Sorry for my ignorance but ... what am i missing here?
Don't i see that the Berne Harquebus has the hook peened through the stock ?
On the other hand, isn't the system of casting the hook to the barrel a 'third generation' development ?
If i well understand, in the first step the gun had a gunstock with a wooden shoulder on the underside, as shown in a specimen in the museum of Pilsen, which dates to around 1400.
But as this design involved severe stress to the wood, which did not withstand the strain for long, the next step was the development of an iron hook with bands or nails being fitted to the shaft, further improved by positioning the hook on the barrel with a band and securing it in the shaft with a cross pin.
It was only after this that, the hook was either forged directly on to the barrel or cast with it, when of bronze.
This is the way i understood an article written by Bernhard Rietsche, in his work Meine gotischen Handfeuerrohre (page 47), which was gently passed to me by a notable person in this Forum

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However i know i don't have the minimum preparation to discuss this subject, so i beg you to correct me if or where i am wrong

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Fernando