{"id":"d2f310a5-5971-4cd4-b9b6-e2354888b283","arxiv_id":"2607.27447","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"low","formal_verification":"none","parameter_count":2,"one_line_summary":"Linewidth broadening in VO2 relaxation oscillators at low frequency comes from thermal jitter in the shallow incubation approach to the IMT, and square-wave 2f injection suppresses it more effectively than sinusoidal locking.","lead":"VO2 relaxation oscillators get noisier at low bias because the slow approach to the insulator-metal switch lets thermal fluctuations scramble the timing. Square-wave injection locking cleans that phase noise better than a sine wave of the same amplitude, which matters for Ising machines and neuromorphic nets built from these devices.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The central claim is an experimental mechanism-plus-control result. The paper supplies the necessary cross-checks (phase-noise slopes, time-domain asymmetry consistent with first-passage statistics, quantitative σ∝(Vs-VIMT)-1 fit, and waveform-dependent locking/Γp). The discharge-negligible premise is the natural place a skeptic would press, yet nothing in the figures or supplement indicates that metallic-state timing contributes comparably; the observed right-skew and slew-rate scaling point specifically at the shallow IMT approach. Because that assumption holds under the data as presented, no verdict adjustment is warranted. The concrete test above is a low-cost verification that would still be worth running on the existing traces.","tokens_in":13647,"tokens_out":475,"duration_ms":11022,"concrete_test":"Re-extract period histograms and FWHM jitter while deliberately windowing only the metallic discharge edge (instead of the IMT rising edge) across the same Vs sweep; if discharge-edge jitter remains ≪ incubation-edge jitter and does not reproduce the inverse-overdrive divergence or the square-vs-sine difference, the negligibility assumption is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest assumption (metallic discharge negligible vs. insulating incubation, so that δt~δV/(dV/dt)th at IMT fully explains voltage-dependent white-frequency noise and square-vs-sine locking) is standard for Pearson-Anson VO2 oscillators and is not contradicted by the data. Free-running Sφ (Fig. 2), intensity-graded traces and right-skewed period histograms (Fig. 3), inverse-overdrive jitter fit extracting VIMT≈1.79 V with ~3.5 ns floor (Supp. Fig. S2), and lower-amplitude locking plus higher Γp under square-wave 2f drive (Fig. 4) form a mutually consistent picture. No internal inconsistency or claim-breaking gap appears; remaining limitations are multi-device statistics and data availability, not soundness of the central mechanism.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript presents an experimental study of phase noise in VO2-based Pearson–Anson relaxation oscillators. It attributes the strong linewidth broadening at low supply voltage (low frequency) to increased thermal susceptibility during the slow capacitor-voltage approach to the insulator-to-metal transition (incubation phase), supported by phase-noise spectrograms/PSDs (flicker-frequency 1/f^3 and white-frequency 1/f^2 regimes), intensity-graded time traces, period histograms with FWHM jitter, and an inverse-overdrive fit extracting V_IMT ≈ 1.79 V with a ~3.5 ns high-bias floor. It further shows that external injection locking at 2f with a square-wave drive suppresses low-offset phase noise more efficiently than a sine drive of equal amplitude, reaches partial/full lock at lower V_sync, and raises the amplitude relaxation frequency Γ_p to ~1–2×10^5 Hz, which the authors link to steeper threshold approach and shortened stochastic incubation time.","tokens_in":13799,"tokens_out":1094,"duration_ms":40334,"significance":"VO2 relaxation oscillators are actively pursued for neuromorphic networks and oscillator Ising machines, where broad linewidth and phase slips limit locking fidelity and time-to-solution. The work supplies a coherent, multi-modal experimental account of the dominant free-running noise mechanism and a practical, waveform-level control knob (square vs. sine at 2f) that improves both phase stability and Γ_p. The Hilbert-transform S_φ extraction, voltage-dependent jitter statistics (including right-skewed first-passage-time histograms), and the inverse-overdrive fit are concrete and falsifiable contributions that strengthen the applied-physics case for using these devices in phase-binarized computing.","major_comments":[],"minor_comments":[{"comment":"Throughout the main text there are numerous missing spaces and run-on words (e.g., “broadlinewidthinoscillatoryneuralnetworks”, “Italsodisturbs”, “relaxationoscillatorschematic”, “V O2” in figure captions). A full copy-edit pass is needed before production.","section":"Full text"},{"comment":"§II after Eq. (1) and the frequency approximation Eq. (4) assert that metallic-state discharge is short and contributes negligibly to period and phase noise. A brief quantitative bound (measured or estimated τ_metal vs. τ_ins, or fraction of the period) would make this standard assumption explicit for non-specialist readers.","section":"§II, Eqs. (1)–(4)"},{"comment":"Fig. 2b and Fig. 4: state explicitly how S_φ is normalized/referenced (rad^2/Hz) and the carrier-tracking or unwrapping procedure used when the free-running linewidth is very broad (Vs = 1.8 V), so that the reported 1/f^2 rise is unambiguously distinguished from amplitude or digitization artifacts.","section":"§III, Fig. 2; Appendix B"},{"comment":"Fig. 4 and the definition of Γ_p: the text identifies Γ_p as the corner of the synchronization plateau (−3 dB from the low-frequency floor). Mark this corner on the plotted curves or give a short table of extracted Γ_p(V_sync) for sine and square drives to make the claimed 1–2×10^5 Hz increase unambiguous.","section":"§V, Fig. 4"},{"comment":"Clarify whether all free-running and locked data are from a single device or representative of multiple devices; if single-device, a short statement on device-to-device spread (or lack of it) would help assess generality for network applications.","section":"§III–V; Appendix A"},{"comment":"Supplementary Fig. S1: the 10 ns sampling-grid ripple artifact is well explained; consider noting it once in the main-text jitter caption (Fig. 3) so readers do not misread the oscillations as physical.","section":"§IV, Fig. 3; Supp. Fig. S1"},{"comment":"PACS line and author affiliations contain minor formatting inconsistencies; arXiv stamp and “July 31, 2026” date should be cleaned for the journal version.","section":"Front matter"}],"recommendation":"minor_revision","confidential_remarks":"Sound experimental measurement paper; central mechanism and square-vs-sine locking claim are well supported and mutually consistent across S_φ, time-domain jitter, and lock plateaus. No load-bearing flaw. Fit for a solid applied-physics / device journal. Minor revision is for presentation and a few clarifying quantitative statements, not for re-opening the physics. Single-device statistics are the main scope limitation but are typical for this class of VO2 oscillator studies and do not warrant major revision."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The useful takeaway is simple: at low bias the white-frequency noise rise is first-passage jitter on a shallow approach to VIMT, and a square edge at 2f cleans that up better than a sine of the same amplitude, also pushing Γp higher. That is incremental but real engineering knowledge for anyone building VO2 Ising or neuromorphic nets.\n\nWhat they did well is the multi-view consistency. Free-running Sφ vs Vs (Fig. 2) shows the 1/f^2 floor climbing while the 1/f^3 piece stays put; intensity-graded traces and right-skewed period histograms (Fig. 3 + Supp. S1) match first-passage statistics; the inverse-overdrive fit extracts VIMT ≈ 1.79 V and a ~3.5 ns floor (Supp. S2); and the square-vs-sine lock comparison (Fig. 4) shows earlier plateaus and higher Γp under the square drive. Methods are complete enough to repeat the Hilbert-phase and jitter pipeline. Citations sit in the right neighborhood (Shukla, Maher, Corti/Karg, etc.) without padding.\n\nSoft spots are ordinary for a single-device applied-physics preprint, not claim-breakers. No multi-device statistics or error bars on the PSD/jitter curves; data not shipped; the metallic discharge is asserted to be negligible (standard Pearson-Anson assumption) rather than measured head-to-head. The 10 ns sampling ripples on the histograms are acknowledged as artifacts. None of that undoes the central picture.\n\nThis is for people who actually couple VO2 oscillators or care about phase slips in oscillator Ising machines. A serious editor should send it to referees; I would cite the square-wave / Γp result if I were locking these devices. Engage.","headline":"Solid experimental map of VO2 relaxation-oscillator phase noise: low-Vs linewidth rise is incubation jitter, and square-wave 2f lock beats sine on both noise and Γp.","tokens_in":14529,"tokens_out":471,"would_cite":true,"duration_ms":10613,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["85.75.-d","05.45.Xt","75.40.Gb","75.47.-m","84.30.Qi"],"model":"grok-4.5","headline":"VO2 oscillator linewidths widen at low frequency because thermal noise hits hardest during the slow approach to the insulator-metal switch, and square-wave injection locks them better than sine waves.","keywords":["VO2 relaxation oscillators","phase noise","insulator-metal transition","incubation time","injection locking","square-wave synchronization","jitter","Ising machines"],"falsifier":"Measure period jitter and phase-noise spectra while independently changing only the metallic-state discharge path (for example by adding a parallel low-resistance shunt or a second switch that dumps the capacitor faster) at fixed insulating charging slope; if metallic discharge is truly negligible, jitter and the 1/f^2 floor should stay unchanged, and square-wave locking should retain its advantage over sine.","tokens_in":14490,"feed_emoji":"⚡","tokens_out":1130,"duration_ms":31100,"temperature":0.7,"pith_summary":"VO2 relaxation oscillators are simple, CMOS-compatible devices used in neuromorphic circuits and Ising machines, but their free-running signals have broad spectral lines that limit locking and phase encoding. This paper shows that the extra broadening at low supply voltage comes from the incubation interval before the insulator-to-metal transition: the capacitor voltage creeps toward threshold with a shallow slope, so thermal fluctuations produce large timing jitter and a rising white-frequency-noise floor. Time-domain histograms become broad and right-skewed, matching first-passage statistics. Injection locking at twice the free-running frequency suppresses that noise, and a square-wave drive does so more efficiently than a sine wave of the same amplitude because its sharp edges steepen the approach to threshold, shorten the stochastic incubation time, and raise the amplitude relaxation rate. The result gives a physical account of the linewidth and a practical waveform choice for more stable VO2 oscillator networks.","feed_headline":"Square waves beat sines at quieting VO2 oscillator noise","feed_subtitle":"Thermal jitter during the slow approach to switching sets the linewidth; sharp injection edges cut it faster.","key_machinery":"Stochastic incubation / first-passage timing at the IMT threshold: timing uncertainty scales as δt ∼ δV / (dV/dt)_th, so jitter and white frequency noise grow as the overdrive (Vs − VIMT) shrinks and the approach slope flattens; square-wave edges raise that slope and shorten the noisy interval.","core_discovery":"The dominant source of linewidth broadening in free-running VO2 Pearson-Anson oscillators at low oscillation frequency is heightened susceptibility to thermal fluctuations during the incubation phase preceding the insulator-to-metal transition, where the capacitor voltage approaches VIMT with reduced slew rate. That mechanism elevates the white-frequency (1/f^2) phase-noise contribution; external synchronization at 2f reduces the phase noise, and a square-wave injection signal does so more effectively than a sinusoidal signal of equal amplitude, reaching partial and full lock at lower drive and increasing the amplitude relaxation frequency Γp to about 1–2×10^5 Hz.","pith_inferences":["The same slew-rate argument should apply to other thermally triggered Mott or phase-change relaxation oscillators, so square-edge injection may be a general fix beyond VO2.","If Γp sets time-to-solution in large Ising arrays, quoting lock bandwidth under square-wave drive becomes as important a figure of merit as free-running linewidth.","Asymmetric first-passage histograms at low overdrive could be turned into a diagnostic of local thermal noise strength or threshold variance across a fabricated array.","Combining moderate overdrive with modest square-wave lock may give a better power-stability tradeoff than pure free-running high-bias operation in dense neuromorphic chips."],"forward_implications":["Operating VO2 oscillators well above the IMT threshold keeps the incubation slope steep and holds white-frequency noise and period jitter near their high-bias floor (~few ns).","Square-wave injection at 2f reaches usable phase-noise plateaus at lower drive amplitude than sine injection and raises Γp, which shortens network convergence time in oscillator Ising machines.","Phase-slip rates and random spin flips in VO2 Ising machines should drop when the free-running incubation noise is suppressed by waveform-shaped locking.","Time-delay and phase encoding in VO2 spiking or oscillatory neural nets become more reliable once the shallow-drift jitter source is identified and controlled.","Device and circuit design can target slew rate at threshold (overdrive and edge shape) as the primary knob for spectral purity rather than only raw thermal noise power."],"fun_headline_variants":["Square injection quells VO2 oscillator thermal phase noise better than sine","Incubation-phase thermal jitter widens VO2 relaxation linewidth","Square-wave lock cuts VO2 oscillator phase noise faster than sine","Thermal fluctuations in slow approach set VO2 oscillator linewidth","External square sync raises VO2 oscillator amplitude relaxation rate"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The short metallic-state capacitor discharge barely affects the period or phase noise, so nearly all of the voltage-dependent jitter and the square-versus-sine locking difference can be blamed on the slow insulating approach to the insulator-metal threshold.","fun_headline_variants_meta":{"raw":{"variants":["Square injection quells VO2 oscillator thermal phase noise better than sine","Incubation-phase thermal jitter widens VO2 relaxation linewidth","Square-wave lock cuts VO2 oscillator phase noise faster than sine","Thermal fluctuations in slow approach set VO2 oscillator linewidth","External square sync raises VO2 oscillator amplitude relaxation rate"]},"model":"grok-4.5","effort":"low","cost_usd":0.003838,"raw_usage":{"total_tokens":1174,"prompt_tokens":747,"num_sources_used":0,"completion_tokens":67,"cost_in_usd_ticks":38384000,"prompt_tokens_details":{"text_tokens":747,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":360,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":747,"tokens_out":67,"duration_ms":6683,"temperature":1.0,"reasoning_tokens":360,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T00:35:15.991134+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Measure period jitter and phase-noise spectra while independently changing only the metallic-state discharge path (for example by adding a parallel low-resistance shunt or a second switch that dumps the capacitor faster) at fixed insulating charging slope; if metallic discharge is truly negligible, jitter and the 1/f^2 floor should stay unchanged, and square-wave locking should retain its advantage over sine.","supporting_citations":[],"review_version":1}