Architectural Thinking Framework

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I’d suggest to to distinguish business function from capability.
Business function is the label given to an asset, capability define the qualitative and quantitative attributes of that asset.
E.g. Automotive—Business function “Production”—quantitative: how many cars I’m able to produce in one day
Qualitative: different kind of cars with (station wagon, spider, crossover and so on).

The Business function is a fixed asset, capabilities can change in terms of quantitity and quality.
I’d put emphasis on capabilities because, in the general blue print of the Organization, the issue to distinguish business functions and (related) capabilities is not important.
But when it comes to evaluate Portfolio, it’s very important to distinguish.

I would move "Architectural Thinking is not a process or discipline." to the end of the paragraph where it appears, not the beginning.  

I am aligned with the motivation of this framework. In fact, I have a similar architecture model as this framework. Where mine differ with ATF is that I break down the Solution further to Application Functions or I would loosely call it architecture building block (ABB). The ABB should be linked to the value streams to provide validation that the ABB are required and necessary. This allows further deliberation at the function level on the qualitative measure of the function eg. how mature is this function, such that it is able to serve the strategic visions or the business capability. Hope this helps

I am not sure what capability means here, although someone already pointed out the confusion with function.

Capabilities are a recent advancement in business thinking.  Prior to World War II there was no concept of capabilities. Everything was explainable through the Coasian model that brought together the resource-based theory of the firm with the marketplace to buy and sell products as the most efficient model.  At the beginning of WWII this had failed to produce a production model that could meet the needs of selling tanks, ships, airplanes, and bullets to the allies, and fight a war where coordination in production was needed. Roosevelt created a commission (leading to a Nobel Prize in Economics for its leader) to solve this problem.  They created a model where academic institutions, the government, and firms, needed to coordinate their production in complimentary ways.  G.B. Richardson in 1976 referred to these mini-markets that existed outside of the Coasian view, as business capabilities. Nelson and Winter would later extend this as part of their view of the evolutionary firm.  Teece, Pisano, and Shuen (1997) changed the name to dynamic capabilities after the confusion caused by Prahalad and Hamel (1990) with their theory of core competencies and Nelson and Winter (1985) extending the definition of capabilities to internal quasi-markets. 

It turned into a mess academically with many trying to further disassociate capabilities from competencies and others falling behind the dynamic capabilities camp.

In business, though, it is useful. I first came across capabilities in 2003 when I was part of one of the largest banks.  We competed based on capabilities. In this case it turned out to be teller services. There is no such thing as a teller function within a bank.  There are accounting, cash disbursement, and more than a dozen functions that go into teller operations, but once these are taken away there is nothing left but a bunch of real estate and people who do things for banking clients. To figure this out the large banks created a quasi-market for teller services that was based on their contrasting abilities.  We were a large retail bank, which in it domicile country, had long lines.  We developed systems that were optimized to be faster than the other banks.  Another bank decided that teller services included personal banking.  Everyone in a branch could provide the customer a 360 degree view of their accounts and a range of services.  Yet another used a brokerage model for their teller services. They had waiting seats, magazines and TV's with tickers.  They also had coffee and cookies for customers to reflect deeper.  This is a capability.  These could also lead to complimentary activities as well. Microsoft created a software ecosystem of competing companies leading to a public that saw these competing companies as complimentary.  AWS has this approach well.  This ecosystem represents a capability for software development.  George Best (2018) discussed how this model was used in the growth of technology in the Boston area, which led to a dynamic change.