{"id":"c1a714aa-9516-43db-83e5-e66a5549b161","arxiv_id":"2508.12913","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":2,"one_line_summary":"The submitted manuscript matches an abstract about multilayer network spectra with a full text about accelerator optimization, making the scientific claims unverifiable from the provided text.","lead":"The abstract promises a random matrix theory study of spectral fluctuations in multilayer networks, with a crossover model and applications to protein structures. The supplied full text is instead an unrelated paper on sparse tensor accelerator design, so the claimed findings cannot be reviewed.","discovery_kind":"unclear","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Full text is a different paper; multilayer spectral analysis and protein results are absent, so the central claim is unverifiable from the submitted manuscript.","rationale":"The reader set the verdict to UNVERDICTED with LOW confidence, primarily because the abstract and full text are different manuscripts. I agree with that verdict: the strongest claim cannot be checked because the supporting body is absent. The reader's identified 'weakest assumption' was the potential circularity of choosing scaling factors after seeing the data to force Wigner-like spectra. That is a substantive methodological concern about the physics, but it presupposes that the scaling and spectral analyses exist in the manuscript. Here the more fundamental, load-bearing problem is that the full text contains none of the claimed analysis at all. I therefore flag the missing support explicitly, as required by the review rules. The concern is not about the authors' intent or about scientific disagreement; it is a straightforward verification blocker: no amount of scrutiny of the supplied SparseMap text can confirm or refute the abstract's claims about multilayer spectral fluctuations. The concrete test offers a decisive check: retrieve the true arXiv record and search for the key terms and structures. If the mismatch is confirmed, UNVERDICTED remains the appropriate verdict and the scorecard should be rebuilt only if the correct manuscript is provided. If the correct manuscript is later supplied, the scaling circularity concern should be re-examined by checking whether the scaling factors are determined a priori from variance equalization or fitted to the spectra. I would not change the reader's verdict, hence UNCHANGED.","tokens_in":24704,"tokens_out":2801,"duration_ms":29297,"concrete_test":"Retrieve the actual arXiv source for 2508.12913 via the arXiv API and extract the full text. Run a literal search for 'multilayer', 'GOE', 'crossover', '1EWT', '1EWK', and '1UW6'. If the body is the SparseMap paper and none of these terms occur outside the abstract, the mismatch is confirmed and the central claim remains unverifiable. If a corrected full text is obtained, then verify Section-by-section that the scaling factors are derived, the crossover model interpolates between two independent GOEs and one GOE, and the protein spectra are computed from the stated PDB structures.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that block-wise scaling equalizes intra- and inter-layer variances and that GOE universality persists across multilayer architectures, supported by a crossover model and protein network analyses. In the supplied full text, none of this appears: the body is the unrelated SparseMap hardware-accelerator paper (arXiv:2508.12906), describing evolution-strategy optimization of sparse tensor accelerators. There is no derivation of the scaling factors, no definition of the crossover parameter, no eigenvalue statistics, no mention of GOE, and no analysis of proteins 1EWT, 1EWK, or 1UW6. The visible header 'JOURNAL OF LATEX CLASS FILES' and the arXiv ID 2508.12906v1 in the body further indicate a different manuscript was supplied. This is a missing-support flag rather than an internal inconsistency: the evidence required to evaluate the abstract's claims is entirely absent. The reader's concern about scaling-after-data circularity is real but secondary; even the existence of the scaling procedure, crossover model, and protein experiments cannot be confirmed from the current text. Consequently, the correctness risk cannot be assessed, and the claim that 'universality of spectral fluctuations persists' has no checkable basis in the submission.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper as submitted claims to investigate spectral fluctuations in multilayer networks within random matrix theory, proposing block-wise variance equalization, a crossover model for bilayer networks, and an application to protein interatomic distance networks. The abstract states that universality of spectral fluctuations persists across multilayer architectures and that the crossover model captures a smooth transition from two independent GOEs to a single GOE. However, the body text supplied with the submission is an unrelated hardware-architecture paper titled \"SparseMap: A Sparse Tensor Accelerator Framework Based on Evolution Strategy,\" with arXiv ID 2508.12906v1. None of the claimed multilayer random matrix theory, spectral statistics, crossover model, scaling factors, or protein analyses appear in the text. As a result, the technical content of the abstract cannot be checked or reproduced from the submitted manuscript.","tokens_in":24814,"tokens_out":3465,"duration_ms":36646,"significance":"If the claims in the abstract were correct, the paper would establish a useful universality statement for multilayer network spectra and demonstrate a concrete application to protein crystal structures. The crossover scenario from two independent GOEs to a single GOE is scientifically interesting and the application to proteins 1EWT, 1EWK, and 1UW6 is potentially valuable. However, the submission provides no derivations, no numerical experiments, no data analysis, and no reproducible code for these claims. The body text is a different manuscript about sparse tensor accelerator optimization. Thus the significance of the claimed result is currently unassessable from the submitted evidence.","major_comments":[{"comment":"The submitted body is not the paper described in the abstract. The header and footer identify \"SparseMap: A Sparse Tensor Accelerator Framework Based on Evolution Strategy,\" and the visible arXiv ID in the body is 2508.12906v1, not 2508.12913. The text concerns hardware design-space exploration for sparse tensor accelerators and contains no discussion of multilayer networks, random matrix ensembles, GOE spectral statistics, eigenvalue spacing, or the proteins 1EWT, 1EWK, and 1UW6. Consequently, the central claim that spectral fluctuations are universal across multilayer architectures has no supporting derivation, plot, table, or protocol in the manuscript. This is a load-bearing missing-support issue that prevents substantive evaluation.","section":"Full text, pages 1–14"},{"comment":"The block-scaling step is stated only as \"Applying appropriate scaling factors for these blocks, we equalize variances across inter- and intra-layers.\" The manuscript supplies no definition of these factors, no formula, and no statement of whether they are predetermined from model parameters or tuned to the data. Without that information, the subsequent universality claim is unfalsifiable and the risk of circularity raised in the review is real: if the factors are chosen to make the rescaled matrix Wigner-like, the observed universality would be put in by construction. A concrete fix would be to give closed-form scaling factors in terms of the model parameters and show that the level-spacing distribution is Wigner-like across a range of connectivities without data-dependent rescaling.","section":"Abstract, third sentence"},{"comment":"The crossover model is not defined anywhere in the submitted text. There is no definition of the crossover parameter, no derivation of the two-GOE to one-GOE transition, and no numerical or analytical results showing a smooth spectral crossover as the inter-layer to intra-layer connection strength varies. The protein network application is also entirely absent: the text does not describe how interatomic distance networks are constructed from the crystal structures, nor does it report spectral statistics for 1EWT, 1EWK, or 1UW6. These omissions are load-bearing because the abstract presents the crossover model and the protein analyses as evidence for the universality claim.","section":"Abstract, fifth sentence"}],"minor_comments":[{"comment":"The journal-template header \"JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021\" is a placeholder, and the arXiv ID printed in the body differs from the submitted paper ID; the manuscript appears to be the wrong document and should be verified before any further review.","section":"Full text, page 1"},{"comment":"Since the body is a different manuscript, I have not catalogued style or typographical issues for the claimed multilayer-network paper; the correct text must be supplied before presentation issues can be meaningfully assessed.","section":"Full text throughout"}],"recommendation":"reject","confidential_remarks":"The submitted full text appears to be the wrong manuscript: the visible arXiv ID is 2508.12906v1 rather than the submitted 2508.12913, and the abstract describes multilayer random matrix theory while the body describes sparse tensor accelerator optimization. This is a submission-integrity issue rather than a scientific disagreement. I recommend verifying the submission with the authors before any substantive review; if the correct manuscript is supplied, the scientific content will need to be evaluated from scratch."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know one thing first: this submission is broken. The abstract on arXiv:2508.12913 describes spectral fluctuations of multilayer networks, a crossover model from two GOEs to one GOE, and applications to protein structures 1EWT, 1EWK, and 1UW6. The full text is a completely different paper, SparseMap (arXiv:2508.12906), about evolution-strategy optimization of sparse tensor accelerators. Nothing in the body—no derivation, no scaling factors, no eigenvalue statistics, no GOE, no protein data—relates to the abstract. This is not a matter of a weak argument; the supporting material for the central claim is simply absent.\n\nTo give credit where it is due: the abstract's idea is reasonable. Equalizing block variances in a multilayer adjacency matrix and asking whether spectral statistics converge to GOE is a sensible extension of known coupled-matrix results. A smooth crossover between two independent GOEs and a single GOE with increasing inter-layer coupling is standard in random matrix theory; showing it explicitly for network models and testing it on protein structures could be a useful, if not groundbreaking, contribution. But that contribution is not in this manuscript. There is no way to check the derivation, the definition of the crossover parameter, the construction of the scaling factors, or the protein experiments.\n\nThe reader's concern about circularity is secondary. Yes, if the scaling factors are tuned after seeing the data to force Wigner-like statistics, the universality claim would be vacuous. But we cannot even confirm that the scaling procedure exists in the submitted text. The missing-text problem dominates.\n\nWho is this for? Someone curious about RMT in multiplex networks might find the abstract worth a look, but they would need the actual paper. As submitted, it is not a paper; it is an abstract attached to the wrong full text. My recommendation: desk reject this version, with clear feedback to the authors that the body does not match the abstract. If the correct manuscript is provided, it deserves a serious referee—the topic is legitimate and the planned analysis, if done honestly, could be publishable. But you cannot peer-review a paper that is not there.","headline":"The abstract promises a multilayer-network RMT paper; the body is an unrelated hardware-accelerator manuscript, so the submission cannot be evaluated.","tokens_in":25445,"tokens_out":1374,"would_cite":false,"duration_ms":16351,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["15B52","60B20","05C82"],"pacs":[],"model":"deepseek-v4-flash","headline":"Multilayer network spectra obey one universal random-matrix curve as layer coupling grows.","keywords":["multilayer networks","random matrix theory","spectral fluctuations","Gaussian orthogonal ensemble","level spacing distribution","crossover model","protein interatomic distance networks","eigenvalue statistics"],"falsifier":"Generate synthetic bilayer matrices with known independent GOE diagonal blocks and controlled inter-layer variance, apply the paper's per-block rescaling, and measure the bulk level-spacing ratio $\\langle r \\rangle$ across coupling strengths. If the measured curve does not follow the model's one-parameter crossover, or if it jumps abruptly from the two-GOE value to the single-GOE value, the universality claim fails. The test should fix the rescaling constants in advance from variance formulas rather than fitting them per spectrum.","tokens_in":24394,"feed_emoji":"🕸️","tokens_out":4645,"duration_ms":49417,"temperature":0.7,"pith_summary":"This paper tries to show that multilayer networks, not just single layers, have universal spectral fluctuations in the random-matrix sense. Writing the adjacency matrix in blocks, the authors rescale each block to equalize variances and then study how eigenvalue statistics change when inter-layer coupling is strengthened. They propose a crossover model in which the spectrum moves smoothly from two independent Gaussian Orthogonal Ensembles at weak coupling to a single Gaussian Orthogonal Ensemble at strong coupling. They test the prediction on interatomic distance networks built from protein crystal structures, arguing that random-matrix theory can serve as a practical probe of real multilayer systems. If correct, the same few spectral statistics that describe atomic and disordered systems would also describe layered biological and technological networks.","feed_headline":"Multilayer spectra follow a single random-matrix curve","feed_subtitle":"Once inter- and intra-layer blocks are variance-scaled, layer coupling drives spectra from two independent GOEs to one.","key_machinery":"The central object is the block adjacency matrix $$\\begin{pmatrix} A_{11} & A_{12} \\\\ A_{21} & A_{22} \\end{pmatrix},$$ where the diagonal blocks hold intra-layer connections and the off-diagonal blocks hold inter-layer connections. The mechanism is variance equalization: a scaling factor per block makes the entries of all blocks comparable in variance, and then a single control parameter, the relative inter-layer to intra-layer strength, drives a one-parameter crossover in the level-spacing statistics. This rescaling is what lets the same Wigner-Dyson fluctuation statistics reappear across different multilayer architectures.","core_discovery":"The central claim is that, after applying one scaling factor per block of a multilayer adjacency matrix to equalize the variances of intra-layer and inter-layer entries, the eigenvalue fluctuations of the network fall into the GOE universality class. As the relative strength of inter-layer to intra-layer connections increases, the spectral statistics interpolate continuously between the statistics of two independent GOE spectra and the statistics of a single GOE spectrum. The paper further claims that this same behavior appears in interatomic distance networks derived from three protein crystal structures, so universality persists beyond synthetic random graphs.","pith_inferences":["If the crossover parameter is identifiable from spectra alone, it could act as a model-free estimator of layer coupling in networks whose true edge weights are unknown or noisy.","The same block-rescaling and crossover logic may apply to graph Laplacians and normalized adjacency matrices, which would extend the result to diffusion and synchronization dynamics on multilayer networks.","The protein application suggests a testable extension: fitted crossover parameters could be checked for correlation with protein size, fold class, or the density of inter-chain contacts.","A natural stress test would be to apply the scaling procedure to multilayer networks with highly heterogeneous intra-layer degrees, where a single per-block scale factor may be too crude to restore GOE statistics."],"forward_implications":["Spectral statistics of multilayer networks can be compared directly across different layer counts and coupling patterns once each block is variance-scaled.","The fitted crossover parameter provides a single number expressing how strongly layers communicate, potentially serving as a spectral measure of coupling strength.","Protein interatomic distance networks with different structures, such as those built from 1EWT, 1EWK, and 1UW6, should show the same universal fluctuation statistics after scaling.","Increasing inter-layer coupling should drive any multilayer system from two-GOE to single-GOE statistics, not to a new class of statistics.","Random-matrix fluctuation measures can be used as a diagnostic of topological and dynamical complexity in real multilayer networks, not merely in synthetic ensembles."],"supporting_citations":[],"fun_headline_variants":["Multilayer spectra unify into one GOE after block scaling","Scaling block variances makes multilayer spectra GOE","From two GOEs to one: the multilayer crossover","Block-scaled multilayer spectra: universal single GOE"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that rescaling each block by one number is enough to bring the whole adjacency matrix into the GOE universality class, so that the observed Wigner-like statistics are not an artifact of choosing the scales after looking at the data.","fun_headline_variants_meta":{"raw":{"variants":["Multilayer spectra unify into one GOE after block scaling","Scaling block variances makes multilayer spectra GOE","From two GOEs to one: the multilayer crossover","Block-scaled multilayer spectra: universal single GOE"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00068,"raw_usage":{"total_tokens":3037,"prompt_tokens":841,"completion_tokens":2196,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":457,"completion_tokens_details":{"reasoning_tokens":2130}},"tokens_in":457,"tokens_out":2196,"duration_ms":17475,"temperature":1.0,"reasoning_tokens":2130,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:16:30.226313+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate synthetic bilayer matrices with known independent GOE diagonal blocks and controlled inter-layer variance, apply the paper's per-block rescaling, and measure the bulk level-spacing ratio $\\langle r \\rangle$ across coupling strengths. If the measured curve does not follow the model's one-parameter crossover, or if it jumps abruptly from the two-GOE value to the single-GOE value, the universality claim fails. The test should fix the rescaling constants in advance from variance formulas rather than fitting them per spectrum.","supporting_citations":[],"review_version":2}