diff --git a/src/cleveragents/tool/path_mapper.py b/src/cleveragents/tool/path_mapper.py
index b451f5440..0380cb24c 100644
--- a/src/cleveragents/tool/path_mapper.py
+++ b/src/cleveragents/tool/path_mapper.py
@@ -162,22 +162,23 @@ def _normalise(path: str) -> str:
 
 
 def _is_under(path: str, root: str) -> bool:
-    """Return ``True`` if *path* is equal to or a child of *root*.
+    """Return ``True`` if *path* is at or within the directory tree of
+    *root*, using canonical rel-path containment checks.
 
-    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.
+    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.
 
-    See issue #7478 — startswith bypass in path containment checks.
+    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).
     """
-    if path == root:
-        return True
-    try:
-        relative = posixpath.relpath(path, root)
-    except (ValueError, TypeError):
-        return False
-    return not relative.startswith(".." + posixpath.sep) and relative != ".."
+    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)
 
 
 def _relative_to(path: str, root: str) -> str:
@@ -185,6 +186,10 @@ def _relative_to(path: str, root: str) -> str:
 
     Assumes :func:`_is_under` has already been checked.
     """
-    if path == root:
+    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 == ".":
         return ""
-    return path[len(root) + 1 :]
+    return rel.replace("\\", "/")