Rigorous Paper Reviewer

2) Review in ordered passes

Always review in this order:

1. structural pass
2. notation pass
3. method-flow / reproducibility pass
4. theorem / proof pass
5. numerical-analysis pass
6. complexity / efficiency pass
7. experiments / figures pass
8. coherence and cross-reference pass

3) Structural pass

Check using Glob and Read:

• title matches actual contribution
• abstract contains gap + method + strongest result
• introduction has contributions and roadmap
• section order is logical
• appendix content is referenced from main text

4) Notation pass

Check using Grep across all .tex files:

• symbols are defined before use
• spaces, dimensions, norms, operators are explicit
• overloaded notation is minimized
• theorem and experiment notation are consistent
• macros are stable and not duplicative (\newcommand vs \providecommand vs \renewcommand)

Flag every undefined or drifting symbol with file:line references.

4a) Method-flow / reproducibility pass

If the paper has a method section, identify the central predictor, operator, or deployment contract and check whether the section unpacks it coherently.

Specifically check:

• whether the task, deployment object, predictor, objective, and constraints are stated before heavy machinery
• whether the central operator is built in dependency order rather than introduced piecemeal
• whether reader-facing intuition and formal tuple or operator definitions are separated cleanly
• whether algorithms match their stated scope
• whether a wrapper algorithm and helper kernel should be split for clarity
• whether algorithm inputs, outputs, instantiated objects, and equation references are exhaustive enough for replication
• whether tables and figures reuse the same contract vocabulary instead of drifting into parallel stories

4b) Progressive introduction check

For every technical term, named concept, axiom, or non-standard notation:

• Find the FIRST occurrence using Grep
• Verify the reader has sufficient context at that point to understand it
• Check that terms follow the progression: plain English → intuitive example → design principle → formal math

Flag violations as:

• TERM BEFORE DEFINITION: technical term used before reader has context
• JARGON IN CAPTION: figure/table caption uses unexplained term (captions must be self-contained)
• DEFINITION WITHOUT MOTIVATION: formal definition appears without prior intuition

Example violation: "the inertia axiom provides temporal persistence" in the introduction, when "inertia axiom" is not defined until §3. Example fix: "temporal persistence (facts persist until contradicted)" in first mention, formal definition later.

5) Theorem / proof pass

For every formal claim ask:

• is the statement complete?
• are assumptions explicit and sufficient-looking?
• is the conclusion stronger than what the proof sketch supports?
• are constants / rates / norms / probability modes explicit?
• does the appendix contain a proof if promised?

Use these labels:

• MISSING PROOF
• MISSING ASSUMPTION
• UNSUPPORTED LEAP
• POSSIBLE ERROR
• PRESENT BUT UNCLEAR

Do not say a proof is correct unless the argument has actually been checked step by step.

6) Numerical-analysis pass

Whenever the paper touches linear algebra, optimization, numerical methods, dynamical systems, PDEs, control, or functional analysis, inspect:

• well-posedness
• regularity assumptions
• stability
• consistency vs approximation vs convergence separation
• conditioning and numerical sensitivity
• discretization/integration details
• hidden dependence on mesh size / time step / rank / tolerance / solver choice

7) Complexity pass

Demand explicit accounting for:

• variables controlling cost
• time complexity
• memory complexity
• dominant bottlenecks
• training vs inference vs preprocessing separation
• hidden assumptions behind asymptotic notation

8) Experiments and figure pass

For each figure/table ask:

• what claim does it support?
• does the caption state the punchline?
• are axes / units / legends readable?
• are comparisons fair?
• are baselines appropriate?
• is there evidence for robustness / ablations / failure cases when needed?

9) Coherence pass

Check:

• intro promises match delivered sections
• roadmap matches actual order
• theorems are referenced when empirically validated
• appendix references resolve
• labels / refs / citations resolve
• conclusions do not overclaim beyond theory + experiments

10) Severity and output format

Report issues grouped by severity:

• BLOCKER: threatens correctness or interpretability
• MAJOR: weakens acceptance readiness substantially
• MINOR: polish, wording, local structure

End with:

• decision-ready summary
• top 5 fixes
• residual mathematical risks that require human expert confirmation

Use the template in assets/review_report_template.md.

11) Tool usage

• Bash: Run python3 ~/.claude/skills/rigorous-paper-reviewer/scripts/verify_latex_paper.py <path> first
• Glob: Find all .tex, .bib, .sty files in the project
• Grep: Search for \label{}, \ref{}, \cite{}, \newcommand, \begin{theorem}, \begin{proof}, notation patterns, macro definitions
• Read: Examine each section thoroughly (read full files, not just snippets)
• Bash: Compile and check: pdflatex -interaction=nonstopmode main.tex then grep -c "undefined" main.log and grep "multiply" main.log

Consult:

• references/review_rubric.md — structured review rubric
• assets/review_report_template.md — output format template