 @@
 #'   same value of the `by` attribute.
 #'
 ### Import the standard ergmTerm documentation template so that it
-### gets indexed in ?ergmTerm.
+### gets indexed in ?ergmTerm. This and other templates can be copied
+### from 'ergm' source code on GitHub, in the man-roxygen/ directory.
 ###
 #' @template ergmTerm-general
 #'
@@ -82,7 +83,6 @@
 ###
 #' @concept undirected
 #' @concept categorical nodal attribute
-#' @concept frequently-used
 ###
 ### No @export!
 InitErgmTerm.mindegree <- function(nw, arglist, ...) {
@@ -116,8 +116,71 @@ InitErgmTerm.mindegree <- function(nw, arglist, ...) {
   )
 }
 
+#' @templateVar name sqrt.triangle
+#'
+#' @title Square root of the number of triangles
+#'
+#' @description These terms add one network statistic to the model,
+#'   the square root of the number of triangles. They demonstrate the
+#'   private and auxiliary storage mechanisms. The change statistic
+#'   for the square root of the number of triangles depends on the
+#'   initial number of triangles, so it is costly to compute -- unless
+#'   one can keep track of the number of triangles. These terms can
+#'   only be used with undirected networks.
+#'
+#' @usage
+#' # binary: sqrt.triangle
+#'
+#' @template ergmTerm-general
+#'
+#' @examples
+#'
+#' data(florentine)
+#'
+#' sqrt(summary(flomarriage~triangle))
+#' summary(flomarriage~sqrt.triangle)
+#'
+#' stopifnot(sqrt(summary(flomarriage~triangle)) == summary(flomarriage~sqrt.triangle))
+#'
+#' @concept undirected
+#' @concept triadic
+InitErgmTerm.sqrt.triangle <- function(nw, arglist, ...) {
+  # No arguments:
+  a <- check.ErgmTerm(nw, arglist, directed=FALSE, bipartite=FALSE)
 
+  # coef.names can have nonstandard characters:
+  list(name = "sqrt_triangle", coef.names = "sqrt(triangle)", dependence = TRUE)
+}
 
+### This also demonstrates how to document multiple terms in one
+### file. The following two Roxygen lines generate code to merge the
+### documentation into the sqrt.triangle-ergmTerm documentation. Note
+### that the alias has to be set manually.
+#' @templateVar name sqrt.triangle
+#' @template ergmTerm-rdname
+#' @aliases sqrt.triangle.aux-ergmTerm
+#' @usage
+#' # binary: sqrt.triangle.aux
+#'
+#' @examples
+#' summary(flomarriage~sqrt.triangle.aux)
+#'
+#' stopifnot(sqrt(summary(flomarriage~triangle)) == summary(flomarriage~sqrt.triangle.aux))
+InitErgmTerm.sqrt.triangle.aux <- function(nw, arglist, ...) {
+  # No arguments:
+  a <- check.ErgmTerm(nw, arglist, directed=FALSE, bipartite=FALSE)
 
+  # coef.names can have nonstandard characters:
+  list(name = "sqrt_triangle_aux", coef.names = "sqrt(triangle)", dependence = TRUE,
+       auxiliaries = ~.triangle) # Request the triangles auxiliary.
+}
 
+### Auxiliaries don't generally get public documentation, since they
+### are not invoked by end-users directly.
+InitErgmTerm..triangle <- function(nw, arglist, ...) {
+  # No arguments:
+  a <- check.ErgmTerm(nw, arglist, directed=FALSE, bipartite=FALSE)
 
+  # coef.names can have nonstandard characters:
+  list(name = "_triangle") # coef.names is an empty vector -> auxiliary
+}
diff --git a/man-roxygen/ergmTerm-rdname.R b/man-roxygen/ergmTerm-rdname.R
new file mode 100644
index 0000000..b668f21
--- /dev/null
+++ b/man-roxygen/ergmTerm-rdname.R
@@ -0,0 +1,11 @@
+#  File man-roxygen/ergmTerm-rdname.R in package ergm, part of the
+#  Statnet suite of packages for network analysis, https://statnet.org .
+#
+#  This software is distributed under the GPL-3 license.  It is free,
+#  open source, and has the attribution requirements (GPL Section 7) at
+#  https://statnet.org/attribution .
+#
+#  Copyright 2003-2025 Statnet Commons
+################################################################################
+#' <% name <- if(startsWith(name, "'")) substr(name, 2, 1000) else name %>
+#' @rdname <%= ergm:::.term.rdname("ergmTerm", name) %>
diff --git a/man/mindegree-ergmTerm-eabdf279.Rd b/man/mindegree-ergmTerm-eabdf279.Rd
index b5b0305..2535fd8 100644
--- a/man/mindegree-ergmTerm-eabdf279.Rd
+++ b/man/mindegree-ergmTerm-eabdf279.Rd
@@ -40,5 +40,4 @@ and conventions.
 \Sexpr[results=rd,stage=render]{ergm:::.formatTermKeywords("ergmTerm", "mindegree", "subsection")}
 }
 \concept{categorical nodal attribute}
-\concept{frequently-used}
 \concept{undirected}
diff --git a/man/sqrttriangle-ergmTerm-c7f8ea09.Rd b/man/sqrttriangle-ergmTerm-c7f8ea09.Rd
new file mode 100644
index 0000000..046bf43
--- /dev/null
+++ b/man/sqrttriangle-ergmTerm-c7f8ea09.Rd
@@ -0,0 +1,42 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/InitErgmTerm.users.R
+\name{sqrt.triangle-ergmTerm}
+\alias{sqrt.triangle-ergmTerm}
+\alias{InitErgmTerm.sqrt.triangle}
+\alias{InitErgmTerm.sqrt.triangle.aux}
+\alias{sqrt.triangle.aux-ergmTerm}
+\title{Square root of the number of triangles}
+\usage{
+# binary: sqrt.triangle
+
+# binary: sqrt.triangle.aux
+}
+\description{
+These terms add one network statistic to the model,
+the square root of the number of triangles. They demonstrate the
+private and auxiliary storage mechanisms. The change statistic
+for the square root of the number of triangles depends on the
+initial number of triangles, so it is costly to compute -- unless
+one can keep track of the number of triangles. These terms can
+only be used with undirected networks.
+}
+\examples{
+
+data(florentine)
+
+sqrt(summary(flomarriage~triangle))
+summary(flomarriage~sqrt.triangle)
+
+stopifnot(sqrt(summary(flomarriage~triangle)) == summary(flomarriage~sqrt.triangle))
+
+summary(flomarriage~sqrt.triangle.aux)
+
+stopifnot(sqrt(summary(flomarriage~triangle)) == summary(flomarriage~sqrt.triangle.aux))
+}
+\seealso{
+\code{\link[ergm:ergmTerm]{ergmTerm}} for index of model terms currently visible to the package.
+
+\Sexpr[results=rd,stage=render]{ergm:::.formatTermKeywords("ergmTerm", "sqrt.triangle", "subsection")}
+}
+\concept{triadic}
+\concept{undirected}
diff --git a/src/changestats.users.c b/src/changestats.users.c
index d81688d..f6576be 100644
--- a/src/changestats.users.c
+++ b/src/changestats.users.c
@@ -7,7 +7,8 @@
  *
  *  Copyright 2012-2019 Statnet Commons
  */
-#include "ergm_changestat.h"
+#include "ergm_changestat.h" // change statistics API and helper functions
+#include "ergm_storage.h" // storage API and helper functions
 
 C_CHANGESTAT_FN(c_mindegree) {
   Rboolean attrflag = IINPUT_PARAM[0];
@@ -39,3 +40,111 @@ C_CHANGESTAT_FN(c_mindegree) {
   }
 }
 
+
+/*****************
+ Square root of triangles: The private storage approach.
+*****************/
+
+/* Initializer: store the number of triangles in its private storage. */
+I_CHANGESTAT_FN(i_sqrt_triangle) {
+  ALLOC_STORAGE(1, double, ntri); /* Allocate private storage for 1 number to store the current number of triangles. */
+
+  /* NB: In an undirected network, tail < head. */
+  EXEC_THROUGH_NET_EDGES(tail, head, e1, { /* For each edge (tail < head) in the network... */
+      EXEC_THROUGH_FOUTEDGES(head, e, node3, { /* and each edge (head < node3)... */
+          *ntri += IS_OUTEDGE(tail, node3); /* a triangle is formed if an edge exists between node3 and tail. */
+      });
+    });
+
+  /* *ntri now contains the number of triangles in the network. */
+}
+
+/* Updater: will be called when toggling (tail, head) with state edgestate is imminent. */
+U_CHANGESTAT_FN(u_sqrt_triangle) {
+  GET_STORAGE(double, ntri); /* Obtain a pointer to private storage and cast it to the correct type. */
+  double change = 0;
+
+  EXEC_THROUGH_EDGES(head, e, node3, { /* For each edge of head... */
+      change += IS_UNDIRECTED_EDGE(node3, tail); /* A shared neighbor between tail and head exists if an edge exists between node3 and tail. */
+    });
+
+  /* Thus the toggle of (tail, head) will change the triangle statistic. */
+  *ntri += edgestate ? -change : change;
+}
+
+/* Cleanup; done automatically when STORAGE != NULL, so not needed in this case. */
+/* F_CHANGESTAT_FN(f_sqrt_triangle) { */
+/*   Free(STORAGE); */
+/* } */
+
+/* Change statistic: can refer to its storage. */
+C_CHANGESTAT_FN(c_sqrt_triangle) {
+  GET_STORAGE(double, ntri); /* Obtain a pointer to private storage and cast it to the correct type. */
+  double change = 0;
+
+  EXEC_THROUGH_EDGES(head, e, node3, { /* For each edge of head... */
+      change += IS_UNDIRECTED_EDGE(node3, tail); /* A shared neighbor between tail and head exists if an edge exists between node3 and tail. */
+    });
+
+  /* Now, we add the new value of the statistic and subtract the old. */
+  CHANGE_STAT[0] += sqrt(*ntri + (edgestate ? -change : change)) - sqrt(*ntri);
+}
+
+
+/*****************
+ Square root of triangles: The auxiliary approach.
+*****************/
+
+/*****
+ This is an auxiliary term .triangle which exports the number of
+ triangles that other change statistics can use. Notice that it
+ doesn't have a c_ or a d_ function.
+ *****/
+
+/* Initializer: store the number of triangles in its private storage. */
+I_CHANGESTAT_FN(i__triangle) {
+  ALLOC_AUX_STORAGE(1, double, ntri); /* Allocate public storage for 1 number to store the current number of triangles. */
+
+  /* NB: In an undirected network, tail < head. */
+  EXEC_THROUGH_NET_EDGES(tail, head, e1, { /* For each edge (tail < head) in the network... */
+      EXEC_THROUGH_FOUTEDGES(head, e, node3, { /* and each edge (head < node3)... */
+          *ntri += IS_OUTEDGE(tail, node3); /* a triangle is formed if an edge exists between node3 and tail. */
+      });
+    });
+
+  /* *ntri now contains the number of triangles in the network. */
+}
+
+/* Updater: will be called when toggling (tail, head) with state edgestate is imminent. */
+U_CHANGESTAT_FN(u__triangle) {
+  GET_AUX_STORAGE(double, ntri); /* Obtain a pointer to its public storage and cast it to the correct type. */
+  double change = 0;
+
+  EXEC_THROUGH_EDGES(head, e, node3, { /* For each edge of head... */
+      change += IS_UNDIRECTED_EDGE(node3, tail); /* A shared neighbor between tail and head exists if an edge exists between node3 and tail. */
+    });
+
+  /* Thus the toggle of (tail, head) will change the triangle statistic. */
+  *ntri += edgestate ? -change : change;
+}
+
+/* Cleanup; done automatically when STORAGE != NULL, so not needed in this case. */
+/* F_CHANGESTAT_FN(f__triangle) { */
+/*   Free(STORAGE); */
+/* } */
+
+/*****
+ This is a change statistic that expects a the number of triangles in its public storage.
+ *****/
+
+C_CHANGESTAT_FN(c_sqrt_triangle_aux) {
+  GET_AUX_STORAGE(double, ntri); /* Obtain a pointer to public storage and cast it to the correct type. */
+  double change = 0;
+
+  EXEC_THROUGH_EDGES(head, e, node3, { /* For each edge of head... */
+      change += IS_UNDIRECTED_EDGE(node3, tail); /* A shared neighbor between tail and head exists if an edge exists between node3 and tail. */
+    });
+
+  /* Now, we add the new value of the statistic and subtract the old. */
+  CHANGE_STAT[0] += sqrt(*ntri + (edgestate ? -change : change)) - sqrt(*ntri);
+}