What is the origination of the mind-stream continuum? What are the basic elements that make up the mind-stream continuum?
Gautama never described an origin. Whether existence had a beginning or end was never defined. Some traditions have taken to saying "beginningless." So if mindstreams have a beginning, the Buddha never said so. The asker was either told that the answer was irrelevant to liberation (hence not worth answering) or that the question did not apply.
The Pali canon relies on dependent origination for explaining where minds come from, but does not describe mindstreams themselves. Later commentators, such as Asanga and and Vasubandhu of the Yogacara school of thought would expound on additional layers of conciousness. From my experience, most talk of mindstreams take their source as the alaya-vijnana; itself a term that has been mentioned by some contemporary Theravadin monks (Ajahn Geoff and Ajahn Sujato).
I believe the orthodox Theravada response would be the parable of the poison arrow, and Mahayana responses would depend on the proclivities of the instructor. A Yogacarin would describe the features of the alaya-vijnana and a Madhyamika (in a Tibetan tradition) would conclude that mindstreams simply are (in conventional terms at least; illusory "like a city of gandharvas" in an ultimate sense).
There is no set "Buddhist" answer here, unfortunately.
Mind is a created thing, further conditioned by experience. The “mind stream” actually isn’t mind at all, since mind is completely dropped in Nibbana. The “unborn, deathless” is what, I think, you are referring to. The unborn is not a static “state”. It flows. In ignorance it flows, creating mind. That-which-flows identifies with mind, creating ego. That-which-flows does not at this point have awareness of itself. That awareness doesn’t happen until one achieves stream entry, the first insight into self-realization. The fruits of stream entry are well known. But when this stage is passed through, one has the “turning in consciousness” spoken of, i.e., full self-realization. I know I am somewhat off the point here, but bear with me, as I think this gives a fuller appreciation of the difference in mind and that-which-flows. When one awakens and reaches Nibbana, mind is dropped but not abandoned completely, else one could not come back and function. Rather, mind changes. A new awareness, of which that-which-flows has achieved, now occupies the mind. (This is obvious from the fact that the mind is created by that-which-flows.) Lastly, you might ask how the unborn flows when it is beyond both time and space. Think of the flow as movement of awareness. It’s not exactly that, but that is a good metaphor for it. Another way is to ask yourself if insight flows. YES! It does. That is what I mean.
the mindstream is merely a element(consciousness) like earth,water,fire,air etc it has always existed and will always exist.it is one of the 5 wisdom lights in vajrayana wich has always existed and will always exist.Vajrayana basis itself on madhyamika,and in madhyamika nothing arises and nothing ceases.dependant arising is an upaya in a sence.the 5 wisdom lights are reified as elements thru (beginingless)ignorance of their true nature,the only difference between a 16th bhumi buddha and a ignorant being is nonconceptual(that is experiential knowledge thus) knowledge of their true nature as empty and as wisdom lights basically according to Dzogchen and mahamudra.
the 5 wisdoms are personal and unique to every sentient being,together they form the basis(Gzhi).there are infinite basises(meaning every sentient being has one basis known also as mind,also known as 5 wisdoms) unique to infinite sentient beings.basically sentient beings have always existed and will always exist.
the reason we percieve the same universe is explained by a container universe yogacara model in vajrayana.
people think madhyamika is saying nothing exists.or that its Nihilism.it isn't saying that.simply that reality is nonestablished and is a contradiction in itself and that it is not arisen .it is simply saying that there is no absolute,without its relative parts and thus there can never be said to be a independant absolute entity.thats it.madhyamika is pretty simple and logical.
In my understanding:
Mind-stream continuum originates from the growth and evolution of tendencies. It is created by the same mechanism that lies behind "the natural evolution of species".
(Phenomena that create causes that either support their continued existence or aid future arising of similar phenomena tend to "survive" and "procreate". These are called tendencies.)
Most phenomena carry imprints of other phenomena, one way or another. Carrying imprints they carry information about (or representation of) other phenomena. These are the basic building blocks mind is made of.
Phenomena that carry imprints of other phenomena can also happen to be like that, cyclical self-supporting tendencies. The more imprints they accumulate, the better their odds for continuation and accumulation of even more imprints.
The rest is explained in the Twelve Nidanas. The cyclical tendency becomes habit to seek similar imprints. This iteratively grows until it becomes an ability to recognize.
Once there's recognition, there's association. Once there's association, there's interpretation of signs. Once there's interpretation of signs there's citta-vrti, the associative loop. Here we go, this is a full-blown Mind-stream.