Scientific Paper Writing

Phase 1: Problem Formulation
  - What is the precise research question?
  - Why does it matter? (motivation)
  - What would a solution look like? (success criteria)
  - What are the boundaries? (scope)

Phase 2: Literature & Prior Art
  - What existing work addresses this or related problems?
  - What are the gaps in existing approaches?
  - How does this work position itself relative to the field?

Phase 3: Methodology & Framework
  - What analytical/computational approach will be used?
  - Why is this approach appropriate? (justify the choice)
  - Define notation, assumptions, and formal setup

Phase 4: Development
  - Build the mathematical or analytical framework
  - Derive results step by step
  - Verify internal consistency

Phase 5: Analysis & Discussion
  - What do the results mean?
  - What are the limitations?
  - What are the practical implications?

Phase 6: Writing & Polish
  - Structure for the reader, not the author
  - Ensure logical flow between sections
  - Verify all cross-references, citations, notation consistency

For detailed guidance on each phase, see references/scientific-method.md.

LaTeX standards

Document setup

Always use these baseline packages unless there is a specific reason not to:

\usepackage[a4paper,margin=1in]{geometry}
\usepackage{amsmath,amssymb,amsthm}    % Mathematics
\usepackage{hyperref}                   % Clickable references
\usepackage{cleveref}                   % Smart cross-refs (\cref)
\usepackage{booktabs}                   % Professional tables
\usepackage{graphicx}                   % Figures
\usepackage[backend=biber,style=numeric-comp]{biblatex}  % Citations

Mathematical typesetting rules

• Operators: Use \operatorname{} or define with \DeclareMathOperator for multi-letter operators (e.g., \operatorname{argmax}, not argmax in math mode)
• Variables: Single italic letters for scalars ($x$), bold for vectors ($\mathbf{v}$), blackboard bold for sets ($\mathbb{R}$)
• Subscripts/superscripts: Use descriptive subscripts: $r_{\text{net}}$, not $r_n$ when $n$ is ambiguous
• Equations: Number all important equations. Use align for multi-line, equation for single-line. Never use eqnarray.
• Definitions: Use \coloneqq (:=) when defining a quantity, = for equality
• Notation table: Include a notation summary table when the paper uses more than 10 symbols

Theorem environments

Define and use proper theorem environments:

\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}

Tables

Use booktabs rules (\toprule, \midrule, \bottomrule). Never use vertical lines. Example:

\begin{table}[htbp]
  \centering
  \caption{Description before the table.}
  \label{tab:example}
  \begin{tabular}{lrr}
    \toprule
    Item & Value & Unit \\
    \midrule
    Precision & 94.3 & \% \\
    Samples   & 1{,}000 & -- \\
    \bottomrule
  \end{tabular}
\end{table}

For complete LaTeX reference, see references/latex-reference.md.

Writing quality standards

• Active voice preferred over passive ("We derive..." not "It is derived...")
• Present tense for established facts and mathematical truths; past tense for describing what was done
• One idea per paragraph. Topic sentence first, then support.
• Transitions between sections and paragraphs — the reader should never wonder "why am I reading this now?"
• Avoid: "it is well known that", "trivially", "clearly", "the reader can easily verify". If it is clear, the reader does not need to be told; if it is not, saying so is condescending.
• Define before use. Every symbol, abbreviation, and technical term must be defined before or at first use.

For detailed style guidelines, see references/writing-style.md.

Workflow for editing existing papers

When asked to work on an existing .tex file:

1. Read the entire file first. Understand structure, notation, and what exists.
2. Identify what is needed. Expand content? Fix errors? Add sections? Improve prose?
3. Maintain consistency. Match existing notation, style, and conventions. Do not introduce new packages or notation that conflicts with what exists.
4. Build on what is there. Extend, do not replace, unless explicitly asked to rewrite.
5. Verify compilation. Ensure no LaTeX errors are introduced.

Workflow for new papers

1. Clarify the research question with the user before writing.
2. Outline first. Propose a section structure and get agreement before writing prose.
3. Design figures and tables early. Determine the key visuals before writing prose — let the figure sequence drive the narrative structure.
4. Write non-linearly. Start with Results/Methods (the most concrete sections), then Discussion, then Introduction, then Abstract. Few successful papers are written start-to-finish.
5. Revise in order: content → structure → style. First ensure correctness and completeness, then logical organization, then prose quality.
6. Writing is iterative. Drafting reveals gaps in reasoning. Expect to revisit earlier sections as later ones develop.

Quality checklist

Before considering a paper section complete:

- [ ] Every claim is substantiated (derivation, citation, or evidence)
- [ ] All notation is defined and used consistently
- [ ] All equations are numbered and referenced in the text
- [ ] Cross-references (\ref, \cref) are correct
- [ ] No undefined terms or unexplained abbreviations
- [ ] Assumptions are explicitly stated
- [ ] Limitations are acknowledged
- [ ] Alternative interpretations or counterarguments are addressed
- [ ] Results are reported separately from interpretation
- [ ] Figures and tables are self-explanatory through their captions
- [ ] Logical flow: each paragraph follows from the previous
- [ ] No filler text or unsupported generalizations