diff --git a/Library/Homebrew/cask/download.rb b/Library/Homebrew/cask/download.rb
index baec2eb63f..0c73efd33a 100644
--- a/Library/Homebrew/cask/download.rb
+++ b/Library/Homebrew/cask/download.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "downloadable"
@@ -13,8 +13,10 @@ module Cask
 
     include Context
 
+    sig { returns(::Cask::Cask) }
     attr_reader :cask
 
+    sig { params(cask: ::Cask::Cask, quarantine: T.nilable(T::Boolean)).void }
     def initialize(cask, quarantine: nil)
       super()
 
@@ -29,9 +31,9 @@ module Cask
 
     sig { override.returns(T.nilable(::URL)) }
     def url
-      return if cask.url.nil?
+      return if (cask_url = cask.url).nil?
 
-      @url ||= ::URL.new(cask.url.to_s, cask.url.specs)
+      @url ||= ::URL.new(cask_url.to_s, cask_url.specs)
     end
 
     sig { override.returns(T.nilable(::Checksum)) }
@@ -70,12 +72,14 @@ module Cask
       downloaded_path
     end
 
+    sig { params(timeout: T.any(Float, Integer, NilClass)).returns([T.nilable(Time), Integer]) }
     def time_file_size(timeout: nil)
       raise ArgumentError, "not supported for this download strategy" unless downloader.is_a?(CurlDownloadStrategy)
 
       T.cast(downloader, CurlDownloadStrategy).resolved_time_file_size(timeout:)
     end
 
+    sig { returns(Pathname) }
     def basename
       downloader.basename
     end
@@ -102,6 +106,7 @@ module Cask
 
     private
 
+    sig { params(path: Pathname).void }
     def quarantine(path)
       return if @quarantine.nil?
       return unless Quarantine.available?
diff --git a/Library/Homebrew/downloadable.rb b/Library/Homebrew/downloadable.rb
index c04bd8aaac..8000da4022 100644
--- a/Library/Homebrew/downloadable.rb
+++ b/Library/Homebrew/downloadable.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "url"
@@ -23,9 +23,16 @@ module Downloadable
 
   sig { void }
   def initialize
+    @url = T.let(nil, T.nilable(URL))
+    @checksum = T.let(nil, T.nilable(Checksum))
     @mirrors = T.let([], T::Array[String])
+    @version = T.let(nil, T.nilable(Version))
+    @download_strategy = T.let(nil, T.nilable(T::Class[AbstractDownloadStrategy]))
+    @downloader = T.let(nil, T.nilable(AbstractDownloadStrategy))
+    @download_name = T.let(nil, T.nilable(String))
   end
 
+  sig { params(other: Object).void }
   def initialize_dup(other)
     super
     @checksum = @checksum.dup
@@ -46,7 +53,8 @@ module Downloadable
 
   sig { returns(String) }
   def download_type
-    T.must(self.class.name&.split("::")&.last).gsub(/([[:lower:]])([[:upper:]])/, '\1 \2').downcase
+    class_name = T.let(self.class, T::Class[Downloadable]).name&.split("::")&.last
+    T.must(class_name).gsub(/([[:lower:]])([[:upper:]])/, '\1 \2').downcase
   end
 
   sig(:final) { returns(T::Boolean) }
@@ -72,9 +80,9 @@ module Downloadable
     version unless version&.null?
   end
 
-  sig { overridable.returns(T.class_of(AbstractDownloadStrategy)) }
+  sig { overridable.returns(T::Class[AbstractDownloadStrategy]) }
   def download_strategy
-    @download_strategy ||= determine_url&.download_strategy
+    @download_strategy ||= T.must(determine_url).download_strategy
   end
 
   sig { overridable.returns(AbstractDownloadStrategy) }
@@ -129,7 +137,7 @@ module Downloadable
 
   sig { overridable.returns(String) }
   def download_name
-    @download_name ||= File.basename(determine_url.to_s)
+    @download_name ||= File.basename(determine_url.to_s).freeze
   end
 
   private
diff --git a/Library/Homebrew/resource.rb b/Library/Homebrew/resource.rb
index 1017c7af9b..2b37c2ec43 100644
--- a/Library/Homebrew/resource.rb
+++ b/Library/Homebrew/resource.rb
@@ -25,15 +25,19 @@ class Resource
   sig { params(name: T.nilable(String), block: T.nilable(T.proc.bind(Resource).void)).void }
   def initialize(name = nil, &block)
     super()
-    # Ensure this is synced with `initialize_dup` and `freeze` (excluding simple objects like integers and booleans)
+    # Generally ensure this is synced with `initialize_dup` and `freeze`
+    # (excluding simple objects like integers & booleans, weak refs like `owner` or permafrozen objects)
     @name = name
+    @source_modified_time = nil
     @patches = []
+    @owner = nil
     @livecheck = Livecheck.new(self)
     @livecheck_defined = false
     @insecure = false
     instance_eval(&block) if block
   end
 
+  sig { params(other: Object).void }
   def initialize_dup(other)
     super
     @name = @name.dup
@@ -108,7 +112,7 @@ class Resource
     current_working_directory = Pathname.pwd
     stage_resource(download_name, debug_symbols:) do |staging|
       downloader.stage do
-        @source_modified_time = downloader.source_modified_time
+        @source_modified_time = downloader.source_modified_time.freeze
         apply_patches
         if block_given?
           yield ResourceStageContext.new(self, staging)
diff --git a/Library/Homebrew/retryable_download.rb b/Library/Homebrew/retryable_download.rb
index a7c7f40d23..63fd5ff5fe 100644
--- a/Library/Homebrew/retryable_download.rb
+++ b/Library/Homebrew/retryable_download.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 module Homebrew
@@ -23,7 +23,7 @@ module Homebrew
       super()
 
       @downloadable = downloadable
-      @try = 0
+      @try = T.let(0, Integer)
       @tries = tries
     end
 
@@ -42,7 +42,7 @@ module Homebrew
     sig { override.returns(T.nilable(Version)) }
     def version = downloadable.version
 
-    sig { override.returns(T.class_of(AbstractDownloadStrategy)) }
+    sig { override.returns(T::Class[AbstractDownloadStrategy]) }
     def download_strategy = downloadable.download_strategy
 
     sig { override.returns(AbstractDownloadStrategy) }