{"id":"42cae48a-3fa3-4011-872f-18a7b685fca2","arxiv_id":"2411.13221","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Direct observation of hybrid skin-topological corner states in a transmission line network using synthetic complex frequency excitation, with HSTE controlled by boundary loss alone.","lead":"The authors use a coaxial-cable transmission line network and synthesized complex-frequency signals to directly observe corner states predicted by the hybrid skin-topological effect (HSTE). A generalist might care because it shows a non-Hermitian topological effect can be driven by loss only at the boundaries and observed without measuring transient complex-frequency dynamics.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The field pattern labeled as the HSTE corner state is a single-time snapshot of a synthesized transient; it may reflect wave-packet dynamics rather than the eigenstate, so the central observation is not yet established.","rationale":"The most load-bearing risk to the abstract's central claim is not the model parameter fitting but the interpretation of the synthetic complex-frequency response. Even if the effective Haldane model is correct, the experiment does not directly measure an eigenstate; it measures a time-domain waveform synthesized from frequency-domain data and then picks a frame. The theoretical justification (Eq. 19) shows the target term grows linearly with t while others oscillate, but this holds only when the excitation frequency is exactly an eigenfrequency and other eigenfrequencies are sufficiently separated in the complex plane. In a 4x5 network with a continuum of bulk states and edge states, the separation may be insufficient. The authors' own admission of upper-left intensity indicates strong hybridization, exactly the regime where the single-mode dominance argument is fragile. The proposed test (time-stability plus full-network eigenmode overlap) directly checks whether the snapshot is the eigenstate. If it fails, the claim of direct observation collapses. The asymmetric transmission claim (Fig. 4g) is also concerning because a passive reciprocal network should have S21=S12, but that is a secondary claim; the corner-state observation is primary. Therefore the verdict remains CONDITIONAL pending this check.","tokens_in":15965,"tokens_out":8396,"duration_ms":91791,"concrete_test":"Vary the synthesis time t across the predicted dominance window (e.g., t = 0.2, 0.57, 1.0 μs) and compute the normalized field pattern from the same experimental data. If the pattern changes substantially (e.g., localization shifts or spreads), the snapshot is not a stable eigenmode. Additionally, diagonalize the full transmission-line network equations (Eq. 4-5) with the measured cable lengths and attenuation parameters, identify the eigenmode nearest (33.49-1.19i) MHz, and correlate its field with the measured snapshot; a Pearson correlation below ~0.9 would indicate the observed pattern is not that eigenstate.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is the direct observation of an HSTE corner eigenstate (Fig. 4d) via synthesized complex-frequency excitation. The method reconstructs a time-dependent response as a superposition of all eigenmodes (Eqs. 12-18). The presented 'eigenstate' is a single-time snapshot at t=0.57 μs, selected because the effective tight-binding model predicts the target mode coefficient dominates in a window (Fig. 7b). This mode-coefficient analysis, however, uses the ideal 3-layer Haldane model, not the actual 4x5 transmission-line network with frequency-dependent coth/sinh couplings and cable attenuation. In the real network, eigenfrequencies are dense and not independently verified; at t=0.57 μs the wave launched from the lower-right corner has only propagated a short distance, so the lower-left intensity could be a traveling boundary wavefront rather than the eigenmode. The authors admit visible upper-left intensity due to finite-size hybridization (Supplementary Note 4), which suggests the eigenstate is strongly hybridized and the target-mode dominance window may not exist. If the pattern is time-window dependent or contaminated by other modes, the observation of the HSTE corner state is not established. Thus, the load-bearing assumption is: the field at the selected time equals the target eigenstate.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports an experimental transmission-line realization of the hybrid skin-topological effect (HSTE), in which topological chiral edge states are argued to collapse into a corner state due to boundary-induced non-Hermitian point gaps. The authors formulate an effective Haldane model in an angular-momentum sector, compute supercell spectra showing that loss distributions breaking the spectral symmetry f(k)=f(-k) produce winding-number-one point gaps, and observe in a 4x5 network a lower-left-localized field pattern under synthesized complex-frequency excitation at f=(33.49-1.19i) MHz. They also present transmission spectra claimed to show asymmetric propagation in the topological band gap and argue that only boundary loss, not bulk loss, is needed for HSTE.","tokens_in":16219,"tokens_out":11983,"duration_ms":130401,"significance":"If all claims hold, the paper would be a useful contribution: it would provide a direct procedure for accessing complex-frequency eigenstates in non-Hermitian topological systems and evidence that boundary-only loss engineering is sufficient for HSTE. The synthesis formalism (Eqs. 7-14) is clearly derived, the periodicity of the synthesized pulse is demonstrated experimentally (T=20 us, Fig. 5), and the supplementary material appears to address robustness, sample shapes, and winding-number variations. However, the central experimental evidence is currently qualitative: single hand-picked snapshots, no quantitative mode-overlap metrics, a small network with acknowledged finite-size hybridization, and fitted attenuation parameters. The strength of the conclusions is therefore not yet commensurate with the claims.","major_comments":[{"comment":"The identification of the lower-left-localized pattern in Fig. 4d as an HSTE corner eigenstate is supported by a single snapshot at t=0.57 us chosen from the synthesized transient (Fig. 6a) and by a mode-coefficient analysis (Fig. 7b) performed with the ideal tight-binding model (t1=-1, t2=-2, gamma=1), not with the physical network equation containing the frequency-dependent coth/sinh couplings and cable attenuation (Eqs. 4-5). Because the 4x5 network has dense eigenfrequencies that are not independently verified, and because the authors acknowledge noticeable upper-left intensity from finite-size coupling (Supplementary Note 4), the dominance window 4<t<10 in Fig. 7b has no demonstrated counterpart at the experimental time. The authors should quantify the overlap between the measured field and the full-network eigenmode, test the stability of the pattern across the predicted time window, and exclude the possibility that the snapshot is a traveling wavefront launched from the lower-right source.","section":"Experimental demonstration; Fig. 4d; Methods Eqs. (12)-(19), Fig. 7b"},{"comment":"For a passive linear network composed of reciprocal coaxial cables and resistive terminators, the two-port scattering matrix must be symmetric, implying |S21|=|S12| for the same two ports. The clear asymmetry in Fig. 4g therefore contradicts reciprocity unless the network contains unmentioned nonreciprocal or active elements, the measurement is not a standard two-port S-parameter measurement, or the ports are not equivalent. Since this asymmetric transmission is presented as a real-frequency manifestation of HSTE, the authors need to specify the exact measured quantity, port definitions, and normalization, and ideally perform a port-swap check. As written, this claim is not supported.","section":"Experimental demonstration; Fig. 4g"},{"comment":"The experimental network is only 4x5 cells, far smaller than the 9x9 model of Fig. 3a used to establish the HSTE corner-state concept. The authors report noticeable intensity at the upper-left corner due to interactions between opposite boundaries (Supplementary Note 4). With such a small sample, the field pattern may be dominated by finite-size hybridization or by boundary-wave propagation rather than by exponential corner localization of an HSTE mode. A finite-size scaling analysis (e.g., localization length extracted from 6x6, 9x9, and larger networks) or a quantitative comparison of the experimental field with the full-network eigenstate is needed to show that the observed localization is a true HSTE eigenstate.","section":"HSTE in the transmission line network; Fig. 3a vs Fig. 4b"},{"comment":"The time window of the mode-dominance calculation is presented in dimensionless tight-binding units ('about 4 < t < 10'), while the experimental snapshot is taken at t=0.57 us. No mapping between the dimensionless time and the physical network time is provided, so the claim that t=0.57 us lies in the dominance window is unsubstantiated. Moreover, the complex excitation frequencies (e.g., f=(33.49-1.19i) MHz) are taken from the model spectrum but are never verified against the realized 4x5 network; the authors should show that these frequencies correspond to actual poles of the measured response, for example by fitting the complex Lorentzian line shape of A(omega) or by measuring the temporal decay rate.","section":"Methods; Fig. 7b; Figs. 4d-f"}],"minor_comments":[{"comment":"There are typos: 'conner' should be 'corner' in the sentence describing Fig. 4f, and 'exitation' should be 'excitation' in the Methods section.","section":"Global"},{"comment":"In the sentence 'Experimental observations of HSTE have been reported in circuit systems 40, photonic crystals41,42, photonic crystals43 and active matter systems 44', the phrase 'photonic crystals' is duplicated; the citation list should be cleaned.","section":"Introduction"},{"comment":"Please specify the units of time and energy in the tight-binding calculation and state how the dimensionless parameters t1=-1, t2=-2, gamma=1 are related to the physical network parameters (cable lengths, permittivity, attenuation).","section":"Fig. 7b"},{"comment":"Report measurement repetitions and error bars for the transmission spectra; the current single spectra do not allow the reader to judge whether the asymmetry exceeds experimental uncertainty.","section":"Fig. 4g"},{"comment":"The text calls the technique 'synthetic complex frequency excitations'; to avoid confusion, clarify earlier that the network is driven at multiple real frequencies and the complex-frequency response is synthesized in post-processing.","section":"Abstract and Introduction"},{"comment":"The statement 'available from the corresponding authors on request' is weaker than current community norms; consider depositing the raw transmission data and simulation scripts in a public repository.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The most serious issue is the apparent violation of reciprocity in Fig. 4g; if the S-parameters are indeed measured as stated, this warrants close scrutiny by the editor. The paper also relies substantially on the authors' own prior work (Ref. 51) for the central tight-binding mapping and effective Haldane model; an independent validation of that mapping would strengthen the report. The stress-test concern about the transient nature of the observed corner state is, in my reading, valid: the current manuscript does not yet distinguish a single eigenstate from a window-selected superposition."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper is worth reading but not worth taking at face value yet. The genuinely new thing is that they excite a complex-frequency corner state directly using synthetic complex-frequency waves in a transmission-line network, and they show that boundary-only loss is enough for the hybrid skin-topological effect. That is a real advance over earlier indirect observations. The paper is also honest about its finite-size limitations.\n\nThe supercell analysis and the point-gap winding argument are standard but carefully done. The experimental and simulated field patterns for the corner state agree qualitatively, and the authors provide a time-resolved evolution showing the signal lingers at the lower-left corner rather than just passing through.\n\nHowever, the central evidence is a single snapshot at t=0.57 μs, and the time-window justification is computed in the ideal tight-binding model, not in the actual frequency-dependent network with cable attenuation. That weakens the claim that the snapshot is the eigenstate. The network is only 4x5, and they admit noticeable upper-left intensity from boundary coupling. These are fixable with quantitative overlap metrics, but right now the evidence is qualitative.\n\nThe asymmetric transmission claim is a bigger problem. In a passive reciprocal network of cables and terminators, S21 and S12 must be equal. The paper reports they differ. Unless the measurement is not a standard S-parameter two-port measurement, or there is some nonlinearity, this contradicts reciprocity. The paper does not address this, and the abstract leans on it. That needs to be sorted out.\n\nThe fitted cable attenuation parameters have no error bars, and data are only on request. Minor.\n\nI'd send it to peer review — the core idea is good and the direct imaging is a contribution — but the referee should push hard on the reciprocity and on a quantitative demonstration that the snapshot is the eigenstate. If those hold up, this is a solid experimental paper.","headline":"Direct imaging of a complex-frequency corner state via synthetic excitation is a real step, but the snapshot evidence is thin and the asymmetric-transmission claim needs to be reconciled with reciprocity.","tokens_in":16762,"tokens_out":3386,"would_cite":true,"duration_ms":36869,"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":"Boundary-only loss creates skin-topological corner states in a transmission-line network.","keywords":["hybrid skin-topological effect","non-Hermitian skin effect","complex frequency excitation","transmission line network","Haldane model","corner states","non-Hermitian photonics","asymmetric transmission"],"falsifier":"Reverse the loss asymmetry by terminating the upper-left corner rather than the lower-left corner; the boundary-control claim predicts the HSTE corner state should move to the new lossy corner. If the corner remains pinned at the lower-left, the claim fails. Alternatively, if the same localized lower-left pattern appears under real-frequency excitation at 33.49 MHz alone, then the complex-frequency synthesis is not necessary for observing the state.","tokens_in":15778,"feed_emoji":"📡","tokens_out":5950,"duration_ms":54620,"temperature":0.7,"pith_summary":"The paper tries to establish that the hybrid skin-topological effect (HSTE) — the collapse of chiral topological edge states into a corner under the non-Hermitian skin effect — can be observed in a passive transmission-line network, and that its occurrence is controlled solely by the loss distribution on the boundaries, not by whether the bulk is lossy. To see the corner states, whose eigenfrequencies are complex, the authors synthesize complex-frequency excitations by Fourier-transforming an array of real-frequency response measurements, a method that recovers the eigenstate field patterns that ordinary real-frequency driving cannot excite. They demonstrate the HSTE corner state at a lower-left corner, observe asymmetric transmission through the topological band gap, and identify a second family of corner states arising from non-chiral boundary modes. If the claim stands, non-Hermitian topological devices such as topological lasers can be designed with Hermitian bulk, and the corner-state position can be relocated by changing only the boundary terminations.","feed_headline":"Boundary-only loss creates skin-topological corner states","feed_subtitle":"A transmission-line experiment directly images complex-frequency eigenstates and finds the bulk can stay Hermitian.","key_machinery":"The load-bearing object is the transmission-line network obeying Eq. (4), whose node voltages map onto a tight-binding model with three stacked honeycomb layers and cyclic interlayer couplings, so that the $m=1$ sector is an effective Haldane model with a topological band gap near 31–36.3 MHz. Non-Hermiticity enters as on-site loss $-i\\gamma$ on B sublattices, implemented by terminators; because only certain boundary meta-atoms are terminated, the point-gap winding number $\\nu$ (Eq. 6) becomes nonzero without altering the bulk. To observe the complex-frequency eigenstates, the experiment measures responses $A(\\omega_j)$ at many real frequencies and reconstructs the complex-frequency response via $\\psi(\\omega_0,t)\\approx \\sum_j [i A(\\omega_j)/(\\omega_j-\\omega_0)] e^{-i\\omega_j t}\\Delta\\omega/2\\pi$, a discrete Fourier synthesis whose time windows isolate the target eigenstate. The combination of a nontrivial point gap in both x- and y-strip geometries causes the chiral edge states to collapse to a single corner, the HSTE corner state.","core_discovery":"The central claim is that a finite two-dimensional transmission-line network, in the angular-momentum sector $m=1$ of an effective Haldane model, develops hybrid skin-topological corner states when on-site loss is applied asymmetrically to the boundary meta-atoms, and that these states can be directly imaged using synthetic complex-frequency excitation. The authors verify this in a $4\\times5$ network with terminators on B sublattices: the complex eigenfrequency spectrum shows a point gap with winding number $\\nu_x=\\nu_y=1$, and the field pattern at $f=(33.49-1.19i)$ MHz is concentrated at the lower-left corner, matching simulation. They also show that removing loss from the bulk does not destroy the effect, while rebalancing the boundary loss removes it, so the boundary non-Hermiticity, not the bulk, is the controlling ingredient. In the real-frequency domain, the same corner state yields asymmetric transmission $|S_{21}|>|S_{12}|$ along the anti-diagonal inside the topological band gap.","pith_inferences":["Because the paper shows the bulk can be Hermitian, a natural extension is to design topological lasers with gain only at chosen edges; the same Fourier-synthesis technique should allow direct imaging of the lasing mode's complex eigenfrequency.","The discrete Fourier synthesis has a temporal periodicity $T=2\\pi/\\Delta\\omega$; in other platforms with faster dynamics, the method's resolution will be limited by the need to keep $T$ larger than the transient response time, a design constraint worth testing.","The boundary-loss control suggests that HSTE corner-state positions could be reprogrammed electronically in circuit or transmission-line networks by toggling terminators, enabling reconfigurable non-Hermitian routing."],"forward_implications":["Topological lasers could be built with Hermitian bulk and loss engineered only at the boundaries, simplifying fabrication.","The corner-state position can be relocated by changing which boundary meta-atoms carry loss, enabling tunable non-Hermitian devices.","Synthetic complex-frequency excitation provides a general route to observe eigenstates with complex eigenfrequencies in passive systems.","Asymmetric transmission in the topological band gap can be used as a real-frequency signature of HSTE."],"supporting_citations":[{"why":"Supplies the transmission-line network implementation and the effective Haldane model with angular-momentum sectors that the experiment is built on.","marker":"[51]"},{"why":"Supplies the synthetic complex-frequency excitation method (Fourier synthesis from real-frequency responses) used to image the complex eigenstates.","marker":"[48]"},{"why":"Predicts gain-loss-induced hybrid skin-topological effect in the non-Hermitian Haldane model, the effect this paper observes experimentally.","marker":"[37]"},{"why":"Shows hybrid skin-topological modes can arise without asymmetric couplings, supporting the boundary-loss-only realization.","marker":"[38]"},{"why":"Establishes the correspondence between point-gap winding numbers and skin-mode localization used to identify the HSTE corner.","marker":"[25]"},{"why":"Earlier observation of chiral edge-state localization by the non-Hermitian skin effect, which this work extends by directly imaging complex-frequency eigenstates.","marker":"[41]"}],"fun_headline_variants":["Synthetic complex frequencies expose hybrid skin-topological corner states","Skin-topological corner states via synthetic complex frequencies","Boundary loss alone induces hybrid skin-topological corner states","Bulk stays Hermitian in new skin-topological corner states"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The identification of the measured lower-left-localized field as an HSTE corner state assumes that the small $4\\times5$ transmission-line network is faithfully described by the effective $m=1$ Haldane tight-binding model with cyclic three-layer couplings and boundary on-site loss, including negligible hybridization between the angular-momentum sectors and between opposite boundaries; the authors themselves note a noticeable upper-left intensity because of the small sample size.","fun_headline_variants_meta":{"raw":{"variants":["Synthetic complex frequencies expose hybrid skin-topological corner states","Skin-topological corner states via synthetic complex frequencies","Boundary loss alone induces hybrid skin-topological corner states","Bulk stays Hermitian in new skin-topological corner states"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000746,"raw_usage":{"total_tokens":3324,"prompt_tokens":946,"completion_tokens":2378,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":562,"completion_tokens_details":{"reasoning_tokens":2312}},"tokens_in":562,"tokens_out":2378,"duration_ms":17398,"temperature":1.0,"reasoning_tokens":2312,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T16:43:46.262341+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Reverse the loss asymmetry by terminating the upper-left corner rather than the lower-left corner; the boundary-control claim predicts the HSTE corner state should move to the new lossy corner. If the corner remains pinned at the lower-left, the claim fails. Alternatively, if the same localized lower-left pattern appears under real-frequency excitation at 33.49 MHz alone, then the complex-frequency synthesis is not necessary for observing the state.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the transmission-line network implementation and the effective Haldane model with angular-momentum sectors that the experiment is built on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the synthetic complex-frequency excitation method (Fourier synthesis from real-frequency responses) used to image the complex eigenstates."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Predicts gain-loss-induced hybrid skin-topological effect in the non-Hermitian Haldane model, the effect this paper observes experimentally."},{"cited_title":"& Liu, Y","cited_arxiv_id":null,"evidence_quote":"Shows hybrid skin-topological modes can arise without asymmetric couplings, supporting the boundary-loss-only realization."},{"cited_title":"& Murakami, S","cited_arxiv_id":null,"evidence_quote":"Establishes the correspondence between point-gap winding numbers and skin-mode localization used to identify the HSTE corner."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier observation of chiral edge-state localization by the non-Hermitian skin effect, which this work extends by directly imaging complex-frequency eigenstates."}],"review_version":1}