Paper Polisher

Purpose

Polish mathematical modeling contest paper sections for language quality, logical clarity, formula consistency, and claim calibration.

This skill operates on already-drafted paper sections. It improves wording, fixes grammar, checks formulas, calibrates hedging to match evidence strength, detects overclaims, and ensures formatting compliance. It does not invent new content, add unsupported claims, or rewrite the paper's scientific argument.

Adapted from nature-polishing design principles: language serves the argument, polish should not hide weak reasoning, and claims must be proportional to evidence.

This skill does not write new paper sections, run experiments, generate figures, or perform final QA.

When to use

Use this skill:

• After paper-section-writer has drafted one or more paper sections.
• Before quality-assurance-auditor.
• When the user says: "polish the paper", "check the English", "fix the grammar", "improve the writing", "calibrate the claims", "check for overclaims", "proofread Q1 section".
• When Chinese-to-English translation has produced rough drafts that need smoothing.
• When formulas, notation, or terminology are inconsistent across sections.

Preconditions

The following should already exist or be provided:

• Paper section drafts under paper/sections/.
• Final method explanations (for formula and notation verification).
• Final result analyses (for claim verification).
• The global symbol table at planning/symbol_table.md (if available).
• Contest formatting requirements (if available).

If paper sections do not exist, hand back to paper-section-writer.

Inputs

Use or request:

• paper/sections/*.md or paper/sections/*.tex — the drafted sections.
• methods/Qx/qx_final_method_explanation.md — for formula and notation verification.
• results/Qx/reports/qx_final_result_analysis.md — for claim verification.
• planning/symbol_table.md — for notation consistency.
• Contest formatting requirements.

Workflow

1. Identify the paper type and section.

   • Mathematical modeling contest papers follow a standard structure: Abstract → Problem Restatement → Problem Analysis → Assumptions → Symbols → Model Construction (per Q) → Model Solution → Results Analysis → Robustness → Strengths & Limitations → Conclusion.
   • Each section has different polishing priorities (see section-specific rules below).

2. Run the 12-point polish checklist (see below).

3. Calibrate claims against evidence.

   • For each numerical or comparative claim, verify it is supported by the final result analysis or robustness report.
   • If a claim overstates the evidence, downgrade the language.
   • If a claim is unsupported, flag it as a blocker (do not silently remove — the writer needs to decide).

4. Check formula and notation consistency.

   • Every symbol must appear in the global symbol table or be defined locally.
   • Same concept must use the same symbol across all sections.
   • Subscripts, superscripts, and indices must be consistent.
   • Formula numbering must be sequential and match references in text.

5. Check terminology consistency.

   • Same concept must use the same term throughout.
   • Method names must match the final method explanation.
   • "Baseline", "main model", "improved model" must be used consistently.

6. Produce polished sections.

   • Show a diff or change summary.
   • Mark any claims that were downgraded and why.
   • Flag any remaining issues that need author attention.

12-Point Polish Checklist

1. Sentence Length

• Split sentences longer than 30 words.
• Vary sentence length: mix short (8-15 words) and medium (15-25 words).
• The first and last sentences of each paragraph should be the clearest.

2. Paragraph Structure

• Each paragraph should have one main point.
• Topic sentence first, support following, transition at end (or beginning of next).
• Paragraphs longer than 5-6 sentences should be split or tightened.

3. Tense Consistency

• Problem restatement / Assumptions / Symbols: Present tense.
• Model construction: Present tense for model description.
• Model solution / Results analysis: Past tense for what was done and found.
• Conclusion: Present tense for final findings, past tense for what was done.
• Do not mix tenses within a single paragraph without reason.

4. Hedging Calibration

Match claim strength to evidence:

Hedging phrases (strongest to weakest):

• demonstrates / shows / establishes → strongest
• indicates / suggests / supports → moderate
• may indicate / appears to / is consistent with → weak
• could potentially / might possibly → weakest (use sparingly)

5. Overclaim Detection

Flag and downgrade or remove:

• Absolute claims: "always", "never", "proves", "guarantees", "optimal" (unless proven).
• Unwarranted causation: "A causes B" when only correlation is shown.
• Scope expansion: "All models benefit from..." when only one model was tested.
• Unverified "first" or "novel" claims.
• "Significantly" without statistical test or defined threshold.
• "Our model outperforms all existing methods" when only 1-2 baselines were compared.
• Numerical precision beyond data support: "The score is 0.883214" → "The score is approximately 0.88".

6. Formula Formatting

• Formulas in display math mode ($$...$$ or \begin{equation}...\end{equation}) for important equations.
• Inline math ($...$) for variable references and short expressions.
• Consistent subscript/superscript style.
• Units after numerical values.
• Variable definitions immediately after first use in a formula.

7. Notation Consistency

• Cross-check every symbol against planning/symbol_table.md.
• Decision variables vs state variables vs parameters must be distinguished.
• Vector/matrix notation must be consistent (bold, arrow, or neither — pick one).

8. Figure and Table References

• Every \ref{fig:...} or "Figure X" must correspond to an actual figure file.
• Figure references must be in order (Fig.1 before Fig.2 in text).
• Every table reference must correspond to an actual table.
• Captions must include the main takeaway, not just a description.

9. Transition and Flow

• Between sections: one bridging sentence connecting to the next section.
• Between paragraphs: logical flow (therefore, however, in contrast, furthermore, specifically).
• Avoid "As mentioned above" / "As discussed previously" — restate briefly instead.
• Avoid "It is worth noting that..." / "It should be mentioned that..." — just state it.

10. Word Choice

• Prefer specific over vague: "RMSE improved by 35%" not "the error got better".
• Prefer simple over ornate: "use" not "utilize", "show" not "elucidate", "about" not "approximately" (unless precision matters).
• Remove filler: "It is important to note that", "Interestingly", "Remarkably".
• Remove redundant pairs: "various different", "basic fundamentals", "advance planning".

11. Voice

• Prefer active voice for clarity: "We applied TOPSIS to the indicator matrix" not "TOPSIS was applied to the indicator matrix".
• Use passive voice sparingly, mainly in Methods/Model Solution: "The weights were computed using the entropy method".
• Use "we" consistently (not "the authors", "this paper", "the research team").
• In Chinese→English translation: avoid literal translation of Chinese academic conventions.

12. Formatting Compliance

• Check contest-specific formatting: word count, page limit, font size, margin requirements.
• Section numbering is consistent.
• Reference format is consistent.
• Appendix materials are properly labeled.