# Geiger TRNG randomness analysis

**Generated:** 2026-07-01T05:14:10Z (duration 10.46 s)
**Git SHA:** b07415ae65db9707fd9a66166370ce82acc5e6be  ·  **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 | 0 |
| `metrics.tsv` rows | 266 |
| `health.csv` rows | 8830 |
| `battery_history.tsv` rows | 104 |

---

## A · Source physics — inter-arrival distribution


*(no data — `events.csv` empty or events window too narrow)*


---

## 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 | 261,846 (49.943%) | 50% |
| bias | -0.00057 | 0 |
| bias 1σ (sampling) | ±0.00069 | – |
| Shannon entropy | 7.9973 bits/byte | 8.0 |
| χ² statistic | 248.27 | ~255 (df) |
| χ² percentile | 60.69% | 5–95% |

**Autocorrelation** at lag 1..32 —
maximum |ρ| = 0.0031 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 = 0.5615 (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
(2026-06-30T05:16:40Z → 2026-07-01T05:14:05Z).

| Metric | mean | std | first | last | min | max |
|---|---|---|---|---|---|---|
| bias | -0.0008 | 0.0056 | -0.0052 | -0.0117 | -0.0131 | 0.0133 |
| ent_bpb | 7.8084 | 0.0163 | 7.8217 | 7.8143 | 7.7580 | 7.8459 |
| chi_pct | 48.2078 | 27.8616 | 77.0500 | 43.5700 | 0.5800 | 98.8400 |
| lag1_bits | -0.0028 | 0.0099 | 0.0005 | -0.0004 | -0.0299 | 0.0213 |
| mean_dt_ms | -11114.5182 | 81027.7200 | 98.5900 | -596536.2900 | -596536.2900 | 108.4700 |
| lag1_dt | 0.0008 | 0.0305 | -0.0037 | -0.0000 | -0.0848 | 0.1149 |
| pileup_pct | 4.8274 | 0.6899 | 4.6900 | 5.0800 | 3.0300 | 7.5200 |



![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)



8830 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 | 8828 | – |
| n pass | 8828 | – |
| n fail | 0 | – |
| count mean | 256.67 | 256.00 |
| count std | 11.15 | 11.31 |


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



**RCT failures logged:** 1



---

## E · Battery history (L3)



104 runs from 2026-05-07T22:45:52Z to 2026-04-30T22:49:10Z.
**47 pass / 57 fail.** Current pass-streak: **6**.

| Metric | Value |
|---|---|
| ent mean | 7.9971 bits/byte |
| ent range | 7.9943 – 7.9977 |
| Rabbit pass-rate | 71.15% |
| Alphabit pass-rate | 93.27% |


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


**Recent runs:**

| ts | ent | chi% | rabbit | alphabit | failures |
|---|---|---|---|---|---|
| 2026-06-30T02:04:46Z | 7.9973 | 62.28 | 1 | 1 | 0 |
| 2026-07-01T02:02:46Z | 7.9972 | 52.99 | 1 | 1 | 0 |
| 2026-04-30T22:49:10Z | 7.9973 | 60.69 | 1 | 1 | 0 |
| 2026-07-01T05:01:11Z | 7.9973 | 60.69 | 1 | 1 | 0 |
| 2026-04-30T22:49:10Z | 7.9973 | 60.69 | 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) | 0.4104 | pass | S_n = -596 |
| Block Frequency | 0.3449 | pass | M=128, N=4096, χ²=4131.56 |
| Runs | 0.0348 | pass | V_n = 262908 (expected 262144) |
| Longest Run of 1s | 0.3764 | pass | M=128, N=49, χ²=5.33 |


![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.

9 runs from 2026-06-22T05:57:08Z to 2026-07-01T05:14:04Z.
**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 **0.8496**,
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.