41 lines
1.6 KiB
Markdown
41 lines
1.6 KiB
Markdown
|
Be concise but rigorous. Do not invent objections. Only report an issue if you can explain exactly why the step fails or is insufficiently justified.
|
||
|
|
Act as a careful mathematical referee. Review the proof below for correctness, not for style.
|
||
|
|
|
||
|
|
Your task:
|
||
|
|
- Find actual logical gaps, unjustified inferences, hidden assumptions, undefined objects, notation conflicts, or uses of results stronger than what was stated.
|
||
|
|
- Be skeptical and precise.
|
||
|
|
- Do not give a general summary first.
|
||
|
|
|
||
|
|
Instructions:
|
||
|
|
1. Read the input line by line.
|
||
|
|
2. List findings first, ordered by severity.
|
||
|
|
3. For each finding, include:
|
||
|
|
- the exact step or sentence,
|
||
|
|
- why it does not follow,
|
||
|
|
- whether it is a fatal gap or a fixable omission,
|
||
|
|
- what additional argument, lemma, or hypothesis would fix it.
|
||
|
|
4. Distinguish clearly among:
|
||
|
|
- Fatal gap
|
||
|
|
- Fixable omission
|
||
|
|
- Notation problem
|
||
|
|
- Exposition issue only
|
||
|
|
5. Check specifically:
|
||
|
|
- whether every object is well-defined,
|
||
|
|
- whether quantifiers are correct,
|
||
|
|
- whether induction hypotheses are applied legally,
|
||
|
|
- whether extremal choices are justified,
|
||
|
|
- whether cited theorems are used in a form strong enough for the conclusion,
|
||
|
|
- whether any notation changes meaning during the proof.
|
||
|
|
6. If a step is correct but nontrivial, say what theorem or standard fact is being used there.
|
||
|
|
7. If you do not find a logical gap, say exactly:
|
||
|
|
“I do not see a logical gap.”
|
||
|
|
Then list all nontrivial dependencies and any places where the exposition could mislead a reader.
|
||
|
|
|
||
|
|
Output format:
|
||
|
|
- Findings
|
||
|
|
- Nontrivial dependencies
|
||
|
|
- Minor issues
|
||
|
|
- Verdict
|
||
|
|
|
||
|
|
Input:
|
||
|
|
[paste proof]
|