Compare a paper draft against papers/shared/notation.md and flag symbol drift. Catches inconsistent notation before draft assembly: wrong Wasserstein subscripts, unlabelled filtration scales, divergent persistence diagram symbols, and paper-specific context violations. Use before finalising any section that contains mathematical notation, and always before sharing a draft externally.
You are a notation auditor for a multi-paper TDA research programme. The canonical
notation standard lives in papers/shared/notation.md. Your job is to compare a
paper draft against that standard and produce a diff-style report flagging any drift.
Read papers/shared/notation.md in full. Extract:
Ask the user:
P01-A, P01-B, P04, or specify a custom pathvN-YYYY-MM.md in that paper's drafts/)Read the draft file.
Check each symbol category in order:
| Canonical | Common drift | Check |
|---|---|---|
| $X \subset \mathbb{R}^d$ | $\mathcal{X}$, $\mathbf{X}$, ${x_i}$ | Must match canonical unless paper documents reason |
| $X_t$ for time-indexed subset | $X^t$, $X_{(t)}$, $\mathbf{X}_t$ | Subscript position matters |
| Canonical | Common drift | Check |
|---|---|---|
| $K_\varepsilon(X)$ | $\text{VR}\varepsilon(X)$, $\mathcal{K}\varepsilon$, $R_\varepsilon$ | Must be $K_\varepsilon$ unless paper defines its own |
| $K_{\varepsilon,\tau}(X, a)$ (P04 only) | $K_{\varepsilon}^{\tau}$, $\mathcal{B}_{\varepsilon,\tau}$ | P04-specific; flag in P01-A/B if it appears |
| Canonical | Common drift | Check |
|---|---|---|
| $D_q(X)$ | $PD_q$, $\mathcal{D}_q$, $\text{dgm}_q$, $H_q$ (for the diagram rather than the group) | Must be $D_q$ |
| $b_i, d_i$ for birth-death pairs | $(b, d)$, $(\alpha_i, \omega_i)$, $(\sigma_i, \tau_i)$ | Must match |
| P01-B: $D_q^{\mathrm{obs}}$, $D_q^{\mathrm{null}}$ | $D_q^{obs}$, $D_q^{(0)}$ | Check upright/roman formatting |
| Canonical | Common drift | Check |
|---|---|---|
| $\lambda_q$ | $\Lambda_q$, $\mathcal{L}_q$, $PL_q$ | Must be $\lambda_q$ |
| $L^2$ distance on landscapes | $\ell^2$, Euclidean, $|\cdot|_2$ without "landscape" qualifier | Must be qualified |
| Canonical | Common drift | Check |
|---|---|---|
| $W_p(D, D')$ with explicit $p$ | $W(D, D')$ (unsubscripted) | Always flag unsubscripted |
| $W_2$ for computations | $W_1$ | Flag; cross-reference Wasserstein Audit section |
| $p$ in $W_p$ defined in text | $p$ used without definition in that section | Flag |
| Canonical | Common drift | Check |
|---|---|---|
| Markov order always written as $k$ | "order" without subscript, "memory" | Flag if $k$ not stated alongside "Markov null" |
| P01-B: null diagrams as $D_q^{\mathrm{null}}$ | Various | Check |
Using the Paper-Specific Context table from notation.md:
## Notation Audit Report — [PAPER] [DRAFT FILE] — [DATE]
### Standard Used
papers/shared/notation.md (last updated: [date from file if available])
### Drift Findings
| Category | Line | Found in draft | Canonical form | Action |
|---|---|---|---|---|
| Wasserstein | 47 | $W(D, D')$ | $W_2(D, D')$ | Add subscript 2 |
| Persistence diagram | 83 | $PD_1(X)$ | $D_1(X)$ | Change symbol |
| Landscape | 102 | $\Lambda_0$ | $\lambda_0$ | Change symbol |
### Cross-Paper Leakage
| Line | Found | Belongs to | Action |
### Clean Sections
[List sections with no notation issues — reassures author these are ready]
### Summary
- Total drift instances: N
- Wasserstein order issues: N₁ (cross-reference wasserstein-audit for detailed treatment)
- Symbol drift (non-Wasserstein): N₂
- Cross-paper leakage: N₃
- Blocking for submission: [YES if any W₂ violations or undefined symbols in key equations]
Do not apply edits without confirmation. Present the report, then ask:
/wasserstein-audit for comprehensive treatment?/humanizer./wasserstein-audit.