Proof of time for domain's challenge period?

I want to bring forward a topic briefly discussed in one of the research team calls, to kick off an elaborate discussion.

Even though block headers include timestamps, these are somewhat prone for manipulation (see here for refuting evidence). Therefore, it is natural to measure “time” in blocks. We had several discussions on how to set the challenge period for domains, mainly in either some number of consensus blocks or domain blocks. The difficulties and challenges that arise in both approaches are outside the scope of this post.

Given these difficulties, one may wonder if there really is a strong reason that prevents us from using timestamps to measure the challenge period. Timelessness (drifts in timestamps) is usually minor, and therefore should not affect the challenge period, if it’s defined to be a relatively long time. On the other hand, the theoretical possibility of someone producing many blocks in a claimed small time frame exists, and if Bitcoin takes that possibility seriously (see here), we should probably not dismiss it. Especially since an attacker may have, in case of optimistic verification, a strong incentive to fork the chain in this manner (it is possible that such a long fork, irrespective of the forged timestamps, is sufficient to get out of the challenge period without a fraud proof, however I do not get into this here).

An alternative is to use proof of time, which is already an integral part of the Subspace protocol. In this case, the challenge period would be defined in some number of iterations completed by the proof of time algorithm, started counting from the beginning of each challenge period (however it is defined today).

There is no good reason to believe that this is a better approach to the pervious ones, for example some kind of a halt in block production (for whatever reason) does not stop time, but the number of accessible blocks in which one can include a fraud proof will decrease (in the extreme case there may be no blocks at all during some time-based challenge period). Therefore, shifting into time-based challenge period should be carefully examined, and I hope we can use this post to discuss the pros and cons of this approach.

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