What's the difference between samādhi, samāhita, samādahati?

I’ve been understanding them as synonyms, but what is the fine difference between them, especially in a sammā samādhi context?

looking up DPR sanskrit dictionary, dhā = ‘put’, and I can’t find an entry for ādahati.

Samādahati [saŋ+ādahati1] to put together S i.169. jotiŋ s. to kindle a fire Vin iv.115; cittaŋ s. to compose the mind, concentrate M i.116; pres. samādheti Th 2 50; pr. part. samādahaŋ S v.312; ppr. med. samādahāna S i.169; aor 3rd pl. samādahaŋsu D ii.254. Pass samādhiyati to be stayed, composed D i.73; M i.37 Miln 289; Caus. II. samādahāpeti Vin iv.115. – pp samāhita.

Samādhi [fr. saŋ+ā+dhā] 1. concentration; a concentrated, self – collected, intent state of mind and meditation which, concomitant with right living, is a necessary condition to the attainment of higher wisdom and emancipation. In the Subha – suttanta of the Dīgha (D i.209 sq.) samādhi – khandha (“section on concentration”) is the title otherwise given to the cittasampadā, …

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(PTS Dict)

Ādahati 1
[a + dahati 1] to put down, put on, settle, fix Vism 289 (samaṁ ā.=samādahati). Cp. sam˚ and ādhiyati.

Dahati 1
(dahate) [Sk. dadhāti to put down, set up; *dhe=Gr. ti/qhmi, Lat. facio, Ohg. tuon, Ags. dōn E. to do. See also dhātu] to put, place; take for (acc or abl.), assume, claim, consider D i.92 (okkākaṁ pitāmahaṁ=ṭhapeti DA i.258); S iii.113 (mittato daheyya) A iv.239 (cittaṁ d. fix the mind on); Sn 825 (bālaṁ dahanti mithu aññamaññaṁ=passanti dakkhanti, etc Nd1 163). Pass dhīyati (q. v.); grd. dheyya (q. v.). Note. dahati is more frequent in combn with prefixes compositions like ā˚, upa˚, pari˚, sad˚, san˚, samā˚, etc pp. ;hita.

Btw: above citation “Vism 289 (samaṁ ā.=samādahati)”:

(Nanamoli Visuddhimagga translation)
“232. (xi) Concentrating (samādahaṃ) the [manner of] consciousness: evenly (samaṃ) placing (ādahanto) the mind, evenly putting it on its object by means of the first jhāna and so on. Or alternatively, when, having entered upon those jhānas and emerged from them, he comprehends with insight the consciousness associated with the jhāna as liable to destruction and to fall, then at the actual time of insight momentary unification of the mind (fn64) arises through the penetration of the characteristics [of impermanence, and so on]. Thus the words, “He trains thus: ‘I shall breathe in … shall breathe out concentrating the [manner of] consciousness,’” are said also of one who evenly places the mind, evenly puts it on its object by means of the momentary unification of the mind arisen thus.”

fn 64. “‘Momentary unification of the mind’: concentration lasting only for a moment. For that too, when it occurs uninterruptedly on its object in a single mode and is not overcome by opposition, fixes the mind immovably, as if in absorption” (Vism-mht 278).

[232 xi] “Samādahaṃ cittanti paṭhamajjhānādivasena ārammaṇe cittaṃ samaṃ ādahanto samaṃ ṭhapento. Tāni vā pana jhānāni samāpajjitvā vuṭṭhāya jhānasampayuttaṃ cittaṃ khayato vayato sampassato vipassanākkhaṇe lakkhaṇapaṭivedhena uppajjati khaṇikacittekaggatā. Evaṃ uppannāya khaṇikacittekaggatāya vasenapi ārammaṇe cittaṃ samaṃ ādahanto samaṃ ṭhapento ‘‘samādahaṃ cittaṃ assasissāmi passasissāmīti sikkhatī’’ti vuccati.

Ādahanto” is apparently present participle of “ādahati” (Nanamoli: “placing”).

Also interesting: the alternative bit (and footnote) mentioning “momentary concentration”(khaṇikacittekaggatā) goes in the direction Mahasi Sayadaw emphasized, though there via pure insight method (without appana-samādhi/jhana) honing what he called “khaṇika-vipassana-samādhi”, which at the advanced stage (just prior to path+fruition) has comparably intensity as in jhana samādhi.

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here’s an example where samāhita is treated as just a conjugated version of samadhi. Notice the two examples that surround it, the undestroyed asava and destroyed asava, and the unestablished vs. established mindfulness.

I came across this example while doing a text search on samādhiyati. There are several other text references where it’s contrasted with samāhita and seem to be synonymous.

MN 17 samahita and samadhi
“Here, bhikkhus, a bhikkhu lives in some jungle thicket.223 “” While he is living there his unestablished mindfulness does not become established, his unconcentrated mind does not become concentrated, his undestroyed taints do not come to destruction,

MN 1, 2. sīhanādavaggo, 7. vanapatthasuttaṃ (MN 17.1), para. 2 ⇒

  1. “idha, bhikkhave, bhikkhu aññataraṃ vanapatthaṃ upanissāya viharati. tassa taṃ vanapatthaṃ upanissāya viharato anupaṭṭhitā ceva sati na upaṭṭhāti, asamāhitañca cittaṃ na samādhiyati, aparikkhīṇā ca āsavā na parikkhayaṃ gacchanti, a

Ok, never mind, I thought Samādhiyati came from “samādhi”, so this doesn’t establish equivalence between samādhi and samādahati.

Samādhiyati is Passive of samādahati.

But here is an example where samādhiyati occurs exactly in the slot for samādhi-sambojjhanga:

DN 1, 2. sāmaññaphalasuttaṃ, nīvaraṇappahānaṃ (DN 2.19), para. 10 ⇒

  1. “tassime pañca nīvaraṇe pahīne attani samanupassato pāmojjaṃ jāyati, pamuditassa pīti jāyati, pītimanassa kāyo passambhati, passaddhakāyo sukhaṃ vedeti, sukhino cittaṃ samādhiyati.

So I do think samādahati can be interpreted as a synonym as samādhi, since that 7sb (bojjhanga) sequences is so frequent.

@cjmacie in another thread proposed that samāhita might be a lower type of samādhi, not as refined as the samādhi in the four jhānas.

I’ve found evidence that definitely proves it’s not the case:

this pericope, which precedes the abhinna, supernormal powers, dozens of times in the EBT

:diamonds: 244. “so evaṃ samāhite citte parisuddhe pariyodāte anaṅgaṇe vigatūpakkilese mudubhūte kammaniye ṭhite āneñjappatte pubbenivāsānussatiñāṇāya

…concentrated mind…imperturbability-attained…

That pericope is sandwiched between four jhanas and the 6 abhinna, or the 3 tejivva subset within the 6 abhinna that occurs so frequently.

So that takes 4th jhana as a prerequisite.