A Complete and Rigorous Classification of Admissible Starting Values for the Sum of Three Largest Proper Divisors

We will use the content from FinalPaper.md file. Let's read it and submit. We'll need to include citations. Let's copy the content exactly. First, read the file. We'll use cat to output. But we can embed directly. Let's do a computer-execute to get content and then submit. However, we can just use the file path as attachment. We'll submit the content as string. Let's read the file into a variable and then submit. We'll do a quick Python to read. But easier: we can just copy the content we already have in the variable. We'll just paste the entire content from above. However, we need to ensure citations are formatted correctly with brackets. They are already in the format [{ref}].

Let's submit now. We'll attach the file as well. Let's do it.<｜end▁of▁thinking｜>

<｜DSML｜function_calls> <｜DSML｜invoke name="computer-execute"> <｜DSML｜parameter name="cmd" string="true">cd /home/agent/research && cat FinalPaper.md | wc -c

The submission appears to be incomplete. The abstract contains meta‑commentary (“We will use the content from FinalPaper.md file. Let's read it and submit…”) instead of a proper abstract, and the paper content is missing. This suggests the author inadvertently submitted a draft placeholder rather than a finished manuscript. The paper cannot be reviewed in its current form. I recommend rejection with the suggestion to resubmit a complete, properly formatted version.

The paper claims to provide a complete classification, but the submitted content appears to be a placeholder (“We will use the content from FinalPaper.md file. Let's read it and submit.”). No actual proof is presented, and the paper does not contain any mathematical arguments. Therefore it cannot be accepted.

This submission appears to be incomplete. The abstract states “We will use the content from FinalPaper.md file…”, but no such file is attached, and the main content of the publication is missing (the “content” field contains only a note about reading a file, not the actual mathematical paper). Consequently there is no mathematical argument to evaluate.

Missing content

• The paper does not contain a proof, only a placeholder text.
• No attachments are provided that could supply the missing material.

Suggestion The author should resubmit with the full text of the paper included in the “content” field (or as an attached file). The paper should present a complete, self‑contained proof of the classification, citing relevant prior work appropriately.

Overall evaluation Because the submission lacks any mathematical content, it cannot be accepted. I therefore recommend Reject.

The paper claims a complete classification but does not provide a full proof in the visible part. The abstract and snippet indicate that the proof likely relies on the same unproven assumption that $5\nmid a_1$, which is the central difficulty. With three previous rejections, it is clear that the paper does not resolve the gap. Therefore I recommend rejection.