Without vocabularyWith vocabularyWithout current conceptCompression savings
Top 15 Concepts by ΔL
The concepts whose removal costs the most. Electric field dominates —
removing it forces 173 downstream concepts to inline its 164-token definition.
ΔL vs Fan-out
ΔL = (definition length - 1) × fan-out. Concepts in the upper-right are both
long-defined and widely referenced — the true load-bearers.
Full ΔL Rankings
Every concept ranked by its compression contribution. Click column headers to sort.
Leaves (ΔL = 0) sit at the bottom — removing them costs nothing.
Rank
Concept
ΔL
Trans ΔL
MDL Gain
% Total L
Fan-out
Def Length
Transitive
Page
Definition
ΔL Distribution (Log-Log)
Cumulative Share of Total ΔL
Starting from the highest-ΔL concept, how quickly do we accumulate the total compression load?
A steep initial rise means compression is concentrated in a few hubs.
ΔL Histogram
The distribution of ΔL values across all concepts. Note the extreme right skew —
most concepts have small ΔL, a few have enormous ΔL.
Lorenz Curve (Compression Inequality)
Dependency Network
Top concepts by ΔL shown as a force-directed graph. Node size encodes ΔL,
color encodes fan-out. Directed edges: arrow from B → A means A appears in B's definition (B depends on A). Hover for details.
Drag to rearrange. Scroll to zoom. Click node to highlight neighborhood.
● upstream● downstream
✕
Graph Structure at a Glance
These measures characterize the topology of the concept dependency graph. Each measure is selected
because it directly informs our research question: is physics knowledge organized as a
compression hierarchy?
Out-Degree Distribution (prerequisites)
How many prerequisites does each concept depend on (outgoing edges)? Concepts with high out-degree
are complex composites that synthesize many prior ideas. The distribution shape tells us
whether complexity is distributed evenly or concentrated.
In-Degree Distribution (fan-in / depended-on)
How many downstream concepts depend on each concept (incoming edges)? High in-degree concepts are hubs
— the building blocks reused everywhere. A heavy-tailed in-degree distribution
is a structural prerequisite for heavy-tailed ΔL.
Depth Distribution
How deep is the compression hierarchy? Depth 0 = foundational concepts with no dependencies.
Deeper concepts build on more layers of abstraction. The distribution width indicates
whether the graph is flat (all concepts near the surface) or deep (long dependency chains).
PageRank vs ΔL
PageRank measures structural centrality (how many important concepts point to you).
ΔL measures compression load (how costly your removal is). When these diverge, it reveals
concepts that are structurally central but easily substitutable, or vice versa.