There is no such thing as a "most basic assumption". Lacan has expressed this in the notion that 'master signifiers are empty'.
(At this point, I did not intend to make a major digression. Please read whatever you want of this and then skip to the bolded 'Yet'...)
His motivating example seems to be Fatherhood. This is a notion that seems to be a basic biological fact, but is instead a social construct that did not exist in early societies. The roles of men as the protectors of specific sets of children is not uniformly associated with biological parentage -- such as in the Mabinogion and other very old epics (including hints in the stories of Abraham), where male privileges and training pass to the nephews of a mother's favorite brother, who is often an adopted friend. Our modern notion of fatherhood comes down from the more general notion of patriarchy, where men guard and guide collections of people, with the nuclear family being the smallest such collection. But not so many generations ago, in many societies the nuclear family's father was subject to his wife's father, or to his own mother, and did not control anyone, including his wife and children. We carried this notion of kingship downward over time, in a way that is not in any way simple. Etc. etc. There ends up being very little about fatherhood that is actually consistent and has meaning.
And in other ways as a 'basic idea' it is a knot of negotiations across time, which don't share anything -- our legal concept of fatherhood, at least in most US states, even proceeds in three directions -- biology, marriage and common law -- which do not agree upon what a father is. A child born to a legally wedded woman has her husband as its father, whoever's biological child it is, even if he abandons the family as a result. Marriage after the birth of the child may or may not confer fatherhood on the new husband, depending upon the level of involvement of the previous husband. A man who supports a child for a given period of time becomes its father even if there is no biological or marital link. Etc. etc. etc.
Yet 'the Father' seems simple and holistic as a symbol and is extremely compelling psychologically, even though it artificially binds up our species overall history of military rulership and male responsibility for acquiring resources from outside the tribe with the tendency of women to be more monogamous than men and to need close friends more intensely, and a bunch of other factors that just aren't simple.
Explanation is necessarily circular, with extremely complex ideas given the status of being simple by the force of culture or by appeal to shared emotional impulses, and extremely simple ideas becoming quite complex as one explores them, because they are only actually simple within a complex context.
This means that parsimony has to do not with absolute meaning, but with emotional resonance. Those concepts are simple which people can be expected to find compelling, and in general that means things that appeal to the broadest shared emotional level. One component of this broadly shared level is logic, so things that take elegant forms and are well-connected logically are often parsimonious. But beyond that, we have only Archetypes.
Concepts like power (safety) and abstraction (mind), and other things we consider to proceed from the religious notion of God (often The Father) are also very broad anthropologically -- but they proceed from a specific path to the notion of God, which succeeds in our shared social trends.
As writers like Starhawk have analyzed, you need to be wary of them, because 'sky gods', the kinds of gods that succeed in cities and other dense populations guarded by military and agricultural strength, are only dominant because those are the kinds of cultures that have taken control of the planet. In periods less given to oversimplification, alongside our God, the Western, Abrahamic traditions have often also had a feminine principle, from Baal down to Mary or the Shekinah. Cultures outside the West have, too. We find such threads less conceptually simple, but only because we have almost uniformly chosen a patriarchal style of life.
In many ways, the most parsimonious theory of God is Jung's: Everyone needs a parent, maybe two, and the ones that we understand too well, are not good enough.
