Read the equation
Blends the old state with the change signal using a golden-ratio-derived coefficient. With φ=(1+√5)/2, ρ is about 0.382 and the retained fraction is about 0.618.
Its role in the build
Blends the old state with the change signal using a golden-ratio-derived coefficient.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | current scalar family state |
| dx | change signal |
| d_x / dx_norm | normalized change signal |
| u / utility | utility input |
| e / err | error input |
| s / stab | stability input |
| φ | golden-ratio constant |
How it works
Read (1-ρ)x + ρ×dx [ρ as the quantity being defined or updated by this relation.
Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
Conditions
The surrounding implementation must define the input scales and any output clipping.
It is a leaky integrator; the field interpretation requires an explicit spatial/state model.
Original context
Exact original notation
(1-ρ)x + ρ×dx [ρ=1/(1+φ)]
Related builds
Sources & provenance
(1-ρ)x + ρ×dx [ρ=1/(1+φ)]