Instrument · one metronome, nine listeners

The rate ladder.

Our transmitter is a metronome: it sends the same short frame at a fixed rate, and every receiver counts the frames that arrive. Speed the metronome up and at some rate the receivers start to miss beats. A rate ladder finds that rate by stepping through it, up and back down, while everything else in the room stays as it was.

In plain words Imagine a metronome in a hall and nine people counting its beats. Speed it up and at some point they start to miss beats; fill the hall with other conversations and they miss more. The fleet runs exactly that: the transmitter steps through a ladder of rates while every receiver counts what arrives.

Episodes Corpus

Declared step rates from the fleet inventory (infra/ansible/inventory/group_vars/csi_nodes.yml); the illuminator's own step sessions and the receivers' reduced minutes from the measurement lake, snapshot 148375 (2026-09-11T10:23+00:00). The reduction that scopes a minute's frame count to our transmitter is reduction schema 4.

Why it matters

Every statistic behind the headcount is computed over the frames that arrive. The Doppler band needs at least thirty frames in a quarter of a second, which is 120 frames a second, and the envelope shares that floor. If the room cannot deliver 120 frames a second, the instrument goes blind before the room goes quiet, and a busy day, with more radios competing for the same channel, may take the floor away exactly when there is most to see. The ladder measures where that happens.

The fleet has run 18 ladders on 3 channels (6, 11, 48): 12 at night and 6 by day, 197 illuminator steps in all. 5 of them have their receivers' minutes reduced, 1140 minutes in all.

§1

What a ladder is

One node is the illuminator. For five minutes it sends 25 frames a second; then 50; then 100, 250 and 500; then back down the same rungs. Each rung is its own capture session on the illuminator, so its start and end are recorded to the second, and the illuminator counts what it sent. The other nodes run one continuous session across all ten rungs, so every rung is judged by the same receivers in the same hour.

sent rate = frames the illuminator reports sent ÷ the rung's seconds (should equal the commanded rate)

Fig. 1 · the staircase · lib-doppler-ladder-2026-09-09-04ch 48 · 2026-09-09 · day

The rungs of this ladder in order. "Commanded" is the rate the inventory declares for the step's profile; "sent" is the illuminator's own count divided by the step's seconds. "Skipped" is the number of frames csid could not send at the cadence.
Step	Profile	Commanded (Hz)	From	To	Seconds	Sent	Sent (Hz)
1	`illum-dop48-250`	250	07:08	07:11	183	45,018	246.0
2	`illum-dop48-090`	90	07:14	07:17	183	16,208	88.6
3	`illum-dop48-045`	45	07:21	07:24	184	8,104	44.0
4	`illum-dop48-090`	90	07:28	07:30	116	10,117	87.2
5	`illum-dop48-250`	250	07:31	07:34	183	45,021	246.0

The commanded rate as a staircase over the ladder's hour, with the illuminator's own sent rate as a dot on each tread. Where the receivers' minutes exist they are drawn as faint marks under the staircase, one per receiver-minute, so a tread and what arrived on it sit on one clock. Hover a tread for its numbers.steps: sessions rows of the illuminator's profiles · commanded: infra/ansible/inventory/group_vars/csi_nodes.yml

§2

What arrives

If every frame reached every receiver, a plot of delivered rate against commanded rate would be a straight line at 45 degrees. The interesting shape is where it bends: the rate above which sending faster no longer delivers faster. Wi-Fi radios share a channel by listening before they talk, so on a busy channel the illuminator itself has to wait its turn, and a receiver can also drop frames it heard but could not process. Both look like a miss. This figure shows the bend per receiver, night ladders and day ladders on one axis, so the two hours can be compared without a percentage in between.

delivered rate at a receiver = our frames it reported in the minute ÷ the minute's seconds

Fig. 2 · delivered against commanded · channel 48night ladders 1 · day ladders 5

Per period, commanded rate and receiver: the minutes inside the rung across every ladder, the median delivered rate and its 10th to 90th percentile. Hertz against hertz.
Period	Commanded (Hz)	Receiver	Minutes	Delivered median (Hz)	p10	p90	Ladders
day	25	monad01	1	24.7	24.7	24.7	1
day	25	monad02	1	24.5	24.5	24.5	1
day	25	monad03	2	13.5	4.5	22.5	1
day	25	monad04	2	9.8	2.1	17.5	1
day	25	monad05	1	24.8	24.8	24.8	1
day	25	monad06	2	7.8	1.6	14.0	1
day	25	monad07	2	12.5	2.5	22.4	1
day	25	monad08	2	15.2	14.9	15.4	1
day	25	monad10	1	24.5	24.5	24.5	1
day	45	monad01	2	44.8	44.7	44.8	1
day	45	monad02	2	44.5	44.5	44.5	1
day	45	monad03	2	44.8	44.7	44.9	1
day	45	monad04	2	44.8	44.7	44.9	1
day	45	monad05	2	43.1	42.7	43.5	1
day	45	monad06	2	44.5	44.4	44.5	1
day	45	monad07	2	44.7	44.5	44.8	1
day	45	monad08	2	43.9	43.2	44.5	1
day	45	monad10	2	44.5	44.5	44.5	1
day	50	monad01	5	49.5	29.2	49.6	1
day	50	monad02	5	48.1	16.4	48.8	1
day	50	monad03	5	49.3	29.0	49.5	1
day	50	monad04	5	49.2	29.0	49.3	1
day	50	monad05	5	49.3	29.4	49.5	1
day	50	monad06	5	48.2	28.5	48.7	1
day	50	monad07	5	49.8	48.4	49.9	1
day	50	monad08	5	48.9	28.4	49.2	1
day	50	monad10	5	47.8	28.4	48.7	1
day	90	monad01	3	88.0	86.4	88.8	1
day	90	monad02	3	85.7	85.5	86.7	1
day	90	monad03	3	90.0	89.6	90.0	1
day	90	monad04	3	89.8	89.6	89.8	1
day	90	monad05	3	88.9	88.7	89.0	1
day	90	monad06	3	88.0	86.1	88.6	1
day	90	monad07	3	89.9	89.6	90.0	1
day	90	monad08	3	88.5	88.3	88.5	1
day	90	monad10	3	86.5	85.6	86.5	1
day	100	monad01	9	98.9	68.5	99.8	1
day	100	monad02	9	96.4	48.5	97.2	1
day	100	monad03	9	98.6	68.5	99.7	1
day	100	monad04	8	98.6	94.2	99.0	1
day	100	monad05	9	98.3	68.5	99.5	1
day	100	monad06	9	97.0	66.7	97.9	1
day	100	monad07	9	99.2	78.8	99.8	1
day	100	monad08	9	97.5	64.9	98.7	1
day	100	monad10	9	97.1	67.4	97.8	1
day	250	monad01	11	247.3	170.1	248.6	2
day	250	monad02	10	241.0	112.8	245.9	2
day	250	monad03	11	246.0	133.4	250.0	2
day	250	monad04	11	247.3	113.5	249.9	2
day	250	monad05	10	247.4	234.6	248.1	2
day	250	monad06	11	246.1	103.9	248.4	2
day	250	monad07	11	247.9	239.1	249.7	2
day	250	monad08	10	228.2	36.2	248.5	2
day	250	monad10	10	236.4	87.1	245.4	2
day	500	monad01	9	496.5	164.7	498.3	1
day	500	monad02	9	485.0	86.0	488.9	1
day	500	monad03	9	496.3	118.5	498.0	1
day	500	monad04	9	494.4	149.8	496.3	1
day	500	monad05	9	494.8	126.7	496.9	1
day	500	monad06	9	488.8	145.1	491.9	1
day	500	monad07	9	497.4	378.9	498.7	1
day	500	monad08	9	489.6	105.3	493.6	1
day	500	monad10	9	485.2	134.4	490.3	1

Delivered against commanded, one line per receiver, solid for night ladders and dashed for day ladders, with the 45-degree line drawn as the ceiling. The band around each fleet point is the 10th to 90th percentile of its minutes. A day line that lies on the night line says the bend belongs to the radios; a day line below it at the same commanded rate says the building's traffic took the difference.Delivered rate is our injector's frames the receiver actually reported in that minute, divided by the minute's seconds: hertz against hertz, never a percentage. The reduction scopes the count to the injector's own address, so ambient traffic on the channel is not in it. A minute counts toward a step only when it lies wholly inside that step's window.

§3

When only the rate moved

The ladder is also a test of the statistics themselves. The room was the same on every rung, so any change in the envelope or the Doppler band between rungs is the instrument responding to its own frame rate, not to a person. A statistic that drifts with the rate has to be read against the rate it was measured at, and the 120 frames a second floor is where both go silent: below it a quarter-second window holds fewer than thirty frames and the reduction refuses to score it.

Fig. 3 · envelope and Doppler by rung · channel 48medians over the rung's minutes

Per period, commanded rate and receiver: the median injector-scoped envelope (dB) and Doppler-band power over the rung's minutes. A dash is a rung whose minutes the reduction could not score.
Period	Commanded (Hz)	Receiver	Minutes	Envelope median (dB)	Doppler 20–60 Hz median
day	25	monad01	1	0.03	—
day	25	monad02	1	0.07	—
day	25	monad03	2	0.06	—
day	25	monad04	2	0.04	—
day	25	monad05	1	0.03	—
day	25	monad06	2	0.07	—
day	25	monad07	2	0.04	—
day	25	monad08	2	0.05	—
day	25	monad10	1	0.07	—
day	45	monad01	2	0.07	—
day	45	monad02	2	0.05	—
day	45	monad03	2	0.06	—
day	45	monad04	2	0.06	—
day	45	monad05	2	0.04	—
day	45	monad06	2	0.05	—
day	45	monad07	2	0.04	—
day	45	monad08	2	0.05	—
day	45	monad10	2	0.05	—
day	50	monad01	5	0.03	—
day	50	monad02	5	0.07	—
day	50	monad03	5	0.07	—
day	50	monad04	5	0.04	—
day	50	monad05	5	0.04	—
day	50	monad06	5	0.06	—
day	50	monad07	5	0.06	—
day	50	monad08	5	0.05	—
day	50	monad10	5	0.08	—
day	90	monad01	3	0.07	—
day	90	monad02	3	0.05	—
day	90	monad03	3	0.06	—
day	90	monad04	3	0.06	—
day	90	monad05	3	0.04	—
day	90	monad06	3	0.05	—
day	90	monad07	3	0.04	—
day	90	monad08	3	0.05	—
day	90	monad10	3	0.05	—
day	100	monad01	9	0.03	—
day	100	monad02	9	0.07	—
day	100	monad03	9	0.07	—
day	100	monad04	8	0.04	—
day	100	monad05	9	0.04	—
day	100	monad06	9	0.06	—
day	100	monad07	9	0.06	—
day	100	monad08	9	0.05	—
day	100	monad10	9	0.07	—
day	250	monad01	11	0.03	0.0033
day	250	monad02	10	0.07	0.0005
day	250	monad03	11	0.07	0.0018
day	250	monad04	11	0.04	0.0068
day	250	monad05	10	0.04	0.0021
day	250	monad06	11	0.06	0.0057
day	250	monad07	11	0.06	0.0026
day	250	monad08	10	0.05	0.0010
day	250	monad10	10	0.07	0.0022
day	500	monad01	9	0.03	0.0018
day	500	monad02	9	0.07	0.0004
day	500	monad03	9	0.07	0.0014
day	500	monad04	9	0.04	0.0033
day	500	monad05	9	0.04	0.0011
day	500	monad06	9	0.06	0.0029
day	500	monad07	9	0.06	0.0017
day	500	monad08	9	0.05	0.0005
day	500	monad10	9	0.08	0.0015

The same rungs and receivers as Fig. 2, with the envelope or the Doppler-band power on the vertical axis (switch above the figure). A flat line across rungs means the statistic does not care how fast the metronome ticks, which is what a good occupancy statistic should do above the floor.inj_ratio_amp_sd_db and inj_doppler_pw_20_60 from the lake's blocks at reduction schema 4

§4

Every ladder the fleet has run

A ladder is listed the moment the lake holds its sessions, whether or not its minutes are reduced. Night and day are the library's clock, 22:00 to 04:00 being night. A ladder with fewer than ten steps lost steps to a timer that did not fire, or is still running when the snapshot was taken.

Every ladder in the snapshot, newest first. "Reduced" is the number of receiver-minutes the lake has scored inside this ladder's rungs; zero means decoded to the frame and not yet reduced. Pick a row to draw its staircase in §1.
Day	Start	Period	Ch	Run	Steps	Rates (Hz)	Receivers	Reduced	Steps with skips
2026-09-09	07:08	day	48	`lib-doppler-ladder-2026-09-09-04`	5	250·90·45	9	61 on 9	0
2026-09-05	21:37	night	6	`lib-rate-ladder-6-2026-09-05-02`	8	50·100·250·500·25	9	165 on 9	0
2026-09-04	08:19	day	48	`lib-rate-ladder-48-day-2026-09-04-09`	10	25·50·100·250·500	9	299 on 9	0
2026-09-02	07:04	day	48	`lib-rate-ladder-48-day-2026-09-02-07`	9	25·50·100·250·500	9	0	0
2026-09-02	23:54	night	6	`lib-rate-ladder-6-2026-09-01-04`	10	25·50·100·250·500	9	303 on 9	1
2026-09-01	20:04	night	11	`lib-rate-ladder-24-2026-09-01-02`	10	25·50·100·250·500	9	312 on 9	1
2026-08-31	01:09	night	6	`lib-rate-ladder-6-2026-08-30-05`	3	25·50·100	9	0	1
2026-08-31	23:53	night	11	`lib-rate-ladder-24-2026-08-30-04`	10	25·50·100·250·500	9	0	0
2026-08-30	20:03	night	48	`lib-rate-ladder-48-2026-08-30-02`	10	25·50·100·250·500	9	0	0
2026-08-26	21:12	night	11	`lib-rate-ladder-24-2026-08-26-02`	10	25·50·100·250·500	9	0	1
2026-08-26	20:03	night	6	`lib-rate-ladder-6-2026-08-26-01`	10	25·50·100·250·500	9	0	0
2026-08-26	00:13	night	11	`lib-rate-ladder-24-2026-08-25-03`	10	25·50·100·250·500	9	0	0
2026-08-26	23:03	night	6	`lib-rate-ladder-6-2026-08-25-02`	10	25·50·100·250·500	9	0	0
2026-08-25	23:53	night	11	`lib-rate-ladder-24-2026-08-24-03`	10	25·50·100·250·500	9	0	1
2026-08-25	22:43	night	6	`lib-rate-ladder-6-2026-08-24-02`	10	25·50·100·250·500	9	0	0
2026-08-23	03:06	day	48	`lib-rate-ladder-48-2026-08-22-02`	10	25·50·100·250·500	8	0	0
2026-08-20	19:56	day	48	`rate-ladder-48-01`	41	25·50·100·250·500	9	0	0
2026-08-16	06:58	day	11	`monad01-ch11-20260816-0858`	11	5·10·25·50·100	5	0	0

Scope of inference. One ladder is one draw of the channel: its ten steps are paired on the same hour, room and roster, so a step against a step is measured, instrument only. A night ladder against a day ladder holds everything fixed but the hour and the people in the building, which is the contrast the day arm was added for. Two ladders on two different days are observed, not measured.