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    Dear MathOverflow community,

    I'd greatly appreciate your help with following question on the AMS journals :

    either directly at academia.SE, or perhaps, if deemed appropriate, after migration to MO.

    Many thanks in advance.

    The answer you got from vonbrand seems exactly right to me. I suppose different journals have different "house-styles" for announcing that a submitted paper is undergoing the review process, but I don't find the wording here confusing. You could just email the editor to ask what it means, if you have lingering doubts.