Here's a link to a write up that indicates that PIA-C-5040E Type III para-cord is being specified for use in
Military C-9 Parachutes .
This article further indicates that PIA-C-5040E Type III was used in the parachutes for the "ACES II ejection seats in F-15, F-16" and "pretty much all current U.S. jet fighters and personal parachutes in cargo airplanes like the C-130."
Also the write-up indicates that "there is no life limit on these . . ." C-9 parachutes. Perhaps that's why the specifications for the C-9 parachutes require a para-cord that's been tested for pH (and meets certain pH standards as to acidity) --- and why PIA-C-5040E is required for these "no life limit" parachutes rather than MIL-C-5040H (which isn't tested for pH).