Throughout the canon the only uses I’ve found of “pariyāya” are about speech, not about future lives. That should be enough evidence, alone, that the phrase “diṭṭheva dhamme upapajje vā apare vā pariyāye” is mistranslated, and I can’t help but wonder how that happened. I have tried hard to find an instance of “pariyāya” being used to mean a “turn at life” in any phrase *other* than “upapajje vā apare vā pariyāye“. I would welcome it if anyone could show me one.
Next follows a list provided by iMeditation over at Ajahn Sujato’s blog, which I also researched:
M i.252 (MN 37 p 345 “It is long, good sir, since you found an opportunity to come here” — the translator apparently couldn’t parse the word pariyaya in the sentence at all so left it out, however since the speaker then launches into a discourse with the visitor, including the word *in* the sentence, it would look like this: “It is long indeed, good sir Morgallana, since you performed a discourse, that is here in this place.”)
M 326 (MN 49 p 424 – same phrase as above )
M iii.7 (MN 107 has “anekapariyāyena” which is translated as “in many ways” — “Master Gotama has made the Dhamma clear in many ways”)
M 62 (MN 115.4-9 “in what way” “might there be another way in which a bhikkhu can be called…” so it is again about how people “speak of”)
S i.142 (SN 6.4 p 237 The same greeting phrase again, in which the speaker greets someone who has been gone long and launches a discourse.)
M i.78 (MN 12 the word is “pariyāyabhattabhojanānuyogamanuyutto” which seems to be translated as “pursuing the practice of taking food at stated intervals” since “bhatta” and “bhoja” are food and “anuyoga” is “practice of” and “anuyutto” is “applying oneself” that leaves “pariyaya” to deal with “stating intervals” — words again)
M i 282 (MN 40 p 373 the word is “pariyāyabhattikassa” part of the phrase translated as “a taker of food at stated intervals — see MN 12 above)
M i 481 (MN 71 “pariyāyamakāsi” or actually “pariyāyam akāsi” and it’s the same phrase as in MN 37)
S ii.51 (SN 12.32 p 568 “In whatever way, Sariputta, a clansman declares final knowledge…” “in whatever way” is about a method of speaking )
A ii.206 (AN 4.198 the word translated is “pariyāyabhattabhojanānuyogamanuyutto” — see MN 12 above)
S i.146 (SN 6.55 p 241 the word is “cetopariyāyakovidā” — a word in a compound is not an accurate source for comparison to the word alone. Plus it’s in the middle of poetry about iddhi but it appears to be about one who can speak what is in other’s minds or read the words in their minds: “skilled in the course of others’ minds” is the translation here, but it is clearly not a reference to rebirth.)