As for the proofs advanced by those who judge it to be a collective duty (farḍ kifāyah), they are the very same proofs cited by those who hold it to be an individual duty (farḍ ʿayn), for the Law permits fighting those who abandon a collective obligation.
Yet this is not a sound inference, because what the Prophet ﷺ threatened them with was killing, and killing is not the same as fighting.
Moreover, had it truly been a collective duty, its obligation would have fallen from the people who stayed behind when the Prophet and those with him performed the prayer, and therefore those absentees would not have neglected a duty for which they deserved punishment.

The proofs put forward by those who oblige it upon each individual, on the other hand, are both authentic and explicit.
Among them is the very ḥadith of Abū Hurayrah now before us, for the Messenger of Allah ﷺ would only contemplate punishing people for one of the major sins.
Another is the report of the blind man who asked the Prophet ﷺ for permission to pray at home because of the rough path and his lack of a guide, yet the Prophet did not grant him a concession.
A third proof is that the congregational prayer has been legislated even in the most critical circumstances—namely, at the time of battle.
Besides these are other clear evidences that admit no re-interpretation.

As for the aḥādīth that merely state a preference, they provide no evidence against obligation, for we have never claimed that the prayer is invalid without a congregation; rather, we say that it is valid but deficient in reward, and that the person who performs it alone without excuse incurs sin.

The chief proof of those who go to extremes—who deem the congregation a condition for the validity of the prayer—is the narration recorded by Ibn Mājah and al-Dāraquṭnī from Ibn ʿAbbās: “Whoever hears the call to prayer and does not come, he has no prayer unless he has an excuse.”
The stronger view is that this ḥadith is mawqūf, not marfūʿ, and scholars have criticised some of its transmitters. Even if it were authentic, it could be interpreted as, “There is no complete prayer except in the mosque,” so that it conforms with the traditions that are sounder than it.
This form of expression is frequent in the Prophet’s speech: the negation of something often signifies the negation of its perfection, not its actual existence.
Likewise, the ḥadith, “Prayer in congregation is twenty-seven degrees superior to the prayer performed alone,” clearly indicates the validity of solitary prayer, for the Lawgiver has allotted it some measure of reward.