Load index table. The kilogram figures are the ETRTO/industry load index values used on truck tyres, single fitment. The dual-fitment rating is the second number moulded on the sidewall (156/150 on a 315/80R22.5, for example) and is always lower than the single figure, because the two tyres in a dual pair share the load and run hotter. Use the dual number when fitted as duals — if your sidewall only shows one figure, take the dual capacity from the tyre data book rather than guessing.
Pressure and heat. With the volume roughly fixed, gauge pressure follows absolute temperature: (P + atmosphere) ÷ T is constant, with T in kelvin. That is the exact correction used above. The industry rule of thumb that drivers use in the yard — about 2% pressure rise per 10°F (5.5°C) of temperature rise — falls out of the same equation over the range tyres actually work in. A tyre that reads far above its mates, or far above the ideal-gas line, is being heated by something other than the road: a dragging brake, a failing bearing, or it was underinflated to start with. Never bleed air out of a hot tyre to match the cold figure.
Tread and matching. US minimum tread depth is 4/32 inch on a steer tyre and 2/32 inch elsewhere (49 CFR 393.75); the EU minimum is 1.6 mm across three quarters of the tread. Most fleets keep dual tyres within about 1/4 inch (6 mm) of each other in diameter, which is about 3/4 inch (19 mm) of circumference, because a larger tyre in a pair is dragged along and both scrub.
Pressures are per the tyre maker's load and inflation table for your size, not a universal number. This tells you whether the numbers you read make sense — the data book tells you what to set.