Fitness Model F(g)

Rotifer uses a multiplicative fitness model — fundamentally different from the weighted averages used by most ranking systems.

The Formula

$$F(g) = \frac{S_r \cdot \ln(1 + C_{util}) \cdot (1 + R_{rob})}{L \cdot R_{cost}}$$

Symbol	Meaning
S_r	Success rate (0–1)
C_util	Caller utility — how useful callers found the result
R_rob	Robustness — resilience to edge cases and adversarial input
L	Latency
Resource_Cost	Compute resources consumed

Why Multiplicative?

In a weighted average (e.g., 0.4×speed + 0.3×quality + 0.3×reliability), a gene with 0% reliability can still score 40% if it’s fast. The weak dimension is masked.

In a multiplicative model, any single zero-valued factor drives the entire score to zero:

• 0% success rate → F(g) = 0, regardless of speed
• Infinite latency → F(g) = 0, regardless of correctness
• Zero utility → F(g) = 0, regardless of robustness

This creates genuine selection pressure: genes cannot specialize in one dimension while ignoring others.

F(g) vs R(g): Two Different Metrics

The website’s developer page displays a Gene Reputation Score:

$$R(g) = 0.5 \times \text{Arena} + 0.3 \times \text{Usage} + 0.2 \times \text{Stability}$$

These are different metrics at different layers:

	F(g) Fitness	R(g) Reputation
Purpose	”How good is this gene right now?"	"How trusted is this gene over time?”
Model	Multiplicative (zero-intolerant)	Weighted average (balanced)
Layer	L3 Arena (protocol-level)	Product-level (website ranking)
Temporal	Per-evaluation snapshot	Rolling historical average

F(g) determines Arena survival. R(g) determines developer-facing visibility.

URAA Layer Assignment

F(g) lives at L3 Competition & Exchange. It is a protocol-level metric, not a product feature. Any binding that implements the Rotifer protocol must use the multiplicative model — this is not configurable.

Further Reading

• Protocol Specification: Overview — formal fitness function definition
• Arena Commands — how to submit genes and view fitness scores