No piṭaka: How did this concept "Ti-piṭaka" (3 baskets) come about?

 In the early suttas, the Buddha only talks about Dhamma (teachings) and Vinaya (monastic code).

There is no Abhidhamma mentioned in the EBT (early buddhist teachings),

there is no tipitaka (3 baskets).

How did this concept "Ti-piṭaka" (3 baskets) come about?

Abhi-dhamma (systematic treatise/analysis of Buddha's Dhamma)  came 100 to 200 years after the Buddha.

Some of it is compatible with EBT (early buddhist teachings), 

some of it is not.

The LBT (late Buddhist teachings) Theravadins wanted to grant Abhidhamma the same status as the Buddha's original words,

so they created a pretty ridiculous origin story claiming Abhidhamma actually was spoken by the Buddha secretly and passed on secretly through only one disciple. 

And then they created the concept of  "Ti-piṭaka" (3 baskets),

putting Abhidhamma as the 3rd basket, along with Dhamma (the Buddha's actual words), and vinaya (monastic code). 

Do you accord a middle manager the same respect and status as the chief executive officer?

This is incredibly arrogant and  presumptuous don't you think? 

Making your own basket and putting it on the same hierarchical level as the Buddha himself?

Maybe that's why the LBT Theravadins had to create a ridiculous origin story that the Buddha himself actually spoke the Abhidhamma and secretly only taught it to his mother in the deva realms, and Sāriputta. 

But will the Real Abhidhamma please stand up?

Of the 18 early Buddhist schools, most of them had their own Abhidharma system,

and they differ radically from the Theravdin Abhidhamma,

along with their origin stories.

The other schools attribute (their version of) Abhidhamma as commentaries made by disciples of Sāriputta, not the Buddha himself. 

So ask yourself this: If the other 18 schools of early Buddhism had nearly identical version of the suttas and vinaya as Theravada, 

but radically different versions of Abhidhamma,

along with a different origin story for their Abhidhamma,

does it seem likely to you that Theravada Abhidhamma is the original words of the Buddha?

Conclusion

There is no "Ti-piṭaka" (3 baskets) in EBT (early buddhist teachings).

There is just Dhamma and Vinaya.

Everything else is a mixed bag, use at your own risk.

You should follow the Buddha's advice in the 4 great references.

    AN ^4.180 - AN 4.180 Mahāpadesa: The Four Great References
        AN ^4.180.1 - (if you hear and memorize Dhamma from one who heard Buddha)
            AN ^4.180.1.1 - (⛔if memory conflicts with suttas and vinaya, you must reject your memory as corrupted Dhamma)
            AN ^4.180.1.2 - (✅☸if memory agrees with suttas and vinaya, your memory of Dhamma is confirmed)