You are given a simulated POSIX-like filesystem and a starting directory `root`. Implement the core of a duplicate-file detector when file contents cannot be read. Each entry in `filesystem` is stored by absolute path and is one of: - `('dir', [child_name1, child_name2, ...], readable)` - `('file', size, inode, readable)` - `('symlink', target_path)` Traverse the tree starting from `root` and find duplicate files using only metadata. Rules: 1. Never follow symlinks. This avoids infinite loops. 2. If a directory is unreadable, count one permission error and do not traverse inside it. 3. If a file is unreadable, count one permission error and skip it. 4. Hard links are represented by multiple file paths with the same inode. They refer to the same physical file, so they must be counted only once. Use the lexicographically smallest readable reachable path as that inode's representative. 5. Under the no-content-read constraint, two files are considered duplicates if they have different inodes but the same size. Return a tuple `(groups, permission_errors)` where: - `groups` is a list of duplicate groups. - Each duplicate group is a lexicographically sorted list of representative file paths. - Only include sizes that have at least 2 distinct representative files. - Order `groups` by increasing file size. This definition can produce false positives in real systems, but for this problem it is the required behavior.