Mario Nistri:
Check out the ymaa embryonic breathing material
Can you give a link to worth reading online resources?
I ask because if you say it just like that it's unlikely that I'm going to spend time in looking for information, considering that Idon't have the competence to distinguish what is foundamental and whatis not, what is good stuff and what isn't; however, if someone experienced in that sort of things gives me an internet page that I can read and go there being sure that what I'm going to read is good stuff, it's likely that I'm going to read that, if I havesome interest in that sort of things.
Other question: if you do that for three months get thesuper-smooth flow that you describe, and then doing something else entirely, how much will the benefits gained throught that kind of practice remain there with time? Will they remain unchanged, will they need some kind of manteinance, will they drop in a couple of days... how does that work?
Sure, any of the posts I've gone on for a length around here

But I'll sum it up briefly right here...
Since the breath is the most coarse and ongoing thing, that is a good logical start for attenuating the various bodily signals. That's a big component of Anapanasati, this attenuating...just "turning down the volume," and thus all of the energy that was going into the "volume level" is now unharnessed, unmanifest...and eventually, the awareness can make use of this additional energy (and it also contributes towards longer breaths.) AKA "settling the heartmind."
Once you learn how to move the diaphragm properly, there's no need to expand the belly (front of abdomen) very far, and eventually its action is mostly dropped from sessions - but here's the answer to your follow up: once you've put in the work and obtained the result, its like riding a bike - you aren't pedaling all the time, there is a time to coast and a time to pedal. Doing the rote work on it reprograms the medulla with this more efficient breathing pattern and it carries forth into all of life, waking, sleeping, etc....so, all that is needed is just a little bit in a session paying attention to the breath mechanics to "give the prayer wheel a little more momentum" and the program you have mindfully written into your subconscious processes is given a furtherance every day, that's really all it takes - let it languish long enough and yeah, it'll disappear, like anything else...just like workouts. I will usually just spend the first few minutes of a session, 5, 10 perhaps if I'm feeling like it, before just letting things spontaneously do their thing, and it starts becoming more Sati than Anapana when things get good. Its a good prep for a session also - putting the entirety of the focus of your awareness into the
feeling of all the breath mechanics...if your awareness is
focused on those breath mechanics, it cant be thinking something - so if your mind is busy, even, it is a good thing to cultivate because it is a break in the thought-form-energy, and when that is ingrained into habit, that is what leads to the ongoing clear states, relatively free of thought or fetter.
So you put in the work until you get very good at it, then meditation really just becomes more "sitting, smiling pleasantly for a few"...and two hours goes by. Of course that doesnt manifest right away, and one cant spend every moment of a session in such a state, but do what you can - the timing of the breath is huge because the additional energetics fuels being able to make breath durations longer and longer. So if one works hard, one obtains the result more quickly.
The fundamental mechanisms:
-Diaphragm
-Psoas
-Hui Yin is the energetic culmination of the perineum
And the front of the abdomen is a sort of 'martial modifier' - when first starting out, use it however you need to make the internal mechanics go properly. As the internal mechanics smooth out, the motion of the front of the abdomen becomes less and less. The qihai point is the energetic culmination point of the front of the abdomen.
-The nose, sinuses, air passageways - everywhere air touches - learn to not use them to facilitate the movement of air. Place the entire onus of breath on the internal mechanism.
The diaphragm is pulled downward from its lower attachment point at the top of the lumbar spine - the motion is assisted "down to the dantien" by the movement of the psoas muscle and that intent continues for the duration of the inhale. Huiyin timed appropriately depending on natural or reverse breath; relax is not prolapse and lift is not clench.
Time all of the energetic culminations to be simultaneous, harmonious. It leads to higher energy potentials. What's the exact timing? Do the gongfu! Think of a dyno readout for a car and where max power vs rpm is, its not where the engine blows up, its usually a bit before the redline starts...so equate "redline" with the energetic culmination of the structure. Smooth diaphragm motion helps settle the heart, since the aorta, vena cava, espphagus & vagus pass through it.
Relax on exhale and begin anew.
Once the energetics about the lower dantien start to become established by this harmonious motion, the reflection of sunlight in the chamber of water will shine at the niwan. Look with the awareness, the mind's internal eye once the energy potential of the lower dantien starts becoming apparent, and then once the niwan begins to resonate with the reflected energy, one may apply intent to the natural waxing and waning of the energy center. Doing both upper and lower at once, on, off...off, on, whichever...is "harmonizing the taiji pole" and works at opening the central energetic channel of the body. But the more poignant bit there is that with the niwan becoming active, the awareness can be effectively brought there.
Bringing the focus into the niwan once these things have been established basically allows you to start "arresting" energypotential that would otherwise manifest as thought-stream-energy and funnel it straight to the awareness.
So it begins by shutting up the 12 cranial nerves via these various gongfus, picking out the energy centers, utilizing their energy, and taming the energy of the body in the process - leaving energy potentials that would otherwise extend out through the senses and leap into spontaneous thoughtforms - unmanifested in their raw true sense. Imho, the habit energy of the ongoing enlightenment experience...but I havent gotten quite that far yet haha

But even after the attainment of buddahood, one still does anapanasati...or so I think I recall reading the buddha having said, hah!