{"id":"9e23b03f-0736-43d6-9d21-e46ddb4d7435","arxiv_id":"2608.11188","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Transmittance spectra of a 1D chain with stealthy hyperuniform disorder contain a sharp edge whose position encodes the stealthiness parameter, and a misfit minimization recovers it for well-resolved cases.","lead":"This paper shows that the stealthiness parameter, a measure of hidden order in certain disordered materials, can be inferred from the electrical transmission spectrum alone. The authors demonstrate this numerically in a one-dimensional chain, which could help experiments characterize correlated photonic and electronic materials without direct structural imaging.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fingerprint claim is supported only by in-sample ensemble-averaged targets and an unspecified misfit window; a single-realization or independent-model test is needed before the practical inversion claim is established.","rationale":"The reader's weakest assumption identifies the same two gaps: validation only against targets generated by the same disorder-ensemble construction, and the unspecified energy window. I agree that these are the load-bearing soft spots. The paper is honest about the small-chi breakdown and finite-size limitations, and the numerical demonstration is internally consistent, so a rejection is not warranted. However, the central claim as stated in the abstract and conclusions extends to realistic transport measurements, and the current evidence does not yet cover a single measured realization or an independent disorder-generation model. The proposed concrete test would distinguish a cosmetic reproducibility issue from a substantive limitation of the fingerprint idea. Since the existing conditional verdict already requires addressing these gaps, no change to the reader's verdict is needed.","tokens_in":13812,"tokens_out":8308,"duration_ms":79225,"concrete_test":"Re-run the Figure 5(a) inversion with the target T_tar(E) taken from a single disorder realization (no 1000-configuration average) generated by an independent transfer-matrix implementation or by adding low-k noise to S(k), and with a fixed a-priori window rule, for example the full band [-2, 0] or a window of width 0.4 centered on the numerically detected transmission edge. If the recovered (W, chi) moves outside the tolerance implied by the current contour plots, or the minimum becomes a shallow valley, the claim that transmittance spectra alone fingerprint stealthy hyperuniform disorder is not supported by the present evidence.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that transmittance spectra are fingerprints from which (W, chi) can be recovered, but the only evidence compares ensemble-averaged target spectra (1000 realizations) with ensemble-averaged trial spectra (200 realizations) drawn from the same Fourier-space construction, Eq. (7), and computed with the same recursive Green's-function code. This is an in-sample consistency check: both sides approximate the same ensemble expectation, so a minimum of F may reflect features of the generative construction (hard Theta cutoff, discrete k grid, RGF implementation) rather than a property of experimentally measurable single-realization spectra. Real transport data are single spectra, not 1000-configuration averages, and real stealthy hyperuniform samples have imperfect or blurred low-k suppression. In addition, Eq. (14) depends on an energy window [E-, E+] whose value and selection rule are never stated; the text only says the window must be 'judiciously selected' to encompass the drop. If the reported minima in Figs. 4 and 5 are not stable under a fixed, a-priori window rule, the recovery is partly an artifact of window tuning. Of these two omissions, the in-sample, ensemble-averaged validation is the more fundamental: without a single-realization or independent-model test, the practical inversion claim exceeds what the numerics establish.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an inverse protocol to recover the stealthiness parameter chi and disorder strength W of a stealthy hyperuniform disordered potential from energy-resolved transmittance spectra. The forward model is a one-dimensional tight-binding chain with on-site disorder generated by a hard cutoff in Fourier space, S(k)=Theta(|k|-K) with K=2 pi chi, and the transmittance is computed with a recursive Green's function method. A misfit function comparing ensemble-averaged target and trial spectra is then minimized over (W, chi). For target parameters W_tar=0.10 and chi_tar=0.30 and 0.20, the authors report clear minima close to the target; for chi_tar=0.10 the minimum is lost. Finite-size scaling up to N=10^6 is also presented, and the authors frame the protocol as a proof of concept for mesoscopic systems.","tokens_in":14054,"tokens_out":5218,"duration_ms":45491,"significance":"If the method is robust, it provides a useful way to extract correlated-disorder parameters from transport measurements without direct structural information, with potential applications in photonic and ultracold-atom platforms. The paper is honest about the limitations, clearly showing the breakdown at small chi, and the numerical implementation is simple and reproducible in principle. However, the significance is currently tempered by the in-sample nature of the validation and by the unspecified energy window, which together leave the central 'fingerprint' claim less strongly supported than the abstract suggests.","major_comments":[{"comment":"The validation is entirely in-sample: the target spectra and the trial spectra are generated with the same disorder-generation rule (Eqs. (4)-(7)), the same configurational averaging (Eq. (13)), and the same recursive Green's function code. Consequently, the reported recovery of (W_tar, chi_tar) is an identifiability check within a single generative model, not a demonstration that experimentally obtainable single-realization transmittance spectra carry the fingerprint. Please add at least one test that breaks this symmetry, e.g., a target generated by an independent forward solver, a target with imperfect (blurred) stealthiness, or a single-realization target, and show that the misfit minimum still approximates the target parameter.","section":"Sec. II.C and Sec. III (Figs. 4 and 5)"},{"comment":"The misfit function F depends explicitly on the integration window [E-, E+], but the paper never states the window used for any of the reported results. The only guidance is that the window must be 'judiciously selected' to encompass the threshold region. Without a fixed, a-priori rule for choosing [E-, E+], the protocol is not reproducible and the apparent minima in Figs. 4 and 5 could be influenced by window tuning. Please specify the exact windows used for each figure and verify that the minima are stable when the window is chosen by a stated rule (e.g., a fixed energy interval around the perturbative E_c).","section":"Sec. II.C, Eq. (14), and Sec. III (Figs. 4 and 5)"},{"comment":"No error bars or confidence intervals are reported for the transmittance spectra or the misfit values, although both are estimated from finite ensembles (1000 configurations for the target and 200 for trial spectra). In the shallower landscapes (e.g., Fig. 5(b) and especially Fig. 5(c)), it is not possible to judge whether the global minimum is statistically significant. Please report the statistical uncertainty of F(W, chi), for instance by bootstrapping over disorder realizations, and indicate the significance of the recovered minima.","section":"Sec. III (Figs. 2-5)"}],"minor_comments":[{"comment":"The normalization of eta_k is not specified; please state the variance (e.g., <|eta_k|^2>=1 or an equivalent convention) so that the disorder strength W is unambiguously defined and the protocol is reproducible.","section":"Sec. II.A, Eq. (7)"},{"comment":"The notation for the number of configurations switches between N_conf and N_conf; please unify it to a single symbol.","section":"Sec. II.C"},{"comment":"The perturbative expression E_c = -2 cos(pi chi) is cited to Ref. [21] without derivation; a one-line derivation or a reference to the specific equation in [21] would improve the self-containedness of the paper.","section":"Sec. III"},{"comment":"The abstract states that the drop position is 'strongly controlled by chi', but the paper later shows that for chi=0.10 (Fig. 5(c)) the drop is not resolved and the method fails; the abstract should qualify this statement by mentioning the regime of validity.","section":"Abstract and Sec. IV"},{"comment":"The numerical thresholds E_c are quoted as -1.18(1), -1.20(1), and -1.22(1) for W=0.05, 0.10, and 0.20, but the meaning of the parenthetical uncertainty is not defined; please specify how these uncertainties were estimated.","section":"Sec. III, Fig. 2 discussion"},{"comment":"The leftmost panel is labeled 'Uncorrelated'; it would be clearer to state explicitly that this corresponds to chi=0, since the dashed boundary between chi=0 and chi>0 is otherwise implicit.","section":"Fig. 1 caption"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and presents a conceptually interesting inverse-problem approach. The main concern is that the numerical demonstration is entirely self-consistent with the same code and disorder model, so the central claim would be considerably strengthened by an independent validation (e.g., a single-realization target or a target generated with a different method). The unspecified energy window is a reproducibility issue that the authors can readily fix. I do not see any reason to doubt the internal consistency of the numerics, but the current evidence is not yet sufficient to support the strong 'fingerprint' claim in the abstract."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version. The paper does something real: it shows for the first time that a transport-based misfit inversion can recover the stealthiness parameter chi in a 1D Anderson-type chain with stealthy hyperuniform disorder, and it maps out where that recovery fails (small chi, large W, or system size exceeding localization length). The numerical work is internally consistent. The finite-size study up to N=10^6 is a good robustness check, and the use of the perturbative edge position E_c = -2 cos(pi chi) to explain the drop location is sound. The authors are also honest about the breakdown at chi=0.1 and about the thermodynamic limit washing out the feature. That honesty should be credited.\n\nThe soft spot is the validation. The target spectra are generated with the same Fourier-space construction (Eq. 7), the same ensemble averaging, and the same recursive Green's function code as the trial spectra. Both sides approximate the same ensemble expectation, so the minimum in the misfit function is an in-sample identifiability check, not an out-of-sample prediction. Real transport data are single spectra, and real stealthy hyperuniform samples have blurred low-k suppression; neither is tested. Until the protocol is run against a single realization as target, or against a different disorder model, the abstract's 'fingerprints' claim overreaches.\n\nSecond is the unspecified energy window in Eq. (14). The text says only that [E-, E+] must be 'judiciously selected' to encompass the drop. No interval is quoted, and no stability test under window choice is shown. That's a reproducibility gap, albeit a fixable one. Related, there are no error bars on the transmittance or on the recovered (W, chi); the misfit contours show shallow valleys at chi=0.2, so a sensitivity analysis matters.\n\nThe forward relation between E_c and chi is a self-citation to the group's PRL, but the paper re-derives the comparison numerically; self-citation alone is not a problem here.\n\nVerdict: the central identifiability claim for the demonstrated range holds up, but the paper as written is a proof of concept needing one out-of-sample test. I would send it to review, with a request for a single-realization or independent-model check and a fixed window rule. For researchers working on correlated-disorder transport or inverse problems, it is worth citing as a conditional proof of concept. I'd bring it to a reading group as a 'maybe' — good discussion material on in-sample validation, but not a definitive result.","headline":"A clean but entirely in-sample numerical proof of concept; the fingerprint claim is plausible but needs a single-realization or independent-model test before it is established.","tokens_in":14630,"tokens_out":3040,"would_cite":true,"duration_ms":27501,"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":"Transmittance spectra can serve as fingerprints of stealthy hyperuniform disorder, and the sharp drop in a one-dimensional transmission curve pins down the stealthiness parameter χ when the edge is well resolved.","keywords":["stealthy hyperuniform disorder","quantum transport","transmittance spectrum","inverse problem","misfit function","tight-binding chain","correlated disorder","localization"],"falsifier":"Take a target transmittance spectrum produced by a structurally different model that still has perfect stealthy hyperuniform correlations (for instance, a real-space collective-coordinate construction rather than the Gaussian Fourier-amplitude recipe) and run the misfit protocol against it: if the recovered (W,χ) drifts away from the true parameters, the claim that transmittance spectra fingerprint stealthiness itself rather than the specific ensemble construction is refuted. A direct measurement on a fabricated stealthy hyperuniform photonic structure whose χ is independently characterized would settle the practical claim.","tokens_in":13600,"feed_emoji":"📉","tokens_out":10859,"duration_ms":80075,"temperature":0.7,"pith_summary":"The paper proposes a conductance-based inverse protocol to recover the stealthiness parameter χ of stealthy hyperuniform disorder from transport data alone. In a one-dimensional tight-binding chain whose on-site disorder is built from a structure factor S(k)=Θ(|k|-K) with K=2πχ, the ensemble-averaged transmittance displays a sharp drop at an energy set almost entirely by χ, while the disorder strength W mainly controls the transmittance magnitude. The paper shows that minimizing a misfit function comparing a target transmittance spectrum against trial spectra yields a clear minimum close to the target (W,χ) whenever the transmission edge is well resolved, demonstrated for χ_tar=0.3 and 0.2. This matters because the microscopic disorder configuration is often inaccessible in realistic samples, so an observable-based route to χ could apply to photonic and atomic transport experiments without structural imaging.","feed_headline":"A spectral drop reveals hidden stealthy disorder parameters","feed_subtitle":"Transport data alone recovers the hidden stealthiness parameter χ and disorder strength W.","key_machinery":"The central object is the misfit function F(Ω)=(1/(E_+ - E_-))∫_{E_-}^{E_+} dE [T_tar(E) - \\bar T(E;Ω)]^2, which compares a target transmittance spectrum with the configurational average over trial disorder parameters Ω=(W,χ). The mechanism that makes the inversion work is the sharp transmittance drop at the perturbation-theory energy E_c≈-2cos(πχ), which separates high- and low-transmittance regions: χ controls the drop's energy position and W controls the transmittance magnitude inside the transparent window, so the two parameters imprint distinct features of the spectrum that the misfit landscape can separate. The recursive Green's function method supplies the spectra efficiently for chains up to N=$10^{6}$, and the paper's finite-size analysis shows the edge feature survives as N grows.","core_discovery":"The central claim is that the energy-dependent transmittance of a disordered conductor carries a recognizable fingerprint of stealthy hyperuniform correlations, and that the fingerprint is invertible: minimizing the misfit function F(W,χ) over trial parameters recovers the parameters that generated a target spectrum, provided the target shows a well-resolved transmission edge. Numerically, for a chain of N=$10^{4}$ sites with disorder generated from S(k)=Θ(|k|-K), the misfit landscape develops a well-defined minimum at (W,χ) close to the target for W_tar=0.10 with χ_tar=0.30 and χ_tar=0.20, while for χ_tar=0.10 the localization length falls below the system size, the edge washes out, and the minimum becomes a shallow degenerate valley. The paper therefore concludes that transmittance spectra can serve as fingerprints of stealthy hyperuniform disorder, offering a practical route to infer correlated-disorder parameters from transport measurements.","pith_inferences":["A natural extension the paper does not pursue is to use the analytic edge relation E_c≈-2cos(πχ) as a direct one-parameter estimator of χ from a single spectrum, bypassing the full two-dimensional misfit minimization; this would be faster and would only need the drop position.","The failure at χ_tar=0.1 implies a fundamental resolution limit in the (W,χ) plane set by the ratio of localization length to system size; mapping that boundary could tell experimentalists which parameter regions are inferable from transport at all.","Realistic stealthy disorder is never perfectly step-like in S(k), so the protocol's robustness to blurred low-k suppression is the most important untested assumption; if the edge survives moderate blurring, the method would transfer to photonic samples, but if not, the practical window narrows considerably.","The same misfit logic could be adapted to two- and three-dimensional stealthy hyperuniform networks by replacing the energy window with a frequency window and using transmission or extinction spectra; the paper's 1D demonstration does not address the multi-mode complications, but the separation of edge position from overall magnitude suggests the signature would persist."],"forward_implications":["In mesoscopic stealthy hyperuniform structures, χ could be determined from a single measured transmission or conductance spectrum by minimizing the misfit function, with no need for structural imaging.","The transmission edge at E_c ≈ -2cos(πχ) provides an analytic anchor: even without running the full inversion, locating the drop gives a first estimate of χ.","Because the edge position is controlled by χ and the magnitude by W, the protocol remains accurate for χ even when the trial value of W differs from the true one, as the misfit minima stay pinned near χ_tar.","The method is inherently mesoscopic: in the thermodynamic limit or for very small χ, where localization suppresses the transmittance across the band, the edge disappears and parameter recovery fails, so the operational regime is N ≲ ξ(E).","The paper's finite-size results (edge visible up to N=10^6) indicate the protocol can be applied to current photonic and atomic experiments, whose system sizes fall in the same mesoscopic range."],"supporting_citations":[{"why":"Defines hyperuniformity as suppressed long-wavelength density fluctuations, the property the stealthy disorder realises.","marker":"[1]"},{"why":"Reviews hyperuniform states of matter and the vanishing small-k structure factor that underlies the S(k)=Θ(|k|-K) model.","marker":"[2]"},{"why":"Introduces the ensemble theory in which the stealthiness parameter χ quantifies the fraction of constrained Fourier modes.","marker":"[6]"},{"why":"Provides the one-dimensional stealthy-disorder tight-binding model and the perturbative transmission-edge energy E_c ≈ -2cos(πχ) that anchors the inversion.","marker":"[21]"},{"why":"Establishes the conductance-based misfit-function inverse problem that this work extends to correlated stealthy disorder.","marker":"[26]"},{"why":"Demonstrates inverse determination of disorder parameters from transmittance spectra, the immediate methodological antecedent for the present protocol.","marker":"[32]"},{"why":"Describes the momentum-space construction of disorder with S(k)=Θ(|k|-K) used to generate the on-site potentials.","marker":"[38]"},{"why":"Supplies the recursive Green's function method for computing 1D conductance that the paper uses to produce spectra.","marker":"[39]"},{"why":"Provides the surface Green's function and self-energy formalism for the recursive Green's function transmission calculation.","marker":"[41]"}],"fun_headline_variants":["Transmittance drop reveals stealthy disorder's hidden parameter","Inverse transport recovers hidden stealthiness parameter","Conductance misfit pinpoints stealthy disorder's χ","Transmission edge fingerprints hidden stealthy correlations","From conductance data to stealthy disorder's fingerprint"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The inversion is validated only against target spectra generated by the same idealized stealthy-disorder construction and the same recursive Green's function code used for the trial spectra, so the demonstration does not test how the protocol performs on experimental data or on disorder with imperfectly suppressed low-k fluctuations; the energy window [E_-, E_+] is also left unspecified, which leaves room for tuning in practice.","fun_headline_variants_meta":{"raw":{"variants":["Transmittance drop reveals stealthy disorder's hidden parameter","Inverse transport recovers hidden stealthiness parameter","Conductance misfit pinpoints stealthy disorder's χ","Transmission edge fingerprints hidden stealthy correlations","From conductance data to stealthy disorder's fingerprint"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000413,"raw_usage":{"total_tokens":2157,"prompt_tokens":989,"completion_tokens":1168,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":605,"completion_tokens_details":{"reasoning_tokens":1093}},"tokens_in":605,"tokens_out":1168,"duration_ms":8449,"temperature":1.0,"reasoning_tokens":1093,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:23:49.481026+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a target transmittance spectrum produced by a structurally different model that still has perfect stealthy hyperuniform correlations (for instance, a real-space collective-coordinate construction rather than the Gaussian Fourier-amplitude recipe) and run the misfit protocol against it: if the recovered (W,χ) drifts away from the true parameters, the claim that transmittance spectra fingerprint stealthiness itself rather than the specific ensemble construction is refuted. A direct measurement on a fabricated stealthy hyperuniform photonic structure whose χ is independently characterized would settle the practical claim.","supporting_citations":[{"cited_title":"Torquato, G","cited_arxiv_id":null,"evidence_quote":"Introduces the ensemble theory in which the stealthiness parameter χ quantifies the fraction of constrained Fourier modes."},{"cited_title":"Vanoni, J","cited_arxiv_id":null,"evidence_quote":"Provides the one-dimensional stealthy-disorder tight-binding model and the perturbative transmission-edge energy E_c ≈ -2cos(πχ) that anchors the inversion."},{"cited_title":"Mukim, F","cited_arxiv_id":null,"evidence_quote":"Establishes the conductance-based misfit-function inverse problem that this work extends to correlated stealthy disorder."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrates inverse determination of disorder parameters from transmittance spectra, the immediate methodological antecedent for the present protocol."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the recursive Green's function method for computing 1D conductance that the paper uses to produce spectra."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the surface Green's function and self-energy formalism for the recursive Green's function transmission calculation."}],"review_version":1}