At 3A per contact and 29 positions, the total current through the header is limited by the pin density and PCB trace width, not the contact itself. The phosphor bronze contact material carries the current with a temperature rise well within the UL94 V-0 housing's thermal limit.
The base product number is 68001; the -129HLF suffix specifies the 29-position, single-row, gold-plated variant.
