☸4nt → 8aam #8: Sammā Samādhi 🌄 → impure jhāna
impure jhāna, is still called "jhāna"
the 4 jhānas in the EBT, can be and are interrupted by impurities from time to time, as SN 40 and many suttas in AN 9 clearly explain. Especially when one is learning. It's just like any skill in life, if you don't practice, your skill erodes. But here is the important point. Even the impure jhāna, the Buddha still calls it "jhāna". . That's the reason for the existence of 4ip (iddhipada) and the suttas on samādhi mastery. They encourage you to remove all the impurities. The impure jhāna is impure, but its still jhāna.
VRJ (Vism. Re-definition of Jhāna) and ABRJ (Ajahn Brahm Re-definition of Jhāna, same as VRJ without abhidhamma theory) which describes a type of samādhi training system that is completely different, and their redefinition of what body and thinking means, contradicts the EBT and causes massive problems.
SN 40 (suttas 1-9) Moggallana's struggles with 8 samādhis
Identical passages occur in SN 21.1, AN 9.34, AN 9.41.
Moggallana is accused by other monks of claiming false samadhi attainment, for hearing sounds while in imperturbable samadhi.
imperturbable can mean fourth jhana, but in that context, it must be one of the arupa samadhis.
The word the Buddha uses to defend moggallana, is that his samadhi is "impure" (parisuddha), but it's still a legitimate imperturbable samadhi, therefore he did not make a false claim.
Look at the passages where the buddha talks about wrong jhana. Especially look at MN 108, KN Snp 4.7.
Jhana in the suttas just means 'meditation', or 'obsessive focus'. The fuel for the meditation/jhana determines it as right or wrong jhana.
B.Bodhi and B.thanissaro usually don't translate 'jhana' as 'jhana' when it's in a 'wrong' context, so you'll have to look at the pali.
So once you realize that wrong jhana is still called 'jhana', and the wrong jhana of KN Snp 4.7 is the identical situation as the impure jhana I cited previously, then it should dawn on you that it's just modern Theravada propaganda that elevates (the naming of) 'jhana' into something more exalted than it actually is in the suttas.
Buddha did not invent jhāna
Another myth of jhana that needs to be cleared up, is that the Buddha invented it. Look in KN Snp vagga 5, especially intro. Other brahmins, before meeting the Buddha, are said to be practicing jhana. And later in that vagga, you see some of them could do arupa samadhis as well.
There is no momentary and access concentration in the EBT. There's just jhana. It can be a wrong jhana, a right jhana, or impure jhana, but the word the Buddha uses is 'jhana'.