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REVIEW 4 major objections 6 minor 4 references

Time Series Analysis of DECAL Sensor Noise for the Generation of Truly Random Numbers

T0 review · 4 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read A particle-detector pixel's noise, whitened by an ARIMA model, yields bits that pass the NIST randomness suite.

desk verdict A clearly-written feasibility study whose 'truly random' conclusion outruns the diagnostics; the Ljung-Box degrees-of-freedom discrepancy deserves a fix before publication. read the letter →

arxiv 2509.02203 v1 pith:O6RGNXMP submitted 2025-09-02 hep-ex hep-lathep-phphysics.ins-det

Dimos Aslanis , Alex Kehagias , Ioannis Kopsalis , Ioannis Theodonis This is my paper · ORCID
classification hep-exhep-lathep-phphysics.ins-det
keywords truerandomnumbergenerationDECALsensornoiseARIMAtimeserieswhiteNISTSP800-22bitextractionparticledetectorcalorimetry
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using the DECAL calorimeter sensor as a test case, the paper claims that a physical pixel's intrinsic noise can be converted into truly random numbers. The authors take threshold-scan data from one pixel, fit a Gaussian to each scan, and model the sequence of Gaussian means as an ARIMA(3,1,5) time series. They then take the sign of each model residual as a bit and apply a deterministic shuffle. The resulting bit stream passes the NIST SP 800-22 suite, the Ljung-Box test, the cumulative periodogram, and random-walk mean-squared-displacement checks. The rate is about 5.4 bits per second in the current setup, so the result is a feasibility proof rather than a high-speed TRNG.

What carries the argument

The load-bearing object is the ARIMA(3,1,5) residual sequence: the fitted model is supposed to strip the sensor's systematic temporal structure, leaving only white noise. The sign of each residual supplies one bit. A segment-based shuffle, whose parameters are derived from the bit stream itself, is then applied to break any small residual correlations. The Box-Jenkins workflow—ACF/PACF inspection, differencing, AIC/BIC order selection, residual diagnostics—is what justifies calling the residuals noise.

What would settle it

Re-run the pipeline with the shuffle removed and with Ljung-Box evaluated at the correct K-q-p degrees of freedom; if the un-shuffled bits or the residuals fail the randomness tests, the claimed sensor entropy is not the sole source of randomness.

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Extended reading notes

Core claim

The central discovery is that the stochastic component of DECAL sensor noise, after ARIMA whitening, behaves as Gaussian white noise whose sign bits pass standard randomness tests. Concretely: discard the first 10,000 scans for warm-up; fit a Gaussian to each threshold-scan count distribution via binned maximum likelihood; take the mean values as a time series; fit an ARIMA(3,1,5) model selected by AIC/BIC; compute the residuals; take the sign of each residual as a bit; apply a segment-based shuffle that swaps bits using patterns in the bit stream itself. The resulting stream passes all applicable NIST tests, and the residuals pass Ljung-Box, periodogram, and random-walk/MSD checks. The auth

Load-bearing premise

The ARIMA residuals are genuine white noise—zero mean, constant variance, and no autocorrelation—so their signs are unbiased independent coin flips.

Editorial extensions

If this is right

  • If the claim holds, DECAL and similar pixel sensors can serve as physical entropy sources for random number generation.
  • The ARIMA residual stream is a statistical characterization of the sensor noise itself, which can inform calibration of future digital calorimetry experiments.
  • The bit-generation step is simple and online, so it can run continuously during normal sensor operation.
  • At 5.4 bits per second the current configuration is not a production TRNG; the paper's own conclusion is that optimizing the data acquisition chain is the path to practical rates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper notes that the Ljung-Box statistic follows K-q rather than K-q-p degrees of freedom and that the Box-Pierce correction is neglected; this leaves open the possibility that some apparent whiteness comes from the fitted model and the shuffle, not the sensor itself. A direct comparison of the pipeline with and without the shuffle would separate those contributions.
  • Only one pixel is analyzed; if the noise streams of the 64 strips are independent, parallel readout could multiply the 5.4 bits per second rate by roughly the number of independent pixels, turning the feasibility result into a usable entropy source.
  • Passing statistical tests establishes local randomness, not physical nondeterminism; for cryptographic use, one would need an entropy model of the sensor and a conservative bias-free extraction rule rather than relying on test-passing alone.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. This paper proposes a TRNG based on DECAL sensor noise. A single pixel's threshold-scan Gaussian means are modeled as ARIMA(3,1,5); the sign of the estimated residuals gives bits, which are then shuffled by a deterministic algorithm. The authors report that the NIST SP 800-22 suite and additional diffusion tests are passed and estimate a bit rate of 5.4 bps. They conclude that the sensor noise can generate truly random numbers.

Significance. The application of time-series analysis to a particle-physics sensor is original and, if the residual-whiteness premise were established, would be a useful feasibility demonstration. The paper is transparent about the slow bit rate and mentions several limitations. However, the conclusion is stronger than the evidence: the residual diagnostics contain an acknowledged degrees-of-freedom discrepancy, the Box-Pierce correction is ignored, the shuffle is a deterministic permutation that cannot add entropy, and no entropy estimate is provided. These are load-bearing gaps.

major comments (4)
  1. [Sec. 3.3, Eq. (5)] The Ljung-Box result is the main evidence for residual whiteness. The observation that Q follows χ²(K−q) rather than χ²(K−q−p) contradicts the null distribution used for estimated ARIMA residuals. The paper calls this "likely suboptimal choice" and "outside the scope", but this is exactly the assumption on which Eq. (4) and bit generation rest. Please report the Q values, p-values, and the result with correct df and with the Box-Pierce correction (Sec. 2.5). Without this, the residuals cannot be claimed white.
  2. [Sec. 2.4, shuffle algorithm] Even if the shuffle is deterministic and efficient, it is a permutation of the input bits and cannot increase entropy. If the residual bits contain bias or dependence, the shuffle may hide them from the NIST tests. The paper should test the unshuffled sign-of-residual stream, or at least show that the shuffle preserves the entropy of an i.i.d. source and quantify the min-entropy/entropy per bit (e.g., NIST SP 800-90B). The phrase "truly random numbers" is not justified by passing statistical tests.
  3. [Secs. 2.3-2.4 and Sec. 4] The residuals are in-sample residuals from a model fitted to the same time series. Such residuals are not an independent sample of the physical innovation process, so NIST tests on them partly validate the fitting algorithm. An out-of-sample procedure (fit on a training interval, generate bits on a held-out interval, re-fit periodically and report parameter stability) would provide much stronger evidence. The current conclusion in Sec. 4 ("truly random numbers") overstates what the design can establish.
  4. [Data availability] The paper does not provide the raw data, processed time series, or code. Since the results depend on a specific pixel, tuning voltage, warm-up cutoff, ARIMA orders, and shuffle parameters, reproducibility is limited. Please include these materials or a detailed reproducibility description, including results for the other pixels claimed to behave similarly.
minor comments (6)
  1. [Eq. (2)-(3)] In Eq. (3), γjt should be γj; the subscript t is used both as index and in the expectation limit, which is confusing.
  2. [Sec. 2.4] The algorithm says "Skip the next Nshuffle segments" and then "when the Nshuffle-th segment is reached", which is inconsistent. Clarify the indexing convention.
  3. [Sec. 2.5] The symbol q is used both for the MA order in Eq. (1) and for (n−2)/2 in the cumulative periodogram bounds. Rename one to avoid ambiguity.
  4. [Sec. 3.3] The residual Q-Q plot and histogram are visual; a formal normality test (e.g., Shapiro-Wilk) would be useful, although sign bits only require zero median.
  5. [Table 1] The caption states that "p-value indicates the probability that the underlying p-values follow the uniform distribution"; this is a misstatement. Revise to describe the P-value of the uniformity test used by NIST.
  6. [Sec. 2.2 / Sec. 3.4] Please clarify how "repeat the scan 2000 times" yields the 100000 scans mentioned in Sec. 3.4 when computing the bit rate.

Circularity Check

1 steps flagged · score 4.0 of 10

Partial circularity: the 'random' bits are the fitted ARIMA residuals, so in-sample whitening tests partly confirm the model rather than the sensor; external NIST tests on the final bitstream mitigate but do not eliminate the concern.

  1. fitted input called prediction [Section 2.4, Eq. (4); Section 3.3]
    "The white noise component is expected to be a time series of uncorrelated, normally distributed random numbers. In principle, this is the end goal of this work: these are hardware generated true random numbers."

    The bits are defined as the sign of the residuals of an ARIMA(3,1,5) model fitted to the same sensor time series (Eq. 4). Thus the residual whiteness tests in Sec. 3.3 (ACF, periodogram, Ljung-Box) evaluate the model's own output, not an independent property of the sensor. If the model is overfitted, residuals can appear white by construction. The paper itself finds the Ljung-Box Q statistic follows χ²(K−q) rather than the theoretical χ²(K−q−p) and defers the discrepancy as 'outside the scope,' yet still concludes the residuals are white noise. Passing NIST on the deterministically shuffled bit stream provides external evidence, but the core 'truly random' claim is partly a re-description of the ARIMA fit.

full rationale

The derivation chain from sensor noise to random bits is: fit ARIMA(3,1,5) to the time series, compute residuals (Eq. 4), take their signs, apply a deterministic shuffle, and test. The residuals are the model's fitted innovations; their whiteness is the model's objective, so in-sample diagnostics (Ljung-Box, ACF, periodogram) partly confirm the fit rather than the physical entropy source. The paper's own Sec. 3.3 reports an unexplained deviation in the Ljung-Box degrees of freedom, undercutting the whiteness conclusion. However, the final bitstream is evaluated against the external NIST SP 800-22 suite and random-walk tests, which would be nontrivial to pass if the residual stream had no entropy. Therefore the circularity is partial: the central claim does not reduce entirely to the model fit because external benchmarks provide independent support. There is also a minor self-citation (ref. [24]) used to assert generality to other pixels, but this is not load-bearing for the single-pixel feasibility result. Overall a score of 4 reflects partial circularity without full collapse.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a standard time-series toolkit applied to a specific sensor; the main fitted inputs are the ARIMA parameters and orders, plus a warm-up cutoff and shuffle constants. No new physical entities are introduced.

free parameters (4)
  • ARIMA(3,1,5) coefficients phi_1..phi_3, theta_1..theta_5, mean = not reported
    Estimated by maximum likelihood from the same DECAL noise time series; these coefficients define the residuals used as random bits.
  • ARIMA model orders p=3, q=5 and differencing order d=1 = 3, 1, 5
    Selected from data using AIC/BIC and residual checks; the model choice affects which part of the signal is classified as noise.
  • Warm-up discard cutoff (first 10000 scans) = 10000
    Chosen by inspecting when the time series stabilizes; a post-hoc data selection that changes the fitted model and residuals.
  • Shuffle/swap window parameters (8-bit segments, Nshuffle/Nswap in 1..4) = L=8, ranges 1..4
    Hand-chosen post-processing constants; they transform the bit stream before NIST testing and are not derived from the physics.
assumptions (5)
  • domain assumption After one differencing, the DECAL noise time series is stationary and is generated by an ARIMA(3,1,5) process with Gaussian white-noise innovations.
    Invoked in Sec. 2.3 and 3.2; if misspecified, residuals are not the true innovations and the randomness claim weakens.
  • domain assumption The threshold scan count distribution is Gaussian, so its mean is a sufficient summary of the noise state.
    Assumed in Sec. 2.2 when fitting with BMLE; supported by a Q-Q plot for one pixel, not for the full dataset.
  • domain assumption The uncontrolled office-desk environment introduces no external periodic or structured signals that survive the ARIMA fit.
    Stated in Sec. 2.1; if false, the randomness may come from environmental artifacts rather than sensor noise.
  • standard math Standard results of ARIMA theory: ACF/PACF identification, MLE properties, Ljung-Box and cumulative periodogram tests, and NIST SP 800-22 test statistics.
    Used throughout Secs. 2.3-2.5 without proof; background textbook material.
  • domain assumption Tuning the pixels to about 1.16 V and waiting 200 clock cycles between scans yields a stable, representative noise series.
    Experimental choices in Sec. 2.2; if the sensor has not stabilized, the warm-up cutoff and model fit are affected.

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Cite this review

Pith. "Pith review of Time Series Analysis of DECAL Sensor Noise for the Generation of Truly Random Numbers." pith.science (2026). https://pith.science/paper/O6RGNXMP

@misc{pith2026250902203,
  author       = {Pith},
  title        = {Pith review of: Time Series Analysis of DECAL Sensor Noise for the Generation of Truly Random Numbers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O6RGNXMP}},
  note         = {Machine review of arXiv:2509.02203}
}
read the original abstract

We explore here the stochastic behavior of the DECAL sensor's noise output, and we evaluate its potential application as a true random number generator (TRNG) using time series analysis. The main objectives are twofold: first, to characterize the intrinsic noise properties of the DECAL sensor in the absence of external stimuli, and second, to determine the feasibility of employing the sensor as a source of randomness. The collected sensor data are examined through statistical and time series methodologies, and subsequently modeled using an auto-regressive integrated moving average (ARIMA) process. This modeling approach enables the transformation of the sensor's raw noise into a Gaussian white noise sequence, which serves as the basis for generating random bits. The resulting random numbers are subjected to a series of statistical tests for randomness, including the NIST test suite. Our findings indicate that the method produces statistically sound random numbers. However, the rate of bit generation is relatively low, limiting its practicality for real-time TRNG applications under the current configuration. Despite this limitation, the results suggest that time series modeling presents a promising framework for extracting randomness from the DECAL sensor, and that with further optimization, the sensor could serve as a reliable and effective TRNG.

Figures

Figures reproduced from arXiv: 2509.02203 by the authors.

Figure 1
Figure 1. The DECAL sensor readout modes: (a) strip mode and (b) pad mode. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Example for the swap algorithm. See text for details. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. The distribution of counts for a threshold scan (left) and the Q-Q plot that compares the empirical distribution [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Histogram of a row of pixels before (a) and after (b) tuning. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 6
Figure 6. Figure 6: Example of time series (top left), histogram (top right), ACF (bottom left), and PACF (bottom right) for a [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Example of time series (top left), histogram (top right), ACF (bottom left), and PACF (bottom right) for a [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Example of time series (top left), histogram (top right), ACF (bottom left), and PACF (bottom right) for a [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Example of a (a) Q-Q plot and (b) cumulative periodogram for the residuals of the ARIMA model fitted to the [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: Histogram of the Ljung-Box Q statistic for the residuals of the ARIMA model fitted to the time series of a pixel of the DECAL sensor. The red continuous line indicates the χ 2 distribution with K − q − p degrees of freedom, the green dashed line indicates the χ 2 dist…
Figure 11
Figure 11. Figure 11: Results of the (a) one-dimensional and (b) two-dimensional random walk tests. See text for details. [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

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Reference graph

Works this paper leans on

4 extracted references · 3 canonical work pages

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