diff --git a/.Rbuildignore b/.Rbuildignore
index 7a15f7d..d4cfa59 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -10,3 +10,4 @@ notes.org
 ^cran-comments\.md$
 ^CRAN-RELEASE$
 ^\.github$
+^CRAN-SUBMISSION$
diff --git a/CRAN-SUBMISSION b/CRAN-SUBMISSION
new file mode 100644
index 0000000..ba17be5
--- /dev/null
+++ b/CRAN-SUBMISSION
@@ -0,0 +1,3 @@
+Version: 1.0.0
+Date: 2024-03-20 01:40:54 UTC
+SHA: dbb09ef6eae8689c3cc8a16aa9dcbdcdc6589db8
diff --git a/DESCRIPTION b/DESCRIPTION
index ce5cbec..f8312f8 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -22,7 +22,8 @@ Encoding: UTF-8
 LazyData: true
 Imports:
     stats,
-    Formula
+    Formula,
+    withr
 Suggests:
     spelling,
     ggplot2,
diff --git a/R/Cbound.R b/R/Cbound.R
index f922725..072db87 100644
--- a/R/Cbound.R
+++ b/R/Cbound.R
@@ -101,31 +101,32 @@ RDSmoothnessBound <- function(object, s, separate=FALSE, multiple=TRUE,
     hatM <- function(D) {
         ts <- abs(D[1, ]/D[2, ]) # sup_t statistic
         maxt <- D[, which.max(ts)]
-        set.seed(42)
+
         Z <- matrix(stats::rnorm(10000*ncol(D)), ncol=ncol(D))
         ## median unbiased point estimate and lower CI
-        hatM <- lower <- 0
+        hatm <- lower <- 0
         if (max(ts) > cv(0, Z, D[2, ], 1/2)) {
-            hatM <- FindZero(function(m) max(ts)-cv(m, Z, D[2, ], 1/2),
+            hatm <- FindZero(function(m) max(ts)-cv(m, Z, D[2, ], 1/2),
                              negative=FALSE)
         }
         if (max(ts) >= cv(0, Z, D[2, ], alpha)) {
             lower <- FindZero(function(m) max(ts)-cv(m, Z, D[2, ], alpha),
                               negative=FALSE)
         }
-        list(estimate=hatM, conf.low=lower,
+        list(estimate=hatm, conf.low=lower,
              diagnostics=c(Delta=maxt[1], sdDelta=maxt[2],
                            y1=maxt[3], y2=maxt[4], y3=maxt[5],
                            I1=maxt[6:7], I2=maxt[8:9], I3=maxt[10:11]))
     }
 
     if (separate) {
-        po <- hatM(Dp)
-        ne <- hatM(Dm)
+        withr::with_seed(42, po <- hatM(Dp))
+        withr::with_seed(42, ne <- hatM(Dm))
         ret <- data.frame(rbind("Below cutoff"=unlist(ne[1:2]),
                                 "Above cutoff"=unlist(po[1:2])))
     } else {
-        ret <- data.frame((hatM(cbind(Dm, Dp))[1:2]))
+        ret <- withr::with_seed(42,
+                                data.frame((hatM(cbind(Dm, Dp))[1:2])))
         rownames(ret) <- c("Pooled")
     }
     ret
diff --git a/cran-comments.md b/cran-comments.md
index 788ed31..9cd4951 100644
--- a/cran-comments.md
+++ b/cran-comments.md
@@ -1,3 +1,11 @@
+## Resubmission
+This is a resubmission. In this version I have:
+
+* avoided using set.seed() inside a function (in R/Cbound.R). Instead, I use
+  withr::with_seed() to ensure that the results are reproducible without
+  modifying the global environment.
+
+
 ## Test environments
 * local Debian 12 (bookworm) install, R 4.3.1
 * Github actions
@@ -23,12 +31,6 @@ Possibly misspelled words in DESCRIPTION:
   Rothe (17:47)
   covariates (18:42)
 
-Found the following (possibly) invalid DOIs:
-  DOI: 10.1257/aer.20160945.
-    From: man/RDHonestBME.Rd
-    Status: 404
-    Message: Not Found
-
 The misspelled words are correct, "covariates" refers to independent variables
 in a regression. "Rothe" is a surname.