Long documents. Please share the quotes and the references. The way it looks to me on a cursory review is that once again you are looking at operational recommendations and actual flight plans rather than aircraft capabilities. But I may have missed the reference.
As regards my post, sorry to say, it wasn't a shill blogger's website that explains mach numbers.
Per wikipedia, here's what NASA says about Mach Numbers:
"An aircraft traveling at Mach 1 at 20°C or 68°F, at sea level, will experience shock waves in much the same manner as when it is traveling at Mach 1 at 11,000 m (36,000 ft) at −50°C or −58F, even though it is traveling at only 86% of its speed at higher temperature like 20°C or 68°F."
National Aeronautics and Space Administration website page "Mach Number", NASA