Page Curves and Bath Deformations

I thank the authors for thoroughly addressing the points made in my previous report. I think the newly-modified introduction is much improved and does a very good job of discussing many of the open issues in the recent developments of black hole evaporation, including with 2D models, nongravitating baths, and doubly-holographic/braneworld constructions. Unfortunately, I must admit that I don't think that these changes substantially address one of my most pressing concerns: namely, of all the ways one could modify the bath, what makes turning on a relevant deformation special? Currently the paper does a very good job of motivating the //general// need to understand properties of the bath and how it affects the physics of the evaporation process, but I don't think it substantially addresses how the //specific// modification being considered here makes headway in addressing this goal. What lesson has been learned? Or if this paper is a first step, what lesson(s) will hopefully be learned in subsequent work as a consequence of studying these sorts of deformations? (To be frank, my current reading of the paper is that a relevant deformation is considered for no other reason than that it's something one can do, which I assume means I'm still missing the authors' physical motivation.)

The authors do mention a potential answer to some of these questions in their response to my first report: that "In the end, our results show that the bath is not a consistent computational tool." What does it mean to be an inconsistent computational tool? Is one of the points of the paper is that models involving baths do not accurately capture the relevant physics of the evaporation process? If so, this would be an very interesting and impactful claim to make. I did not get the sense that this was one of the lessons from reading the paper, but if it is, I think the paper would benefit substantially from making this point much more explicit.

With its current modifications, I think the paper might be appropriate to publish in certain journals as an exploration into possible modifications of the bath using a doubly-holographic setup. However, SciPost's stated acceptance criteria are quite high, and unfortunately without addressing the questions I posed above I don't think the new version of the paper meets them.