# Geiger TRNG randomness analysis

**Generated:** 2026-06-24T03:14:23Z (duration 12.04 s)
**Git SHA:** 0873c6a5a76187fa7ab1ce2b4401eba913efca58  ·  **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 | 144 |
| `metrics.tsv` rows | 263 |
| `health.csv` rows | 3196 |
| `battery_history.tsv` rows | 93 |

---

## 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 | 144 |
| mean Δt | 90311.7 µs |
| median Δt | 64845.8 µs |
| min Δt | 1282.2 µs |
| max Δt | 553130 µs |
| estimated rate | 11.07 Hz (664 CPM) |

**Goodness-of-fit (Kolmogorov-Smirnov vs exponential):**
KS statistic = 0.0891,
p-value = 0.1917 →
**consistent_with_poisson**

**Pile-up cluster** (Δt < 5000 µs, the GM tube + NE555 recovery floor):
3 of 144
(2.08%).


![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 | 261,644 (49.905%) | 50% |
| bias | -0.00095 | 0 |
| bias 1σ (sampling) | ±0.00069 | – |
| Shannon entropy | 7.9971 bits/byte | 8.0 |
| χ² statistic | 266.59 | ~255 (df) |
| χ² percentile | 29.63% | 5–95% |

**Autocorrelation** at lag 1..32 —
maximum |ρ| = 0.0040 at lag 17.


![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 = 0.5624 (1.0 = perfectly flat):

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

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




---

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



263 samples over the trailing 24.0 h
(2026-06-23T03:17:20Z → 2026-06-24T03:14:18Z).

| Metric | mean | std | first | last | min | max |
|---|---|---|---|---|---|---|
| bias | -0.0007 | 0.0057 | 0.0050 | 0.0010 | -0.0199 | 0.0140 |
| ent_bpb | 7.8064 | 0.0169 | 7.7900 | 7.7822 | 7.7535 | 7.8531 |
| chi_pct | 44.9778 | 28.7467 | 6.2600 | 3.4700 | 0.0100 | 99.5400 |
| lag1_bits | -0.0005 | 0.0105 | -0.0063 | 0.0079 | -0.0294 | 0.0242 |
| mean_dt_ms | -978.6338 | 17481.2618 | 106.6800 | -283937.5700 | -283937.5700 | 111.5100 |
| lag1_dt | 0.0009 | 0.0324 | -0.0295 | -0.0010 | -0.0848 | 0.0976 |
| pileup_pct | 4.7522 | 0.6723 | 5.3700 | 4.9800 | 2.9300 | 6.4500 |



![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)



3196 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 | 3194 | – |
| n pass | 3194 | – |
| n fail | 0 | – |
| count mean | 256.49 | 256.00 |
| count std | 10.96 | 11.31 |


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



**RCT failures logged:** 1



---

## E · Battery history (L3)



93 runs from 2026-05-07T22:45:52Z to 2026-06-24T03:14:18Z.
**37 pass / 56 fail.** Current pass-streak: **2**.

| Metric | Value |
|---|---|
| ent mean | 7.9971 bits/byte |
| ent range | 7.9943 – 7.9977 |
| Rabbit pass-rate | 68.82% |
| Alphabit pass-rate | 92.47% |


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


**Recent runs:**

| ts | ent | chi% | rabbit | alphabit | failures |
|---|---|---|---|---|---|
| 2026-06-21T02:02:53Z | 7.9960 | 12.22 | 1 | 1 | 0 |
| 2026-06-22T02:04:54Z | 7.9975 | 85.85 | 1 | 1 | 0 |
| 2026-06-23T02:00:10Z | 7.9977 | 97.84 | 0 | 1 | 1 |
| 2026-06-24T02:01:56Z | 7.9970 | 28.65 | 1 | 1 | 0 |
| 2026-06-24T03:14:18Z | 7.9971 | 30.96 | 1 | 1 | 0 |




---

## 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:** 4 pass / 0 fail.
**Overall: PASS.**

| Test | p-value | Verdict | Detail |
|---|---|---|---|
| Frequency (monobit) | 0.1673 | pass | S_n = -1000 |
| Block Frequency | 0.6508 | pass | M=128, N=4096, χ²=4060.38 |
| Runs | 0.8792 | pass | V_n = 262088 (expected 262143) |
| Longest Run of 1s | 0.4454 | pass | M=128, N=49, χ²=4.76 |


![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.



---

## G · SP 800-90B non-IID min-entropy



NIST SP 800-90B §6 prescribes ten non-IID estimators of min-entropy. We
shell out to NIST's reference `ea_non_iid` over the trailing
1,000,000 unpacked bits of `bits_stream.bin`. The final H_min is the
minimum across all ten — the conservative floor that any cryptographic
claim must respect.

4 runs from 2026-06-22T05:57:08Z to 2026-06-24T03:14:21Z.
**Latest H_min: 0.8717 bits/bit**
(floor set by **compression**;
1,000,000 samples
).

| Estimator | Latest | Spec §6.3 |
|---|---|---|
| Most Common Value | 0.9952 | 6.3.1 |
| Collision | 0.9291 | 6.3.2 |
| Markov | 0.9994 | 6.3.3 |
| Compression | 0.8717 | 6.3.4 |
| T-Tuple | 0.9381 | 6.3.5 |
| LRS | 0.9950 | 6.3.6 |
| MultiMCW | 0.9948 | 6.3.7 |
| Lag | 0.9976 | 6.3.8 |
| MultiMMC | 0.9957 | 6.3.9 |
| LZ78Y | 0.9969 | 6.3.10 |
| **H_min** | **0.8717** | min over all |

H_min across all runs: mean **0.8433**,
range 0.8324 – 0.8717 bits/bit.


![Min-entropy history](plots/min_entropy_history.png)

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


The Compression estimator is the canonical conservative one — it
underestimates for finite samples by design (NIST SP 800-90B §6.3.4
notes its small-sample bias). The cluster of estimators near 1.0
bit/bit reflects how clean the Δt₁ vs Δt₂ construction is: only the
Compression estimator's pessimism keeps the floor below ~0.99.



---

## 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.