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Here is another discovery from the Auckland museum which had it labeled as a rapier!
It has a Kings Head stamped on both sides of the blade, I initially thought it was a Wundes until I realised it faces the wrong way which means it is most likely to be made by Martino Antonio.

Overall Length: 98cm Blade Length: 83cm Weight: 697.3g Balance Point: 13cm
Profile Taper: Shoulder Width: 37mm Point Width: 22mm
Distal Taper: Shoulder Width: 6,5mm Point Width: 2mm