Most important single concept?

The GPA is three dimensional: socio-cultural, cognitive and temporal. In cognitivist theories of second  language acquisition  I would say that the idea of a "mental L2 grammar" is the most important idea. "Acquisition" means modifying that mental object on the basis of experience. In reality, exceedingly little is known with any confidence regarding how that happens. Of course, the cognitive dimension the GPA is concerned not with this speculated mental entity, but with processes that convert acoustic cues into situation models and discursive acts, and also, processes concerned with producing speech which will have these effects in the interlocutors. We'd love to know as much about those processes as possible. Unlike mental grammars, we can be certain that such processes exist and must somehow develop, or be mimicked, as part of growing participation.

However, the cognitive dimension is secondary in the GPA to the sociocultural dimension. Communities ("cultures") use brains to construct and maintain themselves, but the brains, or at least their dispositions resulting from the moulding effects of community, are secondary to the social realities of communities. Thus, prior to cognitive processes are communities characterized by shared practices.

Here's a question: Given the primacy of the sociocultural dimension, what is the most important single concept of the GPA ?

What happened to the Facebook page?

It is still there. https://www.facebook.com/GPApproach/ However, Facebook won't let me access as owner unless I send them copies of business documents and personal identification documents. I hope they'll change their minds. I think I can still post comments there as can any Facebook user. It was there that I tried to introduce the GPA philosophy to people who knew nothing about it. On this Blogspot blog I more assumed people had some training in the GPA. 

Picking up this blog 20 months later. Grammatical cues as processing triggers in comprehensions

What was that? Well I hope I'm back.

Recall that in the GPA grammatical cues are viewed as "hot buttons". For many people grammar is about putting the right bits into the right spots because that is what the mental "competence" grammar happens to specify, and if you want sentences to be grammatical (which is a moral imperative), you do as the grammar specifies. 

We believe instead that grammatical bits (function words, affixes, word order) are cues that trigger complex processes for host listeners. Host listeners are extremely responsive to a variety of cues, from acoustic cues to lexical cues to grammatical cues. That is why we called them hot buttons. 

From this perspective learning is not a matter of putting the right bit in the right places by conscious planning, which over time is replaced automatic processes. Rather it is a matter of becoming increasingly sensitive to cues (through frequent experience) until one is so sensitive that if one throws one's comprehension system a curve--say giving it contradictory or otherwise clashing cues--one's comprehension system reacts to that fact, and one tends then to modify one's speech to give the cues that one's comprehension system expects, since the utterance in question didn't sound right.

That seems pretty reasonable to me at least. It is what my dissertation was about, by the way.  Recently Trenkic, Mirkovic and Altmann, 2013 observed (in the article “Real-time grammar processing by native and non-native speakers,” in _Bilingualism: Language and Cognition) “A vast body of the literature suggests that late second language learners often show inability to process L2 morphosyntactic information in a target-like manner,” (p. 1) and they add that “structures that are difficult to process in comprehension are often the same ones with which L2 users struggle in production” (ibid.). They also cite evidence that “problems in L2 production may be related to the processing strategies used in comprehension…” (p. 2) Well duh! 

This is an important issue to me because as the GPA became more widely used and more popular, this became a refrain: It leads to "non-native-like grammar". Again, well duh. Nothing leads to thoroughgoing native-like (we would say "host-sounding") grammar. There are minor advantages to a certain strategy (such as form focus or correction via prompts) but it is the name of the game that people starting to learn an additional language (languaculture) as adults are quite non-host-sounding, at least for a number of years! So give us a break. I take comfort in the fact that as far as I know those on the offensive against the GPA are on the offensive simply because of its popularity in certain quarters, not because they have actually looked into what it is about!