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"All but dissertation" (ABD) is an unofficial stage in the process of doctoral study at which the student has completed the coursework and other early milestones (such as the qualifying exam) but has not yet submitted a completed dissertation.
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Referencing a mathematical result already obtained
I would suggest submitting your paper.
An appropriate title could be «A proof of [result X] using [technique Y]» or «A study of [Result X] and associated corollaries».
The abstract introduction shou …