I recently heard Leigh Brasington use the word indistractibility (it's not in the dictionary) as the meaning of samadhi. I love listening to other people's way of describing frequently used terms. There are hidden epiphanies in the different use of words. As I've come to expect, there is a wide range of opinions on how the word samadhi should be translated or used. Its use has been traced back to the 1st millennium BCE and in almost all the traditions. Some of the descriptions are:
-meditative absorption, attained by the practice of dhyana.
-the unifying of the mind in a steady, undistracted awareness.-a non-dualistic state of consciousness in which the consciousness of the experiencing subject becomes one with the observing object.
-an abiding in which mind becomes very still but does not merge with the object of attention, and is thus able to observe and gain insight into the changing flow of experience.
-A soundless state of breathlessness. A blissful super consciousness state in which a yogi perceives the identity of the individualized Soul and Cosmic Spirit.
- the enstatic mode of consciousness.     
     You can choose whichever one you like, but I'm going to stick with indistractibility. This is a word that I think can be applied from the first time we sit until the full maturity of the practice. In fact, all training can be seen as about distraction and the end of distraction. Defined in psychology as “having one's attention diverted from the task or thought at hand and turning to another unrelated thought or activity” distraction goes to the root cause of the basic uneasiness and discomfort almost all humans have.      
     Samadhi/indistractibility is essential. From the beginning of practice, we are exercising the ability to stay on one subject-object. This ability grows and eventually, we can come to experience the absolute absence of distractions. This experience changes the way we relate to perceptions. The “diversion” and “turning to another unrelated thought or activity” part of distraction is almost eliminated. Without these elements, attention flows unimpeded. In fact, indistractibility becomes the prevalent mode of functioning. 
​​​​​​​     A caveat, I am just sharing a line of thought that was stimulated by listening to a teacher. This is not a proposal for a new dogma. There are as many ways of explaining the fruits of practice as there are teachers. These contemporary workings of traditional views provide a simpler way of understanding my experience and may help you in understanding yours. Simplicity may be the key to faster success in achieving the goals of practice. I greatly appreciate the effort senior teachers are making in this direction.

There's no link to the source of your essay, Angel, so I want to ask you something: was Leigh referring specifically to samadhi, or to jhana? I ask because he is the modern uber-expert on accessing jhanas. Is jhana the same as samadhi in your view? In Leigh's view?

TIA!

     The reference is to episode 110 of Guru Viking 10:26. https://www.youtube.com/watch?v=kallDKcC_wY
In fact, he is talking of jhana and makes the connection between jhana-concentration-samadhi-indistractibility. This connection between samadhi and jhana is also mentioned in https://en.wikipedia.org/wiki/Samadhi, Comparisons with Buddism: 
"Patanjali's description of samādhi resembles the Buddhist jhānas. According to Jianxin Li, samprajñata samādhi may be compared to the rūpa jhānas of Buddhism.  This interpretation may conflict with Gombrich and Wynne, according to whom the first and second jhāna represent concentration, whereas the third and fourth jhāna combine concentration with mindfulness.  According to Eddie Crangle, the first jhāna resembles Patanjali's samprajñata samādhi, which both share the application of vitarka and vicara."
And this! 
"While Patañjali was influenced by Buddhism, and incorporated Buddhist thought and terminology, the term "nirvikalpa samādhi" is unusual in a Buddhist context, though some authors have equated nirvikalpa samādhi with the formless jhānas and/or nirodha samāpatti."
     I have to stress, this is just information for me. If it can give me insight into my personal experience fine, if not I just let it fly over my head.  You must know by now that phenomenology is king for me.  I only know what I know.

I always called experience of cultivation of skillful qualities as samadhi.
If I cultivate eg. 8th jhana quality then it is 8th jhana samadhi.

Usually these qualities are continuous. The only exception of using term 'samadhi' is what I call Vajra Samadhi, which is momentary experience which connects my mind with everything and with little narrower focus to specific places eg. typically acting as additional sense doors making me experience something I am looking at. The samadhi here is in the name of experience and it is just for two way communication. Experiencing remote qualities is itself not samadhi but if I take the qualities and cultivate them (or something based on them eg. by changing it to its jhanic version) this would be samadhi. In either way name makes sense because for bodhisattva cultivating samadhi for the sake of it is pointless if it cannot be shared.

Adding qualities to qualities is good way to cultivate better versions but typical state of the art is to first separate qualities (vispassanize them) and do cessation of unskillful qualities. If that is to be sent back the instructions for cessation needs to be encoded as the quality, in this case by cultivating 9th jhana and best way to know how is to do cessation with these cultivated qualities rather than by other means. Solving equations made of qualities is hard but like real math becomes easier with practice. One nice about this reality is that it is full of qualities so going out of things to work with is hardly something one have to worry about even when own sheet is worked through