Read the equation
The body forms increment=Dexp(−F)dt, then returns clamp(0.9Ψ_prev+0.1increment+0.5D). The displayed integral contributes one part of this update, but the decay and extra direct decision term materially change the recurrence. It is a bounded driven accumulator rather than a literal unmodified time integral.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| Psi_prev | Previous accumulated state |
| D | Decision score |
| F | Input labelled free energy |
| dt | Step size |
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
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
// T₅₆: D = softmax(W·P + b)
inline double L5_to_L6(double predictive, double w = 2.0, double b = 0.0) {
double z = w * predictive + b;
return std::exp(z) / (1.0 + std::exp(z));
}
// T₆₇: Ψ = ∫D·exp(-F)dt
inline double L6_to_L7(double decision, double free_energy,
double psi_prev, double dt = 0.1) {
double decay = std::exp(-free_energy);
double increment = decision * decay * dt;
return math::clamp(0.9 * psi_prev + 0.1 * increment + 0.5 * decision);
}
// T₇Ω: Ω = Φ·Ψ·C/(1+F)
inline double L7_to_Omega(double psi, double phi, double coherence, double free_energy) {
double numerator = phi * psi * coherence;Exact original notation
T₆₇: Ψ = ∫D·exp(-F)dt