{"id":"a8b6e4c3-a861-4e8f-9803-57e8f30f82f1","arxiv_id":"2502.08882","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A Gaussian process integrated data analysis model for HL-3 plasma density tomography combines FIR line integrals with FMCW point values and reaches 3.60e-4 average relative error in synthetic benchmark tests.","lead":"Researchers combine two plasma density diagnostics on the HL-3 tokamak into one Gaussian process tomography model, using magnetic flux coordinates to map measurements onto a 2D profile. In synthetic tests the integrated model reports an average relative error as low as 3.60e-4, but no experimental data were used and key systematic errors were set aside.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported 3.60e-4 accuracy rests on feeding exact ground-truth values as FMCW point measurements, not on a forward model of FMCW; real FMCW-derived v* carry unmodeled inversion and mapping errors.","rationale":"The paper is internally coherent: the GPR posterior equations are standard, the synthetic tests are clearly described, and the conclusion correctly limits the claim to synthetic validation. The improvement from Cartesian kernels (xi_bar = 5.18e-3) to flux-coordinate kernels (3.60e-4) is a sensible demonstration that including equilibrium structure in the prior helps. The authors are explicit that EFIT systematic errors and experimental application are deferred; no code or data are provided, which already supports a conditional verdict. My stress-test focuses one level deeper: the synthetic FMCW input v* is not derived from a model of FMCW reflectometry at all. FMCW measures group delay as a function of frequency; density profile values are obtained through an inversion algorithm (Appendix B cites HL-2A FMCW development). Treating the exact synthetic profile values at chosen flux locations as 'point measurements' and setting their standard deviation to zero means the GPR conditional in Eq. (2-5) is given exact edge data; the line-integral FIR data then do the remaining work. The reported high accuracy is therefore an interpolation benchmark under idealized v*, not an end-to-end validation of IDA with FMCW. This matters because the abstract promises a 'robust foundation for real application'; real v* will contain systematic errors from FMCW inversion and EFIT mapping that are not in the test. The paper flags the EFIT part but not the identity-measurement assumption for FMCW. A single end-to-end FMCW simulation would settle the issue. The reader's weakest_assumption (EFIT flux accuracy) is adjacent and also valid; my concern is the more upstream assumption that v* are exact direct density observations. Given the absence of code/data and the idealized synthetic FMCW input, the appropriate verdict remains CONDITIONAL: accept only if the authors add an end-to-end synthetic FMCW test or explicitly scope the claim to exact point-value interpolation.","tokens_in":14561,"tokens_out":8817,"duration_ms":87461,"concrete_test":"Replace the Section 3 synthetic FMCW input with an end-to-end simulation: generate synthetic FMCW beat/group-delay traces from the ground-truth profile, run the same conventional FMCW inversion used on HL-2A/HL-3 to obtain v*, add realistic noise (1%, 3%, 5%) and a plausible EFIT flux-coordinate bias, then rerun the IDA reconstruction and recompute xi_bar, xi_max, and rRMSE. If the errors remain at or below ~1e-3, the headline claim survives the test; if they rise by an order of magnitude or more, the 3.60e-4 number should be explicitly re-labeled as an idealized exact-point-value benchmark rather than an integrated-data-analysis accuracy estimate.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The load-bearing step is the construction of v* in the synthetic validation (Section 3). The text says: 'The synthetic values from the virtual diagnostic of FMCW on the electron density profile are obtained as the input v*' and 'The standard deviations of d and v* are set to 0.' This means the FMCW points are the exact values of the known electron density profile at the selected locations, not the output of an FMCW measurement model. In the actual HL-3/HL-2A FMCW reflectometer, the measured quantity is a frequency/group-delay trace, and the local density values v* are obtained only after a separate inversion (Appendix B; refs. 44, 32); that inversion has spatial resolution limits, systematic offsets, and error correlations that are not represented. Section 2 motivates the method by saying it 'eliminates the need for establishing a corresponding forward model for FMCW'—but this also means the validation never exercises the FMCW measurement chain. With exact v* placed in the detection zone and a zero-mean SE-kernel prior on flux coordinates, Eq. (2-5) essentially interpolates the known edge profile through exact data; the FIR likelihood then fixes the remaining degrees of freedom. The reported xi_bar = 3.60e-4 and rRMSE = 1.32e-4 therefore quantify interpolation accuracy of the chosen kernel, not reconstruction accuracy from actual FMCW data. The paper is transparent that EFIT systematic errors are ignored (Section 3) and deferred to future work (Section 5), but it does not separately acknowledge that v* themselves are assumed to be noise-free, unbiased, direct density observations. Since the headline claim is presented as a 'robust foundation for real application' (Abstract), this missing FMCW forward-model step is the most load-bearing unvalidated assumption.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript proposes an integrated data analysis (IDA) model for two-dimensional electron density profile tomography on the HL-3 tokamak. The model combines line-integrated signals d from the 13-channel FIR interferometer with point density values v* from FMCW reflectometry within a Bayesian Gaussian process regression framework. A zero-mean GP prior with a squared-exponential kernel is defined either on Cartesian coordinates or on normalized magnetic flux coordinates obtained from EFIT; the FIR data are entered through a linear response-matrix likelihood, and the posterior is computed by the standard Gaussian conditioning formulas of Eqs. (2-10)-(2-11). The model is validated in a synthetic test: a known 2D density profile, built as a modified tanh function of normalized flux (Appendix C), generates synthetic FIR chord integrals and exact FMCW point values, and the reconstruction is scored against that profile. The headline accuracy is an average relative error xi_bar = 3.60e-4 and rRMSE = 1.32e-4 for the flux-coordinate kernel (Tables 1-2). Sensitivity studies cover grid resolution (14x15 to 56x60, with 28x30 selected as best), the assumed standard deviation of the error model, and 1000 runs with 1-5% random Gaussian noise. The authors conclude that the model provides a robust foundation for application to real HL-3 experimental data.","tokens_in":14862,"tokens_out":12543,"duration_ms":120289,"significance":"The contribution is primarily an application-level synthesis: combining FIR line integrals and FMCW point values through a GP prior in flux coordinates and validating it for the HL-3 diagnostic layout. The derivation is standard GPR with a linear Gaussian likelihood, and Eqs. (2-5), (2-10) and (2-11) are internally consistent; the paper is transparent about its synthetic setup and explicitly acknowledges that EFIT systematic errors are ignored. The BDA-versus-IDA comparison (Tables 1-2) is a useful ablation showing the value of point constraints, and the noise study (Tables 5-7, Figure 8) honestly documents pronounced noise sensitivity. If the reported accuracy were representative of real-data performance, the method would be a practical tool for HL-3. However, the headline accuracy is a self-consistency and interpolation figure obtained under idealized conditions (exact FMCW values, zero measurement noise, same flux mapping used to generate the truth and to define the kernel, and a grid chosen ex post), so the significance of the paper depends on the validation claims being reframed and strengthened.","major_comments":[{"comment":"The headline errors (xi_bar = 3.60e-4, rRMSE = 1.32e-4) are interpolation/self-consistency metrics, not reconstruction accuracies from real FMCW data. The text states that 'The synthetic values from the virtual diagnostic of FMCW on the electron density profile are obtained as the input v*' and that 'The standard deviations of d and v* are set to 0,' so v* contains the exact values of the known profile at the FMCW locations, with no representation of the FMCW measurement chain (frequency/group-delay trace to density inversion, Appendix B and refs. 32, 44). Conditioning Eq. (2-5) on exact point values interpolates the known edge profile, and the zero-noise FIR likelihood (2-7) fixes the remaining degrees of freedom; the experiment therefore measures how well the SE kernel and the 13-chord geometry reproduce a smooth function, not how accurately the method would invert actual HL-3 reflectometer data. To support the 'robust foundation for real application' claim in Section 5, the validation needs a structured-error test in which v* is produced by a model of the reflectometer inversion (including bias and correlated errors) and a test with perturbed EFIT flux mapping.","section":"Section 3 and Table 2"},{"comment":"The flux-coordinate test is circular in a way that guarantees the improvement shown in Table 2. The synthetic profile is constructed as n_e_bar(rho) = A * MTANH(alpha, z) + B, a function of normalized toroidal flux only (Eqs. (5-3)-(5-4)), and the same EFIT equilibrium (Figure 11) is used both to generate that profile and, through the mapping in Section 2.3, to define the kernel distances |psi_j - psi_k| in Eq. (2-13). The model's key assumption, that the electron density is uniform on each flux surface, is therefore exactly true in the test, so Table 2 measures the benefit of injecting that prior when it holds, not its validity for real HL-3 plasmas, where flux-surface asymmetries, MHD activity, and EFIT mapping errors will break F(x) = F(psi). The manuscript acknowledges this in one sentence ('Systematic errors of v* introduced by EFIT equilibrium reconstruction, are ignored in this work'), but the conclusion (Section 5) reports the 87.5%/93.1%/91.5% error reductions without this caveat. It is also unclear whether the kernel coordinates in the synthetic test come from the same EFIT solution used in Appendix C or from the EFITNN mapping cited in Section 2.3; if they differ, an unquantified mapping error is hidden in the test, and if they are identical, the test is fully circular.","section":"Section 3.2 and Appendix C"},{"comment":"The kernel hyperparameters sigma and l are never reported, and the grid resolution was selected using the same metric that is then presented as the headline result. Appendix A says the optimal hyperparameters are determined by evidence maximization, and Section 4.3 states that they 'are fixed,' yet no numerical values for sigma or l appear anywhere in the text or tables, making Tables 1-5 irreproducible. Independent reimplementation is impossible without these numbers. Likewise, Section 4.1 compares four grids and reports that the 840-point (28x30) grid achieves the best xi_max, xi_bar, and rRMSE; choosing the grid that minimizes the reported error and then quoting that minimum as the model's accuracy is a selection-on-the-test-set bias. The authors should report the optimized hyperparameter values and treat the grid choice as part of a declared procedure (for example, selected on a separate validation configuration), or present all four grid resolutions in the main accuracy claims.","section":"Sections 2.3, 4.1 and 4.3"},{"comment":"The robustness claim in the conclusion is not supported by the noise experiments it refers to. Table 5 shows that adding 1% random Gaussian noise raises the mean xi_bar from 5.24e-4 to 3.23e-3 and the mean xi_max from 1.30e-2 to 1.42e-1, and at 5% noise the mean xi_max reaches 6.55e-1, a maximum local error above 65% of the peak density; the text in Section 4.3 itself acknowledges 'pronounced noise sensitivity.' Section 5 nevertheless concludes that 'the model maintains robust inversion capability even when subjected to 10% measurement uncertainty.' This conflates the Section 4.2 experiment, which changes the assumed standard deviations in the error model, with the Section 4.3 experiment, which adds actual random noise; 10% actual noise was never tested. In addition, it is unclear whether Section 4.2 perturbs the data or only inflates Sigma_epsilon and sigma*^2: Figure 7(b) shows back-projections that agree with the synthetic FIR data at all stated standard-deviation levels, which suggests the data were not actually noised. The authors should clarify the design of Section 4.2 and qualify the 'robust' claim accordingly.","section":"Sections 4.2, 4.3 and 5"}],"minor_comments":[{"comment":"Table 3 lists the finest grid as '3660 (56x60)'; this should read '3360 (56x60)' to agree with the count given in the text of Section 4.1.","section":"Table 3"},{"comment":"There are several typos: 'In precious research' should be 'In previous research', 'time-cconsuming' should be 'time-consuming', and the sentence introducing xi_max says 'donates' where 'denotes' is meant.","section":"Section 1 and Section 3"},{"comment":"The appendix equations are labeled (5-1) and (5-2), which is inconsistent with the (2-x)/(3-x) labeling used in the body; they should be relabeled (A-1) and (A-2).","section":"Appendix A"},{"comment":"The zero-mean GP prior is a strong assumption for a strictly nonnegative quantity such as electron density; because extrapolation in the core is weakly constrained (Figure 3(b)), the authors should justify the zero-mean choice or discuss a nonzero mean function based on typical HL-3 profiles.","section":"Section 2.1"},{"comment":"The 'instabilities arising from the numerical calculations' observed at 1890 and 3360 grid points are presented as a preliminary attribution; since Eqs. (2-10)-(2-11) require inverting covariance matrices of size g x g, reporting condition numbers or a Cholesky-based stability check would substantiate the discussion.","section":"Section 4.1"}],"recommendation":"major_revision","confidential_remarks":"This is an application paper built on textbook GPR machinery; its novelty relative to prior IDA-GPR tomography (e.g., Moser et al. 2022, Liu et al. 2022, Kwak et al. 2020, Wang et al. 2018) lies in the specific HL-3 FIR+FMCW combination and the flux-coordinate kernel. The central risk is that the abstract's 'as low as 3.60e-4' and the conclusion's 'robust foundation for real application' will be read by practitioners as statements about real-data performance, when the experiment is an idealized self-consistency test. I would ask the authors to reframe the validation as an interpolation/self-consistency study, report the missing hyperparameters, and add structured-error tests (biased v*, perturbed flux mapping, correlated noise) before the manuscript can support its stated conclusions. With those changes the paper would be a useful contribution to fusion diagnostic integration practice."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a sensible, clearly written extension of existing Bayesian GPR tomography work to HL-3, combining FIR line-integrals with FMCW point values. The math is standard and correctly assembled. The novelty is modest but real: treating FMCW-derived densities as direct observations in a 2D flux-mapped SE kernel, rather than building a forward model for the reflectometer. That is a reasonable first step.\n\nThe problem is what the headline number actually means. In the synthetic validation, the FMCW point values are the exact values of the known profile at those locations, with zero standard deviation, not the output of an FMCW measurement chain. The reflectometer measures frequency traces; the local densities v* come from a separate inversion with its own spatial resolution, offsets, and error correlations. None of that is exercised. So the reported xi_bar = 3.60e-4 is a statement about how well the SE kernel interpolates through exact edge points, not about reconstruction from real FMCW data. The paper acknowledges EFIT systematic errors are ignored, but it does not flag that v* itself is assumed noise-free and unbiased. That is the load-bearing assumption, and it is untested.\n\nThe sensitivity analysis is a plus: the grid, standard deviation, and noise scans are systematic, and the noise sensitivity results give useful reliability benchmarks. The paper is also honest about the core-region limitations without flux mapping. But the grid resolution was chosen post hoc because it scored best, and the kernel hyperparameters are only said to be fixed by Occam's razor, with no values or evidence curves. For a tomography method, that is a reproducibility gap.\n\nThe circularity is real: the synthetic profile is built as a function of normalized flux, which is exactly the model's prior assumption. So the improvement from flux mapping is partly baked in. That does not invalidate the approach, but it means the comparison is a self-consistency check, not an independent validation.\n\nProportionately: the core method is fine, and with a realistic FMCW forward model or real-data demonstration it could be a solid contribution. As is, the abstract's robust foundation for real application overstates what is demonstrated. I would send it to peer review, because it deserves a serious referee, but the referee should push for code and data, reported hyperparameters, and a validation that includes the FMCW measurement chain or at least a clear statement of its absence. For my own work, I would not cite the headline numbers, but the approach might be worth citing as an example of GPR-based IDA.","headline":"A clean GPR-based IDA extension for HL-3, but the headline accuracy is an interpolation benchmark with exact synthetic FMCW values, not a real reconstruction test.","tokens_in":15502,"tokens_out":2955,"would_cite":false,"duration_ms":29332,"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":"By mapping Gaussian-process kernel distances onto normalized magnetic flux, the model fuses FIR and FMCW data into HL-3 electron-density reconstructions with average relative error as low as 3.60e-4 in synthetic validation.","keywords":["Gaussian process regression","integrated data analysis","plasma electron density tomography","HL-3 tokamak","FIR interferometry","FMCW reflectometry","normalized magnetic flux","Bayesian inference"],"falsifier":"Run the same synthetic validation with the equilibrium flux map deliberately perturbed, for example by shifting flux-surface locations by a few centimeters, and record how the average relative error moves from $3.60\\times10^{-4}$. If realistic equilibrium errors push the error up to the level of the Cartesian-kernel reconstruction, the flux-mapping assumption, not the data fusion, is the effect carrying the accuracy claim.","tokens_in":14348,"feed_emoji":"🧲","tokens_out":10606,"duration_ms":95450,"temperature":0.7,"pith_summary":"Integrated data analysis (IDA) on HL-3 is usually done on 1D flux-surface profiles; this paper claims that a Gaussian-process regression model can do genuine 2D tomography by combining line-integral data from the far-infrared interferometer with point values from FMCW reflectometry. The key move is to measure the squared-exponential kernel's distance in normalized magnetic flux rather than Cartesian coordinates, so the 2D geometry is preserved while the profile is forced to respect magnetic surfaces. In synthetic validation the reconstructed profile reaches an average relative error of $3.60\\times10^{-4}$ and rRMSE $1.32\\times10^{-4}$ with a $28\\times30$ grid, about an order of magnitude better than the Bayesian data-analysis baseline with the same diagnostics. Sensitivity tests show the model tolerates up to 10% measurement standard deviation, while added random noise raises errors in a predictable way that sets practical reliability limits. If the claim holds on real data, it gives HL-3 a route to 2D density profiles that use both diagnostics without building a forward model for reflectometry.","feed_headline":"Fusing two diagnostics maps HL-3 density to 3.6e-4","feed_subtitle":"Gaussian-process tomography combines interferometer and reflectometer data into 2D profiles, validated on synthetic HL-3 shots.","key_machinery":"The load-bearing object is the flux-mapped squared-exponential kernel $k_{jk}^{SE}(\\psi_j,\\psi_k)=\\sigma^2\\exp(-|\\psi_j-\\psi_k|^2/(2l^2))$, which replaces the Cartesian distance in the covariance with the distance between normalized magnetic flux values. Because every 2D position is mapped to a flux coordinate by equilibrium reconstruction, the kernel encodes the physical assumption that electron density is uniform on each flux surface while still operating on 2D grid nodes. The rest of the machinery is the standard Gaussian-process conditional update: point values $v^*$ from FMCW enter through Eq. (2-5) as $\\mu_1=\\Sigma_*^T(\\Sigma_{**}+\\sigma_*^2 I)^{-1}v^*$, giving a prior; FIR line integrals enter through the response matrix $R$ in the likelihood Eq. (2-7); the posterior mean and covariance are the closed forms in Eqs. (2-10) and (2-11). The kernel is the only place the magnetic equilibrium enters the model, and it is also the component whose errors would propagate directly into the reconstruction.","core_discovery":"On the paper's own terms, the central discovery is that a Gaussian process prior conditioned on FMCW point measurements, then updated by FIR line integrals through a response-matrix likelihood, yields a 2D electron density reconstruction for HL-3 whose synthetic accuracy is dominated by the choice of kernel distance. With the Cartesian squared-exponential kernel $k_{jk}^{SE}(x_j,x_k)$ the IDA model leaves visible core distortions because FMCW coverage stops around one-third of the minor radius and no line-integral channel passes through the core region. Replacing the distance with $|\\psi_j-\\psi_k|$, the separation in normalized magnetic flux obtained from equilibrium reconstruction, makes the model treat density as uniform on flux surfaces; the average relative error drops from $5.18\\times10^{-3}$ to $3.60\\times10^{-4}$ and rRMSE from $1.56\\times10^{-3}$ to $1.32\\times10^{-4}$. The paper reads this as demonstrating that accurate magnetic-equilibrium information, rather than additional diagnostics, is the main lever for core accuracy in the current HL-3 diagnostic layout.","pith_inferences":["Editorial inference: if the accuracy carries to real data, the agreement between Cartesian-kernel and flux-kernel reconstructions in the core becomes a consistency check on the magnetic equilibrium itself.","Editorial inference: the same GPR prior can absorb other point diagnostics, such as Thomson scattering or electron-cyclotron-emission measurements, with no change to the forward-model machinery.","Editorial inference: because the synthetic test sets the FMCW point-value standard deviation to zero, the headline error is best treated as a lower bound; real calibration and localization errors are likely to dominate.","Editorial inference: a direct stress test is to put a non-flux-aligned density perturbation (localized in Cartesian space) into the synthetic profile and see whether the flux-coordinate kernel smooths it away, since the kernel assumes flux-surface uniformity."],"forward_implications":["With the flux-coordinate kernel, the IDA model reduces average relative error from $2.25\\times10^{-2}$ (BDA) and $5.18\\times10^{-3}$ (Cartesian-kernel IDA) to $3.60\\times10^{-4}$, and rRMSE to $1.32\\times10^{-4}$, on the $28\\times30$ synthetic test.","Adding FMCW point values to the GPR prior removes the need for a dedicated reflectometry forward model while constraining edge reconstruction, as seen in the small errors at 1.2-1.4 m and 2.2-2.4 m.","The $28\\times30$ grid is the best tested configuration; coarser grids lose detail and finer grids introduce core perturbations attributed to numerical instability.","Under 10% measurement standard deviation the mean relative error stays near $6.50\\times10^{-4}$, while 5% added random noise raises mean average relative error to $1.56\\times10^{-2}$, giving a quantitative reliability boundary for real applications.","Without magnetic equilibrium information, FIR plus FMCW data alone cannot reconstruct the core accurately; the paper concludes core coverage must be added or equilibrium information retained."],"supporting_citations":[{"why":"Supplies the Gaussian-process formalism (kernel, conditional mean and covariance) that defines the prior used in Eqs. (2-2) to (2-5).","marker":"[34]"},{"why":"Gives the sensitivity-matrix treatment of linear observations in GPR, used to place diagnostic measurements in flux coordinates.","marker":"[27]"},{"why":"Provides the neural-network equilibrium reconstruction that maps 2D positions to normalized magnetic flux for the kernel.","marker":"[28]"},{"why":"The earlier HL-2A integrated density-profile analysis on which the present IDA model builds.","marker":"[16]"},{"why":"Shows the combined use of laser interferometer and microwave reflectometer for a consistent density profile, the diagnostic pair used here.","marker":"[32]"},{"why":"Shows how magnetic equilibrium information enters Gaussian process tomography, the direct precursor of the flux-coordinate kernel in Eq. (2-13).","marker":"[37]"},{"why":"Establishes the response-matrix Bayesian tomographic inversion underlying the likelihood in Eqs. (2-6) to (2-11).","marker":"[38]"},{"why":"Supplies the modified tanhfit function used to construct the synthetic electron density profile for validation.","marker":"[45]"}],"fun_headline_variants":["Flux-based kernel cuts HL-3 density error to 3.6e-4","GPR tomography: flux coordinates give 14x better HL-3 density","HL-3 density: mapping on flux surfaces beats Cartesian in GPR","Two diagnostics in GPR: flux mapping key to HL-3 accuracy","HL-3 density tomography: flux spacing reduces error 14-fold"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the magnetic flux mapping from equilibrium reconstruction places every measurement on the correct flux surface and that density is constant along each surface; systematic errors in that mapping are explicitly ignored, so a slightly wrong equilibrium would shift the kernel distances, the point-measurement locations, and the reconstructed profile together.","fun_headline_variants_meta":{"raw":{"variants":["Flux-based kernel cuts HL-3 density error to 3.6e-4","GPR tomography: flux coordinates give 14x better HL-3 density","HL-3 density: mapping on flux surfaces beats Cartesian in GPR","Two diagnostics in GPR: flux mapping key to HL-3 accuracy","HL-3 density tomography: flux spacing reduces error 14-fold"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000744,"raw_usage":{"total_tokens":3299,"prompt_tokens":905,"completion_tokens":2394,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":521,"completion_tokens_details":{"reasoning_tokens":2294}},"tokens_in":521,"tokens_out":2394,"duration_ms":16345,"temperature":1.0,"reasoning_tokens":2294,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T23:21:02.381956+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same synthetic validation with the equilibrium flux map deliberately perturbed, for example by shifting flux-surface locations by a few centimeters, and record how the average relative error moves from $3.60\\times10^{-4}$. If realistic equilibrium errors push the error up to the level of the Cartesian-kernel reconstruction, the flux-mapping assumption, not the data fusion, is the effect carrying the accuracy claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Gaussian-process formalism (kernel, conditional mean and covariance) that defines the prior used in Eqs. (2-2) to (2-5)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the sensitivity-matrix treatment of linear observations in GPR, used to place diagnostic measurements in flux coordinates."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The earlier HL-2A integrated density-profile analysis on which the present IDA model builds."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows the combined use of laser interferometer and microwave reflectometer for a consistent density profile, the diagnostic pair used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows how magnetic equilibrium information enters Gaussian process tomography, the direct precursor of the flux-coordinate kernel in Eq. (2-13)."},{"cited_title":"Reconstruction of soft X-ray and tungsten concentration profiles in Tokamaks using Bayesian method","cited_arxiv_id":null,"evidence_quote":"Establishes the response-matrix Bayesian tomographic inversion underlying the likelihood in Eqs. (2-6) to (2-11)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the modified tanhfit function used to construct the synthetic electron density profile for validation."}],"review_version":1}