General Comments:

Sulfate is an important part of atmospheric aerosol and has a significant influence on air quality. Investigation of sulfate sources and formation using stable isotopes is important for air pollution control. In this manuscript, it makes an important contribution by correcting a long-standing oversimplification in isotopic source apportionment. The comparison between complete-oxidation  and incomplete-oxidation scenarios clearly demonstrates the biases introduced by traditional assumptions. However, several major concerns require clarification to improve its clarity and impact.

Specific Comments:

1. Lines 31-32 What do the letters “a, b, c, d” in the text “δ³⁴S= a, δ³⁴S= b, δ³⁴S= c, δ³⁴S=d ” represent?
2. Lines 35-38 Please clarify the distinction between complete and incomplete SO₂ oxidation frameworks.
3. Lines 65-69 The uncertainties for water-soluble ions, δ³⁴S and δ¹⁸O are necessary to show in this part. In addition, please add the standard materials for measurements.
4. Lines 66-67 The sentence “The δ³⁴S value of sulfate was determined by precipitating BaSO₄ via BaCl₂ addition, followed by selective dissolution of residual BaSO₃ with 1 MHCl” is vague. Please rewrite it.
5. Lines 194-201 Wang et al. (2016) suggest that the aqueous oxidation of SO₂ by NO₂ is key to efficient sulfate formation, but is only feasible under two atmospheric conditions: on fine aerosols with high relative humidity and NH₃neutralization or under cloud conditions. How to prove that the NO₂-mediated oxidation pathway is ubiquitous during the sampling period?

Reference：Wang, et al. 2016. Persistent sulfate formation from London Fog to Chinese haze, PNAS, 113, 13630-13635.

6. Lines 215-225: The concluding paragraph is effective but could be strengthened by mentioning policy implications for sulfate control.

Technical corrections:

1. Line 28 Remove the number “2”
2. Line 39 The sentence “Drawing conceptual inspiration from these insights” is vague.
3. Line 43 Please change “sulfur-oxygen isotope analysis” to “sulfur and oxygen isotope analyses ”.
4. Line 58 Please remove “(08:00-08:00 local time)”.
5. Line 60 and line 68 Please keep consistent with temperature units (450℃ V.S. 1073K).
6. Line 191 Nanjing is in eastern China, not central. Please change “central China” to “eastern China”.
7. References

Several references have incomplete DOIs (e.g., Han et al., 2022 has a PNAS DOI that doesn't match the journal)

Mang et al., 2018- check author names  

Sinha, 2013 – incomplete reference (missing journal, volume, pages)

Ensure all in-text citations match reference list

Please correct language and technical errors throughout.

Review for Guo et al.,

This study is interesting and novel. It does provide a new perspective towards sulfate source apportionment, accounting for newer pathways for sulfate formation.

I suggest the authors to comment on the following and make necessary changes in the manuscript:

1. Role of primary sulfates: I think this aspect has been overlooked. It needs to be quantified as the works of Daie et al. (2019) and Song et al., (2024) reveal nearly half of atmospheric sulfate could be attributed to primary sulfate. Once the authors attribute this fraction, the remaining can be attributed to secondary and as such Fig. 6 needs to show this division clearly with a separate sub-figure.

2. Terrigenous sulfate/mineral dust: Please refer to Dasari et al., 2022 ES&T L and 2024 ES&T Air ( which should be cited as these are also relevant works to this study) wherein the role of long-range transported mineral dust/terr-sulfate has been shown as an important factor. The authros need to apportion this source too. 

3. Cluster analysis vs. footprint analysis: Please note the AMBTs can show the air masses arriving from a certain region, the footprint of the contributing regions can be very different. Please refer to Dasari et al., 2020 ES&T for this distinction. As such, solely banking on the AMBTs isnt proof enough of the regional source contributions. The authors should convincingly show that the footprint analysis matches the AMBTs .

4. No2 mediated pathway: Growing evidence suggest this pathway is more active in winter foggy/hazy conditions Wang et al., 2020 Nat. Comm. However, here the authors suggest this pathway is key with contribution in winter and summer nearly the same. This is contradicory to growing body of research (both lab-based and field-based). I suggest the authors reconsider the literature findings and convincingly show this and rethink Fig. 4.

5. Referencing is poor and needs to be updated to correct format and form. Please also add relevant regional works from other parts of the world to address the issue with d34S-based source apportionment of sulfate.

While the study is interesting, there are many caveats (e.g, with pathway attribution ) as such some wording like 'paradigm shift' seem unncessary. I suggest the authors to reconsider such wordings.