{"id":"8d2a9ecf-a3a3-4579-b6a7-9079d037bdfb","arxiv_id":"2510.22081","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Reciprocal flapping propels a granular swimmer via jamming-induced asymmetry at low inertia and coasting-time asymmetry at high inertia, with net direction set by which mechanism dominates.","lead":"A computer simulation of a two-winged 'scallop' swimmer in granular material shows two distinct ways that simple back-and-forth wing flaps produce net motion: grains jamming unevenly around the wings, and the swimmer's own momentum carrying it differently after opening versus closing. The results give physics-based design rules for robots that move through sand, soil, or other granular settings.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quasi-static law Δy/L = αΔN_c depends on an untested hand-chosen force threshold F_c; without a sensitivity analysis over F_c and stiffness, the quantitative claim is not robust.","rationale":"The reader's weakest assumption correctly identifies the untested threshold F_c as the main soft spot. I agree and would emphasize that the issue propagates to Eq. 8: the inertial contribution is isolated by subtracting αΔN_c, so any threshold artifact in α contaminates the dynamic master curve. The qualitative physics is well supported — frictionless simulations suppress locomotion, kinematic fields match X-ray CT, and the direction reversal with inertia is consistent with prior theory. That support reduces correctness risk but does not validate the exact numerical law. A threshold/stiffness sensitivity study and an out-of-sample prediction would settle whether the linear relation is a real order-parameter law or an artifact of calibration. Since the reader already returned CONDITIONAL, my concern does not change the verdict; it strengthens the reason for the condition.","tokens_in":11918,"tokens_out":2899,"duration_ms":28896,"concrete_test":"Recompute ΔN_c and refit α on the same quasi-static dataset for F_c = 0.1, 0.3, 1.0, 3.0, 10.0 mN, and also for Young's modulus rescaled by factors of 0.3 and 3 (both with F_c fixed and with F_c rescaled by the mean contact force). Report α and the goodness-of-fit for each case; if α varies by more than ~50% or linearity breaks, threshold dependence is established. Additionally, leave out the mid-body and one-wing cases from the fit and predict their Δy/L; if these out-of-sample predictions fail, the universality claim is weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (6) defines ΔN_c = N_c(θ_c) − N_c(θ_o), where N_c counts contacts with |F| > F_c = 1.0 mN, chosen as the top 0.1% of the base-case contact-force distribution (Sec. III B, Fig. 4b). The central quantitative support — the linear relation Δy/L = αΔN_c with α = 8.63×10^-6 across varied gap widths, mid-body geometry, and friction — is asserted only for this fixed threshold. DEM contact forces follow the Hertz model (Eq. 1) and depend on Young's modulus, overlap, and packing; F_c is not rescaled when E or the dynamic regime changes. If F_c is lowered, many weak bulk contacts contribute and the opening/closing asymmetry may wash out; if raised, only sparse near-rigid contacts remain and linearity may become noisy. The same α is then subtracted from the dynamic data in Fig. 6b to produce the Eq. 8 master curve, so threshold sensitivity propagates into the inertial collapse. The paper also gives no uncertainty for β and n and no out-of-sample validation. This makes the threshold choice load-bearing for the central quantitative claim: the mechanism may be real, but the paper's central quantification is not yet established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses DEM simulations of a scallop-like reciprocal swimmer in a granular medium to identify two propulsion mechanisms. In the quasi-static regime, the authors quantify jamming-induced symmetry breaking via ΔN_c, the difference in the number of strong contacts (|F| > F_c) between fully closed and fully open wing states, and report a linear relation Δy/L = α ΔN_c with α = 8.63×10^-6 across varied gap widths, mid-body geometry, and friction. In a dynamic regime characterized by a coasting time T_c, they report that net displacement follows Δy/L = α ΔN_c − β(T_c/T)^n with fitted β = 0.24 and n = 0.44, collapsing frictional and frictionless data onto a master curve. The paper validates the base case against prior experiments and includes controls (frictionless medium, one-wing, mid-body).","tokens_in":12346,"tokens_out":2886,"duration_ms":29073,"significance":"If the reported quantitative relations are robust, the paper makes a valuable contribution: it connects mesoscopic force-chain asymmetry (a jamming signature) to net locomotion in a reciprocal granular swimmer, and it demonstrates a distinct inertial propulsion mechanism with a compact order parameter. The simulations are well controlled, with explicit tests of friction, geometry, and inertia, and the qualitative claims are supported by multiple independent observables (coordination number, force chains, swimmer kinematics). The authors are honest that β and n are fitted, and they caution against extrapolating Eq. (8). The main risk is that the central quantitative law depends on a hand-chosen strong-force threshold F_c that is not tested for sensitivity.","major_comments":[{"comment":"The central linear relation Δy/L = αΔN_c is defined using a threshold F_c = 1.0 mN chosen as the top 0.1% of the base-case contact force distribution. This threshold is fixed across all cases, but DEM contact forces scale with Young's modulus, overlap, and packing. The paper does not test how α or the linearity changes when F_c is varied, nor whether a rescaled threshold is needed in the dynamic regime or for different E. If the linear law is an artifact of this particular threshold, the quantitative support for the jamming mechanism fails. Please add a sensitivity analysis varying F_c over at least a decade (including values tied to the force distribution of each case) and show that the linear relation and the inferred α are stable. Report the uncertainty in α from the fit.","section":"Sec. III B, Eq. (6), Fig. 4(b)"},{"comment":"The master curve Eq. (8) is built by subtracting αΔN_c from the dynamic data. This assumes that jamming and inertial contributions add linearly, which is an ad hoc superposition rather than a derived relation. Moreover, β and n are fitted with no uncertainty, and the collapse in Fig. 6(b) is shown only for the training data. To make the inertial scaling convincing, provide uncertainties for β and n, state whether the same power law is obtained if the jamming subtraction uses a different α or threshold, and ideally perform an out-of-sample check (e.g., a configuration not included in the fit).","section":"Sec. III C, Eq. (8), Fig. 6(b)"},{"comment":"The transition from quasi-static to dynamic regime is claimed to occur at T_c/T ≈ 4×10^-3, but the criterion for this crossover is not defined quantitatively. The text describes a plateau and a transition by inspection. If the crossover location is to be used as a physical prediction, please specify an objective criterion (e.g., where the inertial term exceeds the jamming term or where retardation time becomes a fixed fraction of T).","section":"Sec. III C, Fig. 5(c), Fig. 6(a)"}],"minor_comments":[{"comment":"The axis label for the vertical axis appears garbled as '(            -           )' in the provided text; please fix the math rendering. Also clarify whether the plotted quantity is (|Δy_R^c| − |Δy_R^o|)/L.","section":"Fig. 5(c)"},{"comment":"The hydrostatic-like pressure P_s = ρ φ_0 g Z_0 is introduced after its first use in Eq. (7). Define P_s explicitly before or immediately with Eq. (7) so the reader can verify the dimensional analysis.","section":"Sec. III C, Eq. (7)"},{"comment":"Please clarify in the caption or text whether the frictionless point (green triangle) is included in the linear fit for α. If it is included, report its leverage; if excluded, state so. Also add error bars for Δy/L in Fig. 4(b) and Fig. 6, not just in Fig. 4(a).","section":"Fig. 4(b)"},{"comment":"The threshold used to select mobile particles and strong forces is described as 'consistent' across cases. Please state the exact threshold values (force and velocity) in the caption or text.","section":"Sec. III B, Fig. 3"}],"recommendation":"major_revision","confidential_remarks":"The qualitative story is compelling and the simulations are well designed. The main blocker is the lack of sensitivity analysis for the strong-force threshold F_c and the absence of uncertainty quantification for the fitted parameters α, β, n. These are fixable within the scope of the manuscript. If the authors can show the linear law is robust to F_c and provide proper fit uncertainties, I would support acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a careful simulation study with a physically interesting idea, and the qualitative case for both mechanisms is convincing. The quantitative centerpiece, however, rests on a threshold that the paper never tests, so I would not yet call the linear relation a law.\n\nWhat is actually new: two distinct mechanisms for reciprocal scallop-style swimming in a granular medium. The jamming mechanism uses hysteresis in the force network — closing builds stronger, more extensive force chains than opening, and the difference in strong-contact count ΔN_c correlates with forward displacement. The inertia mechanism reverses the direction when the coasting time approaches the stroke period, with clear retardation-time asymmetry. The DEM work is thorough: frictionless control kills the forward motion, the one-wing case bounds the cooperative effect, and the displacement fields match the earlier X-ray CT experiments from [22]. That validation is a genuine independent check, not just self-citation.\n\nSoft spots: the linear law Δy/L = αΔN_c with α = 8.63×10⁻⁶ depends on F_c = 1.0 mN, which is set from the top 0.1% of the base-case contact-force distribution. Nothing in the paper shows the relation survives a change in threshold or in particle stiffness. If F_c moves, you are counting different contacts, and the opening/closing asymmetry could wash out or become noisy. The stress-test note is right that this is load-bearing, because the same α is subtracted to produce the inertia master curve. So the quantitative support for the jamming mechanism is not yet robust. Also, β and n in Eq. 8 are fitted without uncertainty and no out-of-sample validation; the power-law collapse looks nice, but a two-parameter fit can absorb a lot.\n\nThat said, these are not fatal objections. The paper honestly labels what is fitted, and the qualitative evidence is strong. The linear relation across gap widths, mid-body geometry, and friction (including zero friction giving zero ΔN_c) is suggestive even if the slope is threshold-dependent. The inertia regime has clear physical intuition, and the direction matches the Newtonian-fluid prediction [40].\n\nWho it is for: granular locomotion researchers, soft robotics folk, and anyone studying reciprocal strategies in memory-bearing media. An editor should send this to peer review. The referee should ask for sensitivity analysis on F_c and stiffness, plus uncertainty on the fits, but the core mechanisms are worth publishing.","headline":"Solid DEM study with two real propulsion mechanisms, but the headline linear law leans on an untested force threshold and fitted exponents; worth a serious referee, not yet a quantitative law.","tokens_in":12702,"tokens_out":1691,"would_cite":true,"duration_ms":18545,"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":"A reciprocal, time-symmetric scallop-like swimmer can still move through granular media: slow flaps push forward through jamming, while fast flaps reverse direction through inertia.","keywords":["reciprocal swimming","granular media","jamming","scallop theorem","discrete element method","force chains","swimmer inertia","locomotion"],"falsifier":"Rerun the quasi-static parameter sweep with F_c set to, say, the top 0.01%, top 1%, or a fixed multiple of the mean contact force, and check whether Δy/L versus ΔN_c remains on the same straight line; alternatively, in an experiment with a photoelastic granular medium, count force chains above a threshold and compare the predicted displacement per cycle against the measured one.","tokens_in":11840,"feed_emoji":"🏊","tokens_out":7694,"duration_ms":64541,"temperature":0.7,"pith_summary":"This paper uses particle simulations to show that a scallop-like swimmer performing reciprocal (time-reversible) wing flaps can propel itself through dry granular media by two distinct mechanisms. In the slow quasi-static regime, the medium jams more strongly at the end of the closing stroke than at the end of the opening stroke, so the number of strong particle contacts in the fully closed state exceeds that in the fully open state; this excess contact count is linearly proportional to the net forward distance per cycle. In the fast dynamic regime, the swimmer's inertia matters: after each stroke it coasts, and because the closed-wing configuration offers less resistance, the backward coast lasts longer, producing net backward motion. The paper combines both contributions into a single relation, Δy/L = αΔN_c − β(T_c/T)^n, with fitted constants, and shows frictional and frictionless data collapse onto it. A sympathetic reader cares because it identifies measurable order parameters that link microscopic jamming and inertial coasting to macroscale swimming direction and speed.","feed_headline":"Jamming and inertia both move a scallop swimmer through sand","feed_subtitle":"Slow flaps go forward via asymmetric force chains; fast flaps go backward via inertial coasting.","key_machinery":"The central object is the strong-contact count N_c, defined as the number of inter-particle contacts whose force magnitude exceeds a threshold F_c = 1.0 mN (chosen as the top 0.1% of the force distribution in the base case); the order parameter ΔN_c is its difference between the fully closed and fully open states. It captures the jammed stagnant zones that form around the wings and resist translation. The second object is the coasting time T_c = m_s/(P_s L T), a characteristic time for the swimmer to come to rest under medium resistance; the ratio T_c/T measures how much inertia matters within one flapping period. Together these two quantities appear additively in Eq. 8, separating the jammi","core_discovery":"In the quasi-static regime, the cycle-averaged normalized net displacement per cycle, Δy/L, is proportional to ΔN_c = N_c(θ_c) − N_c(θ_o), the difference in the number of contacts carrying forces above a fixed threshold between the fully closed and fully open wing states; the slope is α = 8.63×10^-6 across varied gap widths, a one-wing swimmer, an inert mid-body, and frictional versus frictionless media, with every nonzero case favoring the opening stroke. This linear relation is the paper's quantitative demonstration that jamming-induced hysteresis breaks the symmetry between the two reciprocal strokes and generates forward locomotion. In the dynamic regime, where the flapping period approa","pith_inferences":["A natural extension the paper leaves implicit: ΔN_c could be measured in physical experiments using photoelastic or X-ray imaging of force chains, turning the linear law into a testable design rule for real granular robots rather than a simulation-only result.","The threshold dependence of ΔN_c is untested; an obvious follow-up is to check whether the linear law and slope α survive when F_c is varied over an order of magnitude or redefined per case as a different percentile of the force distribution.","The additive form of Eq. 8 suggests a control knob: for a given swimmer mass, one could choose a flapping frequency at which the jamming and inertial contributions cancel, producing a near-zero net displacement.","Because the inertial mechanism operates even in frictionless media, it may generalize to any dense suspension in which the swimmer's density differs from the medium, bridging the granular results and inertial swimming in ordinary viscous fluids."],"forward_implications":["In the quasi-static regime, net displacement per cycle can be predicted from a single force-network statistic, ΔN_c, without tracking full particle trajectories.","Because the jamming term is linear and additive, geometry changes that raise ΔN_c, such as adding an inert mid-body, proportionately increase forward locomotion.","Friction is necessary for the jamming mechanism: with frictionless particles, ΔN_c is essentially zero and forward locomotion disappears.","In the dynamic regime, increasing swimmer mass or shortening flapping period shifts locomotion from forward to backward, with a power-law dependence on T_c/T.","The two mechanisms are separable: measured displacement minus αΔN_c collapses onto a single master curve in both frictional and frictionless media."],"fun_headline_variants":["Jamming and inertia both move a scallop through sand","Scallop swimmer: slow flaps jam, fast flaps coast","Jamming drives slow strokes, inertia drives fast strokes","Granular scallop uses jamming or inertia to swim"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The linear jamming law rests on the hand-chosen force threshold F_c = 1.0 mN used to define a 'strong contact'; if the linearity or the fitted slope α changes when that threshold is moved, the paper's quantitative jamming claim loses its support.","fun_headline_variants_meta":{"raw":{"variants":["Jamming and inertia both move a scallop through sand","Scallop swimmer: slow flaps jam, fast flaps coast","Jamming drives slow strokes, inertia drives fast strokes","Granular scallop uses jamming or inertia to swim"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001345,"raw_usage":{"total_tokens":5292,"prompt_tokens":726,"completion_tokens":4566,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":470,"completion_tokens_details":{"reasoning_tokens":4507}},"tokens_in":470,"tokens_out":4566,"duration_ms":29522,"temperature":1.0,"reasoning_tokens":4507,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T08:10:32.138888+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rerun the quasi-static parameter sweep with F_c set to, say, the top 0.01%, top 1%, or a fixed multiple of the mean contact force, and check whether Δy/L versus ΔN_c remains on the same straight line; alternatively, in an experiment with a photoelastic granular medium, count force chains above a threshold and compare the predicted displacement per cycle against the measured one.","supporting_citations":[],"review_version":1}