I think this is an interesting topic hopefully worthy of discussion. Much gratitude to anyone who can correct any errors I have made, or give any feedback! I’m just a beginner with Pāli. 
Outiline
In the Susimaparibbājaka Sutta, SN 12.70, we have the following passage:
Sujato:
“Susīma, first comes knowledge of the stability of natural principles. Afterwards there is knowledge of extinguishment.”
“Pubbe kho, susima, dhammaṭṭhitiñāṇaṃ, pacchā nibbāne ñāṇan”ti.
I found the expression ‘the stability of natural principles’ very odd, and not with any apparent decipherable meaning in English. So I looked into this term dhammaṭṭhitiñāṇaṃ.
Searching the canon for dhammaṭṭhit* I found in another seven suttas, two of which I will not discuss as they are from late sections of the KN.
I’ll give my attempt at translating this, and then the extracts of the other occurrences in the canon, followed by my attempts at translating them too, to see if my take on dhammaṭṭhit* holds.
My attempt:
“Susīma, first comes knowledge of the state of things. Afterwards there is knowledge of extinguishment.”
Explanation: It means first get to grips with how this world works, understanding phenomena. In a way we could say how things abide. Then, you can get knowledge of … basically cessation of ‘things’! = nibbāna. It is perhaps including a contrast between lasting (ṭṭhiti), and ceasing (nibbāna) - continuance, and cessation. Here I translated ṭṭhiti as ‘state’. But ‘continuance of things’ might also work. They both have a near meaning, ‘state’ alluding to the continuance, which makes it a state - the ‘way’ that they abide.
DN 9
In the context of doctrines:
When they said this, Poṭṭhapāda said to them:
Evaṃ vutte, poṭṭhapādo paribbājako te paribbājake etadavoca:“I too understand that the ascetic Gotama didn’t make any definitive statement at all regarding whether the cosmos is eternal and so on.
“ahampi kho, bho, na kiñci samaṇassa gotamassa ekaṃsikaṃ dhammaṃ desitaṃ ājānāmi: ‘sassato loko’ti vā, ‘asassato loko’ti vā … pe … ‘neva hoti na na hoti tathāgato paraṃ maraṇā’ti vā;
Nevertheless, the practice that he describes is true, real, and accurate. It is the regularity of natural principles, the invariance of natural principles.
api ca samaṇo gotamo bhūtaṃ tacchaṃ tathaṃ paṭipadaṃ paññapeti dhammaṭṭhitataṃ dhammaniyāmataṃ.
My attempt:
“I too, friend, understand that the ascetic Gotama didn’t expound/teach any definitive/absolute doctrine at all regarding whether the cosmos is eternal and so on.
However/nevertheless, the ascetic Gotama declares/lays out (/elucidates?) the natural/genuine/true true/real/justified true/real path/method/course [all 3 Pāli terms basically referring to the meaning ‘true’]- (that is) the state of things, the fixed nature / natural law/order of things.
Tidy:
“I too, friend, understand that the ascetic Gotama doesn’t teach any definitive doctrine at all regarding whether the cosmos is eternal and so on.
However, the ascetic Gotama lays out the genuine, real, true path - the state of things, natural order of things.
Explanation:
He may be on the one had saying that he’s not talking about whether or not the cosmos is eternal, but the path he teaches ( = Noble Eightfold Path, which includes (Right View) an understanding/doctrine of how things work, in terms of causality, impermanence and so on), is the thing which is ‘eternal’ in a way - he is not talking about whether things really are eternal, but he is talking about how things are, the ‘way’ they are, the way they are existing/happening. And they are impermanent, no-self and so on, and, always will be. That is the state of things. That is the ‘fixed nature’ of things.
And he additionally may be making a pun, with the word dhamma. Because he first says he doesn’t give a dhamma (doctrine) about eternality. And then explains his path also in terms of dhamma, but in this case dhamma as things/phenomena. His doctrine (dhamma) is about the way things (dhamma) are, the natural order. Not about theories of eternality, which when adopted do not further the aim of overcoming dukkha. And in some sense, it is these natural laws which are ‘eternal’.
SN 12.34
A list of knowledges, the last of which is:
And the knowledge that this knowledge of the stability of natural principles is liable to end, vanish, fade away, and cease.
yampissa taṃ dhammaṭṭhitiñāṇaṃ tampi khayadhammaṃ vayadhammaṃ virāgadhammaṃ nirodhadhammanti ñāṇaṃ.
My attempt:
And the knowledge that this knowledge of the state of things(/phenomena) (or: of the state of things that one knows) is [knowledge of(?)] things of decay, things of age/ageing, things that fade away, things that cease.
Meaning: And the knowledge that: the state of things we know (or: what we know about the state of things) - those things are all things that decay, that age, that cease (are annihilated).
SN 12.20
The Buddha said this:
Bhagavā etadavoca:“And what is dependent origination?
“Katamo ca, bhikkhave, paṭiccasamuppādo?Rebirth is a condition for old age and death.
Jātipaccayā, bhikkhave, jarāmaraṇaṃ.Whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles, specific conditionality.
Uppādā vā tathāgatānaṃ anuppādā vā tathāgatānaṃ, ṭhitāva sā dhātudhammaṭṭhitatā dhammaniyāmatā idappaccayatā.A Realized One understands this and comprehends it,
Taṃ tathāgato abhisambujjhati abhisameti.then he explains, teaches, asserts, establishes, clarifies, analyzes, and reveals it.
Abhisambujjhitvā abhisametvā ācikkhati deseti paññāpeti paṭṭhapeti vivarativibhajati uttānīkaroti.
Almost identical to AN 3.136, just one extra word at the end and no monks.
I was curious about the ‘ṭhitāva sā’. I thought that it might be ṭhitāvasā, ṭhita + avasā (avasa: powerless). Is this a possibility? [Edit - this issue was connected to an issue with copying and pasting from the Pāli with Chrome on the new system - it joined dhātu to dhamma making a compound, and leading me on a wild goose chase with ‘ṭhitāva sā’. I now realise there was a space in the original Pāli, and have deleted the section on the above mentioned hypothesis].
Original:
Whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles, specific conditionality.
Uppādā vā tathāgatānaṃ anuppādā vā tathāgatānaṃ, ṭhitāva sā dhātu dhammaṭṭhitatā dhammaniyāmatā idappaccayatā.
My attempt:
“Whether the coming into existence/existence of tathāgatas, or the not coming into existence/existence of tathāgatas, really enduring/persisting/contining (tiṭṭta contrasting with whether tathāgatas arise or not) is that natural condition (dhātu) - the suchness/state of (tā) the state (ṭhita - ‘being, behaving in general’) of things, the suchness/state of fixed nature of things, the-cause-of-this-ness.
Tidier:
Regardless of the coming into existence of tathāgatas or not, that (sā) which really endures/persists/continues is the natural condition (dhātu) - the state of things, the fixed nature of things, the causal nature / state of causality.
Or,
Regardless of the coming into existence of tathāgatas or not, what indeed endures/persists/continues (or ‘what indeed does remain/endure/persist) is that natural condition (dhātu) - the state of things, the fixed nature of things, the causal nature / state of causality.
AN 2.280 (as saddhammaṭṭhitiyā)
… For inspiring confidence in those without it, and increasing confidence in those who have it … For the continuation of the true teaching and the support of the training.
… appasannānaṃ pasādāya, pasannānaṃ bhiyyobhāvāya …saddhammaṭṭhitiyā vinayānuggahāya.
This translation I agree with, using dhamma here in the context of teachings.
AN 3.136
The passage that concerns us is only two words different from SN 12.20 but I wanted to include some context:
“Mendicants, whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles:
“Uppādā vā, bhikkhave, tathāgatānaṃ anuppādā vā tathāgatānaṃ, ṭhitāva sā dhātudhammaṭṭhitatā dhammaniyāmatā.
all conditions are impermanent.
Sabbe saṅkhārā aniccā.
A Realized One understands this and comprehends it,
Taṃ tathāgato abhisambujjhati abhisameti.
then he explains, teaches, asserts, establishes, clarifies, analyzes, and reveals it:
Abhisambujjhitvā abhisametvā ācikkhati deseti paññāpeti paṭṭhapeti vivarati vibhajatiuttānīkaroti:
‘All conditions are impermanent.’
‘sabbe saṅkhārā aniccā’ti.[the same again for:]
all conditions are suffering.
Sabbe saṅkhārā dukkhā.
[…]
all things are not-self.
Sabbe dhammā anattā.
My attempt:
(See SN 12.20 above for reasoning on this translation)
Monks, regardless of the coming into existence of tathāgatas or not, [that which] really endures/persists/continues is that natural condition (dhātu) - the state of things, the fixed nature of things.
AN 10.31
same passage of the list of 10 as AN 2.280