{"id":"d420805b-db33-4915-a265-7574374f4d57","arxiv_id":"2607.10440","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"MOSAIC recovers site-resolved occupancy and displacement fields that produce selected diffuse-scattering features by phase-preserving Fourier filtering of the calculated scattering amplitude.","lead":"MOSAIC turns a known atomic model into maps that show which atoms and displacements create chosen diffuse-scattering features. Materials scientists can use it to interpret large RMC, MD, or STEM-derived structures without guessing motifs by eye.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The Reader correctly identifies both the strongest claim (model-conditioned, phase-preserving filtering with linear additivity) and the weakest assumption (first-order expansion + same-config M-decoder). That assumption is already disclosed in Section 2.3 and is not hidden; the validation cases remain inside the regime where the linear map works well enough for the intended use (feature attribution and spatial topology). The method does not claim unique reconstruction from intensity-only data, so concerns about non-uniqueness or experimental phase retrieval are outside scope. Consequently the ACCEPT verdict stands; no adjustment is warranted.","tokens_in":14519,"tokens_out":459,"duration_ms":9531,"concrete_test":"On the ReO3-type benchmark of Section 4.2, recompute the Displacement-Mode maps after deliberately scaling all true displacements by 2–3\times (so that first-order Eq. 15 is clearly violated); verify that complementary-mask additivity residual remains near zero while magnitude underestimation appears as predicted, confirming that the paper’s own stated limitation is the only soft spot and does not invalidate attribution of feature origin.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is carefully scoped: given a known atomistic configuration and a calculable phase-bearing amplitude, phase-preserving Fourier filtering plus a linear M-decoder recovers site-resolved occupancy and displacement fields that generate selected diffuse features, with exact additivity across disjoint masks. The paper itself states the first-order expansion (Eq. 15) and same-configuration training of M, and shows that for the tested regimes (including ~0.1 Å breathing and 10° rotations) topology and approximate magnitudes are recovered while complementary-mask residuals remain small. Because the method is model-conditioned attribution rather than structure solution from intensity alone, the acknowledged nonlinearity for large displacements and the inheritance of input-model errors do not undermine the stated claim. Synthetic benchmarks (LiFeO2 chemical SRO vs L11, ReO3 rotations vs breathing) and PMN applications supply independent support; open code further reduces risk. No load-bearing internal inconsistency or unstated assumption that would reverse the claim was found.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript introduces MOSAIC, a model-conditioned computational framework that attributes selected diffuse-scattering features to atomic-site-resolved occupancy and displacement fields when an atomistic configuration is available and a phase-bearing scattering amplitude can be calculated. Starting from the Butler–Welberry decomposition of the total amplitude into average and diffuse parts, the method applies phase-preserving reciprocal-space masks, evaluates restricted inverse Fourier transforms at atomic sites (via type-3 NUFFTs in a Map–Reduce pipeline), and recovers chemical contrast (Chemical Mode) and site displacements (Displacement Mode via a linear M-decoder). Exact additivity across disjoint masks is established by construction. Synthetic benchmarks separate coexisting Li/Fe short-range order from L11 nanodomains in a γ-LiFeO2 model and disentangle octahedral rotations from breathing distortions in a ReO3-type framework; applications to published RMC models of PMN and PMN–PT illustrate chemical SRO maps and polar textures. Open-source code is provided.","tokens_in":14754,"tokens_out":1232,"duration_ms":32343,"significance":"If the results hold as presented, MOSAIC fills a practical gap between large-box structural models (RMC, MD, MC) or STEM-derived projections and the interpretation of which real-space motifs generate particular diffuse features. The strictly linear, phase-preserving pipeline with demonstrated additivity, the Chemical/Displacement Mode separation, and the scalable NUFFT Map–Reduce implementation are genuine methodological contributions. Open code, synthetic recovery of known motifs, and application to established PMN/PMN–PT RMC configurations strengthen credibility and usability. The work is carefully scoped as attribution within a supplied model rather than structure solution from intensity alone, which is appropriate and useful for the diffuse-scattering and local-structure communities.","major_comments":[{"comment":"Section 2.3 and the Displacement Mode validation in §4.2: the M-decoder is trained on paired (r_s, u_true_s) samples drawn from the same configuration under analysis, then held fixed across masks. The manuscript acknowledges this and correctly frames the method as model-conditioned attribution, but the main-text language of “recovering” picometer-scale displacements can still be read as independent estimation. Please state explicitly in §2.3 what is being tested (linearity and mask additivity of a fixed decoder; topology and approximate magnitudes of attributed fields) versus what is not (cross-configuration generalization or structure solution from intensity). This is a framing clarification, not a change to the method.","section":null},{"comment":"Section 4.2 (and claim of picometer-scale recovery in the Methods overview): quantitative reconstruction residuals for the ReO3-type benchmark are deferred to Supplementary Fig. S5, while the main text only states that the additivity residual is “negligible compared with the characteristic displacement scale (≈0.1 Å).” For a methods paper whose central quantitative claim is site-resolved displacement recovery, the main text should report at least summary error metrics (e.g., RMSE or |u_all − u_true| distribution for full, rod, and sphere masks) so readers can assess accuracy without the supplement.","section":null}],"minor_comments":[{"comment":"Eq. (15) and §2.3: the first-order expansion and the statement that large displacements cause magnitude underestimation while preserving topology are appropriate; a brief numerical example of the displacement magnitude at which the linear decoder’s error becomes appreciable (for the ReO3 or PMN cases) would help users judge applicability.","section":null},{"comment":"Section 4.1 (LiFeO2 chemical benchmark): the intensity threshold used to display clusters in Fig. 4(d,e) is a free parameter. Please state the threshold criterion (or that it is for visualization only) so the reconstruction is reproducible.","section":null},{"comment":"Section 5.2 / Fig. 7: the projected-column example uses the Fourier representation of the measured displacement field rather than a full kinematic scattering amplitude; this is noted in the text but could be flagged more prominently in the figure caption to avoid confusion with the 3D amplitude pipeline.","section":null},{"comment":"Figure 5: the residual panel (j) and complementary reconstruction (k) are important for the additivity claim; ensuring consistent color scales and a short quantitative residual statement in the caption would improve readability.","section":null},{"comment":"Implementation (§3): the Map–Reduce / NUFFT architecture is well motivated; a short note on typical wall-clock cost or memory for the million-atom / 10^7–10^8 Q-point regime would help practitioners.","section":null},{"comment":"Minor typographical/formatting: “Here, weconsiderascenariowhere…” (start of §2) appears to have missing spaces; similar run-together words appear elsewhere in the provided text and should be cleaned in production.","section":null},{"comment":"References: the prior MOSAIC-related applications [6–8] are appropriately cited; if space allows, a one-sentence contrast with 3D-ΔPDF peak interpretation would further situate the method for readers coming from that literature.","section":null}],"recommendation":"minor_revision","confidential_remarks":"This is a solid, carefully scoped methods paper with open code and useful synthetic and application benchmarks. The same-configuration M-decoder training is not a hidden circularity given the stated claim, but the authors should be pushed to make that framing unmistakable so the paper is not over-cited as a structure-solution method. Fit for a materials/crystallography methods venue is good; I see no novelty or citation-pattern concerns that would affect the editorial decision."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a clean methods paper that does what it claims. Given an atomistic configuration and a calculable phase-bearing amplitude, MOSAIC Fourier-filters selected reciprocal-space regions, does site-centered inverse transforms, and recovers occupancy and displacement fields that generate those features, with exact additivity across disjoint masks. That is the real advance: not structure solution from intensity alone, but quantitative attribution inside models we already have (RMC, MD, MC, or STEM projections).\n\nWhat is new is the packaged linear pipeline: chemical-mode construction that freezes atoms at average positions, a data-driven linear M-decoder that recovers picometer-scale displacements from local patches of the filtered field, and a Map-Reduce NUFFT implementation that scales to million-atom boxes without dense grids. Earlier qualitative image filtering and the group’s own ad-hoc work existed; this makes the operators explicit, linear, and software-ready. Synthetic tests are convincing: LiFeO2 separates matrix SRO from L11 nanodomains; the ReO3-like model cleanly disentangles rotation rods from breathing spheres with negligible additivity residuals. Applications to published PMN/PMN-PT RMC models produce the expected chemical labyrinths and polar textures that were hard to see by eye.\n\nSoft spots are real but proportional. The M-decoder is trained on the same configuration (self-consistency, not cross-model generalization), and the first-order expansion underestimates large displacements while preserving topology. The method inherits whatever is wrong in the input model. None of that breaks the stated claim, which the authors scope carefully. Free parameters (mask shapes, decoder, display thresholds) are ordinary for this kind of analysis. Math, citations, and open code look solid.\n\nThis is for people who already generate large disordered models or STEM projections and need to link specific diffuse features to real-space motifs. It deserves a serious referee. I would engage with it and expect to cite the software when I next need to interrogate an RMC or MD box.","headline":"Solid, usable methods paper that turns known large-box models into site-resolved maps of which atoms produce which diffuse features; scoped carefully and backed by code.","tokens_in":15366,"tokens_out":507,"would_cite":true,"duration_ms":6987,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Fourier filtering of a calculated scattering amplitude recovers the atomic occupancies and displacements that produce selected diffuse-scattering features.","keywords":["diffuse scattering","Fourier filtering","local structure","atomic displacements","chemical short-range order","Reverse Monte Carlo","perovskites","MOSAIC"],"falsifier":"On a controlled perovskite model with known octahedral rotations and breathing distortions, apply complementary cylindrical and spherical masks; if the decoded rotation and breathing fields do not sum to the full-rod reconstruction within residual scale of the known displacements (~0.1 Å), the linear additivity claim fails.","tokens_in":15412,"feed_emoji":"🔬","tokens_out":874,"duration_ms":24114,"temperature":0.7,"pith_summary":"Diffuse scattering encodes local chemical order and atomic displacements, but even a large atomic model that reproduces the pattern often leaves unclear which sites and motifs generate which features. This paper introduces MOSAIC, a framework that starts from a known configuration, computes its complex scattering amplitude, masks chosen reciprocal-space regions, and inverse-transforms those regions back onto the atomic sites. Linear estimators then return site-resolved occupancy contrast and picometer-scale displacement vectors for the selected features. Because every stage is linear, fields from disjoint masks add exactly, so overlapping signals can be separated and recombined as a consistency check. The method applies to reverse Monte Carlo models, molecular-dynamics snapshots, and two-dimensional electron-microscopy projections, giving a practical way to interrogate large disordered structures.","feed_headline":"Fourier filters map diffuse spots back to the atoms that make them","feed_subtitle":"A linear decoder turns masked scattering amplitudes into site occupancy and displacement fields for large atomic models.","key_machinery":"MOSAIC: a phase-preserving Fourier-filtering pipeline that isolates diffuse features in the calculated scattering amplitude and maps them, via site-centered inverse transforms and a linear M-decoder trained on the same configuration, onto occupancy scalars and displacement vectors at each atomic site.","core_discovery":"When an atomistic configuration is available and a phase-bearing scattering amplitude can be calculated, Fourier filtering that amplitude over selected reciprocal-space regions, followed by site-centered inverse transforms and a linear decoder, recovers the atomic-site-resolved occupancy and displacement fields responsible for those features, with exact additivity across disjoint masks.","pith_inferences":["Because the input must already be a phase-bearing configuration, the method complements rather than replaces intensity-only approaches such as three-dimensional difference pair-distribution-function analysis.","Replacing the linear decoder with a compact nonlinear network could improve accuracy for large displacements, but would forfeit exact additivity across masks—an explicit trade-off the paper notes but does not explore.","Slice-wise application to experimental 4D-STEM data might yield real-space order-parameter maps without first building a full atomistic reverse Monte Carlo model.","The additivity property suggests a practical way to partition experimental reciprocal-space volumes into chemically versus displacively dominated contributions once a reliable average structure is known."],"forward_implications":["Specific diffuse rods, peaks, or surfaces can be attributed to particular chemical orderings or distortion modes even when those signals overlap in reciprocal space.","Large reverse Monte Carlo and molecular-dynamics configurations become interpretable site by site for chosen scattering signatures.","Two-dimensional STEM projections can be filtered to reveal polar textures or chemical order that uncorrelated noise otherwise conceals.","Complementary masks can be summed to reconstruct the full field, giving a built-in consistency check on the recovered displacements.","The same operators can be adapted to 4D-STEM scans and to tracking displacement fields of selected vibrational modes along molecular-dynamics trajectories."],"fun_headline_variants":["Fourier filters turn diffuse spots into site occupancy maps","MOSAIC recovers atom displacements from masked scattering amplitudes","Filtered amplitudes decode occupancy and displacement fields","Diffuse features mapped to atomic sites via Fourier filtering","Site-resolved fields from Fourier-filtered scattering amplitudes"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The method assumes displacements stay small enough that a first-order linear map from filtered amplitude patches to site displacements remains accurate; larger shifts make the decoder underestimate magnitudes.","fun_headline_variants_meta":{"raw":{"variants":["Fourier filters turn diffuse spots into site occupancy maps","MOSAIC recovers atom displacements from masked scattering amplitudes","Filtered amplitudes decode occupancy and displacement fields","Diffuse features mapped to atomic sites via Fourier filtering","Site-resolved fields from Fourier-filtered scattering amplitudes"]},"model":"grok-4.5","effort":"low","cost_usd":0.002958,"raw_usage":{"total_tokens":967,"prompt_tokens":663,"num_sources_used":0,"completion_tokens":72,"cost_in_usd_ticks":29580000,"prompt_tokens_details":{"text_tokens":663,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":232,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":663,"tokens_out":72,"duration_ms":3945,"temperature":1.0,"reasoning_tokens":232,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T11:42:32.177276+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"On a controlled perovskite model with known octahedral rotations and breathing distortions, apply complementary cylindrical and spherical masks; if the decoded rotation and breathing fields do not sum to the full-rod reconstruction within residual scale of the known displacements (~0.1 Å), the linear additivity claim fails.","supporting_citations":[],"review_version":1}