# Geiger TRNG randomness analysis

**Generated:** 2026-07-03T03:00:27Z (duration 15.27 s)
**Git SHA:** 1ea05bfaf0b14b4d648f17d7283d33f159db75b4  ·  **Analysis version:** 1.1.0  ·  **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 | 35502 |
| `metrics.tsv` rows | 266 |
| `health.csv` rows | 10307 |
| `battery_history.tsv` rows | 107 |

---

## 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 | 35,502 |
| mean Δt | 101401.8 µs |
| median Δt | 70110.7 µs |
| min Δt | 181.6 µs |
| max Δt | 1222936 µs |
| estimated rate | 9.86 Hz (592 CPM) |

**Goodness-of-fit (Kolmogorov-Smirnov vs exponential):**
KS statistic = 0.0033,
p-value = 0.8370 →
**consistent_with_poisson**

**Pile-up cluster** (Δt < 5000 µs, the GM tube + NE555 recovery floor):
1700 of 35,502
(4.79%).


![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 | 262,196 (50.010%) | 50% |
| bias | +0.00010 | 0 |
| bias 1σ (sampling) | ±0.00069 | – |
| Shannon entropy | 7.9973 bits/byte | 8.0 |
| χ² statistic | 250.34 | ~255 (df) |
| χ² percentile | 57.07% | 5–95% |

**Autocorrelation** at lag 1..32 —
maximum |ρ| = 0.0036 at lag 3.


![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 = 0.5626 (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
(2026-07-02T02:59:00Z → 2026-07-03T02:56:00Z).

| Metric | mean | std | first | last | min | max |
|---|---|---|---|---|---|---|
| bias | -0.0004 | 0.0062 | 0.0081 | -0.0006 | -0.0190 | 0.0165 |
| ent_bpb | 7.8076 | 0.0160 | 7.7956 | 7.8224 | 7.7670 | 7.8544 |
| chi_pct | 46.2830 | 27.7803 | 33.6000 | 71.8700 | 0.1900 | 99.4700 |
| lag1_bits | 0.0007 | 0.0106 | 0.0121 | 0.0074 | -0.0348 | 0.0322 |
| mean_dt_ms | 100.1530 | 3.2927 | 98.7400 | 95.7000 | 91.0400 | 107.0000 |
| lag1_dt | -0.0045 | 0.0298 | 0.0529 | -0.0640 | -0.0771 | 0.0910 |
| pileup_pct | 4.7622 | 0.6595 | 5.3700 | 4.9800 | 2.8300 | 7.1300 |



![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)



10307 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 | 10303 | – |
| n pass | 10303 | – |
| n fail | 0 | – |
| count mean | 256.62 | 256.00 |
| count std | 11.17 | 11.31 |


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



**RCT failures logged:** 3



---

## E · Battery history (L3)



107 runs from 2026-05-07T22:45:52Z to 2026-07-03T02:01:29Z.
**50 pass / 57 fail.** Current pass-streak: **9**.

| Metric | Value |
|---|---|
| ent mean | 7.9971 bits/byte |
| ent range | 7.9943 – 7.9977 |
| Rabbit pass-rate | 71.96% |
| Alphabit pass-rate | 93.46% |


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


**Recent runs:**

| ts | ent | chi% | rabbit | alphabit | failures |
|---|---|---|---|---|---|
| 2026-07-01T05:01:11Z | 7.9973 | 60.69 | 1 | 1 | 0 |
| 2026-04-30T22:49:10Z | 7.9973 | 60.69 | 1 | 1 | 0 |
| 2026-07-01T05:18:53Z | 7.9973 | 60.69 | 1 | 1 | 0 |
| 2026-07-02T02:02:29Z | 7.9974 | 82.06 | 1 | 1 | 0 |
| 2026-07-03T02:01:29Z | 7.9974 | 74.23 | 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) | 0.8858 | pass | S_n = 104 |
| Block Frequency | 0.2980 | pass | M=128, N=4096, χ²=4143.50 |
| Runs | 0.4279 | pass | V_n = 261857 (expected 262144) |
| Longest Run of 1s | 0.8605 | pass | M=128, N=49, χ²=1.92 |


![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.

10 runs from 2026-06-22T05:57:08Z to 2026-07-01T05:23:17Z.
**Latest H_min: 0.8426 bits/bit**
(floor set by **compression**;
1,000,000 samples
).

| Estimator | Latest | Spec §6.3 |
|---|---|---|
| Most Common Value | 0.9946 | 6.3.1 |
| Collision | 0.9330 | 6.3.2 |
| Markov | 0.9991 | 6.3.3 |
| Compression | 0.8426 | 6.3.4 |
| T-Tuple | 0.9191 | 6.3.5 |
| LRS | 0.9430 | 6.3.6 |
| MultiMCW | 0.9952 | 6.3.7 |
| Lag | 0.9938 | 6.3.8 |
| MultiMMC | 0.9983 | 6.3.9 |
| LZ78Y | 0.9967 | 6.3.10 |
| **H_min** | **0.8426** | min over all |

H_min across all runs: mean **0.8489**,
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.



---

## H · Long-term drift & incident timeline



Full-history view of the L2 record — unlike Section C's trailing window,
this loads every `metrics.tsv` row, subtracts the windows in the bench
incident log (`incidents.md`), drops stale/degenerate rows, and looks for
slow structure in what remains.

| | Value |
|---|---|
| span | 63.2 days (2026-04-30T22:49:09Z → 2026-07-03T02:56:00Z) |
| L2 rows | 9,075 (coverage 54.9% at 330 s cadence) |
| masked — incident windows | 39 |
| masked — quality filter | 791 (stale-slice / degenerate rows) |
| clean rows analyzed | 8,245 |

**Rate regimes.** Step-change detection on the daily means (3-day median
shift > 0.45 Hz) splits the
record into 3 eras.
A regime step (e.g. the bench being repositioned) is not drift — the
trend/diurnal/outlier stats below use only the **current era**
(since 2026-05-28,
3,808 rows).

| era start | era end | days | mean rate |
|---|---|---|---|
| 2026-04-30 | 2026-05-10 | 5 | 12.30 Hz |
| 2026-05-11 | 2026-05-27 | 17 | 10.37 Hz |
| 2026-05-28 | 2026-07-03 | 17 | 9.78 Hz |


**Count rate (current era):**
mean 10.005 Hz,
median 9.908 Hz,
σ 0.698,
range 6.69 – 12.91 Hz.

**Linear drift:** +0.0012 Hz/day
(net +0.042 Hz over the span,
r² = 0.000,
p = 4.64e-01) —
not a materially significant trend.
Note: thorium-232's 14-Gyr half-life contributes zero decay-rate drift on
any human timescale; a real trend here is environmental or instrumental.


**Diurnal cycle:** one-way ANOVA across UTC hour-of-day bins gives
F = 10.3,
p = 5.5e-36 —
**significant hour-of-day structure**.
Peak-to-peak swing 4.4%
(fastest ~14:00 UTC,
slowest ~20:00 UTC).
A temperature-mediated rate cycle affects *when* counts arrive, not the
fairness of the Δt₁ vs Δt₂ comparison — the extractor is rate-invariant
by construction.


**Outliers (MAD z > 5):**
215 of 3,808
current-era rows (5.65%),
clustered into 12
episodes.
Sustained episodes not in the incident log deserve investigation — add
confirmed ones to `incidents.md` so future runs mask them.


| start | end | rows | mean rate | peak \|z\| |
|---|---|---|---|---|
| 2026-05-29T02:59:54Z | 2026-05-29T02:59:54Z | 1 | 6.69 Hz | 8.6 |
| 2026-06-19T02:17:04Z | 2026-06-19T13:22:32Z | 64 | 12.05 Hz | 8.1 |
| 2026-06-20T04:41:36Z | 2026-06-20T17:53:08Z | 111 | 12.16 Hz | 7.8 |
| 2026-06-19T14:01:02Z | 2026-06-19T15:07:02Z | 8 | 12.07 Hz | 7.2 |
| 2026-06-19T20:31:02Z | 2026-06-19T22:04:32Z | 9 | 7.92 Hz | 6.2 |




**Incident log** (5 entries from `incidents.md`):

| start (UTC) | end | duration | kind | L2 rows masked |
|---|---|---|---|---|
| 2026-06-18T22:57:50Z | 2026-06-19T02:00:00Z | 182 min | analog / hardware oscillation | 5 |
| 2026-06-20T18:25Z | 2026-06-20T18:55:00Z *(assumed)* | 30 min | silent reboot, cause unknown | 5 |
| 2026-06-24T03:13:57Z | 2026-06-24T03:43:57Z *(assumed)* | 30 min | silent reboot, cause unknown | 6 |
| 2026-06-28T17:44:39Z | 2026-07-01T05:13:34Z | 3569 min | journald stopped writing while system stayed up | not masked (monitoring-only) |
| 2026-07-01T04:55:47Z | 2026-07-01T06:51:47Z | 116 min | compound — silent reboot + hardware disconnect + latent bug | 23 |




![Long-term daily count rate](plots/longterm_rate.png)

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



![Diurnal rate profile](plots/diurnal_profile.png)

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




---

## 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` v1.1.0.