SN 35.95 bahiya, and malyunkaputta, uses 4sp and 6sal: (Re cryptic 4sp formula 'body in body')

One more addition to the article:

• the real meaning of the cryptic formula in 4sp sat...
• I've gone through with a highlighter comparing KN Ud1.10 and SN 35.95 so you can't hide from the truth.

exhibit 1: Bahiya sutta KN Ud 1.10

Bahiya was famous for being the disciple who attained  arahantship the fastest, upon meeting the buddha, hearing this short teaching:

(in reference to the seen, there will only be the seen...)

♦ “tasmātiha te, bāhiya, evaṃ sikkhitabbaṃ —	“Then, Bāhiya, you should train yourself thus:
‘diṭṭhe diṭṭhamattaṃ bhavissati,	In reference to the seen, there will be only the seen.
sute sutamattaṃ bhavissati,	In reference to the heard, only the heard.
mute mutamattaṃ bhavissati,	In reference to the sensed, only the sensed.
viññāte viññātamattaṃ bhavissatī’ti.	In reference to the cognized, only the cognized.
evañhi te, bāhiya, sikkhitabbaṃ.	That is how you should train yourself.
yato kho te, bāhiya,	When for you there will be
diṭṭhe diṭṭhamattaṃ bhavissati,	only the seen in reference to the seen,
sute sutamattaṃ bhavissati,	only the heard in reference to the heard,
mute mutamattaṃ bhavissati,	only the sensed in reference to the sensed,
viññāte viññātamattaṃ bhavissati,	only the cognized in reference to the cognized,
tato tvaṃ, bāhiya, na tena;	then, Bāhiya, there is no you in connection with that.
yato tvaṃ, bāhiya, na tena tato tvaṃ, bāhiya, na tattha;	When there is no you in connection with that,
yato tvaṃ, bāhiya, na tattha,	there is no you there.
tato tvaṃ, bāhiya,	When there is no you there,
nevidha na huraṃ na ubhayamantarena.	you are neither here nor yonder nor between the two.
esevanto dukkhassā”ti.	This, just this, is the end of stress.”2
♦ atha kho bāhiyassa dārucīriyassa bhagavato imāya saṃkhittāya dhammadesanāya tāvadeva anupādāya āsavehi cittaṃ vimucci.	Through hearing this brief explanation of the Dhamma from the Blessed One, the mind of Bāhiya of the Bark-cloth right then and there was released from effluents through lack of clinging/sustenance. Having exhorted Bāhiya of the Bark-cloth with this brief explanation of the Dhamma, the Blessed One left.

4sp formula uses the same model 

Same as the "only the seen in reference to the seen" formula in Bahiya.
In fact, you can even map it in to the 4sp. The "seen"/ditthi, "heard"/sute, "sensed"/mute (corresponds to the other physical sense faculties) all map to the internal and external kaya and vedana anupassi. The cognized/vinnate corresponds to citta-anupassana.

In mālukyaputtasuttaṃ (SN 35.78), where the Buddha gives some commentary on the same teaching to Bahiya, it just confirms what I assert above.

SN 35.95. Māluṅkyaputta

http://lucid24.org/sn/sn35/sn35-v01/toc-addon/index.html

95. Mālukyaputtasutta	95. Māluṅkyaputta
Atha kho āyasmā mālukyaputto yena bhagavā tenupasaṅkami … pe … ekamantaṃ nisinno kho āyasmā mālukyaputto bhagavantaṃ etadavoca:	Then Venerable Māluṅkyaputta went up to the Buddha … and said to him:
“sādhu me, bhante, bhagavā saṃkhittena dhammaṃ desetu, yamahaṃ bhagavato dhammaṃ sutvā eko vūpakaṭṭho appamatto ātāpī pahitatto vihareyyan”ti.	“Sir, may the Buddha please teach me Dhamma in brief. When I’ve heard it, I’ll live alone, withdrawn, diligent, keen, and resolute.”
“Ettha dāni, mālukyaputta, kiṃ dahare bhikkhū vakkhāma.	“Well now, Māluṅkyaputta, what are we to say to the young monks,
Yatra hi nāma tvaṃ, bhikkhu, jiṇṇo vuddho mahallako addhagato vayoanuppatto saṅkhittena ovādaṃ yācasī”ti.	when even an old man like you, elderly and senior, advanced in years, having reached the final stage of life, asks the Realized One for brief advice?”
“Kiñcāpāhaṃ, bhante, jiṇṇo vuddho mahallako addhagato vayoanuppatto.	“Sir, even though I’m an old man, elderly and senior,
Desetu me, bhante, bhagavā saṅkhittena dhammaṃ, desetu sugato saṅkhittena dhammaṃ, appeva nāmāhaṃ bhagavato bhāsitassa atthaṃ ājāneyyaṃ. Appeva nāmāhaṃ bhagavato bhāsitassa dāyādo assan”ti.	may the Buddha please teach me Dhamma in brief! May the Holy one please teach me in brief! Hopefully I can understand the meaning of what the Buddha says. Hopefully I can be an heir of the Buddha’s teaching!”
“Taṃ kiṃ maññasi, mālukyaputta,	“What do you think, Māluṅkyaputta?
ye te cakkhuviññeyyā rūpā adiṭṭhā adiṭṭhapubbā, na ca passasi, na ca te hoti passeyyanti? Atthi te tattha chando vā rāgo vā pemaṃ vā”ti?	Do you have any desire or greed or fondness for sights known by the eye that you haven’t seen, you’ve never seen before, you don’t see, and you don’t think would be seen?”
“No hetaṃ, bhante”.	“No, sir.”
“Ye te sotaviññeyyā saddā assutā assutapubbā, na ca suṇāsi, na ca te hoti suṇeyyanti? Atthi te tattha chando vā rāgo vā pemaṃ vā”ti?	“Do you have any desire or greed or affection for sounds known by the ear …
“No hetaṃ, bhante”.
“Ye te ghānaviññeyyā gandhā aghāyitā aghāyitapubbā, na ca ghāyasi, na ca te hoti ghāyeyyanti? Atthi te tattha chando vā rāgo vā pemaṃ vā”ti?	smells known by the nose …
“No hetaṃ, bhante”.
“Ye te jivhāviññeyyā rasā asāyitā asāyitapubbā, na ca sāyasi, na ca te hoti sāyeyyanti? Atthi te tattha chando vā rāgo vā pemaṃ vā”ti?	tastes known by the tongue …
“No hetaṃ, bhante”.
“Ye te kāyaviññeyyā phoṭṭhabbā asamphuṭṭhā asamphuṭṭhapubbā, na ca phusasi, na ca te hoti phuseyyanti? Atthi te tattha chando vā rāgo vā pemaṃ vā”ti?	touches known by the body …
“No hetaṃ, bhante”.
“Ye te manoviññeyyā dhammā aviññātā aviññātapubbā, na ca vijānāsi, na ca te hoti vijāneyyanti? Atthi te tattha chando vā rāgo vā pemaṃ vā”ti?	thoughts known by the mind that you haven’t cognized, you’ve never cognized before, you don’t cognize, and you don’t think would be cognized?”
“No hetaṃ, bhante”.	“No, sir.”
	(the famous bahiya verse here, with buddha commentary)
“Ettha ca te, mālukyaputta, diṭṭhasutamutaviññātabbesu dhammesu diṭṭhe diṭṭhamattaṃ bhavissati, sute sutamattaṃ bhavissati, mute mutamattaṃ bhavissati, viññāte viññātamattaṃ bhavissati.	“In that case, when it comes to things that are to be seen, heard, thought, and cognized: in the seen will be merely the seen; in the heard will be merely the heard; in the thought will be merely the thought; in the cognized will be merely the cognized.
Yato kho te, mālukyaputta, diṭṭhasutamutaviññātabbesu dhammesu diṭṭhe diṭṭhamattaṃ bhavissati, sute sutamattaṃ bhavissati, mute mutamattaṃ bhavissati, viññāte viññātamattaṃ bhavissati;	When this is the case,
tato tvaṃ, mālukyaputta, na tena.	you won’t be ‘by that’.
Yato tvaṃ, mālukyaputta, na tena;	When you’re not ‘by that’,
tato tvaṃ, mālukyaputta, na tattha.	you won’t be ‘in that’.
Yato tvaṃ, mālukyaputta, na tattha;	When you’re not ‘in that’,
tato tvaṃ, mālukyaputta, nevidha, na huraṃ, na ubhayamantarena.	you won’t be in this world or the world beyond or in between the two.
Esevanto dukkhassā”ti.	Just this is the end of suffering.”
“Imassa khvāhaṃ, bhante, bhagavatā saṅkhittena bhāsitassa vitthārena atthaṃ ājānāmi:	“This is how I understand the detailed meaning of the Buddha’s brief statement:
	(Now look the "sati", repeatedly used  in the same way as the Bayhiya formula)
‘Rūpaṃ disvā sati muṭṭhā,	‘When you see a sight, rememberfulness is confused
Piyaṃ nimittaṃ manasi karoto;	as attention latches on the pleasant aspect.
Sārattacitto vedeti,	Experiencing it with a mind full of desire,
Tañca ajjhosa tiṭṭhati.	you keep clinging to it.
Tassa vaḍḍhanti vedanā,	Many feelings grow
anekā rūpasambhavā;	arising from sights.
Abhijjhā ca vihesā ca,	The mind is damaged
cittamassūpahaññati;	by covetousness and cruelty.
Evaṃ ācinato dukkhaṃ,	Heaping up suffering like this,
ārā nibbāna vuccati.	you’re said to be far from nirvana.
Saddaṃ sutvā sati muṭṭhā,	When you hear a sound, rememberfulness is confused
Piyaṃ nimittaṃ manasi karoto;	as attention latches on the pleasant aspect.
Sārattacitto vedeti,	Experiencing it with a mind full of desire,
Tañca ajjhosa tiṭṭhati.	you keep clinging to it.
Tassa vaḍḍhanti vedanā,	Many feelings grow
anekā saddasambhavā;	arising from sounds.
Abhijjhā ca vihesā ca,	The mind is damaged
cittamassūpahaññati;	by covetousness and cruelty.
Evaṃ ācinato dukkhaṃ,	Heaping up suffering like this,
ārā nibbāna vuccati.	you’re said to be far from nirvana.
Gandhaṃ ghatvā sati muṭṭhā,	When you smell an odor, rememberfulness is confused
Piyaṃ nimittaṃ manasi karoto;	as attention latches on the pleasant aspect.
Sārattacitto vedeti,	Experiencing it with a mind full of desire,
Tañca ajjhosa tiṭṭhati.	you keep clinging to it.
Tassa vaḍḍhanti vedanā,	Many feelings grow
anekā gandhasambhavā;	arising from smells.
Abhijjhā ca vihesā ca,	The mind is damaged
cittamassūpahaññati;	by covetousness and cruelty.
Evaṃ ācinato dukkhaṃ,	Heaping up suffering like this,
ārā nibbāna vuccati.	you’re said to be far from nirvana.
Rasaṃ bhotvā sati muṭṭhā,	When you enjoy a taste, rememberfulness is confused
Piyaṃ nimittaṃ manasi karoto;	as attention latches on the pleasant aspect.
Sārattacitto vedeti,	Experiencing it with a mind full of desire,
Tañca ajjhosa tiṭṭhati.	you keep clinging to it.
Tassa vaḍḍhanti vedanā,	Many feelings grow
anekā rasasambhavā;	arising from tastes.
Abhijjhā ca vihesā ca,	The mind is damaged
cittamassūpahaññati;	by covetousness and cruelty.
Evaṃ ācinato dukkhaṃ,	Heaping up suffering like this,
ārā nibbāna vuccati.	you’re said to be far from nirvana.
Phassaṃ phussa sati muṭṭhā,	When you experience a touch, rememberfulness is confused
Piyaṃ nimittaṃ manasi karoto;	as attention latches on the pleasant aspect.
Sārattacitto vedeti,	Experiencing it with a mind full of desire,
Tañca ajjhosa tiṭṭhati.	you keep clinging to it.
Tassa vaḍḍhanti vedanā,	Many feelings grow
anekā phassasambhavā;	arising from touches.
Abhijjhā ca vihesā ca,	The mind is damaged
cittamassūpahaññati;	by covetousness and cruelty.
Evaṃ ācinato dukkhaṃ,	Heaping up suffering like this,
ārā nibbāna vuccati.	you’re said to be far from nirvana.
Dhammaṃ ñatvā sati muṭṭhā,	When you know a thought, rememberfulness is confused
Piyaṃ nimittaṃ manasi karoto;	as attention latches on the pleasant aspect.
Sārattacitto vedeti,	Experiencing it with a mind full of desire,
Tañca ajjhosa tiṭṭhati.	you keep clinging to it.
Tassa vaḍḍhanti vedanā,	Many feelings grow
anekā dhammasambhavā;	arising from thoughts.
Abhijjhā ca vihesā ca,	The mind is damaged
cittamassūpahaññati;	by covetousness and cruelty.
Evaṃ ācinato dukkhaṃ,	Heaping up suffering like this,
ārā nibbāna vuccati.	you’re said to be far from nirvana.
Na so rajjati rūpesu,	When you see a sight with rememberfulness,
rūpaṃ disvā paṭissato;	there’s no desire for sights.
Virattacitto vedeti,	Experiencing it with a mind free of desire,
tañca nājjhosa tiṭṭhati.	you don’t keep clinging to it.
Yathāssa passato rūpaṃ,	Even as you see a sight
sevato cāpi vedanaṃ;	and undergo a feeling,
Khīyati nopacīyati,	you wear away, you don’t heap up:
evaṃ so caratī sato;	that’s how to live rememberfully.
Evaṃ apacinato dukkhaṃ,	Reducing suffering like this,
santike nibbāna vuccati.	you’re said to be in the presence of nirvana.
Na so rajjati saddesu,	When you hear a sound with rememberfulness,
saddaṃ sutvā paṭissato;	there’s no desire for sounds.
Virattacitto vedeti,	Experiencing it with a mind free of desire,
tañca nājjhosa tiṭṭhati.	you don’t keep clinging to it.
Yathāssa suṇato saddaṃ,	Even as you hear a sound
sevato cāpi vedanaṃ;	and undergo a feeling,
Khīyati nopacīyati,	you wear away, you don’t heap up:
evaṃ so caratī sato;	that’s how to live rememberfully.
Evaṃ apacinato dukkhaṃ,	Reducing suffering like this,
santike nibbāna vuccati.	you’re said to be in the presence of nirvana.
Na so rajjati gandhesu,	When you smell an odor with rememberfulness,
gandhaṃ ghatvā paṭissato;	there’s no desire for smells.
Virattacitto vedeti,	Experiencing it with a mind free of desire,
tañca nājjhosa tiṭṭhati.	you don’t keep clinging to it.
Yathāssa ghāyato gandhaṃ,	Even as you smell an odor
sevato cāpi vedanaṃ;	and undergo a feeling,
Khīyati nopacīyati,	you wear away, you don’t heap up:
evaṃ so caratī sato;	that’s how to live rememberfully.
Evaṃ apacinato dukkhaṃ,	Reducing suffering like this,
santike nibbāna vuccati.	you’re said to be in the presence of nirvana.
Na so rajjati rasesu,	Enjoying a taste with rememberfulness,
rasaṃ bhotvā paṭissato;	there’s no desire for tastes.
Virattacitto vedeti,	Experiencing it with a mind free of desire,
tañca nājjhosa tiṭṭhati.	you don’t keep clinging to it.
Yathāssa sāyato rasaṃ,	Even as you savor a taste
sevato cāpi vedanaṃ;	and undergo a feeling,
Khīyati nopacīyati,	you wear away, you don’t heap up:
evaṃ so caratī sato;	that’s how to live rememberfully.
Evaṃ apacinato dukkhaṃ,	Reducing suffering like this,
santike nibbāna vuccati.	you’re said to be in the presence of nirvana.
Na so rajjati phassesu,	When you experience a touch with rememberfulness,
phassaṃ phussa paṭissato;	there’s no desire for touches.
Virattacitto vedeti,	Experiencing it with a mind free of desire,
tañca nājjhosa tiṭṭhati.	you don’t keep clinging to it.
Yathāssa phusato phassaṃ,	Even as you experience a touch
sevato cāpi vedanaṃ;	and undergo a feeling,
Khīyati nopacīyati,	you wear away, you don’t heap up:
evaṃ so caratī sato;	that’s how to live rememberfully.
Evaṃ apacinato dukkhaṃ,	Reducing suffering like this,
santike nibbāna vuccati.	you’re said to be in the presence of nirvana.
Na so rajjati dhammesu,	When you know a thought with rememberfulness,
dhammaṃ ñatvā paṭissato;	there’s no desire for thoughts.
Virattacitto vedeti,	Experiencing it with a mind free of desire,
tañca nājjhosa tiṭṭhati.	you don’t keep clinging to it.
Yathāssa jānato dhammaṃ,	Even as you know a thought
Sevato cāpi vedanaṃ;	and undergo a feeling,
Khīyati nopacīyati,	you wear away, you don’t heap up:
Evaṃ so caratī sato;	that’s how to live rememberfully.
Evaṃ apacinato dukkhaṃ,	Reducing suffering like this,
Santike nibbāna vuccatī’ti.	you’re said to be in the presence of nirvana.’
Imassa khvāhaṃ, bhante, bhagavatā saṅkhittena bhāsitassa evaṃ vitthārena atthaṃ ājānāmī”ti.	That’s how I understand the detailed meaning of the Buddha’s brief statement.”
“Sādhu sādhu, mālukyaputta.	“Good, good, Māluṅkyaputta!
Sādhu kho tvaṃ, mālukyaputta, mayā saṅkhittena bhāsitassa vitthārena atthaṃ ājānāsi:	It’s good that you understand the detailed meaning of what I’ve said in brief like this.
‘Rūpaṃ disvā sati muṭṭhā,	(The Buddha repeats the verses in full.)
Piyaṃ nimittaṃ manasi karoto;	as attention latches on the pleasant aspect.
Sārattacitto vedeti,
Tañca ajjhosa tiṭṭhati.
Imassa kho, mālukyaputta, mayā saṅkhittena bhāsitassa evaṃ vitthārena attho daṭṭhabbo”ti.	This is how to understand the detailed meaning of what I said in brief.”
Atha kho āyasmā mālukyaputto bhagavato bhāsitaṃ abhinanditvā anumoditvā uṭṭhāyāsanā bhagavantaṃ abhivādetvā padakkhiṇaṃ katvā pakkāmi.	And then Venerable Māluṅkyaputta approved and agreed with what the Buddha said. He got up from his seat, bowed, and respectfully circled the Buddha, keeping him on his right, before leaving.
Atha kho āyasmā mālukyaputto eko vūpakaṭṭho appamatto ātāpī pahitatto viharanto nacirasseva—yassatthāya kulaputtā sammadeva agārasmā anagāriyaṃ pabbajanti, tadanuttaraṃ—brahmacariyapariyosānaṃ diṭṭheva dhamme sayaṃ abhiññā sacchikatvā upasampajja vihāsi.	Then Māluṅkyaputta, living alone, withdrawn, diligent, keen, and resolute, soon realized the supreme end of the spiritual path in this very life. He lived having achieved with his own insight the goal for which people from good families rightly go forth from the lay life to homelessness.
“Khīṇā jāti, vusitaṃ brahmacariyaṃ, kataṃ karaṇīyaṃ, nāparaṃ itthattāyā”ti abbhaññāsi.	He understood: “Rebirth is ended; the spiritual journey has been completed; what had to be done has been done; there is no return to any state of existence.”
Aññataro ca panāyasmā mālukyaputto arahataṃ ahosīti.	And Venerable Māluṅkyaputta became one of the perfected.

conclusion

sati = 4sp satipatthana. Sati is explicitly used to explain the famous bahiya formula, by the Buddha.
So the 4 satipatthana, is giving the same Dhamma teaching, the same teaching that leads to nirvana.

He abides, continuously seeing the body as a body, [as it actually is, according to reality]...

He abides, continuously seeing the experienced-sensations as experienced-sensations, [as it actually is, according to reality]...

He abides, continuously seeing the mind as mind, [as it actually is, according to reality]...

He abides, continuously seeing the ☸Dhamma as ☸Dhamma, [as it actually is, according to reality]...

Whatever grammar nitpicking you want to do, has no bearing here.