This manuscript tested three existing encoding strategies for ensemble TDA on cyclone trajectories to examine the effects of the solar and geomagnetic activity perturbation on the TC. It is revealed that the results are sensitive to different coordinate encoding methods and intrinsic H1 false positive inflation. Overall, this study is only a methodological cautionary one. It neither proposes a new method nor delivers new physical insights, which means that it has relatively weak novelty. Hence, the current version of this manuscript may be unsuitable for publication in current journal. The following are my main concerns.

1.This manuscript only verifies flaws embedded in the existing ensemble TDA. But there are no original methodological advancements proposed to solve the flaws. In other words, the manuscript only discovers methodological defects without fixing them. Whether the author can propose a new strategy or method to overcome the existing flaws? This will be able to improve the novelty of the manuscript.

2.This manuscript is too technical. It has not discussed the fundamental problems of the physical and methodological limitations. Could the author provide substantial physical interpretations regarding the linkage between solar storms, geomagnetic activity and TC? Additionally, from both methodological and physical perspectives, how to understand the phenomenon that different encoding schemes yield contradictory results?

3.If the manuscript does not aim to investigate the physical linkage between solar activity and tropical cyclones and only serves as a methodological diagnostic, the discussions of physical processes in the introduction should be substantially condensed and analyzing methodological flaws should be stressed.

This manuscript applies ensemble topological data analysis (TDA) to tropical cyclone trajectories to test whether extreme geomagnetic events perturb cyclone activity at the ensemble-topology level. The authors construct three longitude encodings and report that H₁ permutation p-values depend critically on encoding choice (0.130, 0.009, 0.214), with H₁ placebo false-positive rates systematically inflated across all encodings (8.2%, 10.2%, 14.3%). While the experimental design is systematic, the manuscript suffers from fundamental weaknesses: the leap from "encoding-dependent results" to "tool cannot test the physical hypothesis" conflates representational robustness with causal robustness without justification; the H₁ inflation diagnosis remains descriptive rather than mechanistic; critical confounds of dimension versus periodicity and climatic variability versus methodological bias are acknowledged but not experimentally separated; the physical background is disproportionate to the explicitly non-physical conclusion; and the proposed minimum protocol is not itself followed. The study has potential value as a methodological diagnostic, but its current form risks being a well-executed yet inconclusive sensitivity study that discovers problems without advancing their solution or theoretical understanding. I recommend Major Revision.

Recommendation: Major revision

This manuscript addresses an important methodological problem: whether persistent-homology results for cyclone trajectories depend on the representation of periodic longitude. The comparison among linear, spherical, and cylindrical encodings is potentially useful, and the manuscript is generally clear and appropriately cautious about making a physical solar–cyclone claim. The reported encoding-dependent H1​ p-values are striking. However, several central conclusions are not yet supported by the experimental and statistical design. Overall, the methodological question is worthwhile, but the title, abstract, and conclusions should be substantially weakened unless the metric comparison, matched-null design, and calibration analysis are revised.

Major comments

1. The encodings change not only longitude periodicity but also coordinate weighting, pairwise distances, ambient geometry, and in the cylindrical case the underlying H1​ topology. The manuscript itself acknowledges that the cylinder can generate a longitude loop with no physical content. Therefore, disagreement among the three results does not by itself demonstrate “encoding fragility”; it may simply reflect comparison of three different geometric models. The main analysis should instead use a common physically defined distance matrix, such as great-circle distance combined with a clearly justified and sensitivity-tested intensity weight.
2. The three events have strongly different seasonal and basin compositions, yet the controls are pooled across the three calendar windows and n storms are sampled uniformly from the complete pool. The null draws should preserve, at minimum, the number of storms from each event window and preferably basin composition. Otherwise, changes in basin and seasonal geometry may dominate the persistence diagrams. It should also be clarified whether all lifetime fixes are included for a storm that merely overlaps the ±15-day window. The methods appear to concatenate all fixes from selected storms, which could introduce observations outside the proposed exposure period and give longer-lived storms greater weight.
3. Only 49 placebos are used, with just 100 null iterations per placebo. The manuscript reports a shared Wilson interval of 1.4–14.7%, but confidence intervals should be calculated around each observed proportion. For example, the Wilson 95% interval for 7/49 is approximately 7.1–26.7%, not the interval reported as the nominal acceptance range. More importantly, no paired comparison demonstrates that H1​ rejects more frequently than H0​; under the linear encoding both rates are exactly 4/49. The three encoding results are also correlated because they use the same placebo dates. A paired calibration analysis, more placebos, and substantially more permutation draws are required before using terms such as “intrinsic inflation.”
4. Multiplying 0.009 by the ratio 10.2/5.0 does not produce a statistically calibrated p-value. Calibration should instead be based on an empirical null distribution of p-values or a nested permutation procedure. Monte Carlo p-values should also use the standard +1 correction and include uncertainty arising from the finite number of permutations.
5. Each sample size appears to be represented by one seeded realization. Non-monotonic p-values across N=400–1000 may therefore reflect ordinary sampling variability rather than a structural noise mechanism. The experiment should be repeated over many independent seeds, using identical sampled point indices across encodings, and should report distributions or confidence intervals rather than single p-values.