Nodes

A Node is a single knowledge unit — a definition, theorem, lemma, and so on. Nodes are the vertices of EulerVertex's knowledge graph, and everything else (facets, pages, edges) attaches to or references them.

Node types

Every node has one of these types:

• Definition — a precise mathematical or conceptual definition
• Theorem — a major proven statement
• Lemma — a supporting statement used to prove theorems
• Corollary — a direct consequence of a theorem
• Proposition — a proven statement of moderate importance
• Axiom — a foundational assumption
• Method — a procedural method or algorithmic approach
• Model — a formal model or framework

The type is metadata only — it doesn't change what fields a node has, just how it's labeled and organized.

Metadata-first: content lives in facets

A node itself only stores metadata (title, type, subject/category/subcategory, tags, prerequisites). The actual written content lives in an attached Facet — specifically a content_variant facet, which every node points to via its default_content_facet_id.

This split matters when you're deciding what to create: if you're writing the primary explanation of a concept, you're creating a node and its main content facet together (the Studio does this in one step). If you're adding an alternative phrasing, a shorter version, or a version for a different audience level, you're adding another content_variant facet to the same node — not a new node.

One node per distinct concept

Two rules keep the graph from fragmenting into near-duplicates:

• Different phrasing, same concept → same node, different facet. If you find yourself writing "here's another way to explain X," that's a new content_variant facet on the existing node, not a new node.
• Same term, different concept → different nodes. The same word can mean genuinely different things in different contexts — a "line bundle" in differential geometry isn't the same concept as one in algebraic geometry. These become two separate nodes, connected by a context_variant edge (see Edges) so readers can find the related concept in the other context.

Keep nodes short and focused

If what you're writing feels like it's covering more than one idea, it's a sign to split it into multiple nodes and connect them with prerequisite edges rather than writing one long node. Short, focused nodes are easier to reuse across pages and courses, and easier to search for.