Thank you jesgord for your research. I think that the conclusion of all this is that the stool with the apparent bolts is an in- house Fritz Hansen design (maybe Søren Hansen) and that Arne Jacobsen somehow improved it. I guess that the role of Jacobsen in the stool design is probably slightly exagerated for marketing reasons...
The problem with this conclusion is that model 3170 encompasses both versions of the stool, the one with the through bolt, and the one without. And model 3170 is credited authoritatively to:
1. Søren Hansen as a person (or company representative),
2. Fritz Hansen as a company (or design department), and
3. Arne Jacobsen.
And Fritz Hansen represents the stool's design as a collaboration.
The simple fact that at one time model 3170 with through bolts was represented as a 'FH' design, and at another time model 3170 without through bolts was represented as an Arne Jacobsen design does indicate much of anything in the context of the Danish furniture industry. It was not uncommon to see design credits change over time between a designer and the manufacturer.
On the evidence presented by Jesgord, I think you can say that Arne Jacobsen was the designer of any version of the stool that was advertised by Fritz Hansen as model 3170. And the same can be said of Søren Hansen (or 'FH'). Probably the most precise way to say it is to quote what Fritz Hansen currently says about the design.
Absent evidence that Fritz Hansen-- simultaneously-- offered the two different versions of model 3170 with different design credits, I don't see how we can reasonably differentiate designers for the different versions.
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