Quality Signal

One number: 0–10,000

sentrux computes a single continuous score called Quality Signal. It’s the geometric mean of 5 root cause metrics, each normalized to [0, 1], then scaled to 0–10,000.

quality_signal = (modularity × acyclicity × depth × equality × redundancy) ^ (1/5) × 10000

Why geometric mean?

The Nash Social Welfare theorem (1950) proves the geometric mean is the unique aggregation satisfying:

1. Pareto optimality — if all scores improve, signal improves
2. Symmetry — all root causes weighted equally
3. Independence — irrelevant dimensions don’t affect the result

Practically: you cannot game one metric while tanking another. The ONLY way to raise the geometric mean is to improve ALL factors. This forces genuine architectural improvement.

Why not letter grades?

Letter grades create artificial boundaries. Score 79 = B, score 81 = A. AI agents game the boundary instead of genuinely improving. With continuous scores, every +1 matters equally. The agent converges naturally when improvements become marginal — like gradient descent.

Why not 20 proxy metrics?

Proxy metrics (coupling ratio, dead code %, function length) measure symptoms, not root causes. An AI agent can game individual proxies — add fake imports to boost cohesion, split functions superficially. The metrics improve but the code doesn’t.

Root cause metrics measure fundamental structural properties that can only improve through genuine architectural change.

The 5 root causes

A codebase is a directed graph G = (V, E) where V = files and E = dependencies. This graph has exactly 5 independent structural properties:

Metric	Theory	What it measures	Edge or Node?
Modularity	Newman 2004	Do edges cluster into modules?	Edge
Acyclicity	Martin 2003	Are there circular edges?	Edge
Depth	Lakos 1996	How deep are edge chains?	Edge
Equality	Gini 1912	Are node properties concentrated?	Node
Redundancy	Kolmogorov	Are there unnecessary nodes?	Node

3 edge properties + 2 node properties = 5 total. Adding more would be redundant.

Normalization

modularity  = (Q + 0.5) / 1.5          # bounded [-0.5, 1] → [0, 1]
acyclicity  = 1 / (1 + cycles)          # unbounded → sigmoid
depth       = 1 / (1 + max_depth / 8)   # unbounded → sigmoid, midpoint 8
equality    = 1 - gini                   # bounded [0, 1] → invert
redundancy  = 1 - ratio                 # bounded [0, 1] → invert

3 of 5 metrics have zero arbitrary parameters. Only 2 need a sigmoid midpoint.

Convergence

Iteration 1: signal = 5800 → equality is lowest (3500)
  → refactor god function → equality improves → signal = 6300

Iteration 2: signal = 6300 → modularity is lowest (5500)
  → extract module → modularity improves → signal = 6900

Iteration 3: signal = 6900 → redundancy is lowest (7200)
  → remove dead functions → redundancy improves → signal = 7400

  ...diminishing returns → natural convergence

No artificial stopping point. The AI converges when marginal improvement per change approaches zero — exactly like gradient descent.

Theoretical foundation

Theory	Year	What it provides
Cybernetics (Wiener)	1948	Feedback loop architecture
Systems Engineering (Tsien)	1954	Decomposition into independent subsystems
Kolmogorov Complexity	1963	Theoretical ground truth
Graph Modularity (Newman)	2004	Modularity Q metric
Nash Bargaining	1950	Geometric mean as optimal aggregation
Gini Coefficient	1912	Inequality measurement
Tarjan’s Algorithm	1972	Cycle detection
Lakos Levelization	1996	Dependency depth