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/notation-clean

Audits and simplifies mathematical notation in LaTeX/markdown to an Econometrica publication standard — one-shot inline symbols, sub-5-use ratios of parameters, Greek letters used for non-parameters, and collisions with reserved notation — triggered only on notation-specific requests.

Category: editing
Field: economics
License: MIT
Updated: 2026-09
Stages: revision-editing

Notation Audit & Cleanup

Audit and simplify mathematical notation in research documents. Enforces the Econometrica-level convention that notation is minimal, consistent, and earns its place.

Trigger conditions

Invoke when the user's request is specifically about notation — the word "notation" or a synonym pointing at symbols ("sub-notation", "symbols", "Greek letters", "shortcuts") is in the request. Representative phrases: "notation audit", "fix the notation", "clean up notation", "simplify notation", "too much notation", "excessive notation", "notation-heavy", "too many symbols", "don't introduce new Greek letters".

Proactive invocation: invoke without being asked only when Claude itself introduced new notation during a derivation in the current conversation (e.g., defined γ ≡ α/β, or used a new Greek for a mid-step quantity) — and it ended up used fewer than 5 times or violates a rule in notation-rules.md. A derivation that is merely long but reuses established symbols does NOT trigger this. Use the fast path below for proactive invocation.

Do not invoke for generic "audit"/"review" (→ /audit-econ), compile errors (→ /latex-doc), code cleanup (→ /simplify), or math correctness (→ /audit-econ). If ambiguous, ask once: "Notation pass, math-correctness audit, or both?"

Before starting

Read references/notation-rules.md — authoritative for Greek/Latin conventions, reserved symbols (β, r, t, T, k, κ, τ, ...), the 5-use rule, and exception handling. Read each run; the user may update it.

Arguments

$ARGUMENTS may contain: - target_path: file(s) or directory. If missing, ask or use current conversation's math. - --mode: audit (report only), fix, both (default). - --agents N: sub-agents for file audits (default 1 for short files and in-conversation, 2 for full papers).

Supported: .tex, .md with LaTeX math. .docx → ask user to export first. Conversation math → use the fast path.

Fast path (in-conversation and short derivations)

Use this when the target is math in the current conversation, a single short section, or a proactive check — NOT a full paper.

  1. Apply the rules in notation-rules.md directly (no sub-agents, no symbol table).
  2. Output using Template D from references/response-templates.md — a compact list of at most 5 items, each with the symbol, the problem in one sentence, and the inlined rewrite.
  3. If the math is clean, one line: "Notation pass: clean."

Skip the rest of the skill. This is the common case for proactive invocation and keeps the quality gate cheap.

Full path (file audits)

For .tex / .md files or multi-section audits. Five phases.

Phase 1: Read and dispatch

Read the full target. Follow \input{} / \include{} in .tex. Building a symbol table is optional scaffolding — do it only if the document is large enough that you need the index to reason about coverage.

Dispatch N sub-agents (default 1 for short files, 2 for full papers) in a single parallel Agent call. Each receives the file path(s), the full contents of notation-rules.md pasted into the prompt, and Template 1 from references/subagent-prompts.md. Sub-agents work independently.

Phase 2: Consensus

Collect FINDING blocks from each sub-agent. Severity guide:

  • High — one-shot symbol (used 1–2×) where inlining clarifies; Greek letter for a non-parameter; reserved standard symbol (β, r, t, T, k, κ, τ) used for a non-standard role.
  • Mid — compound shortcut used 3–4× (below threshold); small/capital Latin stock convention broken; inconsistent decoration.
  • Low — cosmetic; duplicate definition; flagged exception (rule conflict that deserves surfacing).

When sub-agents disagree, pick the stricter reading. Deduplicate findings that refer to the same symbol.

Phase 3: Present findings

Use Template A from references/response-templates.md (findings table). Sort High → Mid → Low, then by location. No commentary outside the table.

Ask the user to pick: Apply all, Apply subset, or Sequential. Stop here if --mode audit.

Phase 4: Apply fixes

For each approved finding: - Inline — replace a compound symbol with its primitive expression; remove the definition. - Rename — keep the object, change its letter to satisfy the convention. - Keep as exception — leave it, add a % Exception: ... comment next to the first definition.

Use Edit with replace_all only when the symbol token is unambiguous (e.g., \gamma_1); otherwise edit with surrounding context. After .tex edits, compile using the /latex-doc protocol and read the log.

Dispatch one verification sub-agent with Template 2 from references/subagent-prompts.md. Iterate if it fails.

Phase 5: Report

Use Template B from references/response-templates.md. List what was applied, what was kept as exception, which file(s) changed. Cite full paths.

Workflow rules

  • Read notation-rules.md every run — don't rely on memory. It is the source of truth for what to flag; this file governs how to run the audit.
  • Never change mathematics. Edit symbols, not meaning. If inlining would require non-trivial algebra, stop and flag.
  • Preserve compile-ability. After any .tex change, compile and check the log.
  • Flag exceptions, don't invent them. When rules conflict or the literature's standard breaks the convention, surface it as a Low-severity flagged exception rather than silently accepting.
  • Table speaks for itself. No commentary outside the findings table. Final report is short.