{"id":"df3265c5-3149-4ce5-8657-624a48996eb9","arxiv_id":"2509.07140","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A single-orientation multislice electron ptychography workflow with physics-based refinement retrieves 3D atomic coordinates of twisted bilayer WSe2 and maps out-of-plane corrugations and vacancy locations.","lead":"Using a single tilted electron microscopy scan, the authors reconstructed 3D atomic positions in twisted bilayer WSe2 with picometer-level claimed precision. The method maps individual vacancies and layer-by-layer bending and spacing changes in moiré materials, information that has been difficult to obtain for buried 2D interfaces.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Z-accuracy benchmark is largely a consequence of the priors: fixed W-Se bond length plus selection to bulk interlayer spacing guarantees ~pm agreement, so the 5.3 pm claim does not independently validate 3D retrieval.","rationale":"The reader identified the bulk-anchoring issue; I agree partially but locate the more fundamental problem in the benchmark itself. The 5.3 pm number is not an independent measure of depth resolution because the model is overdetermined by priors: with fixed bond lengths and near-perfect x,y positions, z coordinates are almost fully determined. The selection step then removes the only remaining free parameter, the mean layer separation. Thus the benchmark demonstrates that the refinement is self-consistent, not that it recovers unknown 3D structure. This matters for the abstract's central claim of picometer-scale 3D accuracy. The relative interlayer spacing variations and vacancy-vs-layer assignments are less affected and appear solid, so the paper still merits conditional acceptance with revised claims. The most useful single test is a synthetic experiment with a perturbed mean spacing; if the pipeline recovers it, the concern is refuted.","tokens_in":19235,"tokens_out":4308,"duration_ms":43268,"concrete_test":"Simulate a new ground truth by taking the MD coordinates used for Fig. 2 and applying a uniform +0.3 Å shift to the z coordinates of the entire top WSe2 layer so that the mean interlayer spacing becomes 6.79 Å instead of 6.49 Å, while keeping all intralayer distances unchanged. Generate 4D-STEM data with the same parameters, run the full peak-finding/refinement pipeline with B=2.5379 Å and selection to 6.49 Å, and compare recovered vs true z positions. If the recovered mean interlayer spacing is pinned near 6.49 Å and the per-atom z rms error jumps from 5.3 pm to tens of pm, the absolute z accuracy is an artifact of the bulk-spacing prior. Also report the curvature maps: if the AA2 bending-mode assignment changes sign under different valid selections among the 401 refinements, that observation is not stable.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central quantitative claim is the post-refinement z rms error of 5.3 pm (Fig. 2D), quoted as evidence of picometer 3D accuracy. However, Eq. S1 enforces every W-Se bond to exactly B=2.5379 Å with weight 51.0 Å^-2. Given the measured x,y accuracy of 4.5 pm, this constraint alone fixes the Se z positions relative to their W atom to within a few pm; the refined z error is therefore dominated by propagation of the in-plane error through a fixed bond length, not by depth information from ptychography. Moreover, the interlayer degree of freedom is not constrained in the loss function; it is selected after the fact from 401 repeated refinements by requiring the mean interlayer spacing to equal the bulk 2H-WSe2 value 6.49 Å (Supplementary Text). The simulation ground truth is an MD structure whose intralayer and interlayer potentials are fitted to the same bulk values, so the benchmark rewards consistency with the priors rather than testing them. For the experimental maps, any uniform deviation of the true mean interlayer spacing from 6.49 Å is removed by construction; the reported absolute AA spacings (6.7-6.9 Å) and the 5.3 pm accuracy are therefore conditional on the priors being exactly correct. The relative AA/AB contrast and layer-resolved vacancy assignments are weaker claims and are probably robust, but the headline 'picometer-scale accuracy' overstates what is actually measured.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports a workflow for retrieving 3D atomic coordinates of twisted bilayer WSe2 from a single tilted multislice electron ptychography (MEP) acquisition. The authors simulate a 4D-STEM dataset (Prismatic multislice, frozen phonons, Poisson noise) from MD coordinates, reconstruct with fold_slice, extract peaks from the 3D phase, and refine coordinates by minimizing a loss function that includes lateral fidelity, a fixed W-Se bond length, vertical spacing, and vertical ordering terms. They report in-plane rms error of 4.5 pm and z rms error improving from 81 pm to 5.3 pm after refinement. In experiment, they map Se vacancies exclusively to the outer Se planes, measure interlayer spacing variations (larger in AA than AB regions), and report mixed breathing and bending corrugations at AA regions. The central claim is picometer-scale 3D accuracy from a single orientation in about 30 seconds of acquisition.","tokens_in":19481,"tokens_out":5643,"duration_ms":49573,"significance":"If the accuracy claim were established, the work would be an important advance: single-orientation MEP with priors could provide routine 3D atomic models of 2D heterointerfaces, including buried layers, defects, and sub-angstrom out-of-plane deformations. The simulation benchmark is well constructed (Prismatic multislice, frozen phonons, Poisson noise) and the refinement loss is explicit and reproducible. The layer-resolved vacancy assignment and the relative AA/AB interlayer contrast are likely robust. However, the quantitative z-accuracy benchmark is not independent of the priors: the fixed bond length and the post-hoc selection of the mean interlayer spacing to bulk values determine much of the reported 5.3 pm, so the headline claim overstates what is actually measured. The experimental absolute interlayer spacings should be interpreted as conditional on the bulk anchoring.","major_comments":[{"comment":"The reported z rms error of 5.3 pm does not independently validate depth retrieval. The refinement enforces every W-Se bond to exactly B = 2.5379 Å with weight 51.0 Å^-2, and among 401 repeated refinements the model whose mean interlayer z spacing is closest to the bulk 2H-WSe2 value of 6.49 Å is selected. Given the in-plane error of 4.5 pm, the bond-length constraint fixes each Se z position relative to its W atom to within a few pm through the geometry of the bond, and the selection removes the dominant systematic error in the interlayer distance, which has a 10th-90th percentile spread of -0.16 to +0.77 Å across refinements (fig. S10A). The MD ground truth is generated from potentials fitted to the same bulk lattice parameters, so the benchmark largely rewards consistency with the priors. The authors should report the z error without the interlayer-spacing selection and quantify how much of the 5.3 pm is attributable to the priors rather than to the ptychographic z information.","section":"Supplementary Text, 'Coordinate refinement'; Eq. S1; Fig. 2D; fig. S10"},{"comment":"The 4.5 pm in-plane rms error is measured after multiplying all x,y coordinates by a global factor 0.991, chosen to align the retrieved coordinates with ground truth. This post-hoc scaling is a fit parameter in the benchmark; without it the raw in-plane error is not reported. The manuscript should report the unscaled in-plane error and justify the rescaling as a calibration procedure rather than an accuracy-enhancing adjustment, or remove the scaling from the headline accuracy claim.","section":"Supplementary Text, 'Rescaling x,y coordinates'; Fig. 2D"},{"comment":"The experimental interlayer spacings of 6.7-6.9 Å in AA regions are produced by a refinement selected to have a mean interlayer spacing equal to the bulk value of 6.49 Å. The absolute values are therefore conditional on the priors being exactly correct; the comparison with MD simulations, which are fitted to the same bulk parameters, is partly by construction. The relative AA-to-AB contrast and the soliton behavior are more robust, and the authors should frame those as the validated experimental results, while presenting the absolute spacings as prior-anchored.","section":"Results, Fig. 4B,D and Supplementary Text 'Coordinate refinement'"}],"minor_comments":[{"comment":"The abstract states that the workflow 'solve[s] the 3D atomic coordinates ... with picometer-scale accuracy', but the accuracy is measured only on simulated data; the experimental coordinates have no ground truth. Suggest rewording to indicate that simulations indicate picometer-scale accuracy.","section":"Abstract and Discussion"},{"comment":"The histograms in Fig. 2D lack axis labels for the error distributions, and the main text does not mention that the mean interlayer spacing anchor is applied; a brief main-text note would help readers interpret the 5.3 pm value correctly.","section":"Fig. 2D and Supplementary Text"},{"comment":"The sentence explaining the 0.991 rescaling should state explicitly that this correction is applied only to the simulation benchmark and not to the experimental coordinates in Fig. 4A.","section":"Supplementary Text, 'Rescaling x,y coordinates'"},{"comment":"The manual steps in coordinate retrieval (labeling Good/Poor/Vacancy, manually adding vacancy sites, and manually shifting misplaced Se atoms) are described in the supplementary but not summarized in the main text; a short paragraph would clarify the degree of human intervention in the reported models.","section":"Materials and Methods, Coordinate retrieval"}],"recommendation":"major_revision","confidential_remarks":"The paper has real merit, but the headline accuracy claim needs to be re-benchmarked without the interlayer-spacing selection and with explicit reporting of the unscaled in-plane error. The authors' transparency in the supplementary is commendable; the main text currently overstates the independence of the z measurement. The referee recommends major revision to reframe the claims around the relative measurements that are robust, while clearly presenting the absolute values as prior-anchored."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline picometer z-accuracy is not established by this paper; the 5.3 pm number is mostly built into the priors rather than measured from the data. That said, the qualitative payload — single-tilt retrieval of six atomic planes, vacancies confined to outer Se layers, and coexisting bending/breathing corrugations — is new and worth taking seriously.\n\nWhat the paper does well: the simulation benchmark is honest and carefully constructed (Prismatic multislice, frozen phonons, Poisson noise, realistic scan parameters), the loss function is written out explicitly, and the supplementary material openly documents the two moves that undermine the headline number. It runs 401 refinements and selects the one whose mean interlayer spacing lands on bulk 2H-WSe2 (6.49 Å), and it pins the W–Se bond length to B = 2.5379 Å with weight 51.0 Å^-2. With in-plane rms accuracy at 4.5 pm, that bond-length constraint alone fixes each Se’s z position relative to its W to within a few pm. The 5.3 pm z-error therefore mostly measures propagation through a prior, not depth information retrieved from ptychography. The simulation ground truth comes from MD potentials fitted to the same bulk values, so the benchmark rewards consistency with the priors rather than testing them.\n\nThe same issue affects the absolute interlayer spacings. The reported AA spacings (6.7–6.9 Å) are anchored to bulk 6.49 Å by selection, so any uniform deviation between twisted bilayer and bulk is removed by construction. The relative AA/AB contrast and the 0.1 Å soliton bump are probably far more robust, and the mixed bending/breathing finding does not depend on the absolute anchor. The x,y rescaling factor of 0.991 is also applied post hoc; minor, but it should be acknowledged as a calibration rather than folded into the error.\n\nWhere the paper holds: the layer-resolved vacancy assignment comes from the tilted ptychographic slices, not from the refinement alone, and the observation of one AA region bending in phase while two breathe out of phase is a useful, unexpected experimental result. The paper is also candid about the absence of drift/incoherence in its simulations and about the manual labeling in coordinate extraction. No data or code are shipped, which is a problem for a workflow this complex.\n\nThis deserves a serious referee, not a desk reject. The referee should ask for a benchmark that does not select against the answer — for example, measuring z accuracy without the bulk-spacing selection, or with a fixed W atom chosen by a rule rather than by outcome — and for absolute spacings reported with uncertainty propagation instead of anchored to bulk. I would bring the paper to reading group and would cite the qualitative mixed-mode observation, but not the 5.3 pm z-accuracy claim.","headline":"The z-accuracy claim is built from priors, but the qualitative 3D model and the mixed corrugation observation deserve attention and review.","tokens_in":20107,"tokens_out":3892,"would_cite":true,"duration_ms":37894,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that a single tilted 30-second 4D-STEM acquisition plus a physics-informed refinement recovers all six atomic planes of twisted bilayer WSe2 with 5.3 pm out-of-plane accuracy.","keywords":["electron ptychography","multislice","twisted bilayer WSe2","3D atomic coordinates","moiré corrugation","interlayer spacing","vacancy mapping","coordinate refinement"],"falsifier":"Simulate 4D-STEM datasets from molecular dynamics structures whose mean interlayer spacing is deliberately varied away from 6.49 Å (for example by ±0.3 Å), run the full retrieval pipeline, and check whether the recovered mean spacing is pulled toward 6.49 Å; if the 5.3 pm z error is achieved only when the truth is the bulk value, the claim of absolute picometer z accuracy is falsified. A complementary experiment would image the same area at +15 and -15 degrees of tilt and require the un-tilted 3D coordinates to agree within the claimed precision.","tokens_in":18981,"feed_emoji":"🔬","tokens_out":7155,"duration_ms":61274,"temperature":0.7,"pith_summary":"Twisted bilayer transition-metal dichalcogenides develop out-of-plane deformations that set their electronic properties, but those deformations have been nearly impossible to measure directly. The paper reports a workflow that recovers all six atomic planes of twisted bilayer WSe2 from a single 30-second tilted 4D-STEM acquisition, using multislice electron ptychography followed by a refinement that nudges noisy depth coordinates toward physically plausible positions. In simulated benchmarks the refined coordinates match ground truth with 4.5 pm in-plane error and 5.3 pm out-of-plane error, so the authors claim picometer-scale accuracy in all three dimensions. On experimental data the model exposes individual selenium vacancies, all confined to the outer Se planes, along with sub-angstrom interlayer spacing variations between AA and AB stacking regions and a mix of breathing- and bending-type moiré corrugations that theory had not predicted in close proximity. The payoff of the claim is that atom-by-atom 3D models of buried 2D interfaces become routine from fast, single-orientation data.","feed_headline":"A 30-second electron scan yields picometer 3D atomic maps","feed_subtitle":"Multislice ptychography plus refinement resolves all six atomic planes of twisted WSe2, including vacancies and corrugation.","key_machinery":"The load-bearing machinery is multislice electron ptychography (MEP), which reconstructs the 3D complex object potential as a stack of slices from 4D-STEM diffraction data. What carries the 3D coordinate claim is the combination of a 15-degree sample tilt, so atoms that share a lateral column are displaced in x,y and can be located with the high lateral precision, and the coordinate-refinement loss of Eq. S1, whose terms keep the x,y positions from ptychography, enforce a fixed W-Se bond length B = 2.5379 Å, weakly hold the z of W atoms near a fixed atom, and use a ReLU penalty to keep Se atoms in the correct layer. A final selection step chooses, among 401 repeated refinements, the model whose mean interlayer spacing is closest to bulk 2H-WSe2, 6.49 Å. The machinery works by letting the precise lateral information compensate for the much poorer depth resolution of ptychography, measured here as 7.5 Å full width at half maximum.","core_discovery":"On the authors' own terms, the discovery is that augmenting multislice electron ptychography with two simple priors, atomicity plus known W-Se bond lengths and the bulk interlayer spacing as a selector, turns a depth-limited 3D phase volume into a genuine 3D atomic model. Tilting the sample by 15 degrees separates the otherwise-overlapping Se columns in the lateral plane, so each of the six planes can be assigned; a coordinate refinement then uses the highly accurate x,y peaks as anchors and the bond-length constraint to correct z positions. The benchmark claims 4.5 pm rms in-plane error and 5.3 pm rms z error after refinement, and the experimental models show vacancies confined to outer Se layers, interlayer spacings of 6.7 to 6.9 Å in AA regions versus 6.2 to 6.4 Å in AB regions, and curvature maps in which two of three AA regions breathe outward while one bends in-phase, a mixed corrugation pattern the authors describe as a new type of structural disorder.","pith_inferences":["The paper's absolute z values inherit the bulk anchor: if the true mean interlayer spacing of the twisted bilayer deviates from 6.49 Å, the reported absolute depths and the 5.3 pm benchmark shift together, while the relative corrugation pattern and layer assignments would survive.","A natural extension is to acquire the same area at two opposite tilts and demand consistent un-tilted coordinates; agreement would remove the need for the bulk anchor and give a direct, prior-free check on absolute z.","The observation that bending and breathing modes coexist at neighbouring AA regions suggests that local strain history and kinetic trapping, not just equilibrium energetics, set the corrugation; in situ heating or repeated imaging could test whether the bending mode anneals away.","The same pipeline should transfer to other 2D stacks whose bond lengths and layer spacings are known, but for heterobilayers with unknown interlayer distance the anchor would need to be replaced by an independent calibration."],"forward_implications":["All six atomic planes of a twisted bilayer can be individually resolved from one tilt direction, so layer-resolved defect counts and stacking assignments no longer require tomography.","Interlayer spacing maps become directly measurable in experiment, enabling direct comparison with molecular dynamics predictions for moiré reconstructions.","The layer assignments of vacancies settle a debate in this sample: the Se vacancies sit only in the two outer planes, pointing to beam or preparation damage rather than intrinsic growth defects.","Mixed breathing- and bending-type corrugations at nearby AA regions imply that out-of-plane disorder is spatially non-uniform, a feature that should enter models of moiré electronic structure.","Because a single dataset takes about 30 seconds to acquire, the approach opens the door to 3D in situ studies of structural transformations in 2D materials."],"supporting_citations":[{"why":"Supplies the multislice electron ptychography reconstruction method and the sub-angstrom lateral-resolution baseline the workflow builds on.","marker":"[25]"},{"why":"Provides the depth-resolved multislice ptychography approach and the layer-regularization weighting used in the reconstructions.","marker":"[27]"},{"why":"Supplies the monolayer exfoliation and bilayer assembly procedures, and demonstrates atom-by-atom imaging in 2D materials by ptychography.","marker":"[26]"},{"why":"Provides the multislice 4D-STEM simulation code used to create the ground-truth benchmark datasets against which the 4.5 pm and 5.3 pm accuracy claims are measured.","marker":"[67]"},{"why":"Supplies the interlayer potential used in the molecular dynamics simulations that generate the ground-truth structure for the simulated benchmark.","marker":"[47]"},{"why":"Supplies the bulk 2H-WSe2 lattice parameters, including the 6.49 Å interlayer spacing used to select among repeated refinements.","marker":"[66]"},{"why":"Predicts that thin samples and high collection angles improve MEP depth resolution, the condition the authors exploit to reach 7.5 Å depth FWHM.","marker":"[33]"},{"why":"Represents prior single-orientation 3D imaging approaches whose out-of-plane accuracy the refinement claims to exceed by an order of magnitude.","marker":"[34]"},{"why":"Documents that the accumulated dose used here is sufficient to create Se vacancies, supporting the beam-damage interpretation of the observed outer-layer vacancies.","marker":"[45]"}],"fun_headline_variants":["3D atom maps of twisted WSe2 from a single 30-s scan","Single-orientation ptychography resolves all 6 layers of twisted WSe2","Picometer 3D atomic models from 30-s electron ptychography","3D defects and corrugation in WSe2 mapped atom-by-atom in 30 s","Mixed bending-breathing corrugations revealed in 3D atomic maps"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The refinement assumes the twisted bilayer's internal bond lengths and mean interlayer spacing equal bulk 2H-WSe2 values, fixing the W-Se bond at 2.5379 Å and selecting the refinement whose average interlayer spacing is closest to 6.49 Å; if the sample deviates from bulk in its average geometry, the absolute z coordinates and the 5.3 pm z-accuracy benchmark are biased.","fun_headline_variants_meta":{"raw":{"variants":["3D atom maps of twisted WSe2 from a single 30-s scan","Single-orientation ptychography resolves all 6 layers of twisted WSe2","Picometer 3D atomic models from 30-s electron ptychography","3D defects and corrugation in WSe2 mapped atom-by-atom in 30 s","Mixed bending-breathing corrugations revealed in 3D atomic maps"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000817,"raw_usage":{"total_tokens":3592,"prompt_tokens":970,"completion_tokens":2622,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":586,"completion_tokens_details":{"reasoning_tokens":2514}},"tokens_in":586,"tokens_out":2622,"duration_ms":15878,"temperature":1.0,"reasoning_tokens":2514,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:13:07.235999+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate 4D-STEM datasets from molecular dynamics structures whose mean interlayer spacing is deliberately varied away from 6.49 Å (for example by ±0.3 Å), run the full retrieval pipeline, and check whether the recovered mean spacing is pulled toward 6.49 Å; if the 5.3 pm z error is achieved only when the truth is the bulk value, the claim of absolute picometer z accuracy is falsified. A complementary experiment would image the same area at +15 and -15 degrees of tilt and require the un-tilted 3D coordinates to agree within the claimed precision.","supporting_citations":[{"cited_title":"opposite","cited_arxiv_id":null,"evidence_quote":"Provides the multislice 4D-STEM simulation code used to create the ground-truth benchmark datasets against which the 4.5 pm and 5.3 pm accuracy claims are measured."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the bulk 2H-WSe2 lattice parameters, including the 6.49 Å interlayer spacing used to select among repeated refinements."},{"cited_title":"Imaging interstitial atoms with multislice electron ptychography","cited_arxiv_id":"2407.18063","evidence_quote":"Predicts that thin samples and high collection angles improve MEP depth resolution, the condition the authors exploit to reach 7.5 Å depth FWHM."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Represents prior single-orientation 3D imaging approaches whose out-of-plane accuracy the refinement claims to exceed by an order of magnitude."},{"cited_title":"Leiter, Y","cited_arxiv_id":null,"evidence_quote":"Documents that the accumulated dose used here is sufficient to create Se vacancies, supporting the beam-damage interpretation of the observed outer-layer vacancies."}],"review_version":2}