diff --git a/Gemfile b/Gemfile
index 846135d..cb689e9 100644
--- a/Gemfile
+++ b/Gemfile
@@ -5,11 +5,12 @@ source "https://rubygems.org"
 gem 'jekyll', "~> 4.0"
 
 group :jekyll_plugins do
+  #plugins in _config.yml
   gem 'jekyll-seo-tag'
   gem 'jekyll-paginate'
   gem 'jekyll-email-protect'
   gem 'jekyll-feed'
+  
+  #dependeny for custom footnote plugin
+  gem 'nokogiri' 
 end
-
-gem "webrick", "~> 1.7"
-gem "nokogiri", "~> 1.15"
diff --git a/Gemfile.lock b/Gemfile.lock
index a3ca3f1..e9f284d 100644
--- a/Gemfile.lock
+++ b/Gemfile.lock
@@ -11,6 +11,7 @@ GEM
     eventmachine (1.2.7)
     ffi (1.16.3)
     forwardable-extended (2.6.0)
+    google-protobuf (3.25.3-arm64-darwin)
     google-protobuf (3.25.3-x86_64-darwin)
     google-protobuf (3.25.3-x86_64-linux)
     http_parser.rb (0.8.0)
@@ -35,9 +36,6 @@ GEM
     jekyll-email-protect (1.1.0)
     jekyll-feed (0.17.0)
       jekyll (>= 3.7, < 5.0)
-    jekyll-last-modified-at (1.3.0)
-      jekyll (>= 3.7, < 5.0)
-      posix-spawn (~> 0.3.9)
     jekyll-paginate (1.1.0)
     jekyll-sass-converter (3.0.0)
       sass-embedded (~> 1.54)
@@ -54,16 +52,16 @@ GEM
       rb-fsevent (~> 0.10, >= 0.10.3)
       rb-inotify (~> 0.9, >= 0.9.10)
     mercenary (0.4.0)
+    nokogiri (1.16.5-arm64-darwin)
+      racc (~> 1.4)
     nokogiri (1.16.5-x86_64-darwin)
       racc (~> 1.4)
     nokogiri (1.16.5-x86_64-linux)
       racc (~> 1.4)
     pathutil (0.16.2)
       forwardable-extended (~> 2.6)
-    posix-spawn (0.3.15)
     public_suffix (5.0.5)
     racc (1.8.0)
-    rake (13.2.1)
     rb-fsevent (0.11.2)
     rb-inotify (0.11.1)
       ffi (~> 1.0)
@@ -71,9 +69,12 @@ GEM
       strscan (>= 3.0.9)
     rouge (4.2.1)
     safe_yaml (1.0.5)
-    sass-embedded (1.69.5)
+    sass-embedded (1.69.5-arm64-darwin)
+      google-protobuf (~> 3.23)
+    sass-embedded (1.69.5-x86_64-darwin)
+      google-protobuf (~> 3.23)
+    sass-embedded (1.69.5-x86_64-linux-gnu)
       google-protobuf (~> 3.23)
-      rake (>= 13.0.0)
     strscan (3.1.0)
     terminal-table (3.0.2)
       unicode-display_width (>= 1.1.1, < 3)
@@ -81,6 +82,7 @@ GEM
     webrick (1.8.1)
 
 PLATFORMS
+  arm64-darwin-23
   x86_64-darwin-21
   x86_64-linux
 
@@ -88,11 +90,9 @@ DEPENDENCIES
   jekyll (~> 4.0)
   jekyll-email-protect
   jekyll-feed
-  jekyll-last-modified-at
   jekyll-paginate
   jekyll-seo-tag
-  nokogiri (~> 1.15)
-  webrick (~> 1.7)
+  nokogiri
 
 BUNDLED WITH
    2.3.22