A continuous normalized-coprime-factor margin estimate with authority-aware quiet-band inference and a two-second response envelope.
The coherent and quiet-band terms answer different observability questions. The first measures the loop where the command excites it. The second fits the output-spectrum shape where the command has little leverage. Weak command activity blends the result to the finite NCF ceiling, preventing displacement feedthrough from becoming false loop evidence.
A 0.5 s sliding DFT is exponentially averaged. Coherence and input power continuously shrink uncertain bins toward the current-authority nominal model; there is no valid/invalid gate.
A scalar loop-gain multiplier is fitted from spectral shape, so unknown noise intensity cancels. Coherent driven-band gain continuously weights this fit: a healthy low-band record stays at ρ = 1, while real damage releases the hazard-band estimate.
One log-integral law handles shedding and recovery. The same observability weight scales its guard and deadband; a 4× rolling prediction horizon accelerates recovery without a deep-shed extrapolation to full authority. There are no latches, counters, cooldowns, or separate recovery mode.
NCF cap: this study retains FABLE’s imposed reporting cap of 1/√2 for direct comparison. It is a software convention, not the intrinsic maximum of the chordal expression, which can reach 1.
Choose a canonical case or the experimental GDBqFpKb replay. Scroll over either plot to zoom in time, drag to pan, and double-click to reset. Both panels share the same time window.
| Requirement | Measured | Limit | Result |
|---|
| Case | FABLE | GPT | GPT warm-up | GPT response | GPT recovery |
|---|
The algorithm exposes structural limits and four meaningful performance values. Frequency bands and the 1/√2 comparison cap describe the experiment; they are not behavioral gates.
| Value | Role | Selected |
|---|---|---|
segment_s | Recent-data span and frequency resolution. | 0.50 s |
memory_s | Exponential spectral memory; determines change detection speed. | 0.35 s |
margin_s | Final continuous margin smoothing. | 0.20 s |
residual_s | Memory of the quiet-band gain fit. | 1.50 s |
warm_s | Finite nominal-prior warm-up. | 2.00 s |
target / guard | Required NCF level and base observability standoff. | 0.55 / 0.020 |
deadband / rate | Base NCF noise band and log-authority gain. | 0.008 / 5.0 |
Results(:,21) is a diagnostic loop-gain multiplier, not an authority command. GPT OSI never receives it; the replay uses only u_osi, dm, and the logged authority that actually acted on the plant. The replay uses the same canonical 0.55 target and default authority law as the ten-case suite.
Because this is an open-loop replay, the plotted diagnostic-gain inverse is context only—not a true authority or acceptance reference. Acceptance checks continuous output, idle behavior before the earthquake, deficit detection at earthquake onset and both destabilizing edges, then post-quiet recovery. Logged FABLE traces remain context only.