A Data-Based Architecture for Flight Test without Test Points

D. Isaiah Harp; Dylan Asmar; John Alora; Joshua Ott

REVIEW 4 major objections 5 minor 1 cited by

A Data-Based Architecture for Flight Test without Test Points

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that a flight-test architecture can eliminate test points: a Gaussian-process reduced-order model, seeded by a physics-based prior and updated with unconstrained maneuver data, predicts T-38 short-period frequency within…

desk verdict The architecture is a real idea; the T-38 demo's headline numbers likely reflect the A-7 prior more than the data. read the letter →

arxiv 2506.02315 v1 pith:45L2BNMC submitted 2025-06-02 cs.LG cs.AIcs.RO

D. Isaiah Harp , Joshua Ott , John Alora , Dylan Asmar This is my paper

classification cs.LGcs.AIcs.RO

keywords flighttestpointsGaussianprocessregressionreduced-ordermodelstabilityderivativesshort-perioddynamicsenvelopeexpansiondata-basedarchitecture

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

Flight test today validates a model by having a pilot hit precisely prescribed test points, and data that miss tolerances are discarded. The paper proposes inverting the hierarchy: treat the data as primary and let it refine a reduced-order model at whatever conditions were actually flown. In a proof-of-concept on the T-38C, roughly five minutes of slow rollercoaster data were fed into a Gaussian process whose mean function was a deliberately wrong generic aerodynamic model. Differentiating the resulting hypersurface at trim conditions produced stability derivatives, and from them short-period frequency and damping curves that sit within 5% (frequency) and 11% (damping) of the scatter internal to the historical record. If the architecture holds, test points, databands, and repeat maneuvers become unnecessary, and the output of flight test becomes a compact, physics-based representation of the aircraft.

What carries the argument

The load-bearing object is a Gaussian process, a distribution over functions updated by observed data, defined over the map from aircraft state to pitching moment coefficient, with a physics-based mean function drawn from a generic aerodynamic model and a neural-network kernel controlling smoothness. The posterior mean is differentiable, so its gradients evaluated at trim conditions give the stability derivatives that enter the short-period frequency and damping formulas. The supporting procedural machinery is the two-stage architecture: offline, a reduced-order model space is built from a high-fidelity model and a model builder is trained on it; online, flight data update the model builder in near real time, and the refined reduced-order model can feed back to update the high-fidelity model. Empirically fitted trim functions for angle of attack and stabilator deflection as functions of dynamic pressure are what convert arbitrary maneuver data into local derivative evaluations at comparable flight conditions.

What would settle it

Rerun the same Gaussian process pipeline on the same rollercoaster data with the generic aerodynamic mean function replaced by a constant mean and by the aerodynamic model of a second, unrelated aircraft, and also with the input data low-pass filtered below 0.0036 Hz. If the recovered T-38C short-period frequency and damping curves shift by more than the paper's reported 5% and 11% margins, the recovery of the high-frequency mode is attributable to the prior rather than to the flight data.

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Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that the fundamental output of developmental flight test should be a direct representation of the physics of the system under test, obtained by inverting the model-test-validate cycle. The demonstration is a single Gaussian-process hypersurface mapping aircraft state (Mach, density, dynamic pressure, body rates, angle of attack, stabilator deflection) to pitching moment coefficient, initialized with the generic aerodynamic mean function of a similar but different aircraft (the A-7) and updated with roughly five minutes of unconstrained rollercoaster data whose input energy is about 1% of the short-period frequency. Posterior differentiation at experimentally determined trim conditions recovers stability derivatives, and a second-order equivalent system then yields short-period frequency and damping as functions of dynamic pressure and Mach. The paper reports that this one function predicts short-period frequency to within 5% of the error internal to the historical record for any dynamic pressure, and damping to within 11% for any dynamic pressure and Mach combination, and that the recovered parameters agree with a published system-identification estimate at 0.7 Mach and 32,000 feet. The authors attribute the recovery of high-frequency modes from low-frequency data to the physics-based prior, explicitly as a hypothesis.

Load-bearing premise

The entire demonstration rests on the hypothesis that a physics-based prior, in the form of a generic aerodynamic mean function, lets a Gaussian process recover high-frequency short-period behavior from rollercoaster data whose input energy is near 0.0036 Hz, about 1% of the short-period frequency, so that if this hypothesis is false, the extracted stability derivatives and frequency and damping curves reflect the prior, not the data.

Editorial extensions

If this is right

Test points disappear as execution requirements: data collected outside databands and tolerances refine the reduced-order model rather than being discarded, which the paper estimates could have accelerated one large program by a factor of six.
The output of a flight-test campaign is a compact, differentiable, physics-based reduced-order model with quantified uncertainty at every point, not a series of spot-check comparisons.
A single hypersurface generated from about five minutes of low-frequency rollercoaster data predicts T-38C short-period frequency within 5% and damping within 11% of the error internal to the historical record, across dynamic pressure and Mach without dedicated test points.
Because the hypersurface embeds dynamic-pressure and Mach dependence implicitly, stability derivatives and short-period parameters can be evaluated at any as-flown condition and updated after each maneuver in near real time.
The refined reduced-order model can be traced back to update the original high-fidelity model, so validation happens simultaneously with model refinement.

Reading between the lines

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

Beyond the paper: the decisive check of the physics-based prior hypothesis is to rerun the pipeline with a constant mean function and with a different generic aircraft as the prior; if the recovered frequency and damping curves move by more than the claimed 5% and 11%, the curves are being supplied by the prior, not the data.
Beyond the paper: the demonstrated error metric compares the new curve to the scatter among historical estimates, not to an absolute ground truth; an independent, dedicated maneuver on the same T-38C airframe at the same trim conditions would be the stronger validation.
Beyond the paper: the architecture turns maneuver planning into optimal experimental design, since flight time should be spent where the posterior variance of the learned hypersurface is largest.
Beyond the paper: the slogan that all data are good data is conditional on the data carrying information; a perfectly steady trim record should barely move the posterior, and the model's own uncertainty would reveal whether a maneuver actually constrained the short-period dynamics.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The architecture is the contribution here, not the numbers. The point-less concept—inverting the predict-test-validate cycle so that any as-flown data refines a reduced-order model instead of spot-checking a point prediction—is genuinely new and clearly argued. The paper is worth engaging on that basis.

The T-38 demo, though, does not carry the weight the authors put on it. The stress-test concern is correct: the GP posterior gradient in Eq. 27 is the A-7 prior gradient plus a data-correction term, and the rollercoaster data have spectral energy around 0.0036 Hz, roughly 1% of the short-period frequency. Those data can constrain a low-frequency combination of Cm_alpha and Cm_Q, but they cannot separately identify the two derivatives that enter omega_SP and zeta_SP. The separation is supplied by the Morelli mean function. The authors themselves flag this in Sec. 4.4 as a hypothesis, and they never show the prior-only curve for comparison. That is a load-bearing gap for the headline claim.

What the paper does well: real T-38 sorties, calibrated data, comparison against four historical sources spanning 1961-2024, and a transparent discussion of the comparison's limitations (non-standard CG, assumed standard atmosphere, hand-plotted scans). The architecture sections are thoughtful about the role of noise, uncertainty, and the connection to outcome-based risk management.

Soft spots, in proportion: missing GP hyperparameters and noise variance make the prior-versus-data weight uncontrolled. The M_alpha_dot = M_q/3 substitution is ad hoc. GP uncertainty is not propagated to omega/zeta. The high-dynamic-pressure region in Table 2 is worse than the historical scatter itself, which is consistent with prior-dominated extrapolation. The '5%/11% of internal error' metric is clever but not as strong as it sounds—it means their curve is within the scatter of the historical record, not that it beats it. All of this is fixable with more analysis, but it does mean the demonstration as presented should not be read as confirmation of the architecture.

Would I referee it? Yes. The concept is timely and could matter for envelope expansion. A serious referee should ask for the GP hyperparameters, a prior-only baseline, identifiability analysis, and uncertainty propagation. That revision would either make the case or expose where it breaks. The paper is a solid, honest proof-of-concept that deserves referee time.

Referee Report

4 major / 5 minor

Summary. The paper proposes a 'point-less' flight test architecture intended to invert the traditional model-test-validate cycle. In this architecture, a Gaussian Process Regression (GPR) model with a physics-based mean function (the A-7E Morelli aerodynamic model) ingests unconstrained, low-frequency 'rollercoaster' maneuver data from a single T-38C sortie. The resulting differentiable hypersurface for the pitching moment coefficient Cm is differentiated at trim conditions to obtain stability derivatives, which are then used to compute short-period frequency and damping as continuous functions of dynamic pressure and Mach. These curves are compared against consolidated historical T-38 data from four sources spanning 1961-2024. The authors claim the frequency curve matches the historical record to within 5% of its internal error and the damping curves to within 11%, concluding that the architecture can eliminate test points and yield a refined reduced-order model from arbitrary 'as-flown' data.

Significance. If the central claim is sustained, the paper would make a noteworthy contribution: it offers a concrete, data-driven alternative to the test-point paradigm, with the potential to reduce the number of required maneuvers and to reuse data that would traditionally be discarded. Credit is due for collecting and presenting actual T-38C flight test data, for consolidating a historically scattered set of comparison points, and for framing the inversion of the model-test-validate cycle in a clear way. However, the demonstration as presented has several load-bearing gaps: the GP hyperparameters and noise variance are not reported, the substitution M_alpha_dot = M_q/3 is unjustified, no uncertainty is propagated from the GP posterior to the derived short-period quantities, and the paper itself labels as a hypothesis the key mechanism by which low-frequency data are claimed to recover high-frequency short-period behavior. The high-dynamic-pressure region of Table 2 also contradicts the headline accuracy claim. These issues mean that the proof-of-concept is plausible but not yet established.

major comments (4)

[Sec. 4.2.2, Eqs. (19)-(20)] The Gaussian process kernel hyperparameters and the noise variance ν are never reported. The posterior mean in Eq. (25) is a weighted combination of the A-7 mean function and the flight data, with the relative weight controlled by ν through A = (K + νI)^(-1)(y - m(X)). Without reporting ν (and any kernel parameters), the reader cannot assess whether the posterior is data-dominated or prior-dominated. Furthermore, although the paper emphasizes uncertainty quantification, the short-period results in Eqs. (28)-(29) are computed from the deterministic posterior mean gradient in Eq. (27) with no propagation of the posterior covariance Σ* from Eq. (16). The claimed uncertainty quantification therefore does not extend to the headline quantities ωSP and ζSP.
[Sec. 4.3.3, Eq. (29)] The replacement M_alpha_dot = M_q/3 is introduced without derivation, citation, or sensitivity analysis, yet ζSP depends directly on this term through Eq. (29). Since the paper's central quantitative claim concerns damping, this substitution is load-bearing. The authors should justify the factor (for example, by providing a reference, by identifying M_alpha_dot from a maneuver that actually excites it, or by demonstrating that the final results are insensitive to reasonable variations in this factor).
[Sec. 4.4, Table 2 and Figs. 12-14] The summary claim that the method predicted short-period frequency 'to within 5% of the error internal to the historical record' and damping 'to within 11%' is not supported across all dynamic pressure regions. In the high-dynamic-pressure row of Table 2, the prediction error for ωSP is 30.2% versus 25.6% for the historical record (4.6 percentage points worse), and for ζSP it is 26.3% versus 15.8% (10.5 percentage points worse). These are the largest discrepancies in the table and are not explained. The conclusion that the method 'exceeded the consistency of the historical record' is only true for the moderate and low dynamic pressure regions. The paper should either restrict its claim, report confidence intervals on the error metrics, or provide a data-region explanation for why performance degrades at high dynamic pressure.
[Sec. 4.4, Eq. (25) and the rollercoaster excitation] The paper itself labels as a hypothesis the recovery of high-frequency short-period modes from 0.0036 Hz rollercoaster input. This is a critical issue because the posterior mean µ(x) = m(x) + k(x,X)^T A is a prior plus a data correction, and during a rollercoaster α and Q are strongly correlated and slowly varying. Such data can constrain only a low-frequency combination of Cmα and CmQ, not the individual derivatives that enter Eqs. (28)-(29). The separation between these derivatives is largely supplied by the A-7 mean function. To support the claim that Figs. 12-14 represent a data-refined T-38 ROM rather than a projection of the A-7 prior, the authors should plot the prior-only short-period curves alongside the posterior curves and quantify the magnitude of the data correction. Without this, the central distinction between 'learning from the data' and 'inheriting the prior' is not demonstrated.

minor comments (5)

[Abstract and Sec. 4.4] The phrase 'within 5% of the error internal to the historical record' is ambiguous: Table 2 reports differences in percentage points, not relative percentages. The abstract should define the metric clearly (e.g., 'within 5 percentage points of the historical internal error').
[Sec. 4.4] The historical comparison data are plotted without uncertainty bars, and the GP-derived curves are shown without posterior uncertainty bands, even though the GPR framework provides such bands. Adding error bars to Figs. 12-14 would make the comparison much more informative.
[Sec. 4.1] The text says the rollercoaster is an 'arbitrary' maneuver, yet the authors targeted particular Mach and altitude combinations for historical comparison. The qualification in footnote 7 is helpful, but the main text should be consistent about what 'arbitrary' means in this context.
[Sec. 4.3.1, Eqs. (21)-(22)] The trim functions αtrim(qbar) and δetrim(qbar) are fitted to data with coefficients a, b, c, d, but no fit quality or uncertainty is reported. Since these functions determine the trim state at which all derivatives are evaluated, reporting their goodness of fit would strengthen the analysis.
[Throughout] There are several typos and formatting artifacts (e.g., 'T est' in the title, 'datbands' for 'databands', 'condescension' in Sec. 2.4). A careful proofread would improve readability.

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity: the central short-period predictions are checked against independent historical data, and the only concrete circular step is a minor in-sample Cm fit presented with prediction language.

fitted input called prediction [Section 4.4, Figure 11 (training setup in Section 4.2.2)]
"The true values of Cm, calculated using equation 3, are represented by the dashed line, serving as the ground truth. The solid line denotes the GP prediction, accompanied by a shaded region that captures the 95% confidence interval, representing the model's uncertainty in its predictions."

The GP was updated using observed data whose targets y(i) are noisy observations of Cm (Section 4.2.2), and the dashed 'ground truth' in Figure 11 is Cm computed by equation 3 from the same maneuver. The comparison therefore shows the posterior mean against its own training targets: the close agreement is an in-sample fit, not a forecast of unseen data. This step is not load-bearing, because the central short-period result is evaluated against four external historical sources (SIDPAC, CIFER, TPS doublets, AFFTC 1961) rather than against this plot.

full rationale

Walking the derivation chain: the forward process uses the external A-7 Morelli generic aerodynamic model [9] as the GP mean function, the GP update equations (15)-(16) are standard, and the short-period formulas (28)-(29) are textbook second-order approximations. The posterior derivative decomposition of Eq. (27) into a prior gradient plus a data correction is exact, not circular. Crucially, the reported omega_SP(qbar) and zeta_SP(qbar, Mach) curves are not fit to the historical omega_SP/zeta_SP values: the historical record is used only to target rollercoaster dynamic pressures and as a final benchmark, so the 'within 5%/11% of historical internal error' claim is an external comparison. The paper contains no load-bearing self-citation chain and no uniqueness theorem imported from the authors. The main caveat is identifiability, not circularity: a rollercoaster excites AOA oscillations at 0.0036 Hz, about 1% of the short-period frequency, so the data may not separately constrain Cm_alpha and Cm_Q; if the data correction in Eq. (27) is uninformative in those directions, the extracted derivatives and hence omega_SP and zeta_SP are inherited from the A-7 prior. The authors explicitly label this mechanism only as a hypothesis ('We hypothesize that we were able to reproduce high-frequency modes with low-frequency experimental content due to our imposition of a physics-based prior'), and they do not report GP hyperparameters, noise variance nu, or a prior-only ablation, leaving the data-versus-prior attribution uncontrolled. That is a validation gap to weigh under correctness risk, not a circular step. The single concrete circularity is Figure 11, where GP 'prediction' is compared with the same Cm values used for training; this is minor and does not support the paper's central claim by itself.

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

The central output, omega_SP(qbar) and zeta_SP(qbar), is a function of the GP posterior, which is fit to flight data via kernel hyperparameters, noise, and trim functions. The A-7 mean function is an input from prior literature, not independently justified for the T-38C. The paper also uses the short-period model it critiques, with an ad hoc substitution. No new physical entities are introduced.

free parameters (4)

Gaussian process kernel hyperparameters = not reported
The neural network kernel in eq 19 has parameters that are fit to the flight data; values are not given in the paper.
Gaussian process noise variance ν = not reported
Appears in eqs 15 and 16 and must be set or estimated; not reported.
Trim function coefficients a, b, c, d = not reported
Fit by regression of experimental trim data in eqs 21-22; values not given.
Short-period damping substitution coefficient = 1/3
Equation 29 replaces M_alpha_dot with (1/3) M_q, an ad hoc modeling choice attributed to Yechout.

assumptions (5)

standard math Rigid-body equations of motion (1-3) with standard notation
Used as the starting point for the short-period derivation.
domain assumption Small perturbation, linearization assumptions for short period
Section A.1/A.2 assumes small deviations, q≈alpha_dot, and neglects higher-order terms.
ad hoc to paper A-7E generic aerodynamic model is a valid mean function for T-38C GPR
The paper intentionally uses a 'known incorrect' model as the physics prior (Section 4.1).
ad hoc to paper Physics-based prior allows recovery of high-frequency modes from low-frequency (0.0036 Hz) data
Section 4.4 labels this as a hypothesis, not a proven result.
domain assumption 2-DOF linear short-period model (eqs 28-29) adequately represents the aircraft despite the paper's claim that 'there is no such thing as the short period'
The paper uses the model it critiques to produce the headline numbers.

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Cite this review

Pith. "Pith review of A Data-Based Architecture for Flight Test without Test Points." pith.science (2026). https://pith.science/paper/45L2BNMC

@misc{pith2026250602315,
  author       = {Pith},
  title        = {Pith review of: A Data-Based Architecture for Flight Test without Test Points},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/45L2BNMC}},
  note         = {Machine review of arXiv:2506.02315}
}

read the original abstract

The justification for the "test point" derives from the test pilot's obligation to reproduce faithfully the pre-specified conditions of some model prediction. Pilot deviation from those conditions invalidates the model assumptions. Flight test aids have been proposed to increase accuracy on more challenging test points. However, the very existence of databands and tolerances is the problem more fundamental than inadequate pilot skill. We propose a novel approach, which eliminates test points. We start with a high-fidelity digital model of an air vehicle. Instead of using this model to generate a point prediction, we use a machine learning method to produce a reduced-order model (ROM). The ROM has two important properties. First, it can generate a prediction based on any set of conditions the pilot flies. Second, if the test result at those conditions differ from the prediction, the ROM can be updated using the new data. The outcome of flight test is thus a refined ROM at whatever conditions were flown. This ROM in turn updates and validates the high-fidelity model. We present a single example of this "point-less" architecture, using T-38C flight test data. We first use a generic aircraft model to build a ROM of longitudinal pitching motion as a hypersurface. We then ingest unconstrained flight test data and use Gaussian Process Regression to update and condition the hypersurface. By proposing a second-order equivalent system for the T-38C, this hypersurface then generates parameters necessary to assess MIL-STD-1797B compliance for longitudinal dynamics.

Figures

Figures reproduced from arXiv: 2506.02315 by the authors.

**Figure 1.** The Model-Test-Validate Cycle The customary hierarchy – model primary, data substantiative – has two important consequences. In the first place, it obligates test pilots to a high degree of precision. Models must be run with some particular set of assumptions: the parameters of the model. As those parameters change, the model outputs also change, sometimes in highly nonlinear or poorly understood ways. Thus, to re… view at source ↗

**Figure 2.** Summing wing and tail moments for a simple airplane model Nelson in fact constructs this model in his monograph on stability and control his sketch of the parameters of interest appears in figure 2 [5]. The sum of the moments in this simplified case is simply the moment due to the wing plus the moment due to the tail, each computed between the airfoil aerodynamic center and the aircraft center of gravity. i.e.,… view at source ↗

**Figure 3.** The forward process in a data-based architecture for flight test This proposal does not alter or break the model-test-validate cycle. In fact, it strengthens it. The model still comes first chronologically. Test follows. However, the outputs of test are used to refine and update the model in near real-time using contemporary data-based methods. Validation of the model then occurs as a natural consequence of (and sim… view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: The inverse process in a data-based architecture for flight test ROM space using a pure imitation-learning (IL) metaphor. If, subject to some set of inputs, each ROM outputs a physical quantity of interest that characterizes the aircraft under test, then we can run eac…

**Figure 5.** Figure 5: The forward process as implemented for a T-38 flight test campaign identified through a model structure determination protocol. For example, the pitching moment coefficient was expressed as Cm ≡ M qS¯ c¯ = θ29 + θ30α + θ31q˜ + θ32δe + θ33αq˜ + θ34α 2 q˜ + θ35α 2 δe + θ…

**Figure 6.** Figure 6: The A-7E Corsair II, the aerodynamics of which were used as a mean function for regressing flight test data for the T-38C. The mathematics of the mean function will be explained more fully in section 4.2.2. However conceptually we adopted the particular ROM of the A…

**Figure 7.** Figure 7: The inverse process as implemented for a T-38 flight test campaign With this generic aerodynamic model of the A-7 as our ROM, we selected Gaussian Process Regression (GPR) as our model builder algorithm for the inverse problem. The theory of GPR as applied in this case…

**Figure 8.** Figure 8: Surface plot showing the relationship between α, Q, and Cm learned by the Gaussian process. The surface is colored by the model’s uncertainty values. 4.3. Prediction of the Short Period One of the key advantages of GPR is that it provides a smooth, differentiable hyper…

**Figure 9.** Figure 9: The consolidated short period data collected for comparison. The symbols cross-reference with figure 12. 4.4. Results To assess the accuracy of our methods, we gathered historical comparison data on the T-38 short period mode from four sources, encompassing a range of …

**Figure 10.** Figure 10: An example of hand-plotted data depicted in the AFFTC test report on the T-38A, from 1961 [18]. temperature), and so a standard atmosphere was assumed. Also, data were not standardized to a common center of gravity (CG) location; it is known that CG location will alte…

**Figure 11.** Figure 11: Cm prediction using our Gaussian process based approach. The linear model is constructed using linear regression between the state vector given in equation 18 and Cm. Method Cmα Cmδe CmQ ωSP ζSP Linear Model -0.285 -0.525 -3.240 0.250 0.219 GP Estimates -0.442 -1.045 …

**Figure 12.** Figure 12: The consolidated short period data collected for comparison, along with a continuous line of values produced using our methods and varying dynamic pressure (denoted as q in this figure). pressure was taken into account; GPR learned how implicit variations in dynamic p…

**Figure 13.** Figure 13: Short period frequency model for dependence on dynamic pressure, along with comparison data. Here, no dependency on Mach was observed. Regions of similar dynamic pressure had values for q¯ within ±40 lb f t2 of each other. This excluded some points from the current an…

**Figure 14.** Figure 14: Short period damping model for dependence on dynamic pressure, along with comparison data. Here, different curves demonstrate the Mach dependence. Dynamic Pressure ωsp Error (%) ζsp Error (%) Prediction Dataset Difference Prediction Dataset Difference High 30.2 25.6 -…

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Forward citations

Cited by 1 Pith paper

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Reference graph

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