cyber/luminosity.md

luminositiesknowledge luminosity
cyber cybernomics cip entity cyber
π 0.01%

Luminosity

Luminosity is a node-level metric in the cyber knowledge graph defined as the product of content size and focus probability:

$$L_i = s_i \cdot \pi_i$$

where s_i is the size of page i (in bytes or words) and π_i is its stationary focus probability from the tri-kernel.

Physical Analogy

In astrophysics, luminosity L = σ × Φ (cross-section × flux) — how much energy a star radiates. The knowledge graph analogy is precise:

Physics Knowledge Graph
Cross-section σ Content size s_i
Photon flux Φ Attention flux π_i
Luminosity L Knowledge radiated into the network

A page with large content but zero focus radiates nothing — a dark body. A page with high focus but no content radiates nothing — a singularity. Luminosity captures what the network actually receives from each node.

Utility

Luminosity answers a question neither size nor focus can answer alone: how much knowledge does this node contribute to the network per unit time?

Metric Measures Blind Spot
Size Content volume Ignores whether anyone reads it
Focus Attention probability Ignores whether there is content to absorb
Luminosity Knowledge throughput None — captures both dimensions

Applications:

  • Identify over-invested nodes: high size, low luminosity → content that nobody reaches
  • Identify under-invested nodes: high focus, low luminosity → attention bottlenecks that need content
  • Resource allocation: luminosity-weighted distribution rewards nodes that actually deliver knowledge

HR Diagram for Knowledge Graphs

In astronomy the Hertzsprung-Russell diagram plots luminosity vs temperature, classifying stars into main sequence, giants, dwarfs, supergiants. The knowledge graph analogue plots luminosity vs focus:

   L ↑
     |  ★ Red Giants               ★ Supergiants
     |    (big content,               (big content,
     |     moderate focus)             high focus)
     |
     |       · · · Main Sequence · · ·
     |         (content proportional to focus)
     |
     |  · White Dwarfs
     |    (small content, high focus)
     |
     +————————————————————————————→ π
Class Profile Example
Red Giant Large s, moderate π Verbose page that accumulated content but lost structural centrality
White Dwarf Small s, high π Hub page — compact, highly linked, concentrates attention
Supergiant Large s, high π Core spec page — comprehensive and central
Main Sequence s ∝ π Healthy pages — content matches the attention they receive

Pages off the main sequence signal structural imbalance: either content should be pruned (red giants) or expanded (white dwarfs).

Conservation

Since Σ π_i = 1, total luminosity equals the focus-weighted average size:

$$L_{total} = \sum_i s_i \cdot \pi_i = \mathbb{E}_\pi[s]$$

This is the expected content size encountered by a random walker — the effective knowledge bandwidth of the graph. Maximizing L_total means either growing content on high-focus pages or increasing focus on content-rich pages.

Relation to gravity

Luminosity is a node metric (what a node radiates). Gravity is a pair metric (how strongly two nodes attract each other). Together they form a complete picture: luminosity determines what each node contributes, gravity determines the structural skeleton through which contributions flow.

Implementation

Computed as a derived metric from focus and file size, available in the publisher build pipeline:

L_i = size_bytes(i) × π_i

Displayed in the files table alongside focus probability π%.

Local Graph