# Geiger TRNG randomness analysis

**Generated:** 2026-06-29T03:01:32Z (duration 13.5 s)
**Git SHA:** 523ab68b8db4ee0894af6ba5e32d3896a66926ee  ·  **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 | 35353 |
| `metrics.tsv` rows | 266 |
| `health.csv` rows | 7167 |
| `battery_history.tsv` rows | 99 |

---

## 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 | 35,353 |
| mean Δt | 101829.8 µs |
| median Δt | 70343.8 µs |
| min Δt | 181.2 µs |
| max Δt | 1298337 µs |
| estimated rate | 9.82 Hz (589 CPM) |

**Goodness-of-fit (Kolmogorov-Smirnov vs exponential):**
KS statistic = 0.0037,
p-value = 0.7231 →
**consistent_with_poisson**

**Pile-up cluster** (Δt < 5000 µs, the GM tube + NE555 recovery floor):
1664 of 35,353
(4.71%).


![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 | 261,921 (49.957%) | 50% |
| bias | -0.00043 | 0 |
| bias 1σ (sampling) | ±0.00069 | – |
| Shannon entropy | 7.9972 bits/byte | 8.0 |
| χ² statistic | 252.40 | ~255 (df) |
| χ² percentile | 53.43% | 5–95% |

**Autocorrelation** at lag 1..32 —
maximum |ρ| = 0.0032 at lag 7.


![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 = 0.5610 (1.0 = perfectly flat):

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

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




---

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



266 samples over the trailing 24.0 h
(2026-06-28T03:01:09Z → 2026-06-29T03:00:20Z).

| Metric | mean | std | first | last | min | max |
|---|---|---|---|---|---|---|
| bias | -0.0002 | 0.0058 | -0.0076 | -0.0004 | -0.0162 | 0.0165 |
| ent_bpb | 7.8059 | 0.0193 | 7.7880 | 7.8023 | 7.7540 | 7.8597 |
| chi_pct | 42.4945 | 31.6160 | 14.9300 | 18.6000 | 0.1200 | 99.8700 |
| lag1_bits | -0.0006 | 0.0100 | -0.0301 | -0.0111 | -0.0319 | 0.0248 |
| mean_dt_ms | 100.9989 | 3.4828 | 100.7300 | 100.4900 | 90.7900 | 110.7600 |
| lag1_dt | 0.0018 | 0.0317 | 0.0028 | -0.0502 | -0.0673 | 0.1009 |
| pileup_pct | 4.7420 | 0.6840 | 3.8100 | 3.8100 | 3.0300 | 6.9300 |



![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)



7167 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 | 7165 | – |
| n pass | 7165 | – |
| n fail | 0 | – |
| count mean | 256.65 | 256.00 |
| count std | 11.09 | 11.31 |


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



**RCT failures logged:** 1



---

## E · Battery history (L3)



99 runs from 2026-05-07T22:45:52Z to 2026-06-29T02:03:47Z.
**42 pass / 57 fail.** Current pass-streak: **1**.

| Metric | Value |
|---|---|
| ent mean | 7.9971 bits/byte |
| ent range | 7.9943 – 7.9977 |
| Rabbit pass-rate | 69.70% |
| Alphabit pass-rate | 92.93% |


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


**Recent runs:**

| ts | ent | chi% | rabbit | alphabit | failures |
|---|---|---|---|---|---|
| 2026-06-25T02:03:47Z | 7.9973 | 69.73 | 1 | 1 | 0 |
| 2026-06-26T02:00:46Z | 7.9975 | 89.02 | 1 | 1 | 0 |
| 2026-06-27T02:00:15Z | 7.9968 | 5.71 | 1 | 1 | 0 |
| 2026-06-28T02:00:47Z | 7.9972 | 41.13 | 0 | 1 | 1 |
| 2026-06-29T02:03:47Z | 7.9973 | 60.52 | 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) | 0.5379 | pass | S_n = -446 |
| Block Frequency | 0.7680 | pass | M=128, N=4096, χ²=4029.41 |
| Runs | 0.9709 | pass | V_n = 262157 (expected 262144) |
| Longest Run of 1s | 0.4800 | pass | M=128, N=49, χ²=4.50 |


![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.

6 runs from 2026-06-22T05:57:08Z to 2026-06-28T01:38:57Z.
**Latest H_min: 0.8998 bits/bit**
(floor set by **compression**;
1,000,000 samples
).

| Estimator | Latest | Spec §6.3 |
|---|---|---|
| Most Common Value | 0.9946 | 6.3.1 |
| Collision | 0.9160 | 6.3.2 |
| Markov | 0.9989 | 6.3.3 |
| Compression | 0.8998 | 6.3.4 |
| T-Tuple | 0.9216 | 6.3.5 |
| LRS | 0.9947 | 6.3.6 |
| MultiMCW | 0.9974 | 6.3.7 |
| Lag | 0.9947 | 6.3.8 |
| MultiMMC | 0.9943 | 6.3.9 |
| LZ78Y | 0.9953 | 6.3.10 |
| **H_min** | **0.8998** | min over all |

H_min across all runs: mean **0.8531**,
range 0.8324 – 0.8998 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.