To analyze the root cause of the CWE-787 (Out-of-bounds Write) vulnerability in the given code slice, let's break down the problematic line and its context:

Root Cause Analysis:

1. Vulnerability Type:
   CWE-787: Out-of-bounds Write

2. Vulnerable Line:
   ```c
   memmove (buf, buf + start, initial_read - start);
   ```

3. Key Issues:

   a. Unchecked buffer boundaries:
      The code doesn't verify if the destination buffer (buf) has enough space to accommodate the data being moved.

   b. Potential negative size:
      The third argument of memmove (initial_read - start) could potentially be negative if start > initial_read, leading to an integer underflow and a very large size value.

   c. Lack of bounds checking:
      There's no check to ensure that start is less than or equal to initial_read.

   d. Implicit trust in input values:
      The code assumes that the calculated start value and initial_read are always valid and within bounds.

4. Contextual Factors:

   a. The start value is calculated based on k, n, and file_size, but there's no validation to ensure it's within the bounds of the buffer.

   b. The condition (initial_read != SIZE_MAX || start < initial_read) doesn't guarantee that the memmove operation will be safe.

   c. The bufsize parameter, which presumably indicates the size of buf, is not used in any bounds checking.

5. Potential Consequences:
   - If (initial_read - start) is larger than the available space in buf, it could lead to a buffer overflow.
   - If start > initial_read, it could cause an integer underflow, potentially leading to a very large move operation.
   - Writing beyond the bounds of buf could corrupt adjacent memory, leading to crashes, data corruption, or even code execution vulnerabilities.

To fix this vulnerability, the code should:
1. Implement proper bounds checking before the memmove operation.
2. Ensure that start is always less than or equal to initial_read.
3. Verify that the destination buffer (buf) has enough space for the move operation.
4. Handle edge cases and potential integer overflows/underflows.

A safer implementation would include checks like:
```c
if (start <= initial_read && initial_read - start <= bufsize) {
    memmove(buf, buf + start, initial_read - start);
} else {
    // Handle error condition
}
```

This analysis highlights the importance of careful buffer management and input validation in C programming, especially when dealing with memory operations and user-influenced data.