Read the equation
The helper first forms r=ΦΨC/(1+F), then returns a clipped cubic r²(3−2r). The cubic is smoothstep and is monotone from zero to one only on r∈[0,1]. The ratio requires F≠−1, and interpreting the result needs the ranges of its component scores.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| Phi | Unity score |
| Psi | Accumulated state |
| C | Coherence-labelled score |
| F | Free-energy-labelled input |
| Omega | Post-transformed output |
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
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;
double denominator = 1.0 + free_energy;
double omega_raw = numerator / denominator;
// Logistic attractor for stability
return math::clamp(omega_raw * omega_raw * (3.0 - 2.0 * omega_raw));
}
}
/**Exact original notation
T₇Ω: Ω = Φ·Ψ·C/(1+F)