test(pps): analyze loop stability and telemetry

soc/software/pps_end_to_end_validation/README.md

@@ -70,6 +70,48 @@ python3 -m pps_end_to_end_validation.pps_end_to_end \
   --trusted-output-delay-ns 35
 ```
 
+## Closed-loop stability and dynamic tuning
+
+The bit-level command above isolates the absolute epoch convention. The
+companion stability analysis connects that result to the fixed-point
+firmware/RTL PI model, replays the real GDOP and tracked-satellite history in
+`fusion/logs/gps_live_5min_20260713.csv`, and synthesizes only the telemetry
+that the repository did not capture:
+
+```bash
+python3 -m pps_end_to_end_validation.stability_analysis
+python3 -m unittest \
+  pps_end_to_end_validation/test_stability_analysis.py
+```
+
+Generated results are in `output/stability/`:
+
+- `stability_report.md`: real-data inventory, discrete poles, absolute phase
+  wander, period jitter, dynamic parameter sweep, and recommendations;
+- `parameter_sweep.csv`: machine-readable results for every scenario/tuning;
+- `synthetic_telemetry.csv`: 5 Hz ABS_SAMPLE, REM_CODE_PHASE, corrected 125 MHz
+  capture, HDOP/VDOP/TDOP/GDOP, C/N0, pseudorange noise, clock sigma/drift,
+  oscillator and timing-error inputs.
+
+The real capture contains 989 GDOP values and 990 tracked-satellite values
+(eight throughout), but no PPS phase/rate, ABS_SAMPLE, C/N0, TDOP/HDOP,
+pseudorange residual, oscillator temperature, or trusted-edge/TIC samples.
+The generated CSV labels its replacements as synthetic; it must not be read as
+board telemetry.
+
+The current acquire, precision, and robust fixed-point poles are inside the
+unit circle at the 200 ms update rate, and the stress analysis observes no
+unlock. It also exposes an important metrics issue: cycle-to-cycle PPS period
+jitter can remain below 20 ns while absolute phase moves slowly through tens
+of nanoseconds. A physical 20 ns maximum therefore requires a common-clock
+time-interval-counter capture and cable/output-delay calibration; a p95 period
+jitter assertion or synthetic run cannot certify it.
+
+The sweep includes the current coefficients, quieter/faster precision loops,
+a robust-noise guard, a larger Doppler-drift gain, and a quality-scheduled
+candidate. The generated report contains the current numerical comparison.
+No production constants are changed by the analysis.
+
 ## 20 ms diagnosis
 
 The current tracking wrapper shifts the current bit into `shift_reg_n`, while