Wasserstein Order Consistency Audit

VerifiedSafe

Scan manuscript drafts and codebase for W₁ vs W₂ inconsistencies. Resolves the blocking Phase 0 deliverable.

Sby Skills Guide Bot
Data & AIIntermediate
007/23/2026
Claude Code
#wasserstein#audit#consistency#manuscript#code

Recommended for

Our review

Scans manuscript drafts and codebase for inconsistencies between Wasserstein orders (W₁ vs W₂) and generates a structured reconciliation report.

Strengths

  • Automatically catches W₁/W₂ mismatches in LaTeX and Markdown files
  • Checks Python wasserenstein_distance calls and TDA library usage for explicit order arguments
  • Outputs a clear report with file locations and suggested fixes
  • Enforces project-wide notation standards

Limitations

  • Does not auto-fix issues; requires manual confirmation
  • Only detects explicit textual patterns, not implicit mathematical usage
  • Relies on the project having a predefined notation standard
When to use it

When you need to align Wasserstein metric usage between a manuscript and its accompanying codebase before publication.

When not to use it

If your project consistently uses a single Wasserstein order (e.g., always W₂) and consistency is not a concern.

Security analysis

Safe
Quality score90/100

The skill only reads files locally and produces a report, with no execution of external commands or modification of files, posing no security risk.

No concerns found

Examples

Full audit of all papers and code
/wasserstein-audit all
Audit only manuscript files
/wasserstein-audit papers
Audit only Python code
/wasserstein-audit code

/wasserstein-audit — Audit Wasserstein Order Consistency

Scan all manuscript drafts and codebase for W₁ vs W₂ inconsistencies. Resolves the blocking Phase 0 deliverable: the legacy P01 manuscript uses W₁ in several places while project convention mandates W₂ as the primary metric.

Usage

/wasserstein-audit
/wasserstein-audit [papers|code|all]

Example: /wasserstein-audit all


What this does

  1. Reads papers/shared/notation.md (canonical notation standard, Wasserstein Audit section)
  2. Scans manuscript .md files under papers/ for W₁, unsubscripted W, ambiguous W_p
  3. Scans Python files under all domain packages for Wasserstein calls without explicit p=2
  4. Cross-references findings against what notation.md already has "verified"
  5. Produces a structured reconciliation report — does not fix anything without confirmation

Manuscript patterns that trigger a flag

| Pattern | Issue | |---|---| | W_1 / $W_1$ / W_{1} | W₁ usage — needs justification or must change to W₂ | | $W$ (unsubscripted) | Always flag — violates notation standard | | bottleneck without alongside Wasserstein | Sole metric violation | | wasserstein without explicit order nearby | Ambiguous |

Code patterns that trigger a flag

| Pattern | Issue | |---|---| | wasserstein_distance(a, b) with no p= arg | Default may not be W₂ in all library versions | | p=1 or order=1 near Wasserstein call | Explicit W₁ usage | | bottleneck_distance(...) | Must not be used as sole metric | | gudhi.wasserstein.wasserstein_distance without order=2 | gudhi default not guaranteed |


Report format

## Wasserstein Audit Report — YYYY-MM-DD

### Manuscript Findings
| File | Line | Found | Issue | Suggested Fix |

### Code Findings
| File | Line | Found | Issue | Suggested Fix |

### Status
- Blocking Phase 0: YES / NO
- Total issues: N (manuscript: N₁, code: N₂)

### Recommended Actions

Library defaults (reference)

  • persim.wasserstein_distance — p=2 by default ✓
  • gudhi.wasserstein.wasserstein_distance — requires explicit order= arg
  • giotto-tda Wasserstein vectorisation — p=2 by default ✓
  • W₁ in theory proofs is acceptable in Methods sections if clearly labelled and distinguished from the computational metric used
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