Pardon me for asking stupid questions, but why not just do something like:

use strict;
use warnings;

my $dir = "/whatever";
my $time = time();
my ($sec, $min, $hour, $mday, $mon, $year, $wday, $yday, $isdst) =
                        localtime($time);
my $btime = $time - $wday * 86400 - $hour * 3600 - $min * 60 - $sec;

if (!-e "$dir/$btime.mrk") {
    # process all records timestamped ($btime - 604799) to $btime
    # create file "$dir/$btime.mrk"
}
[download]

This will process all records from the past week, assuming the server time is set correctly. If the server time is not set correctly, it will still process the records weekly, but the process won't run on the first access Sunday morning.