Brihaspati - I shall now use the term fractal recursivity in its original sense and not in the sense that it has generally been used on this forum (primarily by ME!!) - i.e as a way of showing how the colonized acquires the mind of the colonizer.
The "original" fractal recursivity refers to the phenomenon in which macroscopic differences fade as one enters the microscopic arena where details are mirrored and mimicked in a process that is repeated yet again as you dig deeper into sub-details and sub-sub details.
The "macroscopic" Indic characteristics that we like to talk about appear to be in stark contrast to macroscopic appearance of the Abrahamic faiths and the cultures they fostered. And because of the vast gulf between the macroscopic appearances, there is a tendency for us to think that if we use reductionism and try and dig microscopically into "core principles" one might find that the Indic practices arose from superior core principles and superior ideals while the Abrahamic faiths arose from faulty premises.
I believe that this is wrong. All ancient faiths rose out of the need to explain or cope with the same problems that all humans face - sorrow, disease, death, natural calamity, hunger, disability, infidelity, deceit, subjugation, fear, loneliness and the power of incompetents over others.
If we "cut the crap" and look down to the very origins of the Abrahamic faiths - they were solutions that were mooted for a particular society at a particular time in history. No more. What we see today as the powerful structure of the Abrahamic faiths is merely a mindless historic extrapolation of those rules imposed by military victories on huge areas of the world.
Indic cultures too developed initially as explanations or solutions to those same human problems. But there was no imposition of "one size fits all" solutions but a continuous exploration of all possible solutions.
That is why going back to the core will ultimately get us nowhere - because at the core everyone claims that it all came out of good intentions. The problem is not the core differences but the macroscopic manifestations that we see today.
In some ways the Western solution appears to be good. The Western solution is to downgrade religion - even the Abrahamic religions and bring them under the control of a common law. That common law constitutes the "core ideas" of the Western nation in question. The downside of such abrogation of religion is the mindless pursuit of personal happiness in the absence of religion leading to suicidal societies whose numbers go down as people seek material wealth over the sacrifices and sorrow that family life inevitably brings.
India is in a dilemma - and is sitting up RayC's gum tree. India has tried to replace religion with a common law but has done a half and half job of that. Once again, the modern Indian state, faced with the need to make a firm "this way or that way" decision, has behaved in the Indic fashion and has tried to reach a compromise in which nothing is thrown away and nothing is taken up fully. Modern Indian laws are just one more set of laws that you have the option of following. The behavior of Indians reflects that.
I do not want to thwart you in your quest for a core and for that reason I will (attempt to) leave this thread now. My thought process sees things in such a different way that I will only be destructive I apologise for any hurt feelings I may have caused to anyone. I think my own thoughts about what India looks like to me need to go in a book that I have been threatening to write for over a decade. Only problem is - India is so big that I am spending my entire life learning.
I only hope I can keep my disruptive opinions off this thread by finding some other place to go and park myself.
Also what if your loving girlfriend got squeezed in the process! And what makes you so envious of those who could have multiple wives? Especially in the days before the little blue pills! 
:p