looking for citation, pīti and sukha of 4 jhānas compared to dying of thirst, seeing water in distance, and drinking it

In the context of Jhana, there is a reference a lake with spring-water welling up from within appears in many suttas with regard to the 2nd Jhana (with Piti, Sukha, Ekaggatha) and a pond of the blue lotuses, red and white lotuses, or red lotuses for the 3rd Jhana (with Sukha, Ekaggatha):

• Kuta,danta Sutta
• Mahā Sakuludāyi Sutta
• Dīgha Mahāli Sutta
• Sālavatika Lohicca Sutta
• Kevaḍḍha Sutta
• Mahā Assapura Sutta
• Soṇadaṇḍa Sutta
• (Ānanda) Subha Sutta
• Samādhi Pañc’aṅgika Sutta
• Ambatṭha Sutta
• Kevaḍḍha Sutta

The more famous of the Suttas with this reference is:

• Kāya,gatā,sati Sutta
• Samannaphala Sutta

In the context of Cūḷa Assapura Sutta (MN 40) it means if any person regardless of the divine adobe mediation (4 directions) they practice realises the Dhamma hence quench their thirst. This can be also taken as anyone from the 4 casts can realise the Dhamma and quench their trust. This section appears between the description of divine adobe meditation and description of the people of 4 different casts and seam applicable to both. This Sutta is not about Jhana.

There are lotus pond similies in:

• Kāraṇapālī Sutta - Buddha's clarity of wisdom
• Āghāta Pativinaya Sutta 2 - purity of Sila
• Aputtaka Sutta 1 - proper sure of wealth
• Mahā Sihanāda Sutta - the destruction of mental influxes

what is the citation of that piti sukha simile for the 4 jhanas from?

The citation is from the Visuddhimagga, used to explain piti (rapture) is mental formation (sankhara) rather than a feeling (vedana). Here, the Visuddhimagga says piti is something mental rather than originating from the physical; thus appears to contradict the meaning of 'rupa jhana' and contradicting the sutta terms "vedanāsu vedanānupassī" and "cittasaṅkhārapaṭisaṃvedī" (where 'cittasaṅkhāra' means feelings, per MN 44).

might this sutta, MN 40, be what inspired that simile for jhana piti/sukha differentiation? Should the words piti sukha appear in MN 40 lotus pond, but got lost in transmission?

MN 40 is not about jhana. While, similar to the Visuddhimagga, the pāmojjaṃ (joy) & pīti (rapture) in MN 40 appear to be born of mental formations (sankhara), as said, MN 40 is not about jhana where as Visuddhimagga claims to be about jhana. Therefore, there seems to be a contradiction here between MN 40 and Visuddhimagga. However, if the writer of the Visuddhimagga, similar to FrankK, misinterpreted MN 40, then yes, MN 40 might be what inspired that (false) simile for jhana piti/sukha differentiation

What does the MN 40 lotus pond simile mean on its own terms, just for this sutta? What are the 4 directions referring to?

MN 40 does not appear to be about jhana. MN 40 describes the mental joy of knowing or recognising the mind is pure; similar to the worldly idea of "self-esteem". Using AN 11.2 to explain, MN 40 is describing the joy arising from an absence of remorse.

However, the rapture of jhana is unrelated to any mental recognition, judgment, knowing or perception. The rapture of jhana is "physical" in its origins and is born from the stress in the physical body being thoroughly calmed & dissolved (to the degree that the mind can longer feel/discern the physical body, which consumates the 1st jhana, in which there is no knowing of the physical body, as explained by Bhikkhus Buddhadasa, Brahmavamso, Sujato, etc).

I recall I have explained before the meaning or types "rapture" ("piti") are not always the same. There are at least five different types of rapture found in the suttas, namely:

1. Rapture when hearing about there is a path to an end to suffering (SN 12.23).

2. Rapture when free from remorse and when feeling morally righteous (AN 11.2; MN 40).

3. Rapture when first successfully having mindfulness & insight (SN 45.3; rapture factor of enlightenment).

4. Rapture of neighbourhood concentration (MN 118)

5. Rapture of attainment concentration/jhana (MN 4; MN 19; MN 111).

1. what is the citation of that piti sukha simile for the 4 jhanas from?

It's from the Visuddhimagga-Ch IV.100 (pg. 139):

And wherever the two are associated, happiness is the contentedness at getting a desirable object, and bliss is the actual experiencing of it when got. Where there is happiness there is bliss (pleasure); but where there is bliss there is not necessarily happiness. Happiness is included in the formations aggregate; bliss is included in the feeling aggregate. If a man, exhausted31 in a desert, saw or heard about a pond on the edge of a wood, he would have happiness; if he went into the wood’s shade and used the water, he would have bliss. And it should be understood that this is said because they are obvious on such occasions.

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2. might this sutta, MN 40, be what inspired that simile for jhana piti/sukha differentiation? Should the words piti sukha appear in MN 40 lotus pond, but got lost in transmission?

Possibly. But notice the context is different between MN 40 and Vism IV.100. In MN 40, the lotus pond simile was used to illustrate the benefits of cultivating the Four Divine Abodes and how it benefits everyone; while the Vism's simile was for describing the Piti/Sukha absorption factors of the Jhanas concentration practices.

3. What does the MN 40 lotus pond simile mean on its own terms, just for this sutta? What are the 4 directions referring to?

The Four Divine Abodes.