One-line identity
GSRF Practical is a nonlinear, log-domain soft-servo to a declared normal \(x^*\). It maintains an internal log-state, gently trusts observations through \(\tanh\), and is always spring-pulled toward \(x^*\) by \(k_{\mathrm{return}}\).
That makes it:
- Not a linear low-pass (EMA / MA family)
- Not an unbiased tracker of permanent level shifts
- Yes a bounded-belief stabilizer that compresses peaks and mid-band ring toward “normal”
GSRF Reference is the open-loop twin: same spring/memory, almost no observation use— hugs \(x^*\) and can look “best” on oscillation metrics by flatlining. Not a usable live tracker.
Soft setpoint experiment (wrong \(x^*\))
Bias the declared normal and the mean output follows the wrong setpoint. That is the thermostat, not a passive smoother centre:
| \(x^*\) bias | Mean of GSRF output | Offset from true base 50 |
|---|---|---|
| −30% | 39.9 | −10.1 |
| 0% | 50.0 | ~0 |
| +30% | 58.9 | +8.9 |
| +50% | 64.5 | +14.5 |
\(x^*\) is a soft operating setpoint. Choose it carefully (calm prefix median log, or adaptive trailing median).
Step response = attractor leak
Step 50 → 65 at t=100 with \(x^*=\log 50\) (frozen):
| Method | t=110 | t=200 | t=400 |
|---|---|---|---|
| EMA_low | 60.3 | 65.0 | 65.0 |
| GSRF k_return=0 | 63.4 | 65.0 | 65.0 |
| GSRF Practical | 55.1 | 55.1 | 55.1 |
| GSRF Reference | 50.0 | 50.0 | 50.0 |
Balanced GSRF stops halfway and stays—equilibrium between observation pull and spring. That halfway settle is peak compression. It is also why MAD-to-raw loses. Chart: Evidence · Identity.
What it excels at (and does not)
From excellence hunt v2 + mechanism ablations (pre-declared rules):
- Excels: mid-band oscillation energy (e.g. ~+35% osc31 on phase6.2); peak-dev compression (~38% mean, 49/52 wins)
- Does not excel: tracking MAD (0/52), residual PR-AUC as a detector, delayed plant command smoothing
- Mechanism: \(k_{\mathrm{return}}\) is the soul—turn it off and you get a tracker and lose the niche
Verdict
Use GSRF when the costly failure is ring and spike chase around a known normal. Use EMA/Kalman when the costly failure is lagging the truth. Read When GSRF lost before productizing.
Sources: WHAT_GSRF_REALLY_IS_MASTER.md · EXCELLENCE_FINDING_20260804.md · characterization v4 · mechanism v3 · /evidence