Hi Polarbuddha,
Another decent translation of sati is retention.
There's a nice verse in Theragatha:
1052. ‘‘Gatimanto satimanto, dhitimanto ca yo isi;
Saddhammadhārako thero, ānando ratanākaro.
and related vagga in Anguttara Nikaya:
219. ‘‘Etadaggaṃ, bhikkhave, mama sāvakānaṃ bhikkhūnaṃ bahussutānaṃ yadidaṃ ānando’’.
220. … Satimantānaṃ yadidaṃ ānando.
221. … Gatimantānaṃ yadidaṃ ānando.
222. … Dhitimantānaṃ yadidaṃ ānando.
Regarding
dhāraṇatā, Puggalapaññatti says:
79. Katamo ca puggalo upaṭṭhitassati? Tattha katamā sati? Yā sati anussati paṭissati sati saraṇatā dhāraṇatā apilāpanatā asammusanatā sati satindriyaṃ satibalaṃ sammāsati – ayaṃ vuccati sati. Imāya satiyā samannāgato puggalo ‘‘upaṭṭhitassati’’.
80. Katamo ca puggalo sampajāno? Tattha katamaṃ sampajaññaṃ? Yā paññā pajānanā vicayo pavicayo dhammavicayo sallakkhaṇā upalakkhaṇā paccupalakkhaṇā paṇḍiccaṃ kosallaṃ nepuññaṃ vebhabyā cintā upaparikkhā bhūrī medhā pariṇāyikā vipassanā sampajaññaṃ patodo paññā paññindriyaṃ paññābalaṃ paññāsatthaṃ paññāpāsādo paññāāloko paññāobhāso paññāpajjoto paññāratanaṃ amoho dhammavicayo sammādiṭṭhi – idaṃ vuccati sampajaññaṃ. Iminā sampajaññena samannāgato puggalo ‘‘sampajāno’’.
Mahaniddesa illustrates the contexts of sati:
Satoti catūhi kāraṇehi sato – kāye kāyānupassanāsatipaṭṭhānaṃ bhāvento sato, vedanāsu…pe… citte… dhammesu dhammānupassanāsatipaṭṭhānaṃ bhāvento sato.
Aparehipi catūhi kāraṇehi sato – asatiparivajjanāya sato, satikaraṇīyānaṃ dhammānaṃ katattā sato, satiparibandhānaṃ dhammānaṃ hatattā sato, satinimittānaṃ dhammānaṃ asammuṭṭhattā sato.
Aparehipi catūhi kāraṇehi sato – satiyā samannāgatattā sato, satiyā vasitattā sato, satiyā pāguññatāya sato, satiyā apaccorohaṇatāya sato.
Aparehipi catūhi kāraṇehi sato – sattattā sato, santattā sato, samitattā sato, santadhammasamannāgatattā sato. Buddhānussatiyā sato, dhammānussatiyā sato, saṅghānussatiyā sato, sīlānussatiyā sato, cāgānussatiyā sato, devatānussatiyā sato, ānāpānassatiyā sato, maraṇassatiyā sato, kāyagatāsatiyā sato, upasamānussatiyā sato. Yā sati anussati paṭissati sati saraṇatā dhāraṇatā apilāpanatā asammussanatā sati satindriyaṃ satibalaṃ sammāsati satisambojjhaṅgo ekāyanamaggo, ayaṃ vuccati sati. Imāya satiyā upeto hoti samupeto upagato samupagato upapanno samupapanno samannāgato, so vuccati sato.
Evidently the authors of Atthakatha were not aware of Krishnamurti's 'Choiceless Awareness' and did not incorporate it in their teachings, daring to contradict it:
Satiyeva satipaṭṭhānaṃ. Atha vā saraṇaṭṭhena sati, upaṭṭhānaṭṭhena paṭṭhānaṃ. Iti sati ca sā paṭṭhānaṃ cātipi satipaṭṭhānaṃ. Idamidhādhippetaṃ.
Yadi evaṃ kasmā ‘‘satipaṭṭhānā’’ti bahuvacanaṃ? Satibahuttā. Ārammaṇabhedena hi bahukā etā satiyo.
Mahavagga-Atthakatha 3.753
Tattha ārammaṇe pakkhanditvā upaṭṭhānaṭṭhena paṭṭhānaṃ, satiyeva paṭṭhānaṃ satipaṭṭhānaṃ. Ārammaṇassa pana kāyādivasena catubbidhattā vuttaṃ ‘‘cattāro satipaṭṭhānā’’ti. Tathā hi kāyavedanācittadhammesu subhasukhaniccaattasaññānaṃ pahānato asubhadukkhāniccānattatāgahaṇato ca nesaṃ kāyānupassanādibhāvo vibhatto.
Udana-Atthakatha 304