codex-app-formula-output-rules

name	codex-app-formula-output-rules
description	Formula output rules for Codex App. Use when a reply will contain mathematical expressions, derivations, proofs, or symbol-heavy explanations in Codex App and you need stable rules for displayed equations, prose-vs-equation boundaries, equation numbering, and overflow-safe math layout.

Codex App Formula Output Rules

Use this skill when writing math-heavy answers in Codex App.

This skill focuses on formula output in Codex App, especially displayed equations, prose-versus-equation boundaries, numbering, and layout.

Keep non-formula workflow rules in the host environment's normal instruction set. This published skill covers the formula-output subset only.

This public skill is the rendering companion, not the teaching-route owner. Use a separate explanation skill for mode selection such as concept teaching, prerequisite-chain rebuilds, or sentence-by-sentence paper reading.

The published rule set aims to stay language-agnostic. Keep the math boundary, numbering, and layout rules stable, and localize only short prose labels such as equation-reference wording when needed.

Read references/common-principles.md first.

Read references/codex-app-rules.md when the reply will contain displayed equations, equation references, or dense notation.

Read references/source-map.md when you need to trace the published rule back to the original local rule source.

Quick Start

Apply this skill when the answer includes any of:

• derivations
• proofs
• symbol-heavy explanations
• numbered displayed equations
• comparisons between prose notation and displayed notation

Workflow

1. Load the narrow rule set

• Read references/common-principles.md first.
• Read references/codex-app-rules.md when the reply will contain displayed equations, equation references, or dense notation.
• Read references/source-map.md only when you need source tracing.

2. Choose the right boundary

• Keep dense math out of prose.
• Put LaTeX only in standalone displayed equations.
• Keep prose in plain language or short Unicode symbols when clarity allows.
• If quoted source text contains OCR-style ASCII math fragments, normalize that quote into a readable Unicode form while preserving the original wording and meaning. Use this as a rendering cleanup only. A companion explanation skill should own whether that quote appears and how it fits into a paper-reading workflow.

3. Format the displayed equations

• Use two-level numbering.
• Put numbers on the right.
• Use one shared number for one tightly coupled definition block.

4. Run the prose-math gate

• No raw LaTeX syntax in prose.
• No dense inline symbols that require subscripts, superscripts, or brace groups.
• Use inline code only for short atomic identifiers such as command names, filenames, environment variables, model names, or one bare code symbol.

5. Run the structure gate

• Split long displayed equations before they overflow.
• Prefer short aligned lines for multi-relation or matrix-heavy expressions.
• In long replies, allow long horizontal dividers at major structural transitions such as after a local example, before a synthesis block, or before returning to a lower-level source.
• Treat that divider rule as a narrow layout and readability subset only. A companion explanation skill should still own the teaching-route decision for where those transitions come from.

Focus

• Keep the skill centered on formula rendering, numbering, and layout.
• Keep the published rule set stable, minimal, and environment-specific.
• Leave teaching-mode routing to a companion explanation skill.