What sort of infinite regress to birth is Nagarjuna's MMK arguing for?

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In my understanding, everything Nagarjuna talks about endlessly revolves around one theme - that is of imputation and reification of abstractions, which leads to confusion of the phenomenological with the ontological, which leads to conflicts, and suffering. As was customary in the ancient times he goes over endless examples of the same kind of argument over and over again, to make sure the reader is left with no doubts about the points made.

The initial verse introduces the subject of liberation from reification (paraphrasing Garfield's translation):

I prostrate to the Perfect Buddha, the best of teachers, who taught that everything is dependently arisen -- not dying, not born, not subject to annihilation nor permanence, not coming, not going, with no delineation, no [fixed] identity; -- to liberate from reification.

With arising/birth, just like with every other topic, Nagarjuna uses 'reductio-ad-absurdum' to show that discrete things are reified abstractions we impute onto reality, confusing them with reality itself.

Specifically, speaking about arising/birth, he tries to show that the notion of birth as a moment when something is born is incohesive under close scrutiny. He says, if something arises at point T1, then what is the moment T0 when this arising itself begins (arises). If we look at any such point, we see an infinite regress - not into the past, but into splitting each moment of arising into its "beginning" and the rest of the moment.

Equally, when we look at the moment when something has fully arisen... This notion of "having arisen" is absurd as well. This is where he gives that simile of the lamp, saying that where lamp with its light has fully arisen there is no darkness (absence of light), therefore arising of the lamp could not have possibly caused illumination of the darkness, because by the time lamp with its light fully exists, darkness has gone. This is a similar argument to the "initial moment of arising" argument, except now we're scrutinizing the final moment. As we look closer we see that there is no concrete point in time when something is "fully arisen".

All of this is meant to illustrate that the notion of arising, and therefore the notion of entity, is an abstraction, and that we should stop reifying things as solid and having clear boundaries, because in reality they do not.

In Yogacara's theory of three-fold-svabhava, reality can be analyzed from a perspective of how it appears to a mind of naive reification (i.e. that entities are real), from an analytical perspective of dependent-origination (which explains how entities gradually become more solid as a result of development of the mind of reification), and from an enlightened perspective of Buddha, who look at all this stuff with full understanding of how it works and therefore clearly sees the true "quantum" reality behind both the confused perspective as well as the analytical dependent-origination perspective.

P.S. to those wondering how all this relates to Noble Path and liberation from suffering: in Mahayana, reification of entities as something real and solid is considered the root cause of attachment, therefore of suffering. In Mahayana's interpretation, the ignorance Buddha spoke about, is exactly this naive ignorant reification, not understanding that entities are imputations and therefore grasping onto the phantoms. This in turn leads both to objective conflict because of clashing points of view, and to subjective suffering when things turn out to be different from the way we imagined.

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