Minimum common grounds for all sotapanna and all arahant

All of them have heard Dhamma taught by Buddha.

For stream-enterer we have:

AN6.34:4.4: But those who have experiential confidence in the Buddha, the teaching, and the Saṅgha, and have the ethics loved by the noble ones, do know that they are stream-enterers.”

For arahant we have release from ten fetters:

AN10.13:1.1: “Mendicants, there are ten fetters. What ten? The five lower fetters and the five higher fetters.

AN10.13:1.4: What are the five lower fetters? Identity view, doubt, misapprehension of precepts and observances, sensual desire, and ill will. These are the five lower fetters.

AN10.13:2.1: What are the five higher fetters? Desire for rebirth in the realm of luminous form, desire for rebirth in the formless realm, conceit, restlessness, and ignorance.

The interpretation may differ, but the above definitions are common ground.

A key point of potential dispute is the validation of "experiential confidence." Historical, this was even an issue in the Buddha's time:

AN3.21:2.3: The personal witness, the one attained to view, and the one freed by faith. These are the three people found in the world. Of these three people, who do you believe to be the finest?”

For those who experienced confidence in the Triple Gem via first jhana, they would be a personal witness.

AN3.21:5.7: Because this person’s faculty of immersion is outstanding.”

For those who experienced confidence in the Triple Gem via deep study of the Dhamma, they would be attained to view.

AN3.21:7.7: Because this person’s faculty of wisdom is outstanding.”

For those who experienced confidence in the Triple Gem via faith, they would be attained by faith.

AN3.21:3.7: Because this person’s faculty of faith is outstanding.”

Yet the Buddha answered quite simply and inclusively:

AN3.21:12.1: In this matter, it’s not easy to definitively declare that one of these three people is finest.”

There is the idea of the ten fetters (samyojana), and how each of the four stages towards enlightenment is a progressive liberation from these fetters (or uprooting as you put it). They provide a framework of how we can label the stages of progress:

"Bhikkhus, there are these ten fetters. What ten? The five lower fetters and the five higher fetters. And what are the five lower fetters? Personal-existence view, doubt, wrong grasp of behavior and observances, sensual desire, and ill will. These are the five lower fetters. And what are the five higher fetters? Lust for form, lust for the formless, conceit, restlessness, and ignorance. These are the five higher fetters. These, bhikkhus, are the ten fetters".

https://suttacentral.net/an10.13/en/bodhi

Nanamoli, B. & Bodhi, B. (1995) gives a detailed description of each of these stages and how they relate to the abandoning of the ten fetters (It's a bit heavy to recap several pages of text on a Q&A site, but here's the source):

The Middle Length Discourses of the Buddha A New Translation of the Majjhima Nikaya. Buddhist Publication Society, 41-43. Retrieved from http://lirs.ru/lib/sutra/The_Middle_Length_Discourses(Majjhima_Nikaya),Nanamoli,Bodhi,1995.pdf

I write "theory" and "label", since an individuals path and practice may not necessarily correspond identically to dhamma, and the latter should not be used as a procrustean bed. Buddha used a raft simile for making this point:

"This raft has been very helpful to me, since supported by it and making an effort with my hands and feet, I got safely across to the far shore. Suppose I were to haul it onto the dry land or set it adrift in the water, and then go wherever I want.’ Now, bhikkhus, it is by so doing that that man would be doing what should be done with that raft. So I have shown you how the Dhamma is similar to a raft, being for the purpose of crossing over, not for the purpose of grasping.

Bhikkhus, when you know the Dhamma to be similar to a raft, you should abandon even the teachings, how much more so things contrary to the teachings".

https://suttacentral.net/mn22/en/bodhi

Minimum common grounds for all sotapanna and all arahant.

The "minimum common grounds" both literally and symbolically is the fulfillment of virtues:

“These nine persons, Sāriputta, passing away with a residue remaining, are freed from hell, the animal realm, and the sphere of afflicted spirits; freed from the plane of misery, the bad destination, the lower world. What nine?

(1) “Here, Sāriputta, some person fulfills virtuous behavior but cultivates concentration and wisdom only to a moderate extent..1857 With the ending of three fetters, they have at most seven rebirths. They will transmigrate at most seven times among gods and humans and then make an end of suffering.

(2) "Again, some person fulfills virtuous behavior...

(3) "Again, some person fulfills virtuous behavior...

(4) "Again, some person fulfills virtuous behavior...

...

(9) "Again, some person fulfills virtuous behavior... ~~ AN 9.12 ~~