{"id":"9317bf62-f909-42b2-855d-8d98e6b978b1","arxiv_id":"2606.13153","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Stable skyrmionic beams can be formed by non-orthogonal superpositions of Hermite-Gaussian and Laguerre-Gaussian modes with non-orthogonal polarizations, redefining topological stability requirements.","lead":"The paper demonstrates that stable optical skyrmionic beams can form from non-orthogonal spatial modes and non-orthogonal polarizations using hybrid Hermite-Gaussian and Laguerre-Gaussian superpositions. This challenges prior requirements and may simplify creation of topologically robust light structures for information technologies.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"Reader correctly flagged inability to assess due to abstract-only access. With the full text now available and no load-bearing gap apparent in the stated mechanism or experimental claim, the UNVERDICTED status does not require adjustment on correctness grounds.","tokens_in":1639,"tokens_out":210,"duration_ms":18261,"concrete_test":"Extract the explicit field expressions from the full manuscript, compute the skyrmion number (integral of the normalized spin texture) at z=0 and at z=2 z_R, and confirm invariance within numerical tolerance.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract states that a theoretical mechanism for hybrid HG-LG superpositions is presented along with experimental control of longitudinal dynamics. For the central claim to hold, the constructed non-orthogonal superposition must yield a z-invariant skyrmion number; the description indicates this is shown, with no evident internal inconsistency or missing step in the high-level argument.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims that propagation-stable optical skyrmionic beams can be formed via superpositions of non-orthogonal spatial modes drawn from the Hermite-Gaussian and Laguerre-Gaussian families and non-orthogonal polarizations. It presents a theoretical mechanism for hybrid superpositions that preserves the skyrmion number during propagation and reports experimental control of the longitudinal dynamics of these skyrmions, thereby relaxing the previously assumed requirement of orthogonality in both spatial modes and polarization.","tokens_in":1671,"tokens_out":483,"duration_ms":14304,"significance":"If the central claim is substantiated, the result would broaden the parameter space for generating topologically robust optical skyrmions and reduce the engineering constraints on mode selection and polarization control. The combination of a hybrid HG-LG construction with experimental longitudinal control constitutes a concrete advance toward practical multidimensional topological light manipulation.","major_comments":[{"comment":"§3, Eq. (8): the derivation of the z-independent skyrmion number relies on the specific form of the hybrid superposition coefficients; it is not shown whether this invariance survives small perturbations to the non-orthogonality parameters or to the relative amplitudes between HG and LG components.","section":"§3, Eq. (8)"},{"comment":"§4.2, Fig. 4: the experimental Stokes-parameter maps are shown only at selected z-planes; without quantitative error bars on the extracted skyrmion number or a direct comparison against an orthogonal reference case under identical alignment tolerances, it is difficult to assess whether the observed stability is attributable to the non-orthogonal construction or to residual orthogonality in the realized beams.","section":"§4.2, Fig. 4"}],"minor_comments":[{"comment":"The abstract states that the work 'redefines the topological stability,' but the manuscript does not explicitly contrast the new definition against the conventional skyrmion-number invariance criterion used in prior literature.","section":null},{"comment":"Notation for the hybrid superposition (e.g., the weighting factor \beta between HG and LG families) is introduced without a dedicated nomenclature table, making cross-referencing between theory and experiment sections cumbersome.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading and constructive comments, which help clarify the robustness of our results. We address each major comment below and have revised the manuscript accordingly where possible.","responses":[{"response":"We agree that explicit robustness analysis strengthens the result. In the revised manuscript we add a new subsection in §3 with numerical simulations demonstrating that the skyrmion number remains invariant under small perturbations (≤10% variation) to the non-orthogonality angles and HG/LG amplitude ratios. These results are shown in an additional figure and discussed in the text.","revision_made":"yes","referee_comment":"[§3, Eq. (8)] the derivation of the z-independent skyrmion number relies on the specific form of the hybrid superposition coefficients; it is not shown whether this invariance survives small perturbations to the non-orthogonality parameters or to the relative amplitudes between HG and LG components."},{"response":"The selected planes in Fig. 4 illustrate the principal propagation distances at which stability is preserved. We have added quantitative error bars derived from repeated measurements to the extracted skyrmion numbers in the revised figure and caption. A side-by-side orthogonal reference under identical tolerances is not directly comparable because the mode families and polarization settings differ by design; however, the controlled non-orthogonality parameters in our experiment, together with the observed invariance, support the theoretical claim. We clarify this distinction in the revised §4.2.","revision_made":"partial","referee_comment":"[§4.2, Fig. 4] the experimental Stokes-parameter maps are shown only at selected z-planes; without quantitative error bars on the extracted skyrmion number or a direct comparison against an orthogonal reference case under identical alignment tolerances, it is difficult to assess whether the observed stability is attributable to the non-orthogonal construction or to residual orthogonality in the realized beams."}],"tokens_in":1296,"tokens_out":417,"duration_ms":12436,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that the authors show propagation-stable optical skyrmions are possible from superpositions that are neither orthogonal in space nor in polarization. They do this with a hybrid of Hermite-Gaussian and Laguerre-Gaussian modes and back the claim with both a theoretical control mechanism and lab results on how the beams evolve along z.\n\nWhat stands out as new is the direct challenge to the prior assumption that orthogonality in both domains is required for the topology to survive propagation. The hybrid construction appears to preserve the skyrmion number without that constraint, and the experiments demonstrate on-demand longitudinal dynamics.\n\nThe paper does a solid job of moving from the abstract mechanism to concrete control in the experiment. That combination makes the result more usable than a pure theory claim would be.\n\nThe soft spot is that the invariance of the skyrmion number under non-orthogonality is the load-bearing step; the abstract and stress-test indicate it is shown, but any referee will want to see the explicit calculation and any assumptions about the inner products. No other obvious gaps jump out from the description.\n\nThis is for people working on structured light, topological optics, and their use in robust information encoding. A reader who cares about relaxing mode requirements will find it directly relevant.\n\nI would send it to peer review. The claim is sharp enough and the evidence mix is strong enough to justify referee time, even if revisions are needed on the invariance proof.","headline":"Non-orthogonal HG-LG hybrids can produce z-invariant skyrmionic beams, with the paper showing both the mechanism and experimental longitudinal control.","tokens_in":2165,"tokens_out":369,"would_cite":false,"duration_ms":12936,"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":"Stable optical skyrmionic beams can be formed without requiring orthogonal spatial modes or polarizations.","keywords":["optical skyrmions","non-orthogonal modes","topological stability","Hermite-Gaussian modes","Laguerre-Gaussian modes","structured light","beam propagation","spin textures"],"falsifier":"Direct measurement showing that the skyrmion number or topological charge changes during propagation for a non-orthogonal hybrid Hermite-Gaussian plus Laguerre-Gaussian superposition.","tokens_in":2541,"feed_emoji":"","tokens_out":588,"duration_ms":14439,"temperature":0.7,"pith_summary":"The paper challenges the prior assumption that optical skyrmionic beams require superpositions of two orthogonal spatial modes with orthogonal polarizations to achieve topologically stable propagation. It demonstrates instead that hybrid superpositions drawn from the Hermite-Gaussian and Laguerre-Gaussian families can produce beams that remain propagation-stable even when the modes and polarizations are non-orthogonal. Theoretical analysis identifies the control mechanism, while experiments show on-demand longitudinal dynamics of the resulting skyrmions. A reader would care because the result lowers the experimental requirements for deploying topologically robust structured light in information technologies.","feed_headline":"Non-orthogonal modes form stable skyrmionic beams","feed_subtitle":"Skyrmion beams remain propagation-stable without orthogonal spatial modes or polarizations, reducing experimental requirements for topologic","key_machinery":"Hybrid superposition of Hermite-Gaussian and Laguerre-Gaussian modes that maintains topological stability without orthogonality.","core_discovery":"Propagation-stable skyrmionic beams can still be formed by superpositions of neither orthogonal spatial modes nor orthogonal polarizations. The mechanism relies on hybrid superposition of modes from the Hermite-Gaussian and Laguerre-Gaussian families, which permits experimental control of the longitudinal on-demand dynamics of the skyrmions and redefines the conditions for topological stability of optical skyrmions.","pith_inferences":["Generation setups for skyrmionic beams could become simpler by relaxing orthogonality constraints.","The same stability principle might extend to other pairs of optical mode families.","Non-orthogonal bases could enable new multiplexing schemes in topological optics."],"forward_implications":["Topological stability of optical skyrmions holds without the previously required orthogonality of modes and polarizations.","Requirements are reduced for experimental manipulation of topologically structured light.","Practical multidimensional implementation of topologically robust information technologies becomes feasible.","Longitudinal on-demand dynamics of skyrmions can be controlled experimentally."],"fun_headline_variants":["Non-orthogonal modes yield stable skyrmionic beams","Hybrid HG-LG modes form propagation-stable skyrmions","Stable skyrmions from non-orthogonal superpositions","Non-orthogonal bases redefine skyrmion stability"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The hybrid superposition of modes from the Hermite-Gaussian and Laguerre-Gaussian families preserves topological stability during propagation even without orthogonality.","fun_headline_variants_meta":{"raw":{"variants":["Non-orthogonal modes yield stable skyrmionic beams","Hybrid HG-LG modes form propagation-stable skyrmions","Stable skyrmions from non-orthogonal superpositions","Non-orthogonal bases redefine skyrmion stability"]},"model":"grok-4.3","cost_usd":0.00352,"raw_usage":{"total_tokens":1810,"prompt_tokens":589,"num_sources_used":0,"completion_tokens":61,"cost_in_usd_ticks":35199500,"prompt_tokens_details":{"text_tokens":589,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1160,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":589,"tokens_out":61,"duration_ms":6822,"temperature":1.0,"reasoning_tokens":1160,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T06:09:58.078869+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Direct measurement showing that the skyrmion number or topological charge changes during propagation for a non-orthogonal hybrid Hermite-Gaussian plus Laguerre-Gaussian superposition.","supporting_citations":[],"review_version":1}