| name | no-undefined |
| description | Document-level rigour auditor. Enforces that every term, symbol, abbreviation, experimental label, and formula appears with its definition adjacent to its first occurrence — and re-states it on distant reuse. Also enforces no-step-skipping in math derivations. Invoke whenever writing or reviewing a technical report, paper explanation, or derivation where a reader could encounter an undefined token. Pairs with math-explain (single-formula checklist) and zero-jump-check (inter-step seam auditor) as the outer document-level layer of the rigorous-writing stack. |
no-undefined
Why this skill exists
Readers lose trust the moment something appears without explanation. In a math derivation, an undefined symbol forces the reader to guess. In a technical report, an unexplained abbreviation or experimental label (J1, 3a, agg, mv, fix版…) feels like an in-joke the reader was not invited to. Both failures have the same root cause: the author assumed shared context that does not exist.
This skill removes that assumption entirely. Nothing appears in the document without a definition immediately beside it. Not in a glossary. Not in an appendix. Not in a prior section. Right there, in the same sentence.
This skill is the outer layer of a three-layer rigour stack:
| Layer | Skill | Scope |
|---|
| Outer | no-undefined (this skill) | Entire document: every token of meaning has an adjacent definition |
| Middle | zero-jump-check | Derivation: every inter-step seam is nameable in one phrase |
| Inner | math-explain | Single formula: motivation, symbol defs, assumptions, approximation audit |
The one rule
Every token of meaning must carry its definition at its first occurrence, immediately adjacent — same sentence or the sentence immediately following.
A "token of meaning" is anything a reader cannot decode from plain language alone:
- Technical terms and abbreviations (MoE, RL, agg, mv, GSM8K, RLHF…)
- Mathematical symbols ($\theta$, $\alpha$, $\mathbf{r}$, $\Delta$…)
- Experimental labels and codes (J1–J6, 3a/3b/3c/3d, Stage 1/2/3/4, fix 版…)
- Figure or table labels (Figure 11a, Figure A, Table 2…)
- Method names that are not transparent from plain language (weighted aggregation, majority vote, router logit bias…)
- Numbers or parameters that depend on context (K=4, alpha=0.01, top-8…)
- Measurement or benchmark names (pass@1, GSM8K前100样本…)
Three sub-rules
Sub-rule 1: Definition must be adjacent
Place the definition in parentheses immediately after the term's first occurrence in the document. A glossary section, footnote, or appendix does NOT substitute — the reader must never have to leave the current sentence to decode the term.
Good:
K=4（每个输入做 4 次不同扰动参数的前向传播）聚合解码实测结果如下。
Bad:
K=4 聚合解码实测结果如下。(definition appears in a glossary 2 pages later)
Sub-rule 2: Re-define on distant reuse
If a term reappears more than two ##-level sections away from its first definition, re-state its definition inline as a brief parenthetical. "Brief" means 5–15 words — enough for the reader to recover context without flipping back.
Good (distant reuse, 3 sections later):
在 Stage 4 的 K=4（每个输入做 4 次前向传播）实验中…
Bad:
在 Stage 4 的 K=4 实验中… (no reminder; reader must scroll back 3 sections)
Sub-rule 3: Math — "where" blocks are mandatory, no symbol escapes
For every formula, every symbol that appears in it must be defined in a where … is … block immediately below the formula — even if the symbol was defined earlier. Self-contained symbol blocks are expected and required. See math-explain for the full formula checklist (motivation, term-by-term dissection, assumptions, approximation audit, paper location).
Good:
$$r_i = \sigma(W_r x_i)$$
where $r_i$ is the router score for expert $i$, $\sigma$ is the sigmoid function, $W_r$ is the router weight matrix, and $x_i$ is the hidden state of the current token.
Bad:
$$r_i = \sigma(W_r x_i)$$
(symbols defined three paragraphs earlier; reader must search)
Sub-rule 4: No formula drops from the sky
Never introduce a specialized formula without tracing it from a canonical parent the reader already knows. Write the canonical form first, map symbols, substitute step by step, then label the final line as the paper's or report's formula. See math-explain §Canonical-form-first rule. See zero-jump-check for auditing the inter-step seams of that derivation.
How to apply this skill
Mode A: Writing (proactive)
Before writing any sentence containing a token of meaning, run this decision tree:
Has this token appeared in this document before?
├── No → write token（definition）inline, then continue
├── Yes, within the last 2 sections → use token without re-definition
└── Yes, more than 2 sections ago → write token（brief reminder）inline
For math: apply math-explain to every formula; apply zero-jump-check to every inter-step seam.
For experimental labels: at the START of each new section that mentions a label (J1, 3a, etc.), re-state what it refers to if the label's first definition was in an earlier section.
Mode B: Audit (reviewing existing text)
When invoked on existing text, run four passes:
Pass 1 — Inventory. Extract every token of meaning in document order. List each with its first occurrence location (section + approximate line).
Pass 2 — Definition check. For each token, inspect its first occurrence: is a definition immediately adjacent? Mark ✓ or ✗.
Pass 3 — Distant-reuse check. For each ✓ token, find all subsequent occurrences more than 2 sections away. Does each occurrence have a brief inline reminder? Mark ✓ or ✗.
Pass 4 — Math audit. For every formula, invoke zero-jump-check on its derivation chain. Flag any seam that cannot be named in one phrase.
Report. For every ✗ item: state its location, the token, and the exact parenthetical text to insert.
Patch. Apply all fixes with Edit tool. Verify chapter structure is unchanged after patching.
What does NOT count as a definition
These patterns look like definitions but are not:
| Pattern | Why it fails |
|---|
"MoE models use MoE routing" | Circular — the term explains itself with itself |
"agg is defined in [3]" | External reference — reader must leave the document |
"see Section 2 for K=4" | Remote reference — reader must scroll back |
| Section title as implicit definition | A section titled "J5 Results" does not define "J5" — still needs parenthetical |
| Abbreviation expansion only | "MoE (Mixture of Experts)" is OK for the expansion, but must also add what it means architecturally if that is non-obvious |
Self-check before handing off
After writing any section, verify each item before moving on:
If any box is unchecked, fix it before handing off — do not leave it for the reader to notice.
