What does pari-mukha mean in 16 APS anapana sati?

https://notesonthedhamma.blogspot.com/2019/07/parimukha-57-occurrences-in-pali-suttas.html

excerpt:

parimukha: 57 occurrences in the pali suttas

If you want to be sure of what a pali word means, you need to look at every reference in the suttas and make sure it's coherent and consistent throughout. The conclusion of this study, is that pari-mukha can not mean the physical spatial location "around the mouth", as late Theravada interprets it. In the sitting meditation context, pari-mukha is not about the spatial location "in front" at all. The spatial interpretation just happens to work for 16 APS (breath meditation). But it doesn't work for all of the other Buddhist meditations designated which are non-breath related.

conclusion: Pari-mukha is a figure of speech. Similar to these English figures of speech: 1. Focus on the task at hand 2. A bird in the hand is worth two in the bush. 3. Follow your nose

Pari-mukha is a figure of speech that means, "main priority". pari-mukhaṃ satiṃ upaṭṭhapetvā = Make sati establishment your "main priority".

There's an article discussing the use of that word here -- parimukhaṃ -- which interprets it literally, as you did, by referring to its being used literally in other texts like the Vinaya, the Abhidhamma, the Khuddaka Nikāya, and a Commentary.

Piya Tan disagrees, in his introduction to MN 118 he writes,

2.4 PARIMUKHA
2.4.1 Abhidhamma interpretation.
Unlike in Hatha Yoga, in breath meditation the breath is not deliberately regulated, but a sustained effort is made to fix one’s awareness on the breath as it moves in and out in its natural rhythm. Those who follow the Abhidhamma and Commentarial traditions, teach that mindfulness should be focused at the nostril or the upper lip, wherever the contact of the breath is felt most distinctly. This tradition is mainly based on the Patisambhida,magga and Vibhanga interpretation of parimukham as being “at the tip of the nose or at the centre of the upper lip.”

Parimukha literally means “around (pari) the entrance (mukha),” here always used idiomatically and as an adverb, meaning “in front.” This is the interpretation followed by U Thittila, Maurice Walshe, Soma Thera, and Ñānamoli & Bodhi.

... and he includes a half a dozen footnotes as references for that last sentence.

He also wrote,

In this connection, the Tiantai master, Zhìyǐ 智顗 (538-597), in his Tóngméng zhǐguān 童蒙止觀 (Samatha and Vipasyana for Beginners), gives this advice for dealing with two kinds of distractions:

What is a sinking mind? If during the meditation the mind is dull, confused or unrecordable, while the head drops, this shows a sinking mind. In such a case, it should be fixed on the tip of the nose to nail it there and to prevent it from wandering elsewhere. This is the way to regulate a sinking mind.

What is a floating mind? If during the meditation, it drifts about and is uneasy, while thoughts follow externals, this shows a floating mind. In such a case, it should be pushed down and fixed on the navel to prevent thoughts from rising; thus the mind will be stabilized and will be easily quieted.

Therefore, the absence of the sinking or floating state shows a regulated mind. (Zhìyǐ, Tóngmén Zhǐguān 童蒙止觀 in Lu K’uan Yü, 1964:126;41)

That latter reminds me of the little I was taught about Daoist meditation, incidentally.

It's best take if using it's meaning also mental "bringing it into the front", "focus on it", "make it as target direct for one" in all it's aspects.

"bringing it in foreground"

...reading the options given in the question now, good householder Frank, the third is good when taking the coordiants just one-dimensional, as direction, straight forward, in front, as supporting perception for the mental part of it.

(This "calibration" works good (just as one tool one could try) to perceive such as a robe between ones "bottom" firm on the ground fixed and the crown, taking the breat (strong hand), and pulling the robe straight upward, making the body straight, upright, and with it an even view and focus as well, mental at the same time.)

(note that this Gift of Dhamma is not given for trade, stacks, exchange or entertainment, but for ones work trough maccharia to escape the wheel here and liberation)