{"id":"76ed8a03-a23e-494a-b0e5-9027aef81250","arxiv_id":"2606.04386","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"In a unidirectional double-chain Hatano-Nelson model, the Off-ED regime yields SNR scaling as δ^{-1} instead of the At-ED fractional scaling δ^{-1/2}, while retaining exponential sensitivity with system size N.","lead":"The paper models a double-chain Hatano-Nelson system and shows that operating away from the exceptional deficiency point restores linear SNR scaling with detuning while keeping exponential sensitivity growth with lattice size. A smart generalist might read it to understand a concrete route toward practical non-Hermitian sensors that avoid catastrophic noise amplification.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Whether disorder that suppresses NHSE still preserves the exponential-in-N sensitivity scaling claimed for the Off-ED regime","rationale":"The reader's weakest_assumption directly identifies the modeling choice whose validity determines whether the Off-ED improvement is genuine or an artifact of the chosen coupling and disorder. Because the full text is now available, the concrete numerical check above would settle whether the claimed preservation of exponential scaling holds.","tokens_in":1771,"tokens_out":292,"duration_ms":20689,"concrete_test":"Extract the reported sensitivity vs. N curves (or equivalent data) for both At-ED and Off-ED regimes at fixed disorder strength above the fault-tolerance threshold; fit the exponent of the exponential scaling in each case and check whether the Off-ED exponent remains within 10% of the At-ED value.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The headline result requires that diagonal spatial disorder suppresses the NHSE (and its associated geometric singularity) enough to restore SNR ∝ δ^{-1} while leaving the macroscopically degenerate spectrum's exponential sensitivity to lattice size N intact. The abstract states this occurs “albeit at a slightly reduced absolute sensitivity,” but the unidirectional interlayer coupling plus the specific disorder form must not introduce new uncontrolled perturbations that alter the scaling exponent with N. This modeling assumption, introduced for the double-chain Hatano-Nelson system, is the least-secured step for the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper introduces a double-chain Hatano-Nelson model with unidirectional interlayer coupling and diagonal spatial disorder. At the exceptional deficiency (ED) limit the system exhibits macroscopic spectral degeneracy and NHSE, producing exponential sensitivity scaling with lattice size N that is robust over a wide detuning range. By adding disorder the authors suppress the NHSE, delineate At-ED and Off-ED regimes, and claim that the Off-ED regime restores linear SNR scaling (SNR ∝ δ^{-1}) while preserving the exponential-in-N sensitivity (slightly reduced absolute value), yielding orders-of-magnitude SNR improvement.","tokens_in":1911,"tokens_out":528,"duration_ms":18338,"significance":"If the scaling claims are rigorously verified, the Off-ED construction supplies a concrete operating point that mitigates the sensitivity-noise trade-off in non-Hermitian sensors while retaining the exponential advantage of macroscopic degeneracy. The cosine-similarity diagnostic for the fault-tolerance threshold is a useful quantitative tool. The result would be of interest to the topological-sensing community provided the modeling assumptions do not inadvertently alter the scaling exponent with N.","major_comments":[{"comment":"The central claim that Off-ED operation preserves the exponential sensitivity scaling with N while only reducing absolute sensitivity rests on the modeling assumption that diagonal spatial disorder plus unidirectional interlayer coupling suppresses NHSE without introducing new perturbations that change the scaling exponent. This assumption, introduced in the description of the double-chain Hatano-Nelson system, is load-bearing and requires explicit verification (e.g., scaling plots or analytic argument for multiple N values in the Off-ED regime).","section":"Model and disorder implementation"},{"comment":"The abstract states that the At-ED regime yields SNR ∝ δ^{-1/2} while Off-ED restores SNR ∝ δ^{-1}, yet no derivation or error analysis is supplied showing how these scalings follow from the eigenvalue problem or from the eigenspace geometry once disorder is present. Without this step the claimed orders-of-magnitude SNR enhancement cannot be assessed for robustness.","section":"Results on SNR scaling"}],"minor_comments":[{"comment":"Typo in abstract: 'whith' should be 'with'.","section":"Abstract"},{"comment":"Notation for the detuning parameter δ and the precise definition of the Off-ED operating point should be introduced with an equation or explicit parameter range rather than only descriptive language.","section":"Regime definitions"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful review and constructive feedback. The comments highlight important points regarding verification of scaling claims, which we address below by committing to specific additions in the revised manuscript.","responses":[{"response":"We agree that the preservation of exponential scaling under disorder requires explicit demonstration. In the revised manuscript we will add numerical scaling plots of sensitivity versus N (for N = 10, 20, 40, 80) at fixed disorder strengths inside the Off-ED regime, confirming that the exponent remains unchanged while the prefactor is modestly reduced. A short perturbative argument will also be included showing that the unidirectional interlayer coupling and diagonal disorder primarily suppress the skin-mode localization length without lifting the macroscopic degeneracy that underlies the exponential scaling.","revision_made":"yes","referee_comment":"[Model and disorder implementation] The central claim that Off-ED operation preserves the exponential sensitivity scaling with N while only reducing absolute sensitivity rests on the modeling assumption that diagonal spatial disorder plus unidirectional interlayer coupling suppresses NHSE without introducing new perturbations that change the scaling exponent. This assumption, introduced in the description of the double-chain Hatano-Nelson system, is load-bearing and requires explicit verification (e.g., scaling plots or analytic argument for multiple N values in the Off-ED regime)."},{"response":"We acknowledge the absence of an explicit derivation. The revision will contain a new subsection deriving the SNR scalings directly from the eigenvalue problem and the geometry of the perturbed eigenspace. Starting from the definition SNR = |dE/dδ| / σ_noise and using the cosine-similarity diagnostic to quantify the overlap between left and right eigenvectors, we will show analytically that the At-ED point produces a square-root singularity in the noise variance while the Off-ED point restores a simple pole, yielding the linear scaling. Numerical error bars obtained from ensemble averaging over disorder realizations will be added to the SNR plots to quantify robustness.","revision_made":"yes","referee_comment":"[Results on SNR scaling] The abstract states that the At-ED regime yields SNR ∝ δ^{-1/2} while Off-ED restores SNR ∝ δ^{-1}, yet no derivation or error analysis is supplied showing how these scalings follow from the eigenvalue problem or from the eigenspace geometry once disorder is present. Without this step the claimed orders-of-magnitude SNR enhancement cannot be assessed for robustness."}],"tokens_in":1483,"tokens_out":473,"duration_ms":35142,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The central point here is that the authors separate an At-ED regime from an Off-ED one in their double-chain model. At the exceptional deficiency limit the system has the usual non-Hermitian skin effect and exponential sensitivity with lattice size, but the noise scaling is only square-root. Shifting slightly off that point with diagonal spatial disorder suppresses the skin effect enough to restore ordinary linear SNR scaling and gives several orders of magnitude improvement, at the cost of a modest drop in absolute sensitivity.\n\nThey do a useful job defining the transition with eigenspace cosine similarity and showing a clear fault-tolerance threshold. That gives a concrete way to locate the operating window. The unidirectional interlayer coupling and the specific disorder form are laid out explicitly, so the setup is reproducible in principle.\n\nThe soft spot is that the abstract states the scaling laws without the intermediate steps or error bars, so it is not yet clear whether the linear recovery follows directly from the model or requires fine-tuning of parameters. The stress-test worry about whether the same disorder that kills the skin effect also preserves the exact exponential N-dependence is still open; if the full numerics show the exponent stays intact across the reported detuning range, the claim strengthens, but right now that step rests on the modeling choices.\n\nThis is for people already working on non-Hermitian lattice sensors who need a practical knob to balance sensitivity against noise. It is narrow enough that most readers outside that niche will not need it, but the distinction between the two regimes is a clear enough addition to the existing literature that a serious referee should look at the derivations and the scaling plots.","headline":"The paper's main claim is that operating off the exceptional deficiency point with added disorder in this Hatano-Nelson chain recovers linear SNR scaling while keeping exponential-in-N sensitivity.","tokens_in":2395,"tokens_out":405,"would_cite":false,"duration_ms":22827,"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":"Shifting a non-Hermitian sensor to the Off-ED regime removes geometric noise singularities and restores linear SNR scaling while keeping exponential sensitivity with lattice size.","keywords":["non-Hermitian sensing","exceptional deficiency","non-Hermitian skin effect","sensitivity-noise trade-off","Hatano-Nelson model","topological sensors","spatial disorder"],"falsifier":"A direct measurement of how signal-to-noise ratio scales with detuning δ in a physical realization of the double-chain model, comparing the At-ED and Off-ED regimes, would confirm whether the linear scaling law is recovered in the Off-ED case.","tokens_in":2674,"feed_emoji":"","tokens_out":707,"duration_ms":24210,"temperature":0.7,"pith_summary":"The paper studies a double-chain Hatano-Nelson model with unidirectional interlayer coupling to resolve the sensitivity-noise trade-off in non-Hermitian sensing. At the exceptional deficiency limit the system delivers exponential sensitivity with lattice size N but incurs fractional-order noise amplification. Adding diagonal spatial disorder suppresses the non-Hermitian skin effect and creates a clear separation between At-ED and Off-ED regimes. Operation in the Off-ED regime eliminates the geometric singularity that produces SNR ∝ δ^{-1/2} and recovers the linear law SNR ∝ δ^{-1}, delivering several orders of magnitude improvement while the exponential scaling with N remains intact.","feed_headline":"Off-ED operation restores linear SNR scaling in non-Hermitian sensors","feed_subtitle":"It removes geometric noise singularities while preserving exponential sensitivity to lattice size and yields orders-of-magnitude gains.","key_machinery":"The Off-ED operating regime, defined by progressive suppression of the non-Hermitian skin effect through diagonal spatial disorder in the double-chain Hatano-Nelson model with unidirectional interlayer coupling.","core_discovery":"In the double-chain Hatano-Nelson model, the At-ED configuration imposes fractional-order noise amplification (SNR ∝ δ^{-1/2}) that saturates at a suboptimal plateau, whereas migration to the Off-ED regime eliminates this geometric singularity, restores the linear scaling law SNR ∝ δ^{-1}, and achieves an SNR enhancement of several orders of magnitude while fully preserving the exponential sensitivity scaling with lattice size N, albeit at a slightly reduced absolute sensitivity.","pith_inferences":["The fault-tolerance threshold identified by eigenspace cosine similarity could serve as a practical tuning knob in device fabrication.","Controlled introduction of spatial disorder might be used to switch between regimes in other non-Hermitian lattices that exhibit skin effects.","The approach suggests that topological sensors can be engineered to operate away from exact exceptional points without sacrificing the core scaling advantages."],"forward_implications":["SNR scales linearly as δ^{-1} in the Off-ED regime instead of saturating under fractional amplification.","Several orders of magnitude SNR improvement is obtained while exponential sensitivity with N is retained.","The system remains robust across a six-order-of-magnitude detuning range.","Absolute sensitivity is slightly lower than the strict At-ED limit but the noise immunity is substantially higher."],"fun_headline_variants":["Off-ED restores linear SNR scaling in non-Hermitian sensors","Off-ED fixes SNR scaling in double-chain Hatano-Nelson model","Non-Hermitian sensors use Off-ED for linear noise scaling","Off-ED regime achieves linear SNR scaling with lattice size"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The unidirectional interlayer coupling and the chosen form of diagonal spatial disorder produce a clean separation between At-ED and Off-ED regimes and suppress the non-Hermitian skin effect without additional uncontrolled effects.","fun_headline_variants_meta":{"raw":{"variants":["Off-ED restores linear SNR scaling in non-Hermitian sensors","Off-ED fixes SNR scaling in double-chain Hatano-Nelson model","Non-Hermitian sensors use Off-ED for linear noise scaling","Off-ED regime achieves linear SNR scaling with lattice size"]},"model":"grok-4.3","cost_usd":0.008451,"raw_usage":{"total_tokens":3849,"prompt_tokens":722,"num_sources_used":0,"completion_tokens":69,"cost_in_usd_ticks":84512000,"prompt_tokens_details":{"text_tokens":722,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3058,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":722,"tokens_out":69,"duration_ms":32970,"temperature":1.0,"reasoning_tokens":3058,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T06:29:16.209549+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A direct measurement of how signal-to-noise ratio scales with detuning δ in a physical realization of the double-chain model, comparing the At-ED and Off-ED regimes, would confirm whether the linear scaling law is recovered in the Off-ED case.","supporting_citations":[],"review_version":1}