# Geiger TRNG randomness analysis

**Generated:** 2026-05-13T03:03:14Z (duration 9.99 s)
**Git SHA:** 3945e338141f3380a46fa43bae35ef367c7b2fab  ·  **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 | 47405 |
| `metrics.tsv` rows | 262 |
| `health.csv` rows | 6097 |
| `battery_history.tsv` rows | 8 |

---

## 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 | 47,405 |
| mean Δt | 75939.9 µs |
| median Δt | 52045.5 µs |
| min Δt | 21.9 µs |
| max Δt | 808332 µs |
| estimated rate | 13.17 Hz (790 CPM) |

**Goodness-of-fit (Kolmogorov-Smirnov vs exponential):**
KS statistic = 0.0307,
p-value = 0.0000 →
**departs_from_poisson**

**Pile-up cluster** (Δt < 5000 µs, the GM tube + NE555 recovery floor):
4215 of 47,405
(8.89%).


![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 | 261,933 (49.960%) | 50% |
| bias | -0.00040 | 0 |
| bias 1σ (sampling) | ±0.00069 | – |
| Shannon entropy | 7.9971 bits/byte | 8.0 |
| χ² statistic | 265.02 | ~255 (df) |
| χ² percentile | 32.00% | 5–95% |

**Autocorrelation** at lag 1..32 —
maximum |ρ| = 0.0035 at lag 18.


![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 = 0.5622 (1.0 = perfectly flat):

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

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




---

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



262 samples over the trailing 24.0 h
(2026-05-12T03:05:23Z → 2026-05-13T03:00:53Z).

| Metric | mean | std | first | last | min | max |
|---|---|---|---|---|---|---|
| bias | -0.0004 | 0.0048 | 0.0028 | -0.0059 | -0.0110 | 0.0106 |
| ent_bpb | 7.8068 | 0.0167 | 7.7996 | 7.8071 | 7.7394 | 7.8501 |
| chi_pct | 47.4379 | 29.3227 | 41.8500 | 51.4800 | 0.0600 | 99.1200 |
| lag1_bits | -0.0002 | 0.0113 | 0.0045 | 0.0146 | -0.0397 | 0.0272 |
| mean_dt_ms | 75.5145 | 2.3603 | 73.7600 | 73.2600 | 69.1900 | 82.2200 |
| lag1_dt | 0.0001 | 0.0319 | -0.0279 | -0.0724 | -0.0858 | 0.0917 |
| pileup_pct | 9.3434 | 1.0347 | 7.6200 | 10.4500 | 5.6600 | 11.6200 |



![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)



6097 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 | 6095 | – |
| n pass | 6095 | – |
| n fail | 0 | – |
| count mean | 256.33 | 256.00 |
| count std | 11.13 | 11.31 |


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



**RCT failures logged:** 1



---

## E · Battery history (L3)



8 runs from 2026-05-07T22:45:52Z to 2026-05-13T02:00:26Z.
**8 pass / 0 fail.** Current pass-streak: **8**.

| Metric | Value |
|---|---|
| ent mean | 7.9970 bits/byte |
| ent range | 7.9965 – 7.9977 |
| 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 |
|---|---|---|---|---|---|
| 2026-05-09T02:04:26Z | 7.9977 | 99.11 | 1 | 1 | 0 |
| 2026-05-10T02:03:30Z | 7.9971 | 31.76 | 1 | 1 | 0 |
| 2026-05-11T02:04:26Z | 7.9973 | 64.23 | 1 | 1 | 0 |
| 2026-05-12T02:00:31Z | 7.9969 | 15.79 | 1 | 1 | 0 |
| 2026-05-13T02:00:26Z | 7.9972 | 51.96 | 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.