Here I am a mainly concerned with (iii), (iv), (v) and (vi) of the list above.
CY. (iii) Why is he called the Tathāgata because he has come to the real characteristics (of dhammas)?
(The six elements): The earth element has the characteristic of hardness—that is real, not unreal (tathaṃ avitathaṃ); the water element, of flowing; the fire element, of heat; the wind element, of distending; the space element, of intangibility; the consciousness element, of cognizing.
(The five aggregates): Material form has the characteristic of deformation; feeling, of being felt; perception, of perceiving; the mental formations, of forming; consciousness, of cognizing.
(The jhāna factors): Applied thought has the characteristic of application of mind; sustained thought, of continued pressure; rapture, of pervading; happiness, of gratification; one-pointedness of mind, of non-distraction; contact, of touching.261
(The five faculties): The faculty of faith has the characteristic of resolution; the faculty of energy, of exertion; the faculty of mindfulness, of awareness; the faculty of concentration, of non- distraction; the faculty of wisdom, of understanding.
(The five powers): The power of faith has the characteristic of not wavering because of faithlessness; the power of energy, of not wavering because of laziness; the power of mindfulness, of not wavering because of forgetfulness; the power of concentration, of not wavering because of restlessness; the power of wisdom, of not wavering because of ignorance.
(The seven factors of enlightenment): The enlightenment factor of mindfulness has the characteristic of awareness; the factor of investigation of dhammas, of investigating; the factor of energy, of exertion; the factor of rapture, of pervading; the factor of tranquillity, of subsiding; the factor of concentration, of non-distraction; the factor of equanimity, of detached observation.
(The eight factors of the noble path): right view has the characteristic of seeing; right intention, of application of mind; right speech, of embracing; right action, of originating; right livelihood, of cleansing; right effort, of exertion; right mindfulness, of awareness; right concentration, of non-distraction.
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261. Contact (phassa), though included in the jhānic consciousness, is not a specific jhāna factor. It is puzzling that it is included here.
(The twelve factors of dependent origination): ignorance has the characteristic of unknowing; kamma-formations, of volition; consciousness, of cognizing; mentality, of inclining, and materiality, of deformation; the six sense bases, of actuating; contact, of touching; feeling, of being felt; craving, of causing; clinging, of holding; existence, of accumulating; birth, of production; aging, of decaying, and death, of passing away.
The elements have the characteristics of emptiness; the sense bases, of actuating; the foundations of mindfulness, of awareness; the right endeavors, of endeavoring; the bases of spiritual success, of succeeding; the faculties, of predominance; the powers, of unwavering; the enlightenment factors, of emancipating; the path, of being a cause.
The truths have the characteristic of reality; serenity, of non- distraction; insight, of contemplation; serenity and insight, of having a single flavor; the pairs of complementary opposites,262 of not exceeding one another.
The purification of virtue has the characteristic of restraint; purification of mind, of non-distraction; purification of view, of seeing.
The knowledge of destruction has the characteristic of eradication; the knowledge of non-arising has the characteristic of tranquillity.263
Desire has the characteristics of being the root; attention, of being the originator; contact, of collecting together; feeling, of convergence; concentration, of eminence; mindfulness, of predominance; wisdom, of supremacy; emancipation, of being the essence; and nibbāna, the plunge into the deathless, of being the consummation.
All these characteristics are real, not unreal. Through the movement of his faculty of knowledge he has come to the real characteristic (of all dhammas); he has reached it without falling away from it, fully arrived at it—therefore he is the Tathāgata.
Thus he is the Tathāgata because he has come to the real characteristic.