This manuscript presents a well-structured and insightful study on the role of measurement precision in enhancing the resolvable resolution of ice core water isotope reconstructions, particularly focusing on the Beyond EPICA Oldest Ice Core (BE-OIC). The research is timely and addresses a critical gap in paleoclimate reconstructions by quantifying how measurement noise limits the recovery of high-frequency climate signals through deconvolution techniques. The analytical and numerical approaches are robust, and the results are clearly presented. The manuscript is suitable for publication after minor revisions.

The description of the Wiener deconvolution process and its application to ice core data is technically sound but could be more accessible. Figure 1 shows the conception of how reducing the measurement noise to recovery of higher frequencies. I think the legend of figure 1 should be explained in more details to aid readers unfamiliar with signal processing.

Line 69-73, the authors indicate that the post-depositional processes have a lesser effect on longer timescales. However, the diffusion process is one of the post-depositional processes. Here is a little confused. What kind of the post-depositional processes do you indicate?

The diffusion length profile (Fig. B1) is critical to the analysis but is only briefly mentioned. More details on its derivation, including sensitivity to parameters like geothermal heat flux, would strengthen the manuscript.

The authors should discuss the limitations of the deconvolution method. For example, briefly acknowledge any assumptions in the Wiener deconvolution method that might affect real-world applicability (e.g., linearity of diffusion, stationarity of noise) and discuss potential biases or uncertainties in the diffusion length profile (Appendix B) and how they might influence the results.

Shaw et al report an analytical method to quantify the upper limit of recoverable frequency from diffused ice core isotopic records after deconvolution, with a particular focus on the effect of measurement noise. The authors suggest that the upper part can be analytically solved where white-noise dominates. Then the authors apply the numerical solutions to the Beyond EPICA Oldest Ice Core, for which climate reconstruction is still ongoing. Overall, the study provides valuable insights into the recovery of water isotope signals in deep ice cores, especially the usefulness of the Beyond EPICA Oldest Ice Core in reconstructing climate before the Mid-Pleistocene Transition. I have a few minor comments on the manuscript.

Although the authors provide two surrogate ice core record examples, it would be helpful to generalize how reducing the measurement noise improves the deconvolved depth profile. For instance, only two different diffusion lengths are discussed in the study. How would different diffusion lengths influence the results?

Please check the consistency of the mathematical expressions throughout the manuscript. For instance, P_n and P_n(f) are used interchangeably.

L86-87: it would be beneficial to provide evidence or justification for these choices?

Figure 3b: what is the purple curve?

The diffusion length stated at L184 appears to differ from that in the caption for Figure 7.

Figures 6 and 7: it is unclear how “the true, undiffused” records were obtained.