copied from the channel lineup pdf
If you have an HD-capable television connected via a Cox mini box, you will be able to view TV Starter and TV Essential channels in High Definition by tuning to either the two-digit or three-digit Standard Definition channel or the corresponding HD Channel in the 1000-series range. For example, with a mini box, The Weather Channel may be viewed in HD on either channel 43 or channel 1043 (the Weather Channel numbers in your market may be different). If your television is connected via equipment other than a mini box, such as a Cox HD receiver or a Coxprovided CableCARD together with a CableCARD compatible retail device (and a Cox-provided Digital Tuning Adaptor for certain channels), programming is available in high definition only at the HD Channel position – typically the four-digit number above 1000.
sounds like mini boxes have no option bt to view the HD verion while HD and HD/DVR's and cable have to tune to the 4 digit channel number