{"id":"4ba4bb7c-2241-48f0-8b04-225ace7ab503","arxiv_id":"2502.03100","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A Bayesian framework classifies laser measurements as single-shot or average based on precision versus intrinsic variability, demonstrated at a petawatt laser with a mosaic-filter device.","lead":"This paper introduces a Bayesian framework that defines when a laser measurement can truly resolve individual shots, based on the ratio of measurement precision to intrinsic laser variability. It applies the framework with a new mosaic-filter device at the ATLAS-3000 petawatt laser, reporting the first quantitative uncertainty bounds on pulse front tilt and curvature.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Estimated σ_stoch is not independently validated; unmodeled nonlinear drift or overfitting of the local-linear trend biases the regime threshold and posterior bounds.","rationale":"Good-faith reading. The paper does two things: (1) derive a regime threshold for single-shot resolution from a Kalman-like update, and (2) demonstrate a Bayesian STC reconstructor at ATLAS-3000. The derivation in Section II B is self-consistent: Eq. (8) is the correct stationary variance of the update 1/σ²_post = 1/(σ²_stoch + σ²_post) + 1/σ²_meas, so the threshold σ²_meas = 2σ²_stoch follows algebraically. The vector update in Eqs. (20)–(22) treats a_meas = T⁺d as a direct measurement with covariance T⁺nT⁺ᵀ, which is a sufficient statistic when T has full column rank, so the formalism is sound. The most load-bearing assumption is the identifiability of the stochastic component. Equations (10)–(11) estimate σ²_stoch from the residual variance after subtracting the Holt prediction, but α and β in Eqs. (14)–(15) are fit by maximizing the same Gaussian likelihood over a 20-point window. There is no independent measurement of σ_stoch. If the true deterministic drift inside a 3.3-min window is nonlinear, the residuals are not independent Gaussians; unmodeled curvature inflates σ_stoch, biasing the regime classification toward the distribution-centric side and widening the reported posterior bounds. Conversely, if the local-linear model overfits the stochastic component (a real risk when the update weight exceeds 0.5 in the state-resolving regime), σ_stoch is underestimated and the posterior bounds are overconfident. The paper acknowledges this entanglement in Section II D but only offers self-consistency checks (Fig. 5 histograms) rather than validation against known ground truth. No code or data are provided, so the 54–60% uncertainty reduction cannot be independently reproduced. This concern does not invalidate the theory, but it makes the experimental support for the central claim conditional on assumptions that are plausible but untested. The proposed synthetic injection test would settle the magnitude of the bias; if the bias is large, the ATLAS-3000 conclusions would need re-analysis or a different trend model. Therefore the reader's CONDITIONAL verdict is appropriate; no adjustment is needed.","tokens_in":12742,"tokens_out":9749,"duration_ms":87002,"concrete_test":"Run a synthetic-data injection study: generate 2 hours of data at 0.1 Hz from f(t) = a + b t + c sin(2π t/T) with T ≈ 5–10 min and amplitude comparable to σ_stoch, plus independent Gaussian ε_k and ϵ_k with known σ_stoch and σ_meas (including values straddling the σ_meas² = 2σ_stoch² threshold). Apply the paper's pipeline (Eqs. 13–16 with N=20, SGD fit of σ_stoch). If the recovered σ_stoch deviates from the true value by more than ~20%, or if the state-resolving/distribution-centric classification changes for a fixed σ_meas, the local-linearity assumption is load-bearing and the ATLAS-3000 uncertainty claims need re-analysis.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that single-shot capability is set by σ_meas² = 2σ_stoch² and that the ATLAS-3000 posterior bounds are reliable rests on the identifiability of the trend–stochastic decomposition in Eqs. (1)–(2). In Section II D, σ_stoch is estimated from the residuals Δµ = µ_meas − µ_pred via Eq. (11): σ²_Δµ ≈ σ²_posterior + σ²_stoch + σ²_meas. But µ_pred comes from the local linear approximation in Section II E (Eqs. (13)–(16)), whose parameters α, β are fit on the same N=20 measurement window by maximum likelihood. There is no independent calibration of σ_stoch. If the true deterministic drift within a 3.3-min window is not linear (e.g., thermal transients or slow oscillations), the residuals become autocorrelated and non-Gaussian, so the 'intrinsic stochasticity' absorbs the unmodeled trend. This biases σ_stoch upward, pushing the system toward the distribution-centric regime and widening the posterior bounds; conversely, if α/β overfit the stochastic component (a risk precisely in the state-resolving regime), σ_stoch is biased downward and the posterior uncertainties are overconfident. The paper acknowledges the entanglement in Section II D ('errors in estimating f(tk) will be absorbed into our estimate of εk') but provides only a self-consistency check (histograms matching Eq. (11)), not a validation of the decomposition. Since both the regime classification and the reported 54–60% uncertainty reduction depend on these estimates, the experimental support for the central claim is conditional on the local-linearity and Gaussian-residual assumptions holding at ATLAS-3000.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a Bayesian state-space framework for laser metrology in which each measured parameter is decomposed into a deterministic trend f(t_k) and an independent Gaussian stochastic component with variance sigma_stoch^2, while each measurement adds Gaussian noise sigma_meas^2. Section II derives the scalar Kalman-type update, the steady-state posterior variance in Eq. (8), and the threshold sigma_meas^2 = 2 sigma_stoch^2 separating a distribution-centric from a state-resolving regime. It also presents a frequency-response interpretation and a residual-based maximum-likelihood estimate of sigma_stoch using a local linear (Holt) model. Section III describes a new 'single-shot FALCON' device built from a mosaic 3x3 filter array in front of a Shack-Hartmann sensor, applies the framework at the ATLAS-3000 petawatt laser, and reports posterior-variance reductions of 47--60% compared with pseudo-inverse least squares for pulse-front tilt, curvature, and related modes. The paper claims this provides the first quantitative uncertainty bounds for spatio-temporal coupling measurements.","tokens_in":13033,"tokens_out":8410,"duration_ms":83352,"significance":"If the validation gaps are closed, this is a useful conceptual contribution: it replaces the binary single-shot/multi-shot distinction with a quantitative criterion based on the ratio sigma_meas^2 / sigma_stoch^2, and it produces per-shot posterior bounds for spatio-temporal couplings, which are currently missing from the STC literature. The analytic derivation leading to Eq. (8) is compact, transparent, and internally consistent, and the mosaic-filter device is simple and inexpensive. The paper also deserves credit for an explicit calibration of the measurement-noise covariance, something that is often omitted in STC diagnostics. However, the empirical support for the central quantitative claims is currently limited to self-consistency checks: the intrinsic stochasticity is estimated from the residuals of the same model used for prediction, and the reported uncertainty reduction follows mathematically from the Bayesian update rule. These issues must be addressed before the quantitative regime classification and the claimed first uncertainty bounds are fully established.","major_comments":[{"comment":"The estimate of sigma_stoch is obtained from the residuals of the same local-linear model that is used to form the predictions. Equation (11) defines the residual variance as sigma_posterior^2 + sigma_stoch^2 + sigma_meas^2, but any deterministic trend not captured by the N=20 local-linear fit (e.g., nonlinear thermal drift or slow oscillations) enters the residual and is absorbed into sigma_stoch. The text itself acknowledges this in Section II D: 'errors in estimating f(tk) will be absorbed into our estimate of epsilon_k.' Because the regime classification of Section II B and the posterior bounds of Section III E both depend directly on sigma_stoch, this circularity is load-bearing. The manuscript provides only a self-consistency check (histograms matching Eq. (11)), not an independent validation of the trend--stochastic decomposition. I recommend adding a synthetic-data test with known f(t) and sigma_stoch, plus an independent estimate of sigma_stoch, for example from a second faster diagnostic or from held-out windows, before the reported regime assignment and the uncertainty bounds can be trusted.","section":"Section II D and Section II E (Eqs. (11), (16))"},{"comment":"The reported 54--60% 'uncertainty reduction' is a direct mathematical consequence of Eqs. (5)--(6), not an empirical validation of accuracy. Any informative prior produces a posterior variance smaller than the measurement variance; comparing the posterior variance with the pseudo-inverse's measurement-noise variance quantifies only the amount of prior shrinkage. The histograms in Fig. 5 show that residuals are consistent with Eq. (11), but this is a self-consistency check of the Gaussian assumptions, not evidence that the posterior intervals are calibrated. To support the claim of 'first quantitative uncertainty bounds,' the authors should validate coverage on data with known parameter values, for example by injecting controlled STC changes, or compare posterior predictive intervals against independent measurements.","section":"Section III E (Figs. 5 and 9)"},{"comment":"The assertion that assuming a diagonal intrinsic-stochasticity matrix makes the reconstructed uncertainties 'upper bound values' is not generally valid. Even if mode correlations are neglected, model misspecification in the trend estimate can bias sigma_stoch downward: in the state-resolving regime, each measurement contains a large fraction of the instantaneous fluctuation epsilon_k, and the local-linear fit of Eqs. (14)--(15) can partly absorb that fluctuation into the trend, yielding an overconfident posterior. The opposite bias, inflation of sigma_stoch by unmodeled drift, is also possible. The manuscript argues only one direction of the bias; a formal sensitivity analysis or a simulation with a known trend is needed to establish that the reported bounds are actually conservative.","section":"Section II D and Section II F"},{"comment":"The passage from the scalar update to the vectorial update assumes that T^+ d_k is a sufficient statistic for the modal coefficients. If the transfer matrix T in Eq. (19) is rank-deficient or severely ill-conditioned for the 3x3 sub-aperture configuration, the pseudo-inverse can remove or distort information in the null space, and Eq. (21) is not necessarily the full posterior covariance of the original model in Eq. (19). The paper states that the reconstruction becomes 'well-posed' but does not report the rank or condition number of T, nor does it verify that the coefficient-space update is equivalent to the full Bayesian solution under the assumed noise model. This should be demonstrated explicitly, because the quantitative posterior covariance is the main experimental output.","section":"Section III C (Eqs. (20)--(22))"}],"minor_comments":[{"comment":"There are several wording errors: 'as much diverse information as possible within in a single shot' and 'a few- or multi-shot device can also be a reasonable choice' should be corrected.","section":"Introduction and Section III E"},{"comment":"The upper-right panel is labeled 'Pulse Front Curvature (PFT)/linear defocus'; PFT is used elsewhere in the paper for pulse front tilt, so this label should be corrected (likely 'PFC') to avoid confusion.","section":"Supplemental Material, Fig. 9"},{"comment":"The zoomed panels show the posterior mean and pseudo-inverse mean but do not display uncertainty bands or error bars; showing the posterior uncertainty would make the claimed reduction visible and easier to assess.","section":"Figs. 5 and 9"},{"comment":"The formula for chi_intensity appears to have an unmatched parenthesis; the outer exponent should apply to the entire factor (1 + ...), not just to the numerator term, and the notation should be unambiguous.","section":"Eq. (24)"},{"comment":"The residual model assumes independent, Gaussian residuals, but the paper does not comment on autocorrelation of the residuals shown in Fig. 5. A lag-correlation plot or Durbin--Watson-type statistic would strengthen the self-consistency check and support the diagonal-covariance assumption.","section":"Eq. (12) and Fig. 5"}],"recommendation":"major_revision","confidential_remarks":"To the editor: the paper fits the journal's scope and the conceptual framework is interesting, but the experimental validation is currently too weak for the quantitative claims. The main risk is that the regime threshold and the uncertainty bounds rest on the unvalidated trend--stochastic decomposition and on a by-construction variance reduction. I do not see a scope or novelty problem, and the self-referential caveat in Section II D is honest rather than disqualifying. A major revision with synthetic-data validation, an independent sigma_stoch estimate or held-out cross-validation, and a clarification of the vector update conditions would be appropriate. I would not recommend rejection at this stage."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The attached reader report is about right. The paper's real contribution is the threshold criterion: single-shot capability emerges from the ratio of measurement precision to intrinsic stochasticity, with the boundary at sigma_meas^2 = 2 sigma_stoch^2. That is simple, useful, and not obvious until you write it down. The Bayesian update equations are textbook, but the framing in Section II B, plus the frequency-response analysis in Section II C, gives real insight into what 'single-shot' should mean.\n\nThe experimental part is genuinely new too: first quantitative uncertainty bounds on pulse front tilt and curvature, and a clever mosaic-filter implementation that gets spectral information in one frame. The authors are honest about the main limitation—errors in estimating the deterministic trend get absorbed into sigma_stoch—and they do not overclaim the regime classification (PFT sits at the edge, linear coma is distribution-centric). That honesty earns credit.\n\nThe soft spots are where the reader points. sigma_stoch is estimated from residuals of the same model, and the local-linear trend is fit on a 20-point window. If there is unmodeled drift at timescales longer than about 3 minutes but shorter than the full measurement, it inflates sigma_stoch and biases both the regime classification and the posterior widths. The reported 54–60% uncertainty reduction comes directly from the Bayesian update equation, so it is not a surprise. And there is no code or data, and no independent check against a known ground truth—only histograms of residuals matched to the assumed Gaussian.\n\nNone of this is load-bearing in the sense of invalidating the framework; the central claim is about the concept, not these specific numbers. With a sensitivity analysis on the window size and a synthetic-data test, the demonstration would be much stronger. As it stands, the paper is a solid methods contribution with a plausible but not airtight validation.\n\nThis is for the laser-diagnostic and high-intensity laser community, and the framework could inform adaptive control or predictive modeling. It deserves a serious referee—I would not desk-reject it. I would send it back with a request for synthetic validation and more discussion of trend-identification limits.","headline":"A useful conceptual framework for when a measurement truly resolves single shots, with a plausible but under-validated demonstration; worth reviewing, not desk-rejecting.","tokens_in":13590,"tokens_out":2712,"would_cite":true,"duration_ms":26083,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Single-shot capability in laser metrology is a threshold, set when measurement precision falls below twice the intrinsic shot-to-shot fluctuation — not a built-in property of the device.","keywords":["Bayesian inference","single-shot measurement","spatio-temporal couplings","laser metrology","uncertainty quantification","pulse front tilt","pulse front curvature","state-resolving regime"],"falsifier":"A controlled test would fix a single mode (e.g., pulse front tilt) and take two measurement series with deliberately different measurement noise, one with $\\sigma_{\\mathrm{meas}}^2 = 0.5\\,\\sigma_{\\mathrm{stoch}}^2$ and one with $\\sigma_{\\mathrm{meas}}^2 = 3\\,\\sigma_{\\mathrm{stoch}}^2$; the theory predicts the asymptotic posterior variance falls below $\\sigma_{\\mathrm{stoch}}^2$ only in the first case. If the state-resolving regime appears in the high-noise setting, or fails to appear in the low-noise setting, the threshold $\\sigma_{\\mathrm{meas}}^2 = 2\\sigma_{\\mathrm{stoch}}^2$ is wrong.","tokens_in":12514,"feed_emoji":"⚡","tokens_out":13446,"duration_ms":106504,"temperature":0.7,"pith_summary":"Laser metrology usually labels a device 'single-shot' or 'multi-shot' by how many pulses it consumes. This paper argues that label is wrong: the real question is whether a single measurement can resolve the instantaneous state of the laser, and that is decided by the ratio of measurement noise to the laser's intrinsic shot-to-shot variance. When the measurement variance exceeds twice the stochastic variance, $\\sigma_{\\mathrm{meas}}^2 > 2\\sigma_{\\mathrm{stoch}}^2$, measurements can only describe the statistical distribution; below that threshold, individual shots become distinguishable. The authors build a Bayesian estimator around this threshold, apply it to spatio-temporal couplings at the ATLAS-3000 petawatt laser with a mosaic-filter Shack-Hartmann device, and obtain the first quantitative uncertainty bounds on pulse front tilt and curvature, shrinking posterior uncertainty by up to 60% relative to pseudo-inverse least squares.","feed_headline":"Single-shot laser sensing emerges above a 2:1 noise ratio","feed_subtitle":"A Bayesian reconstruction at the ATLAS-3000 petawatt laser cuts pulse-front uncertainty by up to 60 percent.","key_machinery":"The load-bearing mechanism is the recursive Bayesian update for a Gaussian state-space model, whose self-conjugacy yields an analytic posterior. The state of each Zernike–Taylor coefficient is updated by $\\mu_{k|k} = (1-\\gamma_k)\\mu_{k|k-1} + \\gamma_k y_k$ with $\\gamma_k = \\sigma^2_{k|k-1}/(\\sigma^2_{k|k-1} + \\sigma^2_{\\mathrm{meas}})$. From this update the paper derives the asymptotic variance $\\sigma_{\\infty}^2$ and the threshold $\\sigma_{\\mathrm{meas}}^2 = 2\\sigma_{\\mathrm{stoch}}^2$; the threshold is what separates the distribution-centric from the state-resolving regime. Around this core, the framework couples a local linear model (Holt's exponential smoothing) that tracks the deterministic drift $f(t_k)$, with a maximum-likelihood estimator of the intrinsic stochasticity whose residual variance combines prediction and measurement uncertainty, $\\sigma^2_{\\Delta\\mu} = \\sigma^2_{\\mathrm{pred}} + \\sigma^2_{\\mathrm{meas}} \\approx \\sigma^2_{\\mathrm{posterior}} + \\sigma^2_{\\mathrm{stoch}} + \\sigma^2_{\\mathrm{meas}}$. In the vectorial case, the same update becomes matrix equations with transfer matrix $T$ and pseudo-inverse $T^+$, giving posterior covariances for the retrieved coefficients.","core_discovery":"The central claim is that 'single-shot' capability is an emergent property of the ratio between measurement precision and intrinsic stochasticity, not a fixed attribute of the apparatus. For a Gaussian state-space model where each shot is $x_k = f(t_k) + \\varepsilon_k$ with $\\varepsilon_k \\sim \\mathcal{N}(0, \\sigma_{\\mathrm{stoch}}^2)$ and each measurement is $y_k = x_k + \\epsilon_k$ with $\\epsilon_k \\sim \\mathcal{N}(0, \\sigma_{\\mathrm{meas}}^2)$, the Bayesian posterior variance has an asymptotic limit $\\sigma_{\\infty}^2 = \\frac{\\sqrt{1 + 4(\\sigma_{\\mathrm{meas}}^2/\\sigma_{\\mathrm{stoch}}^2)} - 1}{2}\\,\\sigma_{\\mathrm{stoch}}^2$. When $\\sigma_{\\mathrm{meas}}^2 > 2\\sigma_{\\mathrm{stoch}}^2$ this limit stays above $\\sigma_{\\mathrm{stoch}}^2$, so repeated measurements only characterize the average system (distribution-centric regime); when $\\sigma_{\\mathrm{meas}}^2 < 2\\sigma_{\\mathrm{stoch}}^2$ the limit drops below $\\sigma_{\\mathrm{stoch}}^2$, meaning a single measurement can resolve the instantaneous state (state-resolving regime). The paper further shows that the threshold coincides with the Bayesian update weight $\\gamma = 1/2$ and with a Nyquist-frequency attenuation of about 67%. Demonstrated at the ATLAS-3000 petawatt laser with a single-shot mosaic-filter Shack-Hartmann sensor, this yields per-mode uncertainty bounds on spatio-temporal couplings—the first such quantitative error bars—and the posterior uncertainty on pulse front tilt and curvature is 54–60% smaller than the raw measurement uncertainty.","pith_inferences":["The same Gaussian update and threshold argument should apply to any metrology scheme where a parameter carries both measurement noise and process noise—e.g., beam-position monitors, wavefront sensors in adaptive optics, or even particle-beam diagnostics—so the definition of 'single-shot' could be exported beyond laser science.","Since the paper diagonalizes the stochasticity matrix for simplicity and calls the resulting uncertainties upper bounds, a natural extension is a full covariance or Gaussian-process model over time; this could lower the bounds further and reveal correlations between coupled Zernike modes.","The separating point in the spectra of Fig. 7 (around 8 minutes for pulse front tilt, 20–40 minutes for linear coma) suggests that the framework could be used online to detect when unresolved dynamics are masquerading as stochasticity, a use the paper does not explicitly develop.","The calibrated measurement-noise decomposition (focal-spot-position error plus a model-fit term of 0.6 pixels) is itself a new component for STC diagnostics; applying the same calibration to other sensors would let facilities compare their 'single-shotness' on a common scale."],"forward_implications":["For a given laser mode, the regime boundary is a number, not a label: the same device can be state-resolving for tilt while distribution-centric for linear coma, exactly as observed in the ATLAS-3000 data.","With per-shot posterior distributions, spatio-temporal couplings become inputs to closed-loop control: the posterior mean plus its uncertainty can drive beam stabilization, and modes whose fluctuations are stochastic set a floor that no a priori correction can remove.","The measured pulse-front-tilt stochasticity corresponds to a 0.3–5.5% loss in focal intensity at ATLAS-3000, giving a quantitative lower bound on peak-intensity fluctuations for an otherwise perfect laser.","Because the threshold depends on the ratio, improving the sensor (smaller spot-finding error or better calibration of the model-fit term) can move a mode across the boundary without touching the laser, so the framework doubles as a design rule for diagnostics.","The frequency-response analysis implies a tunable trade-off: increasing the update weight improves temporal resolution of shot-to-shot dynamics, while decreasing it suppresses measurement noise; at the threshold the Nyquist frequency is attenuated to roughly 67%, which can serve as an operating-point guideline."],"supporting_citations":[{"why":"Supplies the FALCON modal reconstruction formalism and Zernike–Taylor basis that the single-shot device extends.","marker":"[13]"},{"why":"IMPALA, the few-shot comparison method, used to motivate what a single-shot alternative must beat on acquisition time.","marker":"[14]"},{"why":"The survey noting that current STC diagnostics lack uncertainty quantification, the gap this work fills.","marker":"[20]"},{"why":"Time-series models for slow laser drifts, the basis for separating predictable evolution from stochastic variation.","marker":"[21]"},{"why":"Adaptive Kalman filter shown to overestimate system noise, motivating the two-step detrend-then-estimate procedure.","marker":"[27]"},{"why":"Holt's linear exponential smoothing used for the local linear approximation of deterministic drift.","marker":"[28]"},{"why":"Analytic formula for focal intensity loss from pulse front tilt, used to convert stochasticity into a peak-intensity floor.","marker":"[30]"}],"fun_headline_variants":["Single-shot metrology: a 2:1 noise ratio flips the regime","Petawatt laser: Bayesian sensing cuts pulse-front error 60%","Single-shot capability emerges from noise ratio, not device","Noise threshold separates single-shot from average measurement","Bayesian method redefines single-shot at ATLAS-3000 laser"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The framework assumes that after removing the local linear trend, the remaining shot-to-shot fluctuations are independent and Gaussian with a fixed, diagonal covariance, and that this stochastic variance can be estimated reliably from the same data; if the deterministic drift is not captured well by the local linear model, the estimated stochasticity is inflated and the regime classification and uncertainty bounds become biased.","fun_headline_variants_meta":{"raw":{"variants":["Single-shot metrology: a 2:1 noise ratio flips the regime","Petawatt laser: Bayesian sensing cuts pulse-front error 60%","Single-shot capability emerges from noise ratio, not device","Noise threshold separates single-shot from average measurement","Bayesian method redefines single-shot at ATLAS-3000 laser"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000268,"raw_usage":{"total_tokens":1680,"prompt_tokens":1071,"completion_tokens":609,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":687,"completion_tokens_details":{"reasoning_tokens":520}},"tokens_in":687,"tokens_out":609,"duration_ms":5851,"temperature":1.0,"reasoning_tokens":520,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T05:54:51.402290+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A controlled test would fix a single mode (e.g., pulse front tilt) and take two measurement series with deliberately different measurement noise, one with $\\sigma_{\\mathrm{meas}}^2 = 0.5\\,\\sigma_{\\mathrm{stoch}}^2$ and one with $\\sigma_{\\mathrm{meas}}^2 = 3\\,\\sigma_{\\mathrm{stoch}}^2$; the theory predicts the asymptotic posterior variance falls below $\\sigma_{\\mathrm{stoch}}^2$ only in the first case. If the state-resolving regime appears in the high-noise setting, or fails to appear in the low-noise setting, the threshold $\\sigma_{\\mathrm{meas}}^2 = 2\\sigma_{\\mathrm{stoch}}^2$ is wrong.","supporting_citations":[{"cited_title":"Weisse, J","cited_arxiv_id":null,"evidence_quote":"Supplies the FALCON modal reconstruction formalism and Zernike–Taylor basis that the single-shot device extends."},{"cited_title":"Smartsev, A","cited_arxiv_id":null,"evidence_quote":"IMPALA, the few-shot comparison method, used to motivate what a single-shot alternative must beat on acquisition time."},{"cited_title":"Alonso, A","cited_arxiv_id":null,"evidence_quote":"The survey noting that current STC diagnostics lack uncertainty quantification, the gap this work fills."},{"cited_title":"D¨ opp, C","cited_arxiv_id":null,"evidence_quote":"Time-series models for slow laser drifts, the basis for separating predictable evolution from stochastic variation."},{"cited_title":"Mohamed and K","cited_arxiv_id":null,"evidence_quote":"Adaptive Kalman filter shown to overestimate system noise, motivating the two-step detrend-then-estimate procedure."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Holt's linear exponential smoothing used for the local linear approximation of deterministic drift."},{"cited_title":"Pretzler, A","cited_arxiv_id":null,"evidence_quote":"Analytic formula for focal intensity loss from pulse front tilt, used to convert stochasticity into a peak-intensity floor."}],"review_version":1}