Read the equation
The first line advances an agent state by dt times its current derivative estimate. The second clips that proposal into [0,1]. This makes every stored scalar bounded for finite arithmetic, while the resulting projected recurrence can differ substantially from the unconstrained continuous-time equation near the boundaries.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| S_i | Agent state |
| dt | Time step |
| dS_i_dt | Derivative from the federation equation |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
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Original context
Read the surrounding source passage
## 11.2 Discrete Update
```
S_i(t+1) = S_i(t) + dt · dS_i/dt
S_i(t+1) = clamp₀₁(S_i(t+1))
```
**Explanation**: Euler integration of the continuous dynamics with clamping for stability.
## 11.3 Federation Coherence
```
Coherence_fed = (2/(n(n-1))) · Σ_{i<j} C_ij
```
**Explanation**: Average pairwise coherence across all agent pairs in the federation.
---
# 12. Activation Functions
## 12.1 Softsign
```
softsign(x) = x / (1 + |x|)Exact original notation
S_i(t+1) = S_i(t) + dt · dS_i/dt S_i(t+1) = clamp₀₁(S_i(t+1))