diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 1d25782..35e2796 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -43,19 +43,26 @@ jobs:
   # The Rails-facing specs against the oldest supported ActiveSupport
   # lines (the main matrix already exercises the newest release): the
   # drop-in's quirks_mode path and the encoder seam differ across them.
+  #
+  # json is pinned per line, never left to resolve: unpinned, it follows
+  # whatever standard's rubocop allows, and standard 1.57 let json 3 in
+  # overnight. ActiveSupport 7.1 and 8.0 pass quirks_mode to JSON.generate
+  # and JSON.parse, which json 3 rejects even without nosj, so they stay
+  # on json 2; 7.2 and 8.1 run on json 3.
   rails-compat:
-    name: Rails compat (activesupport ${{ matrix.activesupport }})
+    name: Rails compat (activesupport ${{ matrix.activesupport }}, json ${{ matrix.json }})
     runs-on: ubuntu-latest
     strategy:
       fail-fast: false
       matrix:
         include:
-          - { activesupport: "~> 7.1.0", ruby: "3.3" }
-          - { activesupport: "~> 7.2.0", ruby: "3.4" }
-          - { activesupport: "~> 8.0.0", ruby: "3.4" }
-          - { activesupport: "~> 8.1.0", ruby: "4.0" }
+          - { activesupport: "~> 7.1.0", json: "< 3", ruby: "3.3" }
+          - { activesupport: "~> 7.2.0", json: "~> 3.0", ruby: "3.4" }
+          - { activesupport: "~> 8.0.0", json: "< 3", ruby: "3.4" }
+          - { activesupport: "~> 8.1.0", json: "~> 3.0", ruby: "4.0" }
     env:
       NOSJ_ACTIVESUPPORT_VERSION: ${{ matrix.activesupport }}
+      NOSJ_JSON_VERSION: ${{ matrix.json }}
 
     steps:
       - uses: actions/checkout@v6
@@ -67,8 +74,8 @@ jobs:
           cargo-cache: true
 
       # The committed lockfile resolves the newest ActiveSupport; the
-      # pin needs a fresh resolution.
-      - name: Bundle with the pinned ActiveSupport
+      # pins need a fresh resolution.
+      - name: Bundle with the pinned ActiveSupport and json
         run: |
           rm Gemfile.lock
           bundle install
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 40ddbc3..f0977fe 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,13 @@
+## [0.5.1] - 2026-10-06
+
+- Fixed: `NOSJ.patch` read a `path` without the leading slash (`"a"`
+  instead of `"/a"`) as the root pointer, so `add`, `copy`, and `move`
+  silently replaced the whole document with the value instead of
+  raising, and `remove` reported `cannot remove the root`. Such paths
+  now raise the same `ArgumentError` as `NOSJ.at_pointer`
+  (`JSON Pointer must be empty or start with '/'`) in every op. The
+  bug dates back to 0.3.0. Found by fuzzing.
+
 ## [0.5.0] - 2026-09-25
 
 **json 3.0 compatibility.** nosj now matches the behavior of the json
diff --git a/Cargo.lock b/Cargo.lock
index 99f88ab..557f080 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -200,7 +200,7 @@ dependencies = [
 
 [[package]]
 name = "nosj_native"
-version = "0.5.0"
+version = "0.5.1"
 dependencies = [
  "ahash",
  "magnus",
diff --git a/Gemfile.lock b/Gemfile.lock
index 73d21f9..be507a7 100644
--- a/Gemfile.lock
+++ b/Gemfile.lock
@@ -1,7 +1,7 @@
 PATH
   remote: .
   specs:
-    nosj (0.5.0)
+    nosj (0.5.1)
       rb_sys (~> 0.9.91)
 
 GEM
diff --git a/ext/nosj/Cargo.toml b/ext/nosj/Cargo.toml
index 3c97fe4..c28133e 100644
--- a/ext/nosj/Cargo.toml
+++ b/ext/nosj/Cargo.toml
@@ -5,7 +5,7 @@
 # required by lib/nosj.rb as "nosj/nosj" (Init_nosj set explicitly in
 # lib.rs). Gem name, module, and API are plain nosj.
 name = "nosj_native"
-version = "0.5.0"
+version = "0.5.1"
 edition = "2021"
 authors = ["Yaroslav Markin <yaroslav@markin.net>"]
 license = "MIT"
diff --git a/ext/nosj/fuzz/seeds/lines/overflow_float.ndjson b/ext/nosj/fuzz/seeds/lines/overflow_float.ndjson
new file mode 100644
index 0000000..98e5ef3
--- /dev/null
+++ b/ext/nosj/fuzz/seeds/lines/overflow_float.ndjson
@@ -0,0 +1,2 @@
+{"big":1e999}
+-124.4e044754
diff --git a/ext/nosj/fuzz/seeds/patch/overflow_literal.bin b/ext/nosj/fuzz/seeds/patch/overflow_literal.bin
new file mode 100644
index 0000000..ab5eb62
Binary files /dev/null and b/ext/nosj/fuzz/seeds/patch/overflow_literal.bin differ
diff --git a/ext/nosj/fuzz/seeds/patch/overflow_splice.bin b/ext/nosj/fuzz/seeds/patch/overflow_splice.bin
new file mode 100644
index 0000000..3f151f9
Binary files /dev/null and b/ext/nosj/fuzz/seeds/patch/overflow_splice.bin differ
diff --git a/ext/nosj/fuzz/seeds/patch/overflow_value.bin b/ext/nosj/fuzz/seeds/patch/overflow_value.bin
new file mode 100644
index 0000000..bed45f2
Binary files /dev/null and b/ext/nosj/fuzz/seeds/patch/overflow_value.bin differ
diff --git a/ext/nosj/fuzz/seeds/patch/slashless_path.bin b/ext/nosj/fuzz/seeds/patch/slashless_path.bin
new file mode 100644
index 0000000..8f5d453
Binary files /dev/null and b/ext/nosj/fuzz/seeds/patch/slashless_path.bin differ
diff --git a/ext/nosj/fuzz/src/prelude.rb b/ext/nosj/fuzz/src/prelude.rb
index d6aacdb..5ed4ad0 100644
--- a/ext/nosj/fuzz/src/prelude.rb
+++ b/ext/nosj/fuzz/src/prelude.rb
@@ -140,11 +140,19 @@ def lines_case(bytes)
     raise "yielded values diverge from per-line parses" unless yielded.eql?(reference)
 
     if status == :ok && !yielded.empty?
-      # Parsed values are always generable: parse refuses lone
-      # surrogates, the only source of unencodable strings.
-      ndjson = stage("generate_lines") { NOSJ.generate_lines_native(yielded, nil) }
+      # Parse refuses lone surrogates, the only unencodable strings, but
+      # an overflow float (1e999, 124.4e044754) parses to Infinity, which
+      # generates only under allow_nan; it lifts exactly that refusal,
+      # and the round-trip then reads Infinity back under it too.
+      opts = nil
+      ndjson = begin
+        NOSJ.generate_lines_native(yielded, nil)
+      rescue NOSJ::GeneratorError
+        opts = {allow_nan: true}
+        stage("generate_lines with allow_nan") { NOSJ.generate_lines_native(yielded, opts) }
+      end
       back = []
-      NOSJ.each_line_native(ndjson, nil) { |v| back << v }
+      NOSJ.each_line_native(ndjson, opts) { |v| back << v }
       raise "generate_lines does not round-trip" unless back.eql?(yielded)
     end
     nil
@@ -227,6 +235,7 @@ def rfc6902_case(doc, tree_status, tree, ops)
   # --- the pure-Ruby reference implementations ------------------------
 
   def ref_splice(tree, edits)
+    edits.each_value { |value| generable(value) }
     token_lists = edits.keys.map { |ptr| ptr_tokens(ptr) }
     token_lists.combination(2) do |a, b|
       short, long = (a.length <= b.length) ? [a, b] : [b, a]
@@ -262,8 +271,8 @@ def ref_patch(tree, ops)
       path = op["path"]
       raise RefFail unless path.is_a?(String)
       case name
-      when "add" then ref_add(box, ptr_tokens(path), fetch_value(op))
-      when "replace" then ref_replace(box, ptr_tokens(path), fetch_value(op))
+      when "add" then ref_add(box, ptr_tokens(path), generable(fetch_value(op)))
+      when "replace" then ref_replace(box, ptr_tokens(path), generable(fetch_value(op)))
       when "remove" then ref_remove(box, ptr_tokens(path))
       when "move"
         from = op["from"]
@@ -366,6 +375,24 @@ def fetch_value(op)
     op["value"]
   end
 
+  # splice, add, and replace generate their values with default options,
+  # which refuse non-finite floats, and an overflow literal in the spec
+  # (1e999) parses to Infinity. test compares, and move/copy splice raw
+  # document bytes, so a 1e999 already in the document passes there.
+  def generable(value)
+    raise RefFail unless finite_floats?(value)
+    value
+  end
+
+  def finite_floats?(v)
+    case v
+    when Float then v.finite?
+    when Array then v.all? { |e| finite_floats?(e) }
+    when Hash then v.each_value.all? { |e| finite_floats?(e) }
+    else true
+    end
+  end
+
   def deep_dup(v)
     case v
     when Hash then v.transform_values { |e| deep_dup(e) }
diff --git a/ext/nosj/src/patch.rs b/ext/nosj/src/patch.rs
index 8e983e7..0259292 100644
--- a/ext/nosj/src/patch.rs
+++ b/ext/nosj/src/patch.rs
@@ -119,11 +119,25 @@ fn container_children(
 }
 
 /// Split an RFC 6901 pointer into (parent, unescaped last token).
-/// Returns None for the root pointer "".
-fn split_pointer(pointer: &str) -> Option<(&str, String)> {
-    let cut = pointer.rfind('/')?;
+/// Returns None for the root pointer "" only: any other pointer must
+/// start with '/', else the crate's own InvalidPointer error raises as
+/// ArgumentError, exactly like `span_at`. (A slash-free path once read
+/// as the root, and `add` replaced the whole document.)
+fn split_pointer<'p>(ruby: &Ruby, pointer: &'p str) -> Result<Option<(&'p str, String)>, Error> {
+    if pointer.is_empty() {
+        return Ok(None);
+    }
+    if !pointer.starts_with('/') {
+        // Byte 0 is where the crate reports a missing leading slash.
+        let invalid = nosj::ParseError {
+            offset: 0,
+            kind: nosj::ErrorKind::InvalidPointer,
+        };
+        return Err(arg_error(ruby, invalid.to_string()));
+    }
+    let cut = pointer.rfind('/').unwrap_or(0);
     let token = pointer[cut + 1..].replace("~1", "/").replace("~0", "~");
-    Some((&pointer[..cut], token))
+    Ok(Some((&pointer[..cut], token)))
 }
 
 /// RFC 6902 array index token: digits only, no leading zeros.
@@ -211,7 +225,7 @@ fn op_add(
     value: &Insert,
     cfg: &GenConfig,
 ) -> Result<Vec<u8>, Error> {
-    let Some((parent, token)) = split_pointer(path) else {
+    let Some((parent, token)) = split_pointer(ruby, path)? else {
         // Root: the value becomes the entire document.
         return apply_edit(ruby, doc, 0, doc.len(), value, cfg);
     };
@@ -295,7 +309,7 @@ fn extend_insert(
 /// RFC 6902 `remove`: the entry disappears along with its key and one
 /// separating comma; surrounding formatting stays.
 fn op_remove(ruby: &Ruby, doc: &[u8], path: &str) -> Result<Vec<u8>, Error> {
-    let Some((parent, token)) = split_pointer(path) else {
+    let Some((parent, token)) = split_pointer(ruby, path)? else {
         return Err(patch_error(ruby, "cannot remove the root".into()));
     };
     let Some((pstart, pend)) = span_at(ruby, doc, parent)? else {
diff --git a/lib/nosj/version.rb b/lib/nosj/version.rb
index b942fa9..cf91bd2 100644
--- a/lib/nosj/version.rb
+++ b/lib/nosj/version.rb
@@ -2,5 +2,5 @@
 
 module NOSJ
   # The gem version.
-  VERSION = "0.5.0"
+  VERSION = "0.5.1"
 end
diff --git a/spec/patch_spec.rb b/spec/patch_spec.rb
index 762536f..4d08363 100644
--- a/spec/patch_spec.rb
+++ b/spec/patch_spec.rb
@@ -215,6 +215,28 @@ def apply(doc, patch)
       end
     end
 
+    # Found by the patch fuzzer: a slash-free path used to read as the
+    # root, so add replaced the whole document.
+    it "refuses pointers without a leading slash like at_pointer, never as the root" do
+      doc = %({"a":1})
+      message = begin
+        NOSJ.at_pointer(doc, "a")
+      rescue ArgumentError => e
+        e.message
+      end
+      [
+        {"op" => "add", "path" => "a", "value" => 2},
+        {"op" => "remove", "path" => "a"},
+        {"op" => "replace", "path" => "a", "value" => 2},
+        {"op" => "test", "path" => "a", "value" => 1},
+        {"op" => "move", "from" => "/a", "path" => "b"},
+        {"op" => "copy", "from" => "/a", "path" => "b"},
+        {"op" => "copy", "from" => "a", "path" => "/b"}
+      ].each do |op|
+        expect { NOSJ.patch(doc, [op]) }.to raise_error(ArgumentError, message), op.inspect
+      end
+    end
+
     it "move onto itself is a no-op" do
       expect(NOSJ.patch(%({"a":1}), [{"op" => "move", "from" => "/a", "path" => "/a"}]))
         .to eq(%({"a":1}))