{"id":"8a18b892-7896-4417-af8d-7f29a16e9ecc","arxiv_id":"2605.31107","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Introduces composition-based coordination number metric and percolation scaling for APT clustering that compensates for dilations and outperforms density methods in artifact-inclusive simulations.","lead":"The paper proposes a coordination-number metric for clustering atom probe tomography data and scales parameters using percolation thresholds to create an invariant variable. This could allow more reliable detection of nanoscale phase nuclei in materials despite common reconstruction artifacts.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Percolation threshold identification may not be robust when coordination-number metric is applied to mixed solvent-solute APT volumes with detection losses.","rationale":"The reader’s weakest assumption directly identifies the same load-bearing step (percolation scaling under realistic APT incompleteness). Because the full text was not supplied in the initial query the original verdict was UNVERDICTED; the concrete simulation check above would resolve whether the assumption holds inside the authors’ own modeling framework, moving the verdict to CONDITIONAL pending that result.","tokens_in":1708,"tokens_out":371,"duration_ms":15320,"concrete_test":"Generate 50 independent APT-like point clouds (L=40 nm, 10 at.% solute, detection efficiency stepped from 35% to 80%) with the same reconstruction artifacts used in the paper; for each efficiency compute the coordination-number percolation threshold p_c via the same algorithm as §3, then evaluate the scaled clustering variable at fixed physical precipitate size; if the standard deviation of the scaled variable across efficiencies exceeds 8% the invariance claim is falsified.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that percolation thresholds remain identifiable and usable for scaling even after the composition-based coordination metric is computed on incomplete point sets. In typical APT data the solvent atoms dominate the graph; random removal of 20-60% of atoms (standard detection efficiency) alters local coordination numbers non-uniformly near interfaces and in dilute regions. If the resulting percolation threshold shifts or becomes ill-defined, the self-similar variable loses invariance and the claimed compensation for heterogeneous dilations fails. The abstract states that the metric “effectively compensates” in simulations, but this hinges on the untested premise that the threshold can still be extracted reliably from the same noisy graphs.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript introduces a coordination-number metric derived from local composition for clustering in atom probe tomography (APT) data. It applies this metric within a higher-order clustering framework, identifies percolation thresholds in typical APT structures (solvent + solute), and scales clustering properties to those thresholds to obtain a self-similar variable claimed to be nearly invariant to metric choice, clustering parameters, and structural disorder. The work further examines characteristic clustering in small precipitates, the effect of the precipitate-matrix interface on the composition spectrum, and demonstrates via simulations that incorporate finite spatial resolution, detection efficiency, and reconstruction artifacts that the coordination-number approach compensates for heterogeneous dilations and outperforms conventional solute-density methods in all tested cases.","tokens_in":1843,"tokens_out":566,"duration_ms":20053,"significance":"If the central claims hold, the self-similar variable and associated parameter-transfer procedure would constitute a useful methodological advance for reducing user-parameter sensitivity in APT clustering analysis. The explicit inclusion of detection efficiency and reconstruction artifacts in the validation simulations is a strength; reproducible demonstration that the percolation threshold remains extractable under realistic atom-loss conditions would strengthen the result.","major_comments":[{"comment":"The central claim that the coordination-number metric “effectively compensates for heterogeneous dilations” in the presence of detection efficiency (20–60 % atom removal) rests on the untested premise that percolation thresholds remain identifiable and stable on the resulting incomplete graphs. The abstract states that simulations include detection efficiency, but without explicit quantification of threshold shift or loss of percolation signature near interfaces and in dilute regions, the invariance of the self-similar variable cannot be verified.","section":"Simulations section (detection-efficiency results)"},{"comment":"The self-similar variable is defined by scaling to percolation thresholds measured on the same data set to which the coordination metric is applied. If the threshold extraction itself depends on the metric and on the same incomplete point set, the claimed parameter-free invariance may be partly by construction; an independent validation (e.g., against known synthetic precipitates or cross-validation with an external length scale) is needed to establish that the scaling is not circular.","section":"Percolation-threshold definition and self-similar variable"}],"minor_comments":[{"comment":"The abstract is information-dense; splitting the final sentence or adding a short clause on the range of detection efficiencies tested would improve readability.","section":"Abstract"},{"comment":"Notation for the coordination number (e.g., whether it is a local average or a graph degree) should be defined at first use with an explicit equation.","section":"Methods / metric definition"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed and constructive review. The two major comments raise important points about the robustness of the percolation analysis under detection efficiency and the potential circularity in the self-similar variable. We address each below and will revise the manuscript accordingly.","responses":[{"response":"We agree that explicit quantification of percolation threshold stability under atom removal would strengthen the claims. While the simulations section already incorporates detection efficiencies of 20–60 % and shows the coordination-number metric outperforming density-based methods, we did not provide a dedicated quantification of threshold shifts or signature loss near interfaces. In the revised manuscript we will add a new panel or supplementary figure reporting the percolation threshold as a function of detection efficiency, including separate curves for interface and dilute regions, to directly verify that the signature remains identifiable and the self-similar variable remains stable.","revision_made":"yes","referee_comment":"The central claim that the coordination-number metric “effectively compensates for heterogeneous dilations” in the presence of detection efficiency (20–60 % atom removal) rests on the untested premise that percolation thresholds remain identifiable and stable on the resulting incomplete graphs. The abstract states that simulations include detection efficiency, but without explicit quantification of threshold shift or loss of percolation signature near interfaces and in dilute regions, the invariance of the self-similar variable cannot be verified."},{"response":"We acknowledge the referee’s concern that scaling to a threshold extracted from the same incomplete point set could introduce some degree of circularity. The current manuscript demonstrates invariance across metrics and parameters on the same data, which supports transferability, but does not include an external check against known ground-truth structures. In the revision we will add a validation subsection using synthetic precipitates of known size and composition; we will show that the scaled variable recovers the expected clustering behavior when compared against these independent length scales, thereby confirming that the invariance is not solely an artifact of the threshold definition.","revision_made":"yes","referee_comment":"The self-similar variable is defined by scaling to percolation thresholds measured on the same data set to which the coordination metric is applied. If the threshold extraction itself depends on the metric and on the same incomplete point set, the claimed parameter-free invariance may be partly by construction; an independent validation (e.g., against known synthetic precipitates or cross-validation with an external length scale) is needed to establish that the scaling is not circular."}],"tokens_in":1442,"tokens_out":518,"duration_ms":26542,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is a new coordination-number metric that folds in solvent atoms instead of discarding them, paired with a percolation-threshold scaling to create a self-similar variable for moving parameters between clustering methods.\n\nWhat is actually new is the shift to a composition-derived coordination metric applied to higher-order clustering, plus the use of measured percolation thresholds to normalize across metrics, parameters, and disorder. They also quantify how small precipitates and matrix interfaces broaden the clustering curve and alter the composition spectrum. The simulations add finite resolution, detection efficiency, and reconstruction artifacts, and the abstract states the approach compensates for heterogeneous dilations better than solute-density methods across the tested cases.\n\nThat inclusion of solvent atoms is a sensible move because they carry most of the spatial structure. The self-similar variable is a clean way to make parameter choice less arbitrary if the scaling really holds.\n\nThe soft spot is whether percolation thresholds stay reliably identifiable once the metric is computed on the incomplete point sets that result from 20-60% detection losses. Random atom removal can change local coordinations non-uniformly near interfaces and in dilute zones, which might shift or blur the threshold and break the claimed invariance. The abstract says the simulations support outperformance, but that hinges on the thresholds remaining usable; without the actual graphs or threshold extraction details it is hard to judge how well this holds.\n\nThis is for APT practitioners who analyze nanoscale clustering in materials. A reader working on phase separation or interface studies would get practical value from the method if the robustness checks out.\n\nI would send it for peer review. The idea is distinct enough from standard distance-based work and targets a real limitation in the technique.","headline":"The paper introduces a composition-based coordination number metric plus percolation scaling for APT clustering, but the robustness claim under detection losses needs the full results to confirm.","tokens_in":2315,"tokens_out":413,"would_cite":false,"duration_ms":16579,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A composition-based coordination number metric combined with percolation scaling improves clustering of nanoscale features in atom probe tomography data and compensates for reconstruction artifacts better than solute-density approaches.","keywords":["atom probe tomography","clustering","coordination number","percolation","precipitates","size effects","reconstruction artifacts","phase nucleation"],"falsifier":"A direct comparison on simulated APT datasets with known precipitate locations and controlled heterogeneous dilation artifacts in which the coordination-number method shows no improvement or produces a scaled variable that varies strongly with metric choice.","tokens_in":2595,"feed_emoji":"🔬","tokens_out":673,"duration_ms":14232,"temperature":0.7,"pith_summary":"The paper develops a clustering method for atom probe tomography that uses a coordination-number metric defined from local atomic composition rather than Euclidean distances or solute atoms alone. It scales clustering properties to percolation thresholds to produce a self-similar variable that stays nearly constant across metrics, parameters, and structural variations. Simulations incorporating detection efficiency, spatial resolution limits, and other typical artifacts show that this coordination approach handles heterogeneous dilations more effectively and yields better results than conventional solute-density methods, including for small precipitates where matrix interfaces broaden the clustering response.","feed_headline":"Coordination metric outperforms density clustering in APT","feed_subtitle":"Scaling to percolation thresholds yields an invariant variable that compensates for reconstruction artifacts in nanoscale precipitate detect","key_machinery":"The coordination-number metric based on local composition, which incorporates solvent atoms and is scaled to percolation thresholds to yield an invariant self-similar clustering variable.","core_discovery":"The central claim is that a coordination-number metric based on composition, when combined with scaling of clustering properties to the corresponding percolation thresholds, defines a self-similar variable that is nearly invariant with respect to the choice of metric, clustering parameters, and structural disorder; this variable enables formal transfer of optimal parameters between methods and, in simulations that include finite spatial resolution, detection efficiency, and reconstruction artifacts, the coordination-number approach compensates for heterogeneous dilations and outperforms solute-density-based methods in all tested scenarios.","pith_inferences":["The same percolation-scaling step might reduce sensitivity to reconstruction algorithm choices across different atom probe instruments.","The approach could be tested on experimental datasets where precipitate sizes are independently verified by another microscopy technique to check consistency of the invariant variable.","Extending the coordination definition to include higher-order neighbor shells might further stabilize the scaled variable in very dilute alloys."],"forward_implications":["Optimal clustering parameters identified with one metric can be transferred to another metric via the self-similar variable.","Small precipitates exhibit broadened clustering curves because the precipitate-matrix interface alters the local composition spectrum.","The method remains effective when typical APT artifacts such as limited detection efficiency and spatial resolution are present.","Clustering descriptions become largely independent of the specific distance or density metric once scaled to the percolation threshold."],"fun_headline_variants":["Percolation scaling makes coordination metric invariant in APT","Coordination metric outperforms solute density clustering in APT","Invariant variable transfers optimal parameters across APT methods","Coordination approach compensates heterogeneous dilations in APT"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"Percolation thresholds can be reliably identified and used for scaling in mixed solvent-solute APT structures, and the composition-based coordination definition captures relevant spatial information without new biases from detection efficiency or reconstruction artifacts.","fun_headline_variants_meta":{"raw":{"variants":["Percolation scaling makes coordination metric invariant in APT","Coordination metric outperforms solute density clustering in APT","Invariant variable transfers optimal parameters across APT methods","Coordination approach compensates heterogeneous dilations in APT"]},"model":"grok-4.3","cost_usd":0.007362,"raw_usage":{"total_tokens":3386,"prompt_tokens":667,"num_sources_used":0,"completion_tokens":58,"cost_in_usd_ticks":73624500,"prompt_tokens_details":{"text_tokens":667,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2661,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":667,"tokens_out":58,"duration_ms":17803,"temperature":1.0,"reasoning_tokens":2661,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T22:01:47.801781+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A direct comparison on simulated APT datasets with known precipitate locations and controlled heterogeneous dilation artifacts in which the coordination-number method shows no improvement or produces a scaled variable that varies strongly with metric choice.","supporting_citations":[],"review_version":1}