Hello bhildred, and welcome to the Monastery!

The sizes of the integer templates 'i' and 'I' are variable by design. For fixed-size integers, use one of following (signed/unsigned): c/C (8 bits), s/S (16 bits), l/L (32 bits), q/Q (64 bits). Since you specify an “unsigned 32-bit number”, use 'L':

$packed = pack   'L', $count;
...
$count  = unpack 'L', $packed;
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(The template sizes are clearly documented on page 801 of the Camel Book, 4^th Edition, 2012. L is “An unsigned long value, always 32 bits”.)

Hope that helps,