{"id":"45aab85a-1ba0-4eca-8f45-da8b10f9a55b","arxiv_id":"2509.11608","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Stochastic resetting erases memory in non-Markovian escape from a harmonic trap, turning heavy-tailed first-passage distributions near-exponential and enabling an optimal reset protocol.","lead":"This paper studies how restarting a random motion (stochastic resetting) changes the time a particle takes to escape a trap when the motion is non-Markovian, meaning it remembers its past. It shows that resetting erases this memory, makes escape times nearly exponential, and can either speed up or slow down escape depending on how often and where the motion is restarted.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (11) computes 'survival' from the unrestricted resetting propagator, so the FPT distribution and MFPT are not true first-passage quantities; in the Markovian limit S(t) tends to a positive constant and the MFPT integral diverges.","rationale":"The reader's verdict CONDITIONAL focuses on the validity of the FPE Eq. (3) and its use with an absorbing boundary. I agree the FPE/absorbing-boundary step is the weak point, but the precise failure is one step later and even more direct: Eq. (11) does not compute a survival probability at all. It integrates the unrestricted resetting propagator over the domain, which counts trajectories that have previously crossed the boundary and returned. This is not a first-passage quantity. The Markovian limit provides a crisp falsification: Eq. (11) gives S∞>0, so the associated 'FPT distribution' has mass less than 1 and the 'MFPT' diverges. The paper's own caveat that the MFPT is 'analogous, not exact' does not fix the problem; it concedes the central quantitative claim is not rigorously established. Because the near-exponential FPT distribution and the optimal reset protocol are both built from this defective S(t), the central claims are unsupported. This is a REJECT-level concern, not merely a missing citation or an untightened approximation.","tokens_in":18802,"tokens_out":11372,"duration_ms":149820,"concrete_test":"Run the Markovian limiting case H=1/2 with D=kBT/(mω²)=1, x_a=3, x0=0. (i) Evaluate Eq. (11b) at t=100: χ=e^{-100}, so S≈0.9995 and ∫ f dt≈0.0005. (ii) Solve the exact OU FPE with absorbing boundary P(x_a,t)=0 on (-∞,x_a) numerically or via eigenfunction expansion, and compute the true S_true(t) and f_true(t). The exact solution has S_true→0 and ∫ f_true dt=1. A mismatch at, say, t=10 proves that Eq. (11) is not a first-passage survival probability. Optionally repeat with Brownian dynamics with absorption for the same parameters and compare histograms.","verdict_should_be":"REJECT","load_bearing_attack":"The most load-bearing flaw is the definition of S(t|x0) in Eq. (11a). It is obtained by integrating the no-absorbing-boundary propagator P(x,t|x0) of Eq. (8) over x < x_a. But that is the probability that the free resetting process is left of x_a at time t; it is not the probability that the particle has never hit x_a. True survival requires solving the FPE on the half-line with P(x_a,t)=0, or using the standard renewal S_r(t)=e^{-rt}S_0(t)+r∫_0^t dτ e^{-rτ} S_0(τ)S_r(t-τ) in terms of the true no-reset survival S_0. The paper uses neither. The defect appears already in the model's own Markovian limit: for H=1/2, χ(t)=e^{-t}, and with x0=0, Eq. (11b) gives S∞=(1/2)[1+erf(x_a/√(2D))] > 0, so f(t) has total mass 1-S∞ < 1 and the MFPT ∫S dt diverges. The paper's finite-time integration of S(t) cannot cure this, since the positive tail makes the full integral infinite. Thus Figs. 3-5 describe the free propagator, not first-passage statistics of the GLE with an absorbing boundary. The simulation comparison in Fig. 4 uses an absorbing boundary and therefore is not a valid check of Eq. (11); the analytical distribution is defective and cannot be a normalized first-passage density.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies first-passage escape from a harmonic well for an overdamped generalized Langevin equation driven by fractional Gaussian noise, under Poissonian stochastic resetting. It derives a Fokker-Planck equation for the one-point density, solves the full-space propagator with a Mittag-Leffler relaxation function, uses a renewal equation to obtain the resetting steady state, and then defines the survival probability as the integral of this unrestricted propagator over the region left of an absorbing boundary. From this it extracts a first-passage-time distribution and a mean first-passage time, reporting an exponential tail induced by resetting and an optimal reset rate. The position-distribution part is supported by simulations, and code is provided. The central first-passage claim, however, is based on an incorrect identification of occupancy with survival.","tokens_in":19114,"tokens_out":5575,"duration_ms":77595,"significance":"If the first-passage analysis were correct, the paper would provide a useful closed-form treatment of resetting in a non-Markovian harmonic system, with practical implications for escape kinetics and optimal reset protocols. The paper has genuine strengths: the derivation of the time-local FPE for the marginal density is non-trivial, the full-space propagator is explicit, the renewal construction for the position distribution is standard, and the simulations are reproduced with shared code. These strengths, however, do not rescue the FPT claims, because the quantity computed as survival is not the survival probability of a process with an absorbing boundary. The central quantitative results in Figs. 3--5 are therefore not established.","major_comments":[{"comment":"The object S(t|x0) defined in Eq. (5) and evaluated in Eq. (11) is not a survival probability. It is the integral over x<x_a of the full-space, no-absorbing-boundary propagator P(x,t|x0) from Eq. (8). That is the probability that the process is to the left of x_a at time t; it does not condition on the trajectory never having hit x_a. A true survival probability requires solving the FPE on the half-line with P(x_a,t)=0, or using the renewal relation S_r(t)=e^{-rt} S_0(t)+r∫_0^t dτ e^{-rτ} S_0(τ) S_r(t-τ) with S_0 the true no-reset survival probability. Eq. (11a) contains neither ingredient. Consequently f(t)=-dS/dt in Eq. (6) is not a first-passage-time density and Eq. (7) is not the MFPT. This is the load-bearing step of the paper.","section":"Section II, Eqs. (5), (6), (7), (11)"},{"comment":"The defect is visible already in the model's own Markovian limit. For H=1/2, χ(t)=e^{-t/τ_0}. From Eq. (11b), S∞ = (1/2)[1+erf(x_a√(mω²/(2k_BT)))] (for x_0=0), which is positive for any finite absorbing boundary. Thus f(t) has total mass 1-S∞<1, and the integral in Eq. (7) diverges because S(t) tends to a positive constant. The paper's finite-time integration in Fig. 5, and the text's admission that the result is 'not the exact MFPT', cannot cure a positive tail. This directly contradicts the assumption S(∞)=0 used in Eq. (7). The issue is not a numerical truncation; the computed object is defective as a first-passage distribution.","section":"Eq. (11b) and Markovian limit H=1/2"},{"comment":"The FPT simulations in Appendix C use an absorbing boundary at x=x_a and stop trajectories at the first hitting time. That is the correct protocol for first-passage statistics. The analytical curve in Fig. 4, however, is derived from the derivative of the unrestricted-propagator quantity in Eq. (11). These two objects are not the same: the analytical density is defective in the sense described above, whereas the simulated histogram is a genuine first-passage-time density. Therefore Fig. 4 cannot validate Eq. (11). The reported agreement is unexplained and, as a matter of principle, cannot hold in the tail region. This invalidates the paper's main comparison and the claims of exponential-tail and optimal-reset behavior in Figs. 3--5.","section":"Fig. 4 and Appendix C"}],"minor_comments":[{"comment":"In the second term of the expression for I', the Laplace transform should be \\(\\bar K(z_2)\\), not \\(\\bar K(z_1)\\); the subsequent formula appears to use the corrected version. Please fix the typo.","section":"Appendix D, Eq. (D33)"},{"comment":"The notation mω²_B appears with a subscript B in several equations (e.g., D1, D22, D38) but is defined nowhere; the main text uses mω². Please clarify whether this subscript is meaningful or a typographical artifact.","section":"Appendix D and main text"},{"comment":"The text states that S(t) beyond the plotted range is constant and that the finite-time sum is 'analogous to the MFPT (not the exact MFPT)'. This admission should be prominently connected to the fact that a constant survival tail makes the exact MFPT infinite for the quantity defined in Eq. (11). As written, the figure axes label the finite-time sum as MFPT, which is misleading.","section":"Fig. 5 discussion"}],"recommendation":"reject","confidential_remarks":"I agree with the stress-test concern: the identification of the unrestricted propagator integral with survival probability is not a minor technical slip but the foundation of all first-passage claims. The paper itself acknowledges the finite-time integration and that the result is 'not the exact MFPT', which confirms the problem. Replacing Eq. (11) with a true half-line solution or a correct renewal equation would require redoing the FPT analysis and all figures, which is beyond a revision of the present manuscript. The position-distribution part and code are useful, but the paper as submitted cannot support its central conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: the paper has a genuine analytical core and a useful construction for position distributions of a non-Markovian process under resetting, but the first-passage part doesn't survive scrutiny. Equation (11) integrates the unrestricted propagator over x<xa and calls it the survival probability. That is the occupation probability of the half-line, not the probability that the particle never hit xa. In the Markovian limit, I(t) tends to a positive constant, so S(∞)>0, the FPT density has total mass less than one, and the MFPT integral diverges. The paper itself admits the MFPT is “analogous” and integrates only a finite time range, so the optimal reset rate plots are not rigorous. This is not a minor gap; it is the load-bearing claim of the paper.\n\nWhat is good: Appendix D is a careful derivation of a time-local FPE from the GLE for a harmonic trap using Novikov's theorem, Appendix E solves the propagator explicitly, and Eq. (8) is a correct renewal equation for the position distribution. The histograms in Fig. 2 confirm that the unrestricted P(x,t) matches simulations, and the code is on GitHub. That is real, reproducible work.\n\nBeyond Eq. (11): the “resetting induces Markovianity” claim is qualitative—no tail exponent is computed. The FPE with an absorbing boundary is not justified for non-Markovian dynamics; even a half-line solution would not be exact because the absorbing boundary couples to memory. The paper does not cite prior work on resetting in non-Markovian systems, so the novelty claim needs a literature check, though I haven't done one. Fig. 4's good agreement is suspicious: the simulations use an absorbing boundary while the analytic f(t) is not a true first-passage density, so the match must be coincidental or confined to early times.\n\nThis paper is for readers who want the position statistics and the FPE construction; it should not be cited for FPT/MFPT results in its current form. A serious referee could push the authors to either solve the true absorbing-boundary problem or reframe the paper as a study of occupation probability. I would send it to review, but with the expectation of major revision or substantive reframing.","headline":"Real FPE derivation and position statistics, but Eq. (11) is not a survival probability—the FPT/MFPT claims don't hold as written.","tokens_in":19677,"tokens_out":3721,"would_cite":false,"duration_ms":48657,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82C31","60G22","60J70"],"pacs":["05.40.-a","05.10.Gg"],"model":"deepseek-v4-flash","headline":"Resetting erases the memory of a non-Markovian particle, turning its heavy-tailed escape distribution into a near-exponential one and enabling an optimal reset rate for fast escape.","keywords":["stochastic resetting","non-Markovian dynamics","first-passage time","fractional Gaussian noise","generalized Langevin equation","Mittag-Leffler relaxation","escape kinetics","optimal reset rate"],"falsifier":"Run direct numerical integration of the original generalized Langevin equation (with power-law kernel and fractional Gaussian noise) in the same harmonic well with an absorbing boundary at x_a, collect a large number of first-passage times at a fixed reset rate r, and compare the empirical survival probability with Eq. (11). A statistically significant deviation in the exponential tail or in the location of the MFPT-vs-r minimum would falsify the exact Markovianization claim.","tokens_in":18603,"feed_emoji":"⏱️","tokens_out":5940,"duration_ms":66487,"temperature":0.7,"pith_summary":"The paper studies a harmonically trapped overdamped particle driven by fractional Gaussian noise, a memory-carrying noise with power-law correlations, and asks what Poissonian stochastic resetting does to escape over an absorbing boundary. It builds an analytical framework by combining a time-local Fokker-Planck equation with a time-dependent diffusion coefficient, a Gaussian propagator with Mittag-Leffler relaxation, and a renewal equation that stitches together intervals between resets. The central claim is that resetting breaks the memory: the first-passage time distribution, which without resetting has a heavy non-exponential tail, becomes near-exponential once resetting is introduced, and an optimal reset rate minimizes the mean escape time when the reset point is away from the well minimum. A sympathetic reader would care because this gives a concrete, closed-form prescription for accelerating escape in viscoelastic and other memory-driven environments, and identifies resetting as a control that effectively erases temporal correlations.","feed_headline":"Resetting turns heavy-tailed escape into near-exponential","feed_subtitle":"Poissonian resets erase memory in a harmonic well, giving an optimal rate that minimizes mean escape time.","key_machinery":"The central machinery is the renewal equation P(x,t|x0) = e^{-rt}G(x,t|x0) + r ∫_0^t dτ e^{-rτ}G(x,τ|x_r), which is exact for Poissonian resetting because reset times are independent of the system dynamics. It is coupled to the Fokker-Planck equation with time-dependent coefficient eta(t) = -d/dt ln chi(t), where chi(t) = E_b[-(t/tau_0)^b] is the Mittag-Leffler relaxation function; this is the object that carries the memory of the non-Markovian process. The Gaussian propagator constructed from this FPE is then integrated up to the absorbing boundary to produce survival and first-passage statistics. The machinery works by turning the non-Markovian memory into a single time-dependent coefficie","core_discovery":"For a linear restoring force and fractional Gaussian noise with Hurst index H in [1/2,1), the paper claims that the non-Markovian generalized Langevin equation can be reduced to a Fokker-Planck equation with a time-dependent diffusion coefficient eta(t) = -d/dt ln chi(t), where chi(t) is a Mittag-Leffler relaxation function. The corresponding propagator is Gaussian, and combining it with a renewal equation for Poissonian resetting yields closed-form survival probabilities and first-passage time distributions. The central discovery is that resetting induces Markovianity: the heavy-tailed, non-exponential first-passage distribution becomes near-exponential, with an optimal reset rate that mini","pith_inferences":["A direct test the paper does not run: simulate the original generalized Langevin equation with an absorbing boundary, collect first-passage times, and compare the empirical survival probability with Eq. (11); this would settle whether any non-local memory survives the reset at the absorbing boundary.","The exact Markovianization likely depends on the harmonic force. A testable extension is to apply the same resetting protocol to an anharmonic or bistable well and check whether the first-passage distribution remains exponential; the FPE reduction would need modification there.","The paper's MFPT figures are based on integrating survival over a finite time window, which the paper itself notes is 'analogous' rather than exact; an exact tail extrapolation might shift the reported optimal reset rates.","The renewal equation's exactness relies on Poissonian reset times. An extension not pursued in the paper is whether periodic or power-law reset schedules preserve the memory-erasing effect or produce different optimal rates."],"forward_implications":["If the central claim holds, resetting is a practical control strategy: one tunable rate r can convert slow heavy-tailed escape into a Poisson-like fast escape in viscoelastic and other memory-driven environments.","The optimal reset rate is not universal: it increases with memory strength H, so strongly correlated baths need more frequent restarts, while weakly correlated baths need only occasional resets.","Resetting at the harmonic well minimum is counterproductive and can increase mean escape time; reset positions away from the minimum are required for the speed-up.","The survival formula with the Gaussian propagator provides closed-form first-passage statistics that can be used to fit single-molecule escape experiments in memory-driven systems.","Direct numerical simulation of the generalized Langevin equation confirms the analytical renewal formulas for position distributions and first-passage time histograms over the parameter range studied."],"fun_headline_variants":["Resetting erases memory, making escape near-exponential","Stochastic resetting turns heavy tail into exponential","Optimal reset rate found for memory-driven escape","Resetting makes non-Markovian escape near-exponential"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that the non-Markovian generalized Langevin dynamics with fractional Gaussian noise in a harmonic well is exactly equivalent to a time-local Fokker-Planck equation whose only memory trace is the time-dependent coefficient eta(t); if residual non-local memory survives at an absorbing boundary, the renewal-based escape statistics are approximations.","fun_headline_variants_meta":{"raw":{"variants":["Resetting erases memory, making escape near-exponential","Stochastic resetting turns heavy tail into exponential","Optimal reset rate found for memory-driven escape","Resetting makes non-Markovian escape near-exponential"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000559,"raw_usage":{"total_tokens":2468,"prompt_tokens":693,"completion_tokens":1775,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":437,"completion_tokens_details":{"reasoning_tokens":1711}},"tokens_in":437,"tokens_out":1775,"duration_ms":15842,"temperature":1.0,"reasoning_tokens":1711,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T16:43:05.074960+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run direct numerical integration of the original generalized Langevin equation (with power-law kernel and fractional Gaussian noise) in the same harmonic well with an absorbing boundary at x_a, collect a large number of first-passage times at a fixed reset rate r, and compare the empirical survival probability with Eq. (11). A statistically significant deviation in the exponential tail or in the location of the MFPT-vs-r minimum would falsify the exact Markovianization claim.","supporting_citations":[],"review_version":1}