In their work "Pinch-point Singularities in Stress-Stress Correlations Reveal Rigidity in Colloidal Gels" the authors present the results of a study of the computational model of a two-dimensional colloidal gel in the light of a vector charge theory of solids.

The article is well-written and serves two purposes: it provides a simplified account of the vector-charge theory of solids and an illustration in a concrete case where data is available.

The numerical data is mostly convincing. It is a bit harder to understand to what extent the assumptions and the key results of the theory are tested: are there any features of the data that could be explained solely by the VCTG approach? It would seem that the symmetries and shapes of the correlation functions would point in that direction, but it is not immediately clear from the reading of the article. I would recommend that the authors be more explicit on this point and clarify the limits of applicability.

In conclusion, I think the article is perfectly suitable for Soft Matter and publishable as it is. Still, I invite the authors to consider the following remarks to clarify a few points further:

• Could one explain better what is meant by "geometric compatibility" and how this translates to 3D?
• In section 2.1 "extensively applied" refers to two works: are there more to cite? is the work emerging, or are there fundamental challenges (approximations/role of annealed or quenched disorder, etc.) that limit its applicability?
• As I was reading about the VCTG mapping (section 2.2), I was wondering whether there is any connection (or analogy) between the stress-only ensemble of the theory and the statistical ensemble proposed by Edwards used for granular materials: Could the authors help the readers understand whether there is any link or what the main differences may be. It may be useful to quickly compare with the Edwards ensemble to guide the readers.

• For the Fits of figure 1, could the authors help the readers understand how the forms where chosen and it what sense these are products of the theory (or whether one could one reach the same model functions simply by symmetry arguments)

• I am slightly confused by the Fig2 snapshots: are we seeing the entire system? Where are the particles located? is the data binned on a grid? What do the high-stress regions correspond to geometrically? Maybe the answers to these questions are immaterial (or even orthogonal) to the spirit of the approach, but it seems appropriate to address them in some way, which could be a parallel figure with the particle locations, or some overlayed circles or a brief discussion in the text on why the particle positions and arrangements would not be informative.

• Fig 2 focuses on the floppy side of the transition. Is there a particular reason not to show the rigid side?
• It is stated that the maps of Fig 3(a,b,c) show that the pinch point exists only for configurations with percolations in two directions. This should be 3a, if I understand correctly. While I do see a qualitative difference between 3a and 3c (the contour maps have no "neck" at qx = 0 for 3c), the 3b case seems somewhat intermediate. This is illustrated by the comparisons of Figures 3(d,e,f): it would seem that (d) and (e) have very similar shapes (at qx=0) and that the main difference resides in the intensity being a factor 2-3 smaller at low qs for (e) compared to (d). These differences are discussed in the text. However, based on this very same discussion, the notion of a pinch-point seems somewhat blurred and dependent on the strength of correlations at low q. Since this signal depends on the averaging ensemble, what does it actually tell us about the configurations? Isn't the distinction between two-way or one-way percolation somewhat artificial and inherently dependent on finite sizes? With this, I mean that a sufficiently large simulation box (at the percolation transition) should show a negligible number of 1-direction percolating configurations since there is no particular reason to prefer one direction with respect to another. Is the statement that the chosen simulation box is able to reveal such distinction precisely because its sizes are comparable to the correlation length of the stress correlator? Maybe this could signify that one could exploit finite-size effects to probe this length scale (which should be analogous to the screening length scale) by solely measuring the proportion of configurations spanning in one or two dimensions.
• It is not very clear how Figure 4d demonstrates agreement with the VCTG theory: what would be the theoretical prediction for the modulus-pressure relationship?