diff --git a/src/cleveragents/tool/path_mapper.py b/src/cleveragents/tool/path_mapper.py
index 0380cb24c..e1895ac58 100644
--- a/src/cleveragents/tool/path_mapper.py
+++ b/src/cleveragents/tool/path_mapper.py
@@ -12,7 +12,6 @@ Based on issue #515 — container-aware tool execution and I/O forwarding.
 
 from __future__ import annotations
 
-import os
 import posixpath
 from dataclasses import dataclass
 
@@ -162,23 +161,22 @@ def _normalise(path: str) -> str:
 
 
 def _is_under(path: str, root: str) -> bool:
-    """Return ``True`` if *path* is at or within the directory tree of
-    *root*, using canonical rel-path containment checks.
+    """Return ``True`` if *path* is equal to or a child of *root*.
 
-    This replaces the former ``path.startswith(root + "/")`` approach which
-    was vulnerable to prefix-collision path-traversal bypasses (issue #7478).
-    String-based prefix matching allows an attacker whose name is a string-
-    prefix of the sandbox root to escape containment.
+    Uses semantic path containment via posixpath.relpath instead of
+    string prefix matching (str.startswith). String prefix matching
+    is vulnerable to sibling-directory prefix-collision attacks where
+    /tmp/sandbox would incorrectly match /tmp/sandboxmalicious/file.
 
-    Uses ``os.path.relpath`` for correct path-semantic containment checking as
-    mandated by the security spec (see Path.is_relative_to semantics on paths
-    where files may not exist).
+    See issue #7478 — startswith bypass in path containment checks.
     """
-    rel = os.path.relpath(path, root)
-    # Rel-path returns empty string ('') when equal, "." or a non-".."-prefixed
-    # path when contained, or "../..." when *outside* the root.
-    components = rel.replace("\\", "/").split("/")
-    return all(c != ".." for c in components)
+    if path == root:
+        return True
+    try:
+        relative = posixpath.relpath(path, root)
+    except (ValueError, TypeError):
+        return False
+    return not relative.startswith(".." + posixpath.sep) and relative != ".."
 
 
 def _relative_to(path: str, root: str) -> str:
@@ -186,10 +184,6 @@ def _relative_to(path: str, root: str) -> str:
 
     Assumes :func:`_is_under` has already been checked.
     """
-    rel = os.path.relpath(path, root)
-    # Strip leading "." for a child path (relpath returns "." when path
-    # equals root).  When the path equals the root we get "" which is fine
-    # for callers that check for that separately.
-    if rel == ".":
+    if path == root:
         return ""
-    return rel.replace("\\", "/")
+    return path[len(root) + 1 :]