GSRF Practical does not smooth the raw level with a linear IIR. It maintains an internal state in log-space, updates that state, then maps back with exp.
Why log-space
- Positive industrial / physiological magnitudes behave more multiplicatively
- Observation errors are bounded with tanh in log domain
- The spring to x* is a soft setpoint in the same space
Hard constraints for users
- Positive signals only (snippet clamps with epsilon)
- Set x* from a calm prefix (median log) or adapt it when regimes truly move
- Not a drop-in for bipolar AC with zero crossings without redesign
Public formula (identity, not full production pack)
update ≈ baseline + k_return·(−(x − x*)) + mem·tanh(Δx) + w_obs·tanh(x_obs − x)
output = exp(x)
output = exp(x)
Verdict
Log-space + spring is the product identity. Full runnable loop: /try. Theory narrative: What GSRF really is.
Sources: public Practical identity · try snippet · WHAT_GSRF_REALLY_IS_MASTER