# Geiger TRNG randomness analysis

**Generated:** 2026-05-28T15:57:56Z (duration 11.84 s)
**Git SHA:** ddc908188f687667118ff13ab82554c02e68c783  ·  **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 | 185 |
| `metrics.tsv` rows | 191 |
| `health.csv` rows | 15372 |
| `battery_history.tsv` rows | 38 |

---

## 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 | 185 |
| mean Δt | 101983.6 µs |
| median Δt | 69173.7 µs |
| min Δt | 539.0 µs |
| max Δt | 570258 µs |
| estimated rate | 9.81 Hz (588 CPM) |

**Goodness-of-fit (Kolmogorov-Smirnov vs exponential):**
KS statistic = 0.0297,
p-value = 0.9952 →
**consistent_with_poisson**

**Pile-up cluster** (Δt < 5000 µs, the GM tube + NE555 recovery floor):
9 of 185
(4.86%).


![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 | 261,913 (49.956%) | 50% |
| bias | -0.00044 | 0 |
| bias 1σ (sampling) | ±0.00069 | – |
| Shannon entropy | 7.9973 bits/byte | 8.0 |
| χ² statistic | 243.59 | ~255 (df) |
| χ² percentile | 68.56% | 5–95% |

**Autocorrelation** at lag 1..32 —
maximum |ρ| = 0.0036 at lag 14.


![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 = 0.5613 (1.0 = perfectly flat):

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

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




---

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



191 samples over the trailing 24.0 h
(2026-05-27T22:21:19Z → 2026-05-28T15:57:52Z).

| Metric | mean | std | first | last | min | max |
|---|---|---|---|---|---|---|
| bias | 0.0009 | 0.0051 | 0.0060 | -0.0049 | -0.0161 | 0.0122 |
| ent_bpb | 7.8122 | 0.0180 | 7.8037 | 7.8272 | 7.7723 | 7.8640 |
| chi_pct | 55.6157 | 30.9120 | 18.0400 | 88.2400 | 0.7700 | 99.9800 |
| lag1_bits | 0.0005 | 0.0103 | -0.0193 | 0.0093 | -0.0335 | 0.0225 |
| mean_dt_ms | -1361.9146 | 13026.3493 | -159951.1000 | -59936.1400 | -159951.1000 | 113.9400 |
| lag1_dt | -0.0003 | 0.0321 | -0.0010 | -0.0010 | -0.0706 | 0.0920 |
| pileup_pct | 4.4790 | 0.7129 | 4.6900 | 3.9100 | 3.1200 | 9.7700 |



![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)



15372 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 | 15366 | – |
| n pass | 15366 | – |
| n fail | 0 | – |
| count mean | 256.61 | 256.00 |
| count std | 11.31 | 11.31 |


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



**RCT failures logged:** 5



---

## E · Battery history (L3)



38 runs from 2026-05-07T22:45:52Z to 2026-04-30T22:49:08Z.
**29 pass / 9 fail.** Current pass-streak: **0**.

| Metric | Value |
|---|---|
| ent mean | 7.9971 bits/byte |
| ent range | 7.9965 – 7.9977 |
| Rabbit pass-rate | 84.21% |
| Alphabit pass-rate | 86.84% |


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


**Recent runs:**

| ts | ent | chi% | rabbit | alphabit | failures |
|---|---|---|---|---|---|
| 2026-04-30T22:49:08Z | 7.9974 | 79.33 | 1 | 1 | 0 |
| 2026-05-27T22:22:58Z | 7.9974 | 80.66 | 1 | 1 | 0 |
| 2026-05-28T02:04:11Z | 7.9975 | 87.56 | 1 | 1 | 0 |
| 2026-04-30T22:49:08Z | 7.9973 | 70.06 | 1 | 1 | 1 |
| 2026-04-30T22:49:08Z | 7.9973 | 69.24 | 1 | 1 | 1 |




---

## F · NIST SP 800-22 STS subset



A subset of the NIST SP 800-22 Statistical Test Suite, computed
directly from the loaded bit window (524,288
bits). The decision rule is **pass if p ≥ α**, with α = 0.01
(the canonical NIST threshold).

**Summary:** 3 pass / 1 fail.
**Overall: FAIL.**

| Test | p-value | Verdict | Detail |
|---|---|---|---|
| Frequency (monobit) | 0.5234 | pass | S_n = -462 |
| Block Frequency | 0.0014 | **fail** | M=128, N=4096, χ²=4372.84 |
| Runs | 0.3946 | pass | V_n = 262452 (expected 262144) |
| Longest Run of 1s | 0.4407 | pass | M=128, N=49, χ²=4.80 |


![NIST STS subset p-values](plots/nist_pvalues.png)

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


The four tests cover progressively finer structure:
- **Frequency** — global 0/1 balance.
- **Block Frequency** — per-block balance (catches local drift).
- **Runs** — bit-flip frequency vs the random expectation.
- **Longest Run of 1s** — local clustering, sensitive to dead-time
  artefacts the others miss.

With our default 64 KB load (≈ 524 K bits), Longest Run runs in the
NIST M=128 / N=49 regime. To activate the larger M=10,000 / N=75
regime, run an ad-hoc analysis with `--bits-window-bytes 131072`
(≥ 1 M bits) once `bits_stream.bin` is big enough.



---

## 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.