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what is vitakka and vicara doing in breath meditation?

What are the canonical definitions of vitarka-vicara in the Tripitaka
https://buddhism.stackexchange.com/questions/34897/what-are-the-canonical-definitions-of-vitarka-vicara-in-the-tripitaka-or-related/34910#34910

The quote below defines Vitarka-vicara as:

Ardency (atappa) + mindfulness (sati) => combines to make vitakka
Ardency (atappa) + alertness (sampajañña) => combines to make vicara
As Ajaan Lee, my teacher’s teacher, once noted, mindfulness combined with ardency turns into the concentration factor called vitakka, or directed thought, where you keep your thoughts consistently focused on one object, such as the breath. Alertness combined with ardency turns into another concentration factor: vicāra, or evaluation

Head & Heart Together, by Ṭhānissaro Bhikkhu, Chapter: Mindfulness Defined

No citation from the cannon have been given in this discussion.

What are the Tipitaka, commentary, sub commentary sources, including primary, secondary or tertiary source with citations, which defines Vitarka-vicara as such?

Are there other definitions of Vitarka-vicara from Tipitaka, commentaries, sub commentaries, including primary, secondary or tertiary source with citations?


See SN 46.3 http://lucid24.org/sn/sn46/sn46-003/index.html

 sati-sambojjhanga remembers Dhamma-teaching, then thinks (vitakka) about that Dharma.
Dhamma-vicaya-sambojjhnaga investigates that Dharma-teaching recollected by sati, by means of vicara (evaluation) paññāya (same word as the sampajano, what B. thanissaro translates as 'alertness').
ātāpi = ardency, is equivalent to the 3rd awakening factor vigor/viriya, also equivalent to 4 aspects of right effort.

 So what Ajahn Lee is saying sounds idiosyncratic at first, but it is solidly based on EBT sutta.
frankk

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