This seems to have different interpretation and translations? What are the different interpretations and translations and what might be the most correct interpretation according to different line of practice? How is the particular interpretation rationalised?
What are the different interpretations and translations and what might be the most correct interpretation according to the different lines of practice? How are they rationalized?
Here are some:
pari- is a prefix used with the connotation of around, about, all over, or that of completeness. Thus dhāvati means 'to run' and paridhāvati means 'to run about'; vajati - 'to go/ proceed' becomes paribbajati, 'to wander about', ie. 'to live the life of a religious mendicant'; carati - 'to walk' becomes paricarati - 'to walk around, ie. to serve, honour'; gaṇeti, 'to count' becomes parigaṇeti - 'to calculate'.
mukhaṃ means primarily and literally 'mouth', by extension 'face' and figuratively 'entrance', 'opening', 'brim', then in a more abstract meaning 'the front', 'the foremost' and finally 'that which is an entrance into something', ie. 'a mean', 'a cause'.
Strictly from the point of view of semantics (ie. neglecting contextual information), the following meanings could reasonably be derived from the juxtaposition of these two components: around the mouth, all over the mouth, completely on the mouth, around the face, all over the face, completely on the face, around the entrance, all over the entrance, completely on the entrance, around the front, all over the front, completely on the front
Note: The above link also has references to commentaries & later Pāḷi literature.
Thanissaro Bhikkhu: To the fore (parimukhaṃ): The Abhidhamma takes an etymological approach to this term, defining it as around (pari-) the mouth (mukhaṃ). In the Vinaya, however, it is used in a context (Cv.V.27.4) where it undoubtedly means the front of the chest. There is also the possibility that the term could be used idiomatically as "to the front," which is how I have translated it here.
Ānandajoti Bhikkhu: Parimukhaṃ means at the front, or perhaps, around the mouth, i.e. it is a vague area, not meant to be confined to one particular spot or place, which would have been easy to designate if that is what was meant (like specifying oṭṭha, the lip). It is of course the mindfulness that is important in the practice, not the breathing as such, which only provides a basis for the mindfulness.
Anālayo Bhikkhu: Once the posture is set up, mindfulness is to be established “in front”. The injunction “in front” (parimukhaṃ) can be understood literally or figuratively. Following the more literal understanding, “in front” indicates the nostril area as the most appropriate for attention to the in- and out-breaths. Alternatively, “in front” understood more figuratively suggests a firm establishment of sati, sati being mentally “in front” in the sense of meditative composure and attentiveness.
Sujato Bhikkhu: In the gradual training, sati and upatthana occur together in the common idiom parimukhaṃ satim upatthapeti. Here the term parimukha is one of those simple words that is so hard to interpret. It modern renderings usually use something vague like 'in front'. However the phrase frequently occurs in contexts outside of anapanasati, making the interpretation 'at the nose-tip', or any literal spatial interpretation, unlikely. The Sanskrit has a different reading, pratimukha. This has many meanings, among which are 'reflection' and 'presence'. Both of these would be appropriate in meditative context. But the word usually, as here, occurs in close conjunction with upatthana, which also means 'presence'. I think here we have another example of that common feature of Pali or Sanskrit, a conjunction of synonyms for emphasis: literally, 'one makes present a presence of presence of mind', or more happily, 'one establishes presence of mindfulness'.
S. N. Goenka: The awareness is established around the mouth, the entrance to the nostrils: parimukhaṃ. Certain traditions translate this as "in the front," as if the awareness is imagined to be in front of the person, but this sets up a duality. Actually you have to feel the breath coming and going around the mouth, above the upper lip, which is parimukhaṃ.
This is an extremely important issue when it comes to jhana practice. The etymology is as per the above, mouth first, face second, front I would put third from a review of it's contextual uses where it's 50/50 mouth/face a little bit of the rest. Mouth of a river, face of the moon, etc.
In actual meditation experience testing the idea as mouth, face, and forefront (as it is often translated 'bring mindfulness to the forefront' or 'make mindfulness the purpose of one's sitting') I found advantages to all three ... over mindlessness. All three together as a progression is also interesting. Using 'face' one roams the face and discovers and releases facial tension. Since facial tension reflects one's reactions to sense stimuli it is the point where these tensions can be let go and so the result is an over-all release of tension. More effective in attaining concentration as a factor of jhana, is focus around the mouth. The idea is: "Take the mind and place the focus around (pari) the mouth. Then, in the same way, focus on the breathing." This is the answer to the debate as to where and how to place the attention on the breathing. You do it in the same way as you just put your mind onto the area around your mouth. It is not one spot because that spot is not there that stands still even for a second. When the idea is around the mouth in general one finds it relatively easy to maintain focus for prolonged periods. Again, to have gone directly to the breath would not have provided such a concrete example of how to do it.
There is also the residual benefit of the fact that after sit-down practice the idea of focusing on the mouth hangs around and as most of us know, it is from the mouth (after the mind) that most of our trouble begins.
An important thing to understand is what 'mindfulness' means. The word sati means remembrance but also mind. The two are actually the same thing from one point of view: that is that the mind consists of memory (think computers). A better translation would be simply 'mind' as in what the babysitter does with the baby. She does not keep her eye on the baby without a break. She checks it sufficiently often to establish awareness that everything is ok. Mind your manners. Mind your own business. Mind the time.
I think it is used idiomatically, but as one contributor stated pratimukha in Sanskrit could mean , "reflection" or "presence". If we look back to Ajhan Geoff's statement, that supports his idea. But the reason I started typing, is we can put aside the definition and see how we naturally start to relax in accord with the basic instruction. If you mediate like me, you will find great benefit from allowing the awareness of the breath through out the entire body, to develop the first foundation well. Well, how about if it could mean all three or four of the meanings, from the most limited to the most expansive...?
Excerpt from the Anapanasati Sutta " Breathing in long, he discerns, 'I am breathing in long'; or breathing out long, he discerns, 'I am breathing out long.'  Or breathing in short, he discerns, 'I am breathing in short'; or breathing out short, he discerns, 'I am breathing out short.'  He trains himself, 'I will breathe in sensitive to the entire body.' He trains himself, 'I will breathe out sensitive to the entire body.'  He trains himself, 'I will breathe in calming bodily fabrication.' He trains himself, 'I will breathe out calming bodily fabrication.' So, My brief conclusion is, If we follow the instructions, to calm bodily fabrications, then we probably will not want to have our main focus on the the tip of the nose. Otherwise we would have to work our attention too hard, attending to the breath and the nose, in a focused way and also calming bodily fabrications. I think we need to see the bigger picture, and relax deeply.