I think it is a kind of loyalty to “what is important” to us. That we hold this as an intention.

• Authenticity is a measure of whether an asserted “what is important” is actually “what is important”
• Martin Heidegger talk about authenticity as congruence between one’s potentiality & actuality

Werner Erhard says

“Being authentic is being and acting consistent with who you hold yourself out to be for others, and who you hold yourself to be for yourself. When leading, being authentic leaves you grounded, and able to be straight with others without the use of force”

Authenticity does not begin with being authentic. Authenticity begins with being authentic about your inauthenticity.

/The only actionable access to authenticity is being authentic about your own inauthenticities./

Heidegger says

“For Heidegger, there are two dominant modes of being human: authenticity and inauthenticity. Furthermore, we have a choice to make between these two modes: the choice is whether to be oneself or not to be oneself, to be author of oneself and self-authorising or not.”

Being and Time, part 2: On 'mineness' | Simon Critchley