{"id":"e740c76a-23d4-4185-850d-6a09f4e8456c","arxiv_id":"2607.00618","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Analytical formulas derived via symbolic regression for soliton boundaries in non-Hermitian Kerr waveguide arrays, with continuum approximations showing NHSE-driven edge localization corroborated by numerics.","lead":"This paper examines light propagation and soliton formation in non-Hermitian optical waveguide arrays that include Kerr nonlinearity. It reports analytical formulas for soliton existence boundaries and shows that the non-Hermitian skin effect drives strong edge localization.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Symbolic regression formula for soliton existence boundary lacks reported validation against held-out simulations or first-principles derivation","rationale":"The reader's weakest_assumption directly identifies the symbolic-regression validity issue as load-bearing; the full text does not resolve it with additional safeguards, so the concern stands. This moves the verdict from UNVERDICTED to CONDITIONAL pending the concrete check.","tokens_in":1721,"tokens_out":303,"duration_ms":12773,"concrete_test":"Extract the symbolic-regression formula and the exact set of simulation points used to generate it; recompute the boundary on 20 new (g, γ) pairs drawn from the same range but not used in training; if the formula deviates by >15% on more than 3 points, the expression is not reliable.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The headline result for single-channel excitation rests on an analytical expression for the existence boundary obtained via symbolic regression. For the claim to hold, this expression must be a robust, physically interpretable relation rather than a fit to the specific numerical trajectories used in training. The manuscript provides no details on the regression search space, regularization, cross-validation procedure, or quantitative error on independent parameter points; without these, the formula could be an overfit artifact whose apparent agreement with numerics is circular. The continuum approximation for broad pulses is less central to the strongest claim and appears numerically corroborated in the text.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript studies nonlinear light propagation in non-Hermitian waveguide arrays with Kerr nonlinearity. Single-channel excitation is shown to produce stable solitons via the interplay of Kerr nonlinearity and the non-Hermitian skin effect (NHSE); an analytical expression for the soliton existence boundary is obtained by symbolic regression. For broad-pulse initial conditions, perturbed soliton solutions are derived in the continuum approximation and stated to be corroborated by numerics, with NHSE driving edge localization. Stationary solutions are also identified: nonlinear bulk modes in the Hermitian limit that become compressed toward the edge under non-reciprocality, and near-edge skin solitons in the non-Hermitian regime.","tokens_in":1838,"tokens_out":524,"duration_ms":15605,"significance":"If the symbolic-regression formula proves robust and the numerical validations hold, the work supplies concrete analytical and numerical results on nonlinear extensions of the NHSE in both discrete and continuum settings. The explicit formula for the existence boundary and the demonstration of NHSE-driven localization constitute potentially useful benchmarks for experiments in non-Hermitian nonlinear optics.","major_comments":[{"comment":"The central analytical result—the closed-form expression for the soliton existence boundary—is obtained exclusively via symbolic regression. No information is provided on the regression search space, regularization, cross-validation procedure, or quantitative error metrics evaluated on independent parameter points outside the training set. Without these, it is impossible to determine whether the formula is a physically interpretable relation or an overfit artifact whose agreement with the reported trajectories is circular (§ on single-channel excitation and symbolic regression).","section":"single-channel excitation / symbolic regression section"},{"comment":"The claim that the continuum approximation remains accurate for broad-pulse dynamics rests on numerical corroboration, yet the manuscript does not report quantitative measures (e.g., L2 error between continuum solution and discrete lattice evolution, or dependence on lattice spacing) that would confirm the approximation's validity across the parameter range used for the existence boundary.","section":"broad-pulse excitation / continuum approximation"}],"minor_comments":[{"comment":"Notation for the non-reciprocal coupling parameters and the Kerr coefficient should be introduced once with explicit definitions before being used in multiple sections.","section":null},{"comment":"Figure captions for the soliton profiles should state the precise values of the non-Hermitian parameter and nonlinearity strength used in each panel.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive and detailed report. We address each major comment below and will revise the manuscript to incorporate the requested clarifications and quantitative validations.","responses":[{"response":"We agree that additional methodological details are required to establish the robustness of the symbolic-regression result. In the revised manuscript we will expand the relevant section to specify the search space of operators and functions, any regularization employed, the cross-validation protocol, and quantitative error metrics (e.g., RMSE) evaluated on an independent test set of parameter points. These additions will demonstrate that the formula is not an overfitting artifact and that the numerical trajectories used for comparison were generated independently of the regression training data.","revision_made":"yes","referee_comment":"[single-channel excitation / symbolic regression section] The central analytical result—the closed-form expression for the soliton existence boundary—is obtained exclusively via symbolic regression. No information is provided on the regression search space, regularization, cross-validation procedure, or quantitative error metrics evaluated on independent parameter points outside the training set. Without these, it is impossible to determine whether the formula is a physically interpretable relation or an overfit artifact whose agreement with the reported trajectories is circular (§ on single-channel excitation and symbolic regression)."},{"response":"We concur that quantitative error measures are necessary to substantiate the continuum approximation. In the revision we will add explicit L2-error comparisons between the continuum solutions and discrete-lattice simulations, together with the dependence of this error on lattice spacing, evaluated across the parameter regime of the existence boundary. These metrics will replace the current visual corroboration and confirm the approximation's accuracy.","revision_made":"yes","referee_comment":"[broad-pulse excitation / continuum approximation] The claim that the continuum approximation remains accurate for broad-pulse dynamics rests on numerical corroboration, yet the manuscript does not report quantitative measures (e.g., L2 error between continuum solution and discrete lattice evolution, or dependence on lattice spacing) that would confirm the approximation's validity across the parameter range used for the existence boundary."}],"tokens_in":1415,"tokens_out":441,"duration_ms":19532,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's core contribution is an analytical expression for the existence boundary of solitons from single-channel excitation in non-Hermitian waveguide arrays, derived via symbolic regression, plus some continuum solutions for broad pulses that show NHSE driving localization at the edge. They also identify stationary nonlinear bulk modes and near-edge skin solitons.\n\nThe work does a decent job laying out two excitation regimes and claiming numerical support for the continuum part. Extending the skin effect into the nonlinear Kerr regime in discrete arrays is a natural next step from the linear literature they cite, and the distinction between Hermitian bulk modes and non-Hermitian skin solitons adds a bit of structure.\n\nThe soft spot is the symbolic regression result. The stress-test concern is on point: without details on the search space, regularization, cross-validation, or error on held-out parameter sets, the formula risks being an overfit to the training trajectories rather than a robust physical relation. The abstract and stress-test note give no sign those checks were done, so that part needs more evidence before it can be taken as solid.\n\nThe continuum approximation for broad pulses looks less shaky since the paper claims direct numerical corroboration there.\n\nThis is for specialists already working on non-Hermitian optics or discrete nonlinear waveguides. A reader in that narrow area might pick up the analytical boundary formula or the acceleration mechanism to try in their own setups.\n\nIt deserves peer review so the regression procedure can be examined directly. I'd send it on.","headline":"The symbolic regression formula for the soliton existence boundary is the main new claim but needs validation details to hold up, while the NHSE extension to nonlinear skin solitons is a reasonable incremental step.","tokens_in":2307,"tokens_out":384,"would_cite":false,"duration_ms":17130,"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":"Kerr nonlinearity and the non-Hermitian skin effect together generate stable skin solitons localized at the edge of waveguide arrays.","keywords":["non-Hermitian skin effect","Kerr nonlinearity","waveguide arrays","skin solitons","symbolic regression","soliton existence boundary","non-reciprocal couplings","edge localization"],"falsifier":"Direct numerical integration of the discrete lattice equations that either confirms or refutes the persistence of stable solitons for parameter values lying just inside versus just outside the analytically predicted existence boundary.","tokens_in":2622,"feed_emoji":"","tokens_out":753,"duration_ms":18852,"temperature":0.7,"pith_summary":"The paper examines light propagation in non-reciprocal waveguide arrays under the Kerr nonlinearity. Single-channel excitation produces stable solitons through the combined action of nonlinearity and the non-Hermitian skin effect. Symbolic regression supplies a closed-form expression for the boundary of soliton existence. Broad initial pulses evolve into perturbed solitons whose propagation is accelerated by the skin effect, resulting in strong edge localization. Stationary solutions include nonlinear bulk modes that are driven toward the edge when non-reciprocality is present, constituting a nonlinear version of the skin effect.","feed_headline":"Kerr effect and skin effect create stable edge solitons in waveguide arrays","feed_subtitle":"Single-channel excitation yields localized states whose existence boundary is given by symbolic regression; broad pulses tighten at the edge","key_machinery":"The non-Hermitian skin effect in interplay with Kerr nonlinearity, which supports stable localized solitons and supplies the mechanism for edge compression of bulk modes.","core_discovery":"Single-channel excitation creates stable solitons supported by the interplay of the Kerr nonlinearity and non-Hermitian skin effect. An analytical formula defining the soliton existence boundary is obtained by the symbolic-regression method. For broad-pulse excitation, perturbed soliton solutions are derived in the continuum approximation and show that the skin effect accelerates propagation toward the boundary, ultimately causing tight localization at the edge. Stationary nonlinear bulk modes in the Hermitian regime become compressed toward the edge under non-reciprocality, which is identified as the nonlinear extension of the non-Hermitian skin effect.","pith_inferences":["The derived boundary formula could be used to predict the minimal nonlinearity strength needed for edge localization in similar discrete non-Hermitian lattices.","The observed acceleration of broad pulses suggests that non-Hermitian couplings might serve as a passive mechanism for routing optical power to boundaries without external modulation.","The nonlinear skin-effect compression of bulk modes may extend to other conservative nonlinearities, offering a route to edge-mode engineering in photonic arrays.","Testing the same initial conditions in a continuum non-Hermitian nonlinear Schrödinger equation would check whether the localization persists without lattice discreteness."],"forward_implications":["Single-channel initial conditions reliably produce stable solitons localized by the skin effect.","The existence region of these solitons is delimited by an explicit analytical formula obtained from symbolic regression.","Broad pulses experience accelerated motion to the array edge and form tightly localized states.","Nonlinear bulk modes are compressed toward the edge once non-reciprocal couplings are introduced.","Near-edge skin solitons appear as stationary solutions in the non-Hermitian regime."],"fun_headline_variants":["Skin-Kerr interplay stabilizes solitons at non-Hermitian waveguide edges","Symbolic regression yields soliton boundary in skin-effect waveguides","NHSE drives broad solitons to tight edge localization in arrays","Non-Hermitian couplings compress nonlinear modes to array edges"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The symbolic-regression procedure produces a physically valid closed-form expression for the existence boundary rather than an overfit artifact, and the continuum approximation remains accurate for the broad-pulse dynamics in the discrete lattice.","fun_headline_variants_meta":{"raw":{"variants":["Skin-Kerr interplay stabilizes solitons at non-Hermitian waveguide edges","Symbolic regression yields soliton boundary in skin-effect waveguides","NHSE drives broad solitons to tight edge localization in arrays","Non-Hermitian couplings compress nonlinear modes to array edges"]},"model":"grok-4.3","cost_usd":0.00663,"raw_usage":{"total_tokens":3107,"prompt_tokens":695,"num_sources_used":0,"completion_tokens":67,"cost_in_usd_ticks":66299500,"prompt_tokens_details":{"text_tokens":695,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2345,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":695,"tokens_out":67,"duration_ms":16430,"temperature":1.0,"reasoning_tokens":2345,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-02T07:26:28.166436+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Direct numerical integration of the discrete lattice equations that either confirms or refutes the persistence of stable solitons for parameter values lying just inside versus just outside the analytically predicted existence boundary.","supporting_citations":[],"review_version":1}