SKILL

Enrich Mathematical Content

Add domain-specific typed relations to a mathematical page’s frontmatter based on the Mathematical ASR specification.

Procedure

1. Read the target page. Note its current type:, defines:, tags:, and any existing relations.

2. Determine the mathematical content type. Based on the page body:

   • Does it establish the meaning of a term or structure? → definition
   • Does it state a proposition taken as given? → axiom
   • Does it state and prove a result? → theorem (or lemma, proposition, corollary)
   • Does it demonstrate a result is true? → proof
   • Does it state an unproven conjecture? → conjecture
   • Does it give a concrete instance? → example or counterexample
   • If none of these apply, keep the general ASR type (term, concept, text).

3. Identify required relations. Consult the content types specification for MUST and SHOULD requirements:

   Type	MUST have	SHOULD have
   definition	defines:	has-example:, requires:, extends:
   axiom	part-of:	enables:
   theorem	proven-by:, requires:	corollaries:
   proof	proves:, uses:	technique:
   lemma	proven-by:, requires:	supports:
   corollary	follows-from:, proven-by:	—
   conjecture	— (MUST NOT proven-by:)	evidence:
   example	illustrates:	—
   counterexample	refutes:	—

4. Read the page body for implicit relations. Look for:

   • Inline links or references to other pages → candidates for requires: or uses:
   • Phrases like “extends,” “generalizes,” “builds on” → extends:
   • Phrases like “for example” → has-example:
   • The page’s position in a dependency chain (e.g., group requires monoid)

5. Add relations to frontmatter. Only add relations that are accurate based on the page content. Do not invent relations the content does not support.

6. Update type: if appropriate. If the current type is term but the content is actually a mathematical definition with formal context, consider updating to definition. Only change if the new type is clearly more accurate.

7. Verify. Re-read the page to confirm the frontmatter is consistent with the body.

Constraints

• Do not modify body content. This skill only touches frontmatter.
• Do not add relations to pages you have not read.
• Prefer existing page paths for relation targets. If a target page does not exist, use a descriptive string value instead of a broken path.
• If unsure whether a relation applies, leave it out. Missing SHOULD relations produce warnings, not errors.