I must revise this answer for 'the world' with a pertinent quote from SN 12.10, namely:
‘Alas, this world has fallen into trouble. It’s born, grows old, dies,
passes away and follows on as before'.
‘kicchaṁ vatāyaṁ loko āpanno jāyati ca jīyati ca mīyati ca cavati ca
The word 'jāyati' (verbal form of 'jati') above does not mean physical birth. For example, AN 4.200 & Dhp 212 say:
Cattārimāni, bhikkhave, pemāni jāyanti. Katamāni cattāri? Pemā pemaṃ
jāyati, pemā doso jāyati, dosā pemaṃ jāyati, dosā doso jāyati.
Monks, these four things are born. Which four? Affection is born of
affection. Aversion is born of affection. Affection is born of
aversion. Aversion is born of aversion.
Piyato jāyatī soko, piyato jāyatī bhayaṃ
From affection is grief born, from affection is fear born.
SN 12.2 defines "jati" as the birth of a "category of beings" ("satta nikaye"). SN 23.2 defines "a being" ("satta") as "strong attachment". SN 5.10 defines "a being" ("satta") as "a view"; "a convention"; "a word".
Therefore, when SN 12.10 says "the world is born", this means "the world is born from self-views". In other words, it is from self-views that grief & fear are born. Thus "the world" is that has the nature of grief, fear & sorrow. Thus AN 8.6 says:
Bhikkhus, these eight worldly conditions revolve around the world, and
the world revolves around these eight worldly conditions. What eight?
Gain and loss, disrepute and fame, blame and praise, and pleasure and
pain. These eight worldly conditions revolve around the world, and the
world revolves around these eight worldly conditions.
In SN 2.26, SN 12.44 & SN 12.15, it appears the term "world" is a synonym for "suffering" ("dukkha"). SN 12.15, in particular, says:
For one who sees the origin of the world as it really is with correct wisdom.... for one who sees the cessation of the world as it really is with correct wisdom... This world, Kaccana, is for the most part shackled by engagement,
clinging and adherence. But this one with right view does not become
engaged and cling through that engagement and clinging, mental
standpoint, adherence, underlying tendency; he does not take a stand
about ‘my self.’ He has no perplexity or doubt that what arises is
only suffering arising, what ceases is only suffering ceasing.
The word 'patiṭṭhito' is found in suttas such as AN 3.76 & SN 22.53. Here, 'patiṭṭhito' is about when craving causes consciousness to be "established" or "fixated" in a sense object. In AN 3.76, it appears 'patiṭṭhito' explains or defines what 'bhava' ('becoming') is.
While am no Pali expert & while the following distinction is not important, the term "dukkhe" appears to be of locative case. Thus, I would translate the phrase: "the world is established in suffering" rather than "the world is established on suffering".
Therefore, per SN 12.15, it appears the phrase 'dukkhe loko patiṭṭhito' means 'the world is established in the self-views that are suffering'.
To reiterate from SN 12.15:
For one who sees the origin of the world as it really is with correct wisdom.... this world, Kaccana, is for the most part shackled by engagement,
clinging and adherence... a stand
about ‘my self’... what arises is
only suffering arising...
Similarly, SN 5.10, which is about the worldly wrong view & convention of "a being" ("satta"), says:
Why now do you assume 'a being'? Mara, have you grasped a view?
Just as, with an assemblage of parts, The word 'chariot' is used, So,
when the aggregates are present, There's the convention 'a being.'
It's only suffering that comes to be, Nothing but suffering comes to
Therefore, again, it appears the world is established in the self-views of "beings" that are suffering.
Again, to note, SN 23.2 defines "a being" ("satta") as "strong attachment" ("visatta").