{"id":"90eafb1f-228a-4c06-af5c-d7271d201ad6","arxiv_id":"2501.10434","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A superconducting circuit lattice with uniaxial second-neighbor inductance realizes tunable tilted Dirac-like microwave cones, with a fitted tilt of 0.59.","lead":"Researchers built 731-site superconducting honeycomb circuits with an extra inductance along one direction, which tilts the cone-shaped microwave spectrum. The measured spectrum matches the tilted-cone model with tilts up to 59%, a step toward emulating curved spacetime in the lab.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 59% tilt claim depends on one-to-one eigenvalue pairing relative to the Dirac point; with 11 of 731 modes missed, a shifted pairing could bias the fitted ζ upward (fitted 0.434/0.590 vs designed 0.40/0.52).","rationale":"The paper has genuine strengths: three 731-site devices with controlled L', a two-parameter fit to essentially the entire spectrum, and a clear change in DOS asymmetry with the added second-neighbor coupling. These support the qualitative conclusion that uniaxial second-neighbor coupling tilts the microwave cone. The load-bearing quantitative claim is the 59% tilt, which comes from the fitted ζ values in SI Sec. 4C. That extraction rests on the assumption that each detected resonance is correctly paired to a specific finite-lattice eigenmode index relative to the Dirac point. With 11 modes missed (720 of 731 detected) and explicit acknowledgment that misses occur in noisy and crowded ranges, a systematic pairing shift is plausible and would bias the fitted ζ. The observed fitted values lie systematically above the designed values (0.434 vs 0.40, 0.590 vs 0.52), and the main text incorrectly labels the fitted 59% and 43% as designed values, further emphasizing that the headline depends on the fit. The proposed synthetic test would directly determine whether the missed-mode pattern biases the recovered ζ; until that test is done, the central quantitative claim should be treated as conditional. I therefore see no reason to change the reader's CONDITIONAL verdict.","tokens_in":21850,"tokens_out":12348,"duration_ms":124730,"concrete_test":"Run a synthetic pipeline test: generate noiseless transmission spectra from the 731-site finite-lattice model for ζ=0, 0.40, and 0.52 with the stated L and C values. Emulate the measurement by adding realistic noise, applying the authors' phase-gradient/|S21| peak-detection algorithm, deleting 11 resonances preferentially in the <1 GHz and >9 GHz ranges and near the Dirac point, then applying the SI Sec. 4C pairing and least-squares fitting routine to recover ζ. If the recovered ζ differs from the input by more than 0.02 (about 5% relative) for any device, the extracted tilt values are not robust to missed modes, and the headline 59% would need to be re-derived using a robust matching algorithm or with the released data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim in Section 4 and the abstract is that the fitted tilt parameter ζ extracts the cone tilt, with values up to 59%. The extraction (SI Sec. 4C, Fig. S11) works by labeling the measured resonance closest to the theoretical Dirac frequency as mode 0 and pairing all other measured resonances to finite-lattice eigenmodes by their index relative to this point. However, the peak-detection algorithm finds only 720 of the 731 modes; the SI explicitly notes missed modes in the noisy sub-1 GHz range, the crowded ~9 GHz range, and possibly near the Dirac point. If the missed modes are not symmetrically distributed around the Dirac point, the index shift accumulates for every subsequent mode, and the least-squares fit can partially absorb that shift by increasing ζ and adjusting ω0. The direction of the observed bias is consistent with this: the fitted values ζ=0.434 and 0.590 exceed the designed values 2L/L'=0.40 and 0.52 by about 8% and 13%, respectively. The main text's statement that these 'match the theoretical designed values of 59% and 43%' mislabels fitted numbers as designed; the headline '59%' is the fitted value, and its reliability depends entirely on pairing correctness. If the pairing is biased, the quantitative claim of deterministic tilt control is not yet established, even though the qualitative trend across devices is credible.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports the realization of tilted Dirac-like microwave cones in three 731-site superconducting LC-resonator honeycomb lattices. The tilt is engineered by adding uniaxial second-neighbor inductances L′ to the honeycomb lattice, with designed tilt parameters ζ = 2L/L′ of 0, 0.40, and 0.52. The authors measure microwave transmission spectra at 15 mK, detect on the order of 720 of the 731 expected resonances, and fit the measured resonance frequencies to a finite-lattice tight-binding model with two free parameters, the frequency scale ω0 and the tilt parameter ζ. From the fit they report tilt values of 43% and 59% in the relative difference of opposite-direction group velocities, and they display the corresponding model band structures and DOS as evidence of tilted cones. The paper also interprets the tilted cone as an emergent spacetime metric and discusses possible gravity-emulation experiments.","tokens_in":22142,"tokens_out":5721,"duration_ms":56802,"significance":"If the central claim is established, this is a significant experimental advance: a compact lumped-element superconducting circuit architecture that can host hundreds of low-loss microwave modes, with a simple inductance-ratio knob that deterministically controls the tilt of a Dirac-like crossing. The two-parameter fit to roughly 730 spectral lines across three devices is a strength, and the qualitative trend of increasing fitted tilt with decreasing L′ is credible. The quantitative claim, however, is model-inferred rather than directly observed, and the current presentation overstates the agreement with design values. The platform could be of wide interest for circuit-QED lattices and analogue-gravity studies, but the quantitative tilt values need additional robustness evidence.","major_comments":[{"comment":"The tilt-extraction procedure anchors the mode numbering on the single resonance closest to the theoretical Dirac frequency and pairs every other measured resonance to a finite-lattice eigenmode by index relative to this anchor. The peak detector finds only 720 of 731 modes, and the SI explicitly lists missed modes in the noisy sub-1 GHz range, the crowded ~9 GHz range, and possibly near the Dirac point. If the missed modes are not index-symmetric around the anchor, the index offset accumulates for all subsequent modes and can be partly absorbed by the two free parameters f0 and ζ. The observed offset direction is consistent with this bias: the fitted ζ values of 0.434 and 0.590 exceed the designed values of 0.40 and 0.52 by about 8% and 13%, respectively. I therefore ask for a robustness analysis: repeat the fit under alternative worst-case pairings, for example by shifting the anchor by ±1 mode or by deleting the same number of low- and high-frequency modes as the experiment misses, and report how much the fitted ζ changes; alternatively, demonstrate that the missed-mode distribution is index symmetric around the Dirac point.","section":"SI Sec. 4C; Fig. S11"},{"comment":"The headline value of a 59% tilt is a fitted parameter, not a directly measured tilt. The DOS bar plots in Figs. 3c-e are measured, but the band structures in Figs. 3f-k and the cone cross-sections in Figs. 3i-k are the infinite-lattice dispersion evaluated at the fitted f0 and ζ, so those plots do not independently confirm the tilt. The statement in Sec. 4 that the measured tilts match \"the theoretical designed values of 59% and 43%\" is also inaccurate: the designed ζ values stated in Sec. 3 are 0.40 and 0.52, so the fit overestimates the design by roughly 8% to 13%. The text should clearly distinguish extracted model parameters from directly observed quantities, and the design-versus-fit comparison should be given with consistent notation.","section":"Abstract; Sec. 4; Figs. 3f-k"},{"comment":"The extraction assumes that the fabricated lattice is exactly described by uniform L, C, and L′ and that parasitic couplings and fabrication disorder are negligible. This assumption is load-bearing because the two fitted parameters can absorb disorder-induced spectral shifts into a biased ζ, and a disorder-broadened or disorder-shifted spectrum near the Dirac point could mimic part of the DOS asymmetry attributed to tilt. The authors should provide an independent estimate of the disorder, for example from statistics of individually characterized resonators or from test-structure arrays, and show that the fitted ζ is stable when disorder of this magnitude is included in simulated spectra of the finite lattice.","section":"Sec. 3; SI Sec. 2"}],"minor_comments":[{"comment":"The author name \"Tobias J. Kippenebrg\" appears to be a typo for \"Tobias J. Kippenberg.\"","section":"Author line"},{"comment":"The sentence \"for initially designed value of ζ = 2/5.02 ≈ 0.2\" is internally inconsistent because 2/5.02 ≈ 0.398; the intended quantity is likely ζ/2 = L/L′ ≈ 0.2. Please correct the notation.","section":"SI Sec. 4C"},{"comment":"The phrase \"the theoretical designed values of 59% and 43%\" should be corrected to the actual designed values of 52% and 40%; the current phrasing mixes fitted and design values.","section":"Sec. 4"},{"comment":"Fig. S11 reports fitted values of ζ/2 = 0.217 and 0.295, while the main text and Eq. (4) use ζ; the notation should be defined so that readers can compare these values with the designed ζ/2 = L/L′ = 0.20 and 0.26.","section":"Fig. S11"},{"comment":"The data-availability statement says the data and code \"will be available on Zenodo\" but gives no DOI or repository identifier; please provide a permanent link or DOI at the time of submission.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's quantitative claim is stronger than the present evidence supports. The platform and the qualitative demonstration of tilt control are promising, but the reported tilt values are fit outputs and the pairing sensitivity has not been quantified. I would ask the authors to add a robustness analysis of the mode-pairing procedure and an independent disorder estimate before reconsidering the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a real experimental advance. The 731-site lumped-element superconducting circuit lattice with meander inductors and parallel-plate capacitors is a compact, low-disorder architecture that beats CPW lattices by orders of magnitude in footprint. The DOS measured from three devices with different second-neighbor couplings clearly shows the expected evolution, and the two-parameter fit to the resonance spectrum over 731 modes is strong evidence that the tight-binding model captures the device. The quality factors above 1000 and narrow linewidths make the data credible. I buy the platform and the qualitative tilt trend.\n\nThe soft spots are real but not fatal. First, the tilt is not directly observed; it is reconstructed from a fit. That is acceptable if the fit is robust, but the extraction depends on pairing every detected resonance to a model eigenmode relative to the Dirac point. Only 720 of 731 modes are detected, and the missing modes are not necessarily symmetric. The stress-test concern is legitimate: if missed modes reorder the pairing near the Dirac point or in the noisy low/high frequency ranges, the fitted ζ can absorb the error. The observed fitted values (0.434, 0.590) are systematically about 8–13% above the designed values (0.40, 0.52), which is consistent with such a bias. The qualitative trend across devices survives, but the quantitative \"deterministic tilt control\" claim needs a robustness check.\n\nSecond, the main text says the tilting \"matches the theoretical designed values of 59% and 43%,\" but the designed values are 52% and 40%. They quoted the fitted numbers as if they were designed. That is a mislabeling, and it feeds the circularity concern: the agreement is partly built into the fit. This should be corrected.\n\nThe theory is from the authors' own prior work (ref [40]), which is fine because that is published and this paper's contribution is the experimental realization. The data and code are only promised, not yet released; that should be fixed.\n\nThe paper is worth a serious referee. I would send it out, but the authors need to fix the mislabeling, add a sensitivity analysis of the pairing, and release the data. The platform is genuinely useful for analogue-gravity studies and large-scale circuit lattices, and the paper deserves to be engaged with seriously.","headline":"A genuinely new large-scale circuit platform with a credible 731-mode fit, but the headline tilt value is fitted, not directly measured, and the main text mislabels it as designed.","tokens_in":22688,"tokens_out":2113,"would_cite":true,"duration_ms":22042,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper reports that adding a preferred-axis second-neighbor inductance to a 731-site honeycomb LC lattice tilts the microwave Dirac cone, with fitted tilts up to 59% group-velocity asymmetry.","keywords":["tilted Dirac cone","superconducting circuit lattice","lumped-element LC resonator","honeycomb lattice","second-neighbor coupling","density of states reconstruction","emergent spacetime","microwave photonics"],"falsifier":"Take one of the tilted devices and redo the least-squares fit with the mode numbering shifted by one at the Dirac point: if the extracted $\\zeta$ moves by more than the stated uncertainty, the tilt value is not robust to pairing ambiguity. Alternatively, measure a single-site local density of states at a corner and in the bulk: if the DOS dip at the Dirac frequency is absent where the model says it must be, the fit's starting point is wrong.","tokens_in":21668,"feed_emoji":"📡","tokens_out":8120,"duration_ms":75561,"temperature":0.7,"pith_summary":"This paper reports an experimental platform in which a Dirac-like microwave cone is tilted by a designer amount, rather than by the fixed conditions of a particular material. Three superconducting honeycomb lattices made of 731 lumped LC resonators each show a cone whose tilt is set by the ratio of a first-neighbor inductance $L$ to a uniaxial second-neighbor inductance $L'$, with measured tilts reaching a 59% asymmetry between opposite-direction group velocities. The authors reconstruct the density of states from measured microwave transmission spectra and match it to a finite-lattice tight-binding model, extracting the tilt as an inductance ratio $\\zeta = 2L/L'$. If correct, the result turns the tilt of a band crossing from a material property into a circuit-design parameter, which the authors argue is a step toward imprinting curved-spacetime metrics onto a chip.","feed_headline":"Microwave Dirac cones tilted up to 59 percent in circuit lattices","feed_subtitle":"Three 731-site superconducting lattices show tilt set by an inductance ratio, a step toward curved spacetime on a chip.","key_machinery":"The load-bearing object is the honeycomb lattice as a circuit graph: every node is a parallel-plate capacitor $C$ to ground, connected to its three nearest neighbors by inductance $L$ and, along one preferred axis, to two of its second neighbors by inductance $L'$. Kirchhoff's laws reduce to the eigenvalue problem $DV = (\\omega/\\omega_0)^2 V$ with $\\omega_0 = 1/\\sqrt{LC}$, and the Bloch Hamiltonian acquires a $\\mathbf{k}\\cdot\\zeta$ term proportional to the identity matrix, which tilts the cone; the identity $\\zeta = 2L/L'$ is what makes the tilt a design knob. The measurement pipeline—peak detection in the transmission $S_{21}$ using phase gradients and amplitude, Lorentzian/Fano fits for linewidths, histogram construction of the density of states, and least-squares pairing of detected resonances to the finite-lattice model anchored at the Dirac frequency—is the machinery that turns raw microwave data into the quoted tilt values.","core_discovery":"The central claim is that uniaxial second-neighbor coupling in a honeycomb circuit lattice deterministically tilts the Dirac-like microwave cone, and that the tilt can be read out from the spectrum of a large finite lattice. Concretely, the paper shows that a honeycomb lattice of LC resonators with first-neighbor inductors $L$ and selective second-neighbor inductors $L'$ realizes a tight-binding model with tilt parameter $\\zeta = 2L/L'$, giving opposite tilt at the $K$ and $K'$ valleys while leaving the crossing gapless. Three fabricated devices with designed $\\zeta = 0$, $0.40$, and $0.52$ were measured at 15 mK; fitting the measured resonance frequencies to a 731-site model yields $\\zeta \\approx 0$, $0.43$, and $0.59$, i.e., up to 59% relative difference in opposite-direction group velocities. The paper presents this as the first deterministic, large-scale tuning of cone tilt in a superconducting circuit platform, and as a foundation for engineering an emergent spacetime metric through spatially varying $\\zeta$.","pith_inferences":["One direct extension the authors do not test: push $\\zeta$ toward 1 by choosing $L' \\approx L/2$, which would bring one group velocity to zero—the type-I/type-II transition—and would test whether the cone remains gapless at the critical tilt.","A local probe that images constant-frequency contours, rather than a global DOS fit, could independently verify the tilt and would also reveal whether mode-pairing near the Dirac point is the fragile step in the extraction.","The uniaxial second-neighbor recipe is symmetry-based, so the same lumped-element circuits should be able to tilt cones in other Bravais lattices, not just honeycomb, whenever a $C_{2v}$-preserving sublattice-diagonal coupling can be wired in.","If the paper's 'time dilation' prediction is right, identical LC probe resonators placed in regions of different $\\zeta$ should show frequency shifts scaling as $1/\\sqrt{1-\\zeta^2}$, a measurement within current cryogenic techniques."],"forward_implications":["Because the tilt is set by an inductance ratio, the same 731-site architecture can realize many $\\zeta$ values without changing materials or atomic structure.","A spatially graded $L'$ would produce $\\zeta(\\mathbf{x})$, which the paper interprets as a moving-frame velocity that varies in space—equivalent to a curved Painlevé–Gullstrand spacetime metric.","Vortex-like tilt profiles would act as a synthetic gravitomagnetic field, with predicted cyclotron-like orbits and Landau quantization of microwaves.","Flux-tunable Josephson inductors would allow time-dependent $\\zeta$, a route to generating synthetic gravitational waves in the lattice.","Coupling superconducting qubits into such tilted lattices offers a test bed for curved-spacetime-mediated entanglement."],"supporting_citations":[{"why":"Provides the tight-binding circuit model and the identity $\\zeta = 2L/L'$ that the experiment is designed to test.","marker":"[40]"},{"why":"Motivates the symmetry-breaking mechanism: uniaxial second-neighbor coupling tilts a Dirac cone, which the circuit implements with inductors.","marker":"[65]"},{"why":"Supplies the circuit-QED Lagrangian/Hamiltonian formalism used to map the lumped-element circuit to the tight-binding model.","marker":"[17]"},{"why":"Establishes the low-disorder microwave cavity lattice platform that the lumped-element architecture scales beyond.","marker":"[55]"},{"why":"Gives the moving-frame and metric interpretation of tilt used to connect the measured $\\zeta$ to synthetic spacetime.","marker":"[24]"},{"why":"Predicts gravitomagnetic effects in tilted Dirac systems that the outlook section uses for vortex-tilt measurements.","marker":"[14]"}],"fun_headline_variants":["Circuit lattices tilt Dirac cones up to 59%","Superconducting circuit lattices achieve 59% Dirac cone tilt","Tilted Dirac cones realized on chip via superconducting lattices","Engineered tilt in Dirac-like cones hits 59% in circuits"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central measurement depends on pairing every detected resonance with a specific eigenmode index relative to the Dirac frequency, and on assuming the fabricated 731-site chip matches the ideal uniform $L$, $C$, $L'$ model; if modes are missed or reordered near the Dirac point, or if disorder or parasitics distort the spectrum, the fitted tilt would be biased.","fun_headline_variants_meta":{"raw":{"variants":["Circuit lattices tilt Dirac cones up to 59%","Superconducting circuit lattices achieve 59% Dirac cone tilt","Tilted Dirac cones realized on chip via superconducting lattices","Engineered tilt in Dirac-like cones hits 59% in circuits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000746,"raw_usage":{"total_tokens":3316,"prompt_tokens":926,"completion_tokens":2390,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":542,"completion_tokens_details":{"reasoning_tokens":2318}},"tokens_in":542,"tokens_out":2390,"duration_ms":17183,"temperature":1.0,"reasoning_tokens":2318,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:50:43.156763+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take one of the tilted devices and redo the least-squares fit with the mode numbering shifted by one at the Dirac point: if the extracted $\\zeta$ moves by more than the stated uncertainty, the tilt value is not robust to pairing ambiguity. Alternatively, measure a single-site local density of states at a corner and in the bulk: if the DOS dip at the Dirac frequency is absent where the model says it must be, the fit's starting point is wrong.","supporting_citations":[{"cited_title":"Ma˜nes, Fernando de Juan, Mauricio Sturla, and Mar ´ ıa A","cited_arxiv_id":null,"evidence_quote":"Provides the tight-binding circuit model and the identity $\\zeta = 2L/L'$ that the experiment is designed to test."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Motivates the symmetry-breaking mechanism: uniaxial second-neighbor coupling tilts a Dirac cone, which the circuit implements with inductors."},{"cited_title":"Cooling of a levitated nanoparticle to the mo- tional quantum ground state","cited_arxiv_id":null,"evidence_quote":"Supplies the circuit-QED Lagrangian/Hamiltonian formalism used to map the lumped-element circuit to the tight-binding model."},{"cited_title":"Anomalous heat flow in 8pmmn borophene with tilted Dirac cones","cited_arxiv_id":null,"evidence_quote":"Establishes the low-disorder microwave cavity lattice platform that the lumped-element architecture scales beyond."},{"cited_title":"Escape from black hole analogs in materials: Type-II weyl semimet- als and generic edge states","cited_arxiv_id":null,"evidence_quote":"Gives the moving-frame and metric interpretation of tilt used to connect the measured $\\zeta$ to synthetic spacetime."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Predicts gravitomagnetic effects in tilted Dirac systems that the outlook section uses for vortex-tilt measurements."}],"review_version":1}