docs(monitor): the firing-rate channel cannot be calibrated, and here is why

[mspinola]

"An arrival-process test would give it a stated false-alarm rate" sat at the top of docs/edge_monitor.md's open list from the day the monitor shipped, resting on the claim that trade arrivals are approximately Poisson. Building it showed the claim is false. It is removed rather than softened, and the measurements are recorded so nobody builds it twice.

The prize was real, and worth stating: a count-based detector spots a halved firing rate in 0.6 years against 5.1 for the expectancy CUSUM — about eight times faster, on the failure the other two channels cannot see.

Arrivals are not Poisson

Dispersion index 3.43 against Poisson's 1.0. Roughly 40% is a secular trend (+0.49 trades/yr per year, r=+0.63); the rest is sub-annual clustering, with lag-1 autocorrelation of detrended annual counts at +0.04.

Three detectors, each designed for a 10-year budget, measured against the book's own arrivals:

Detector	Delivered	vs stated
exponential CUSUM on gaps, full span	3.6 yr	0.36x
...7-year window	3.5 yr	0.35x
...5-year window	1.8 yr	0.18x
Poisson CUSUM on monthly counts	3.2 yr	0.32x

All fire 3x to 5x more often than stated, and in the dangerous direction: the expectancy CUSUM's 1.39x skew inflation buys margin, this spends it.

Two of my hypotheses failed, and both are recorded

• "A recent window restores the Poisson model." Annual-count dispersion does fall to 0.68 at 7 years, but a CUSUM runs on individual gaps, not annual counts, and those stay non-exponential at every window. Coarse and fine scale came apart, and the 5-year window is the worst of the four.
• "Then calibrate h empirically." The honest fallback, and it fixes the centre: h moves 4.26 → 6.22. But bootstrapping the calibration, h ranges 4.15–8.18 and the delivered budget ranges 5.3 to 77.9 years. A stated 10-year rate that is truly somewhere in 5–78 is not a stated rate.

Root cause is data, not model

34 trades/yr gives 82 monthly periods in a 7-year window, and run length depends on a tail that 82 samples cannot pin down. The gap detector is worse: crossing its boundary needs two or three of the largest gaps back to back, so it is a rare-combination test over the tail of a 233-gap sample, and its ARL curve is visibly stepped as a result.

So the channel keeps its ratio rule and its SLIPPING cap. An uncalibrated rule that says so beats a calibrated-looking one wrong by 3x, and manufacturing a stated rate to satisfy "only calibrated detectors may escalate" would defeat the rule it was meant to satisfy.

Reproducer

tests/test_frequency_calibration.py pins the general claims synthetically — 80 periods leave an 8.6x spread in the delivered budget where 2,000 leave 1.3x — so the limit is re-derivable without the private book. It also asserts the DEGRADED path still runs only through the calibrated CUSUM, and points a future reader at the measurements if they change it.

390 tests pass, ruff clean, mkdocs build --strict clean.

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