# Geiger TRNG randomness analysis

**Generated:** 2026-05-08T15:26:42Z (duration 12.67 s)
**Git SHA:** 8217fa8cf3daa11ada10758a0388c9127b04a12e  ·  **Analysis version:** 1.0.0  ·  **Python:** 3.13.5

## Parameters

| Knob | Value |
|---|---|
| bits window | 65536 bytes (524,288 bits) |
| events window | 60.0 min |
| metrics window | 24.0 h |
| pile-up cutoff | 5000 µs |
| ACF max lag | 32 |

## Inputs

| Source | Loaded |
|---|---|
| `bits_stream.bin` (last N) | 65536 bytes |
| `events.csv` deltas | 46295 |
| `metrics.tsv` rows | 192 |
| `health.csv` rows | 1624 |
| `battery_history.tsv` rows | 3 |

---

## A · Source physics — inter-arrival distribution



The Geiger source is a Poisson process: the probability of an event in any
infinitesimal interval is constant. Inter-arrival times of a Poisson process
are exponentially distributed.

**Observed:**

| Statistic | Value |
|---|---|
| n deltas | 46,295 |
| mean Δt | 77762.0 µs |
| median Δt | 53718.9 µs |
| min Δt | 118.0 µs |
| max Δt | 805329 µs |
| estimated rate | 12.86 Hz (772 CPM) |

**Goodness-of-fit (Kolmogorov-Smirnov vs exponential):**
KS statistic = 0.0216,
p-value = 0.0000 →
**departs_from_poisson**

**Pile-up cluster** (Δt < 5000 µs, the GM tube + NE555 recovery floor):
3727 of 46,295
(8.05%).


![Inter-arrival log-log histogram](plots/interarrival_loglog.png)

*([interactive HTML](plots/interarrival_loglog.html))*



The pile-up cluster shows up as the spike below the cutoff line: events that
arrived faster than the recovery dynamics. These come from genuine random
arrivals binned by the dead-time floor:

![Pile-up cluster histogram](plots/pileup_cluster.png)

*([interactive HTML](plots/pileup_cluster.html))*




---

## B · Bit-level statistics



The Δt₁ vs Δt₂ disjoint-pair extractor emits 1 if Δt₁ > Δt₂, 0 otherwise.
With independent samples and constant dead time, the symmetry argument gives
unbiased output. With non-constant dead time (which we have — see Section A)
we filter by `--reject-us`.

| Statistic | Value | Target |
|---|---|---|
| n bits | 524,288 | – |
| ones | 261,960 (49.965%) | 50% |
| bias | -0.00035 | 0 |
| bias 1σ (sampling) | ±0.00069 | – |
| Shannon entropy | 7.9975 bits/byte | 8.0 |
| χ² statistic | 223.13 | ~255 (df) |
| χ² percentile | 92.57% | 5–95% |

**Autocorrelation** at lag 1..32 —
maximum |ρ| = 0.0023 at lag 13.


![Bit-stream autocorrelation](plots/bit_acf.png)

*([interactive HTML](plots/bit_acf.html))*



**Byte distribution** (0..255):

![Byte-value histogram](plots/byte_histogram.png)

*([interactive HTML](plots/byte_histogram.html))*



**Frequency-domain check.** A truly uniform bit stream has a flat power
spectrum (white noise). Any structural bias shows up as a peak.
Spectral flatness = 0.5601 (1.0 = perfectly flat):

![FFT power spectrum](plots/fft_power.png)

*([interactive HTML](plots/fft_power.html))*




---

## C · Drift over time (L2 rolling stats)



192 samples over the trailing 24.0 h
(2026-05-07T22:04:23Z → 2026-05-08T15:26:37Z).

| Metric | mean | std | first | last | min | max |
|---|---|---|---|---|---|---|
| bias | 0.0003 | 0.0054 | 0.0006 | -0.0023 | -0.0176 | 0.0137 |
| ent_bpb | 7.8112 | 0.0183 | 7.8281 | 7.8068 | 7.7617 | 7.8600 |
| chi_pct | 53.7063 | 30.2419 | 79.7700 | 71.8700 | 0.6500 | 99.9400 |
| lag1_bits | -0.0011 | 0.0119 | -0.0116 | 0.0099 | -0.0360 | 0.0249 |
| mean_dt_ms | 78.4165 | 2.8052 | 82.9800 | 77.8000 | 71.7000 | 86.2200 |
| lag1_dt | -0.0015 | 0.0318 | 0.0111 | -0.0028 | -0.0810 | 0.0906 |
| pileup_pct | 8.2270 | 1.9434 | 5.5700 | 6.6400 | 4.4900 | 15.8200 |



![Bias timeline](plots/bias_timeline.png)


![Entropy timeline](plots/entropy_timeline.png)


![χ² percentile timeline](plots/chi_timeline.png)


![Pile-up % timeline](plots/pileup_timeline.png)




---

## D · Health-test history (L1)



1624 rows in `health.csv`.


**Adaptive Proportion Test** — counts of bits matching the first bit of each
W=512 window. NIST cutoff: 310.

| | Observed | Theoretical |
|---|---|---|
| n verdicts | 1623 | – |
| n pass | 1623 | – |
| n fail | 0 | – |
| count mean | 256.41 | 256.00 |
| count std | 11.06 | 11.31 |


![APT count distribution vs Bin(W, 0.5)](plots/apt_distribution.png)



**RCT failures logged:** 0



---

## E · Battery history (L3)



3 runs from 2026-05-07T22:45:52Z to 2026-05-08T02:03:56Z.
**3 pass / 0 fail.** Current pass-streak: **3**.

| Metric | Value |
|---|---|
| ent mean | 7.9966 bits/byte |
| ent range | 7.9965 – 7.9967 |
| Rabbit pass-rate | 100.00% |
| Alphabit pass-rate | 100.00% |


![Daily battery history](plots/battery_history.png)


**Recent runs:**

| ts | ent | chi% | rabbit | alphabit | failures |
|---|---|---|---|---|---|
| 2026-05-07T22:45:52Z | 7.9965 | 6.38 | 1 | 1 | 0 |
| 2026-05-07T22:47:18Z | 7.9965 | 6.33 | 1 | 1 | 0 |
| 2026-05-08T02:03:56Z | 7.9967 | 3.99 | 1 | 1 | 0 |




---

## Notes

- Static PNGs in `plots/` (rendered inline above) are produced via matplotlib.
- Interactive Plotly charts live alongside as `plots/*.html` (linked under
  Section A/B; for Section C/D/E open them directly from a clone).
- Source data slices used for this run are in `raw/` (if `keep_raw=True`).
- Numeric values are also available machine-readable in `stats.json`.
- This report is generated by `analysis/runner.py` v1.0.0.