{"id":"b5ba4550-423e-4947-b8fc-7862cdf896ad","arxiv_id":"2501.10973","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A cantilever experiment finds no spin-velocity exotic force below 10 micrometers and sets a new bound f4+5 <= 2.2e-9 at 2.1 micrometers.","lead":"This paper searches for a new spin- and velocity-dependent force between electrons and nucleons at micrometer distances using a vibrating magnetic stripe source and a cantilever. No force is seen, so the authors set the strongest limit yet on the coupling strength below 10 micrometers.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Real-to-imaginary leakage at the 10th harmonic is the load-bearing assumption; the End Matter \"phase error less than 1 mrad\" claim is not quantitatively verified against the fitted imaginary amplitude.","rationale":"The reader correctly identified the demodulation-separation assumption as the weakest point. I agree that this is the single most load-bearing condition for the central claim. My additional point is that the existing empirical support is not strong enough to close the concern. The residual-potential control in Fig. 3 shows that the imaginary-image standard deviation is insensitive to a deliberately enhanced real force, but the fitted f4+5 is determined by the coherent imaginary image, not by its standard deviation. A coherent leakage of about 1 fN could be buried in the 5 fN image noise while still biasing the fit at the level of the statistical uncertainty. The claimed 1 mrad phase error is stated without a measurement protocol or a propagation into the imaginary quadrature. Since the check I propose is purely computational and uses data the authors already have, it is a feasible requirement before the limit can be considered final. If the check passes, the central claim stands; if it fails, the bound would need to be weakened or re-derived with a corrected demodulation. Thus I would make acceptance conditional on this verification rather than reject the paper outright.","tokens_in":7574,"tokens_out":26184,"duration_ms":321944,"concrete_test":"Using the recorded time series and the measured source displacement x(t), run a synthetic-injection test: set the cantilever deflection equal to the response to a known position-dependent force with the same spatial period as the spin source, F_s(x) = A cos(2πx/Λ), choosing A equal to the largest real-signal amplitude observed during acquisition (or at a deliberate contact-potential offset such as +68 mV). Process this synthetic signal through the exact t'-reparameterization and 10th-harmonic quadrature of Eqs. (4)-(5). If the resulting imaginary component is not zero at a level below roughly 0.1 fN, or if the shift in the fitted f4+5 exceeds the reported statistical error, then the separation assumption fails and the quoted bound requires a systematic correction or an enlarged uncertainty.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central null result rests on the assumption in Eqs. (4)-(5) and End Matter that the imaginary part of the 10th-harmonic signal is uncontaminated by position-dependent (real) forces. The nonlinear piezo response is corrected by redefining a time t' so that the measured source displacement x(t') is a pure cosine, and the paper asserts an initial phase error below 1 mrad. However, this assertion is not supported by a measured residual waveform distortion or by a direct calibration of real-to-imaginary leakage. The empirical check in Fig. 3, where the residual potential is varied by -33 mV and +68 mV, compares the standard deviation of the imaginary images (5-6 fN). That test is insensitive to a periodic leakage of order 1 fN: a coherent leaked pattern of 1 fN would barely change a 5.2 fN image standard deviation yet could shift the fitted f4+5 significantly, since the statistical uncertainty on the fitted coupling corresponds to roughly 0.1 fN per image. Moreover, the t' reparameterization cannot perfectly remove all harmonic distortion of x(t); residual distortion at the 10th harmonic can mix a real force with spatial frequency into the imaginary quadrature at an amplitude proportional to the distortion times the real force. Without a quantitative bound on that product, the null imaginary image does not by itself set the claimed limit.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper reports an experimental search for a spin- and velocity-dependent exotic interaction between nucleons and electrons, using a cantilever with a gold sphere and a microfabricated, periodically magnetized spin source. The source is driven at 18.85 Hz with an amplitude of about 28.7 um, and the cantilever force signal is demodulated at the 10th harmonic of the drive frequency. The central result is a null observation: the imaginary part of the 10th-harmonic signal shows no periodic pattern, and a maximum-likelihood fit yields f4+5 = (-8.8 +/- 6.7) x 10^-10 at lambda = 2.1 um, leading to a 95% upper limit of 2.2 x 10^-9 and improving previous limits by about a factor of ten for interaction ranges below 10 um. The improvements come from a larger oscillation velocity, a thicker and higher-remnant-magnetization spin source, a thinner cover layer, and demodulation at a higher harmonic to suppress position-dependent background forces.","tokens_in":7843,"tokens_out":4969,"duration_ms":57665,"significance":"If the central result holds, it is a valuable experimental constraint: it improves the best published limits on f4+5 in the micrometer range by roughly an order of magnitude and provides an independent cross-check through the spatial pattern of the imaginary force image. The paper gives a concrete error budget in Table I, an explicit null result, internal consistency checks in Fig. 3, and a clear comparison with prior limits. The main caveat is that the background-rejection argument relies on a quantitative claim about demodulation phase error that is asserted but not directly demonstrated; this needs to be supported by a dedicated leakage calibration before the limit can be considered fully established.","major_comments":[{"comment":"The clean separation of the imaginary (velocity-dependent) signal from the real (position-dependent) background is the load-bearing assumption of the experiment. The End Matter states that, after redefining the time variable t' so that the measured source displacement is x(t') = x0 + A_d cos(2*pi*f_d t'), the residual initial phase error is less than 1 mrad, but no measured residual waveform, fit quality metric, or direct calibration of the real-to-imaginary leakage is provided. The check in Fig. 3, where the residual potential is varied by -33 mV and +68 mV and the standard deviations of the imaginary images remain in the 5.1-6.2 fN range, is not sensitive to a coherent leaked pattern at the level of about 1 fN: such a pattern would barely change the image standard deviation yet could bias the fitted coupling constant appreciably, since the statistical uncertainty of the fit corresponds to a small fraction of the 5.2 fN image standard deviation. I request a quantitative leakage test, for example by applying a known position-dependent force (such as a controlled electrostatic force with a modulated residual voltage), processing the data through the same t' reparametrization and 10th-harmonic demodulation, and reporting the residual imaginary amplitude; alternatively, the paper should propagate the measured residual phase error through Eqs. (2) and (3) and bound the induced imaginary signal. Without this bound, the null imaginary image does not by itself establish the claimed limit.","section":"Table I and fit procedure"},{"comment":"The paper reports the fit result f4+5 = (-8.8 +/- 6.7) x 10^-10 and lists parameter uncertainties in Table I, but it does not explain how the parameter errors are combined with the statistical uncertainty of the maximum-likelihood fit, nor does it state which errors are included in the final quoted uncertainty. In particular, the uncertainty on the phase-error leakage discussed above is not included, and no total systematic error is given. Please state the likelihood function, the treatment of parameter uncertainties, and the final statistical and systematic contributions separately; this is needed to assess whether the reported 95% limit is robust.","section":"Table I and fit procedure"}],"minor_comments":[{"comment":"The phrase 'used to measured the force' in the abstract should read 'used to measure the force'.","section":"Abstract"},{"comment":"The procedure for defining t' from the measured x(t) is not fully specified. Please state how t' is computed from the fitted Fourier coefficients, and discuss the uniqueness and monotonicity conditions of the mapping, since a non-monotonic x(t) would make the reparametrization ambiguous.","section":"End Matter"},{"comment":"The caption says the numbers at the corners are the standard deviations of the entire image, but only the values for the imaginary images are visible in the text. For completeness, report the standard deviations of the real images as well, since they quantify the periodic background that the imaginary-quadrature rejection is meant to suppress.","section":"Fig. 3"},{"comment":"The entries 'FeCo width W1' and 'FeCo width W2' should be defined explicitly in the text or in the Fig. 1 caption, since the two widths are not identified in the main text.","section":"Table I"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the reported improvement is plausible and interesting. My main concern is the unverified real-to-imaginary leakage bound; this is a load-bearing point for the null result. The requested calibration is a well-defined experimental check and seems feasible, so major revision rather than rejection is appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline is that this is a careful null result that tightens the constraint on the spin-velocity-dependent coupling f4+5 below 10 μm by about an order of magnitude, with the best limit at 2.1 μm of f4+5 ≤ 2.2×10^-9. The improvement comes from a harder drive, a higher harmonic (10th), and a better spin source (FeCo, thicker, higher remnant magnetization). The error budget in Table I is thorough, and the internal checks (residual potential variations, reference distance) are good practice. The citation pattern looks fine, and the result is genuinely new, not a reanalysis of old data.\n\nThe soft spot is the separation of the imaginary part. The method—measuring the actual source displacement, fitting it to a Fourier series, and reparameterizing time so that x(t') is a pure cosine—is reasonable, and the claim of phase error <1 mrad is plausible. But it is not quantitatively supported. The fit residual at the 10th harmonic is not reported, and the empirical check in Fig. 3 is not sensitive: varying the residual potential changes the real force but the standard deviation of the imaginary images stays ~5 fN, which cannot rule out a coherent leakage of order 1 fN. Since the statistical uncertainty on the fitted coupling corresponds to roughly 0.1 fN per image, a 1 fN leak would be a significant systematic shift. So the central null result rests on an assumption that is not fully verified.\n\nThat said, I don't think this is a fatal flaw. The leakage from a real force with amplitude tens of fN at 1 mrad phase error is sub-fN, so it may be within the statistical error. But the paper should provide a quantitative bound on the leakage, for example by measuring the residual distortion or by applying a known real force. A referee should ask for that.\n\nWho is this for? People working on exotic spin-dependent interactions and precision force microscopy. It's a solid incremental result, not a breakthrough, but it's the kind of data point that matters for beyond-Standard-Model searches.\n\nRecommendation: send to peer review. A good referee can get the authors to quantify the leakage and possibly tighten the error budget. The paper is worth engaging with.","headline":"Solid null result that improves micrometer-range limits on f4+5 by about 10x, but the real-to-imaginary leakage is under-verified and needs a quantitative bound.","tokens_in":8367,"tokens_out":5708,"would_cite":true,"duration_ms":63387,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.80.Cc"],"model":"deepseek-v4-flash","headline":"A cantilever-and-spin-source experiment finds no spin- and velocity-dependent exotic force in the micrometer range and sets a 95% upper limit $f_{4+5} \\le 2.2\\times10^{-9}$ at 2.1 µm.","keywords":["exotic interaction","spin-dependent force","velocity-dependent force","fifth-force search","cantilever force sensor","harmonic demodulation","micrometer-range limits","coupling constant bound"],"falsifier":"A controlled test where the contact-potential difference is deliberately stepped over a wide range, with the imaginary image's standard deviation monitored: if it rises above the roughly 5 fN noise floor in step with the real image amplitude, the phase-correction assumption would fail and the null imaginary image would not directly bound $f_{4+5}$.","tokens_in":7385,"feed_emoji":"🔬","tokens_out":5740,"duration_ms":62266,"temperature":0.7,"pith_summary":"This paper reports a tabletop search for a hypothetical force between electron spins and nucleons whose strength depends on their relative velocity, a possible signature of new bosons beyond the Standard Model. The experiment drove a striped magnetic spin source back and forth under a gold sphere mounted on a soft cantilever and demodulated the force at the tenth harmonic of the drive frequency. Because the sought-after force is proportional to velocity, only its part in quadrature with the displacement should appear in the imaginary channel, while ordinary position-dependent backgrounds such as electrostatic and Casimir forces should appear only in the real channel. No periodic imaginary signal was seen, and the authors convert the noise into an upper limit on the coupling constant, $f_{4+5} \\le 2.2\\times10^{-9}$ at an interaction range $\\lambda = 2.1\\,\\mu\\mathrm{m}$, roughly ten times more stringent than earlier micrometer-range bounds. A null result tightens the excluded parameter space for light mediators and demonstrates that harmonic separation can suppress short-range backgrounds.","feed_headline":"No exotic spin-velocity force found; limits tighten 10x","feed_subtitle":"Cantilever search in the micrometer range cuts the allowed coupling about tenfold, narrowing room for new light mediators.","key_machinery":"The load-bearing mechanism is demodulation at the 10th harmonic of the source oscillation, using a phase reference built from an interferometric measurement of the actual source displacement. Equation (2) shows that a velocity-proportional force contributes only to the imaginary component, while Eq. (3) shows that position-only forces contribute only to the real component. The measured displacement is fitted to a Fourier series and reparametrized as a pure cosine $x(t')$, reducing the phase error below 1 mrad, so leakage of the real image into the imaginary channel is negligible. This separation is what lets a null imaginary image set a limit on the exotic coupling.","core_discovery":"The central claim is that the imaginary part of the 10th-harmonic force signal contains no periodic spatial structure correlated with the spin-source stripes, and that the remaining noise therefore bounds the spin- and velocity-dependent coupling. Using a maximum-likelihood fit to the imaginary image, the authors obtain $f_{4+5} = (-8.8 \\pm 6.7)\\times10^{-10}$ at $\\lambda = 2.1\\,\\mu\\mathrm{m}$, consistent with zero, and quote a 95% confidence upper limit $f_{4+5} \\le 2.2\\times10^{-9}$ at that range. They state that this improves the limits for interaction ranges below $10\\,\\mu\\mathrm{m}$, with the bound at $\\lambda = 2.1\\,\\mu\\mathrm{m}$ about ten times more stringent than the current limit.","pith_inferences":["If the imaginary-channel separation works at smaller separations, the limit could improve sharply because the potential scales roughly as $1/r^2$ near the surface; reducing the 809 nm gap is the obvious next step, and the paper's own conclusion points to reducing electrostatic force for this purpose.","The phase-corrected harmonic-demodulation technique is transferable to other short-range force searches: any force with a known velocity or phase dependence could be isolated from position-dependent backgrounds at a chosen harmonic.","Because the current bound is set by thermal noise rather than systematics, cryogenic operation or higher-quality cantilevers would push the limit to smaller couplings, and the isolation assumption should be tested with larger residual potential differences.","The limit on $f_{4+5}$ alone does not distinguish vector from scalar mediators; combining it with independent spin-dependent measurements that weight the vector and scalar couplings differently could separate those channels."],"forward_implications":["Any new boson with the assumed couplings in the interaction range below $10\\,\\mu\\mathrm{m}$ must have $f_{4+5}$ below the reported curve, which at $\\lambda = 2.1\\,\\mu\\mathrm{m}$ means below $2.2\\times10^{-9}$.","The excluded region covers mediator masses around $m_b = \\hbar/(\\lambda c) \\sim 0.1\\,\\mathrm{eV}$ for this channel, complementing constraints from magnetometer and NV-center searches.","Because the dominant backgrounds are separated into the real channel, the limit is set by cantilever thermal noise rather than by electrostatic, Casimir, or magnetostatic forces, so quieter cantilevers would translate directly into stronger bounds.","The upper limit constrains combinations of vector and scalar couplings, $f_{4+5}=\\tfrac{1}{2}g_e^V g_N^V$ or $\\tfrac{1}{2}g_e^s g_N^s$, for light mediators."],"supporting_citations":[{"why":"Supplies the theoretical potential in Eq. (1) and the identification of $f_{4+5}$ with combinations of vector or scalar couplings.","marker":"[19]"},{"why":"Prior cantilever experiment with the same general scheme and spin-modulated source whose limits this work extends.","marker":"[32]"},{"why":"Recent micrometer-scale limit from an ensemble NV-diamond magnetometer that this work claims to improve.","marker":"[30]"},{"why":"Spin-mechanical quantum chip measurement in the micrometer range used as a comparison baseline.","marker":"[31]"},{"why":"Provides the method for calibrating the cantilever spring constant by matching simulated and measured resonance frequencies.","marker":"[33]"},{"why":"Provides the maximum-likelihood fitting procedure used to convert the imaginary image into a coupling-constant estimate.","marker":"[34]"}],"fun_headline_variants":["Micron-range probe tightens spin-velocity exotic limits 10x","No spin-velocity exotic force; limits cut tenfold at 2.1 μm","Cantilever search bounds spin-velocity exotic interaction tighter","Micrometer exotic force search yields 10x better spin-velocity limits"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result depends on the assumption that, after the timing correction, nothing leaks from ordinary position-dependent forces into the imaginary part of the 10th-harmonic signal.","fun_headline_variants_meta":{"raw":{"variants":["Micron-range probe tightens spin-velocity exotic limits 10x","No spin-velocity exotic force; limits cut tenfold at 2.1 μm","Cantilever search bounds spin-velocity exotic interaction tighter","Micrometer exotic force search yields 10x better spin-velocity limits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000804,"raw_usage":{"total_tokens":3511,"prompt_tokens":900,"completion_tokens":2611,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":516,"completion_tokens_details":{"reasoning_tokens":2532}},"tokens_in":516,"tokens_out":2611,"duration_ms":20665,"temperature":1.0,"reasoning_tokens":2532,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T18:45:55.278473+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A controlled test where the contact-potential difference is deliberately stepped over a wide range, with the imaginary image's standard deviation monitored: if it rises above the roughly 5 fN noise floor in step with the real image amplitude, the phase-correction assumption would fail and the null imaginary image would not directly bound $f_{4+5}$.","supporting_citations":[{"cited_title":"Fadeev, Y","cited_arxiv_id":null,"evidence_quote":"Supplies the theoretical potential in Eq. (1) and the identification of $f_{4+5}$ with combinations of vector or scalar couplings."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior cantilever experiment with the same general scheme and spin-modulated source whose limits this work extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Recent micrometer-scale limit from an ensemble NV-diamond magnetometer that this work claims to improve."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Spin-mechanical quantum chip measurement in the micrometer range used as a comparison baseline."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the method for calibrating the cantilever spring constant by matching simulated and measured resonance frequencies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the maximum-likelihood fitting procedure used to convert the imaginary image into a coupling-constant estimate."}],"review_version":1}