{"id":"b570843b-07be-4cb2-b252-df121144551b","arxiv_id":"2511.11815","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Mixed-age starfish embryos transition from a traveling, flocking state to a fluctuating crystal as their pairwise nonreciprocity weakens, and a new 'topological flowscape' framework quantifies this transition.","lead":"Starfish embryos at two developmental stages chase each other asymmetrically, and the authors map how this nonreciprocal push-pull reshapes their collective motion and structure. They introduce 'topological flowscapes' to track structural change and use them to locate the traveling-to-crystal transition in the embryos.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Nonreciprocal self-healing and the N≈0.5 order peak are computed with transverse interactions scaled to 10% of inferred values and with no noise; the central state diagram may not survive a parameter sweep.","rationale":"The reader's weakest_assumption identifies the same load-bearing modeling premise: the simulated state diagram — and specifically the nonreciprocal self-healing effect — depends on transverse interactions being scaled to 10% of the experimentally inferred values, on a weak central potential, and on the absence of noise. I agree that this is the central soft spot because the paper's broadest claim, 'weak nonreciprocity promotes structural order while stronger asymmetry disrupts it,' is established almost entirely through these simulations. The experimental observation of traveling-to-fluctuating transition and the flowscape rate shift are credible and independently supported by several measures (velocity polarization, entropy-production bound, information rate), but they do not directly establish the N≈0.5 ordering peak. The concern is not that the model is wrong, but that its headline prediction has not been shown to be robust to the stated parameter choices. A focused parameter sweep would settle whether the claimed effect is a feature of the inferred interactions or an artifact of the ad hoc reductions. For this reason the existing CONDITIONAL verdict should stand; I do not see grounds for rejection, since the experimental phenomenology is real and the framework is promising, but the general claim should not be accepted unconditionally until the simulation sensitivity is tested.","tokens_in":34832,"tokens_out":5506,"duration_ms":55003,"concrete_test":"Rerun the SI III simulations for N ∈ {0, 0.25, 0.5, 0.75, 1, 1.25} with (a) f_T at the full inferred magnitude, (b) f_T at 50% of inferred, and (c) the inferred noise Δ from SI Eq. (2) added, keeping all other settings identical. Also run a variant with fr=0 and a hard-wall confinement instead of the harmonic trap. If the ⟨dhex⟩ minimum near N=0.5 or the jump near N=1 disappears, shifts by more than one grid point in N, or changes sign under any of these perturbations, the central state diagram is not robust to the stated modeling premise.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's widest claim is the simulation state diagram (Fig. 2d) and, in particular, the 'nonreciprocal self-healing' minimum in ⟨dhex⟩ near N=0.5 (Fig. 2c; SI IV.D). This result is produced by Eq. (SI 14) with three hand-set ingredients stated in SI III.A: transverse interaction strengths f_T are reduced to 10% of the values inferred from the experimental trajectories, a weak harmonic trap fr=2e-4 is added to mimic the curved interface, and noise is set to zero. The inference in Eq. (SI 2) includes a fitted noise amplitude Δ; dropping it changes the effective dynamics, and the trap changes boundary conditions, yet their influence on the order peak and on the N=1 fragmentation jump is never quantified. If the 10% transverse scaling is too aggressive, the chiral rotational stresses present in the real embryos could destroy the annealed crystal before N reaches 0.5, shifting or eliminating the minimum. If noise is restored, defect dynamics and annealing may change qualitatively. Because the experimental evidence for the 'weak nonreciprocity promotes order' claim is a single trajectory in which time-segmented inference shows N(t) only decreasing from ≈1.2 to ≈0.9 (SI II.B), the claim is essentially a model prediction whose robustness to these hand-set terms has not been established. The paper's own SI VI.D notes that the experimental transition path differs from any fixed-N model steady state, which further weakens the quantitative mapping but does not directly address this simulation sensitivity.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies starfish-embryo mixtures with two developmental stages (E1, E2) that interact nonreciprocally through fluid-mediated forces. It infers pairwise longitudinal and transverse interactions from experimental trajectories, then builds an overdamped inference-based model in which the longitudinal inter-type nonreciprocity is tuned by a parameter N (with N=0 reciprocal and N=1 the experimentally inferred value). Simulations with varying N produce four states—crystalline, self-propelled crystalline, flocking, and fragmented—summarized in a state diagram (Fig. 2d). The authors introduce a topological metric (distance to hexagonal packing in a T1-motif graph), a topological landscape (kernel-density representation of motif frequencies on a low-dimensional manifold), and a topological flowscape (KL-divergence-based trajectory of time-evolving landscapes). The experimental trajectory is interpreted as a transition from an N≈1 flocking-like state to an N≈0 crystalline state, and the flowscape, entropy-production estimates, and information-rate measures all show a rate shift around 3 h that coincides with the independently measured traveling-to-fluctuating transition.","tokens_in":35288,"tokens_out":4045,"duration_ms":42783,"significance":"If the central claims hold, the paper offers a broadly applicable framework for quantifying nonequilibrium structural transitions in active and living matter, connecting interaction asymmetry to topology and to information-theoretic rate signatures. The combination of quantitative imaging, Bayesian interaction inference, and topological packing statistics is ambitious, and the falsifiable state diagram is a useful organizing hypothesis. The topological landscape/flowscape construction is conceptually novel and could be applied to other soft-matter systems. However, the quantitative conclusions depend on a simulation model whose hand-set ingredients are not stress-tested, and the experimental inference of decreasing nonreciprocity lacks uncertainty quantification. These gaps currently prevent the paper from fully supporting its strongest claims about nonreciprocal self-healing and the precise model–experiment mapping.","major_comments":[{"comment":"The central simulation results—the ⟨dhex⟩ minimum near N=0.5 (nonreciprocal self-healing) and the sharp destabilization at N=1—are produced with three hand-set modeling choices: transverse interactions reduced to 10% of inferred values, a central potential fr=2e-4, and zero noise. The inference in Eq. (SI 2) explicitly includes a fitted noise amplitude Δ, and the transverse forces are part of the experimentally inferred interaction set; dropping/scaling these terms by fiat may change the effective dynamics qualitatively. The paper gives no sensitivity analysis. I ask the authors to quantify how the ⟨dhex⟩ curve and the N=1 fragmentation transition depend on (i) the transverse scaling factor (e.g., 0, 0.1, 0.5, 1 times the inferred f_T), (ii) adding noise at the inferred Δ, and (iii) varying fr. Without this, the claim that weak nonreciprocity promotes order is a model prediction resting","section":"SI III.A, Eq. (SI 14); Fig. 2c,d"},{"comment":"The time-segmented inference of N(t) is presented with no error bars or confidence intervals, and the text states the decrease is 'approximately 30%' while Fig. S10 appears to show a decrease from about 1.2 to 0.9 (about 25%). This inferred N(t) is also computed from the same trajectory data that produce the experimental topological landscapes and flowscape, so the model–experiment correspondence is partly a fit to the same data. The authors should provide bootstrap or posterior-uncertainty estimates for N(t), test whether the decrease is statistically significant, and state explicitly whether the N=1→N≈0.9 range is actually sufficient to cross any of the model's distinct states. This matters because the main-text narrative assigns the observed transition to a decrease in nonreciprocity.","section":"SI II.B, Fig. S10"},{"comment":"The paper candidly states in SI VI.D that the experimental flowscape path deviates from the fixed-N model path, and that the experimental transition state is a 'hollow crystal' not present in any fixed-N steady state. This is a limitation statement in the manuscript itself and it directly qualifies the central quantitative mapping. If the experimental transition cannot be reproduced by any fixed-N model, then the claim that the traveling-to-fluctuating transition is 'captured' by the topological flowscape as a nonreciprocity-driven transition is weakened. The authors should either (a) extend the model to include candidate higher-order mechanisms (e.g., time-dependent interaction changes, density changes, embryo aging, boundary/interface effects) and show which mechanism produces the hollow-crystal states, or (b) explicitly reframe the conclusions so that the flowscape is a phenomenologic","section":"SI VI.C–D; Fig. S21–S22"},{"comment":"The sharp rate shift in the flowscape diagonal displacement and the independently estimated entropy-production rate is a key supporting observation, but no error bars or significance tests are provided for either quantity. The EPR estimate in Eq. (25) depends on the choice of time gap τ (set to 20 s) and on the motif transition statistics; the statistical distance and activity shown in Fig. S26 appear smooth, but the resulting rate-shift time is not quantified with confidence intervals. The authors should report bootstrap or block-resampling uncertainties for the rate-shift time, and ideally for the EPR curve, so that the claimed coincidence with the traveling-to-fluctuating transition can be assessed as more than a visual similarity.","section":"Fig. 4e,f; SI VII.A"}],"minor_comments":[{"comment":"The abstract says 'Experiments, interaction inference, and topological analysis yield a nonreciprocal state diagram,' but the state diagram in Fig. 2d is generated from the inference-based simulation, not from the experiments directly. Please rephrase to avoid giving the impression that the experimental data alone determine the phase boundaries.","section":"Abstract"},{"comment":"The statement 'We also neglect noise, based on the assumption that self-generated flows captured by pairwise interactions dominate the embryo dynamics' is an assumption that should be tested rather than asserted. At minimum, the authors should report the inferred noise amplitude Δ from Eq. (SI 2) and discuss its magnitude relative to the inferred forces, since the stress-test sensitivity analysis requested above depends on this comparison.","section":"SI III.A"},{"comment":"The motif occurrence cutoff (>10 occurrences) captures 99.7% of probability for N=0.5 but only 50% for N=2.0 and 65% for N=1.5. The claim that the cutoff 'adequately captures the diversity' of the higher-nonreciprocity states should be supported by a convergence check (e.g., recomputing ⟨dhex⟩ with a lower cutoff or with the full motif set), because the high-N behavior is precisely where the paper draws its fragmentation conclusions.","section":"SI IV.B, Table I"},{"comment":"The flowscape coordinates use KL divergences to Gaussian reference distributions whose width σM is matched to the experimental kernel width. The sensitivity of the resulting trajectory to σM is not shown. A small figure or statement showing the trajectory over a plausible range of σ would help establish that the observed rate shift is not an artifact of the chosen reference width.","section":"Main text, Fig. 4c; SI VI.B"},{"comment":"The notation ΣHS is introduced as 'net Hatano-Sasa entropy production' and later used as a per-interval quantity; please define the units and the integration bounds explicitly. Also, the statement that this is a 'well-known speed limit' is fine, but the reader must know that the estimate is a lower bound, not a direct measurement of total EPR.","section":"SI VII.A, Eq. (24)"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely to be of high interest to the soft-matter and active-matter community, and the topological landscape/flowscape framework is a genuinely useful addition. However, the main quantitative claims currently hinge on several hand-set simulation parameters and on an experimental N(t) with no uncertainty. I would not reject: the experimental phenomenology is rich, and the missing robustness checks, error bars, and explicit handling of the hollow-crystal discrepancy are, in principle, achievable within the scope of a revision. If the authors can supply a sensitivity analysis of the transverse-force scaling and noise, quantify the N(t) decrease, and either extend the model to reproduce the experimental transition states or carefully delimit the scope of the flowscape claims, the paper could become a strong contribution. I would not recommend rejection on editorial grounds, but the revision is substantial rather than cosmetic."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper is worth reading for the topological landscape and flowscape framework, and the starfish embryo experiment is a solid, interesting observation. But the central claim about nonreciprocal self-healing is a model prediction that depends on parameters the paper does not sweep, so I would not treat the state diagram as established.\n\nWhat is actually new: applying T1-motif statistics to a nonreciprocal living mixture, building the low-dimensional motif manifold, and the flowscape idea of embedding landscape evolution via KL divergences to chosen references. That is a useful, generalizable way to visualize nonequilibrium structural transitions, and the entropy production rate estimate from speed limits is a nice independent check. The experimental traveling-to-fluctuating transition, with polarization rotation and the later ordered lattice, looks credible and well documented.\n\nThe soft spots are real. In SI III.A the model reduces transverse interactions to 10% of the inferred values, adds a weak harmonic trap, and sets noise to zero, while the inference itself includes a fitted noise amplitude. The nonreciprocal self-healing minimum near N=0.5 and the sharp jump at N=1 come from that model. The authors do not quantify how these choices affect the location or existence of the minimum, which is a genuine gap. The time-segmented N(t) has no error bars and is inferred from the same trajectory data used to build the experimental flowscape, so part of the model-experiment correspondence is a fit rather than an independent test. The paper itself admits (SI VI.D) that the experimental path passes through hollow-crystal states not seen in fixed-N simulations, which is honest but weakens the quantitative mapping.\n\nI do not think these issues are fatal. The framework stands on its own as an analysis tool, the experiment is a real observation, and the authors are explicit about the deviations. But the sweeping phrasing in the abstract and discussion goes beyond what the simulation robustness supports.\n\nAudience: people working on nonreciprocal active matter, living crystals, and topological characterization of structure. I would cite it for the flowscape, and probably not for the self-healing result unless the parameter sensitivity is resolved.\n\nRecommendation: send to peer review, yes. Ask the authors for a parameter sweep over the transverse scaling and noise amplitude, error bars on inferred N(t), and release of data and code.","headline":"Topological landscape/flowscape is a genuinely new analysis tool and the experimental transition is credible, but the 'weak nonreciprocity promotes order' result rests on a simulation with hand-set transverse scaling and no noise, so treat the state diagram as tentative.","tokens_in":35738,"tokens_out":1614,"would_cite":true,"duration_ms":16375,"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":"Weak nonreciprocity orders embryo mixtures into crystals; strong asymmetry fragments them.","keywords":["nonreciprocal interactions","active matter","starfish embryos","topological motifs","T1 transitions","structural order parameter","topological flowscape","state transitions"],"falsifier":"Run the same mixture with independently varied age gaps (for example 12, 36, and 60 hours post-fertilization): if the d_hex minimum does not occur at an intermediate gap, or if the traveling-to-fluctuating transition time does not track the time-segmented inferred N, the central claim fails. In simulation, repeating the state diagram with transverse interactions at 100% instead of 10% of the inferred values is a direct check; losing the N=0.5 order dip would show that the peak is an artifact of that rescaling.","tokens_in":34769,"feed_emoji":"⭐","tokens_out":4748,"duration_ms":44371,"temperature":0.7,"pith_summary":"This paper claims that the asymmetry of forces between two developmental stages of starfish embryos is a control knob for collective structure: a little asymmetry heals defects and stabilizes crystals, while more asymmetry drives the mixture through self-propelled crystals, flocking, and fragmented states. It supports this with tracking experiments, Bayesian inference of pairwise forces, and simulations in which only the inter-type nonreciprocity is scaled. To see transitions that velocity polarization misses, the authors count local topological rearrangements (T1 flips) relative to a perfect hexagon and map the evolving distribution of motifs as a 'topological landscape' and its time trajectory as a 'flowscape.' The flowscape shows the experimentally observed traveling-to-fluctuating transition as a sharp rate shift, corroborated by an entropy-production estimate. A sympathetic reader would care because the paper offers a general way to read structural state diagrams out of living matter and tie them to information-theoretic and thermodynamic signatures.","feed_headline":"Asymmetry tunes embryo swarms from crystals to flocks to fragments","feed_subtitle":"Topological landscapes locate the traveling-to-fluctuating transition in living starfish embryo mixtures.","key_machinery":"The load-bearing object is a one-parameter family of pairwise force models built from experimentally inferred interactions: the E1–E2 longitudinal force is split into symmetric and antisymmetric parts and the antisymmetric part is scaled by N. The diagnostics are topological: d_hex counts local T1 bond-flips needed to reach a perfect hexagonal motif; topological landscapes embed roughly 15,000 motifs on a manifold by pairwise T1 distance and plot motif frequencies as height; topological flowscapes track a system state by its KL divergences from M1-like and M2-like reference distributions.","core_discovery":"The central claim is that nonreciprocity N, defined by the antisymmetric part of the inferred E1–E2 longitudinal interaction, organizes a state diagram: at N=0 a clockwise crystalline state; for 0<N<1 a self-propelled crystalline state that is more ordered than the reciprocal crystal ('nonreciprocal self-healing'); at the experimentally inferred N=1 a flocking state with merging and fragmenting clusters; and for N>1 a fragmented state. The structural order parameter d_hex — the average number of T1 topological transitions needed to turn each local neighborhood into a perfect hexagon — falls to a minimum near N=0.5 and jumps sharply at N=1. The experimental transition from a traveling to a fl","pith_inferences":["A testable extension: the 'nonreciprocal self-healing' mechanism suggests that controlled asymmetry could anneal defects that equilibrium crystallization cannot remove, which could be probed in colloidal or active-metamaterial experiments by slowly cycling N.","Because the inferred N decreases during development, the same framework could serve as a structural developmental clock, reading embryo age from the trajectory of motif distributions rather than from cell labels.","The experimental transition passes through a hollow-crystal state that the fixed-N simulations do not produce, implying an additional mechanistic ingredient—possibly interface adhesion or cluster-scale elasticity—that a next-generation model would need to include.","The flowscape is defined for any time series of probability distributions, so in principle it could be applied to neural population activity, tissue morphogenesis, or other high-dimensional evolving states without modification."],"forward_implications":["If N is the control parameter, tuning developmental age differences or any pairwise asymmetry should move a real active mixture continuously through the four states, with peak crystalline order at intermediate N.","The pair of order parameters — velocity polarization for dynamics and d_hex for structure — distinguishes states that look identical in velocity alone, such as self-propelled crystals versus fragmented clusters.","The first-order-like coexistence of M1 and M2 motifs near N=1 predicts that the traveling-to-fluctuating transition is an indirect, mediated structural transition rather than a single sharp bond flip.","The topological flowscape yields a rate shift coinciding with the independently measured polarization transition, so structural information alone can locate a macroscopic state transition.","Topological motif frequencies and the topological earth-mover distance generalize the structural order parameter to defect-rich and anisotropic arrangements beyond simple crystals."],"fun_headline_variants":["Asymmetry steers embryo swarms: crystal, flock, then fragments","Nonreciprocity flips starfish embryos from ordered to fragmented","Weak asymmetry orders starfish swarms; strong asymmetry breaks them","Flowscape maps embryo transitions: from crystal to flock to fragments"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The quantitative state diagram rests on the simulation assumption that the sideways (transverse) forces between embryos are only 10% of their measured strength and that a weak central trap stands in for the curved air-water surface; if that sideways scaling is inaccurate, the predicted order peak and fragmentation boundary could shift.","fun_headline_variants_meta":{"raw":{"variants":["Asymmetry steers embryo swarms: crystal, flock, then fragments","Nonreciprocity flips starfish embryos from ordered to fragmented","Weak asymmetry orders starfish swarms; strong asymmetry breaks them","Flowscape maps embryo transitions: from crystal to flock to fragments"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000515,"raw_usage":{"total_tokens":2314,"prompt_tokens":696,"completion_tokens":1618,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":440,"completion_tokens_details":{"reasoning_tokens":1543}},"tokens_in":440,"tokens_out":1618,"duration_ms":10894,"temperature":1.0,"reasoning_tokens":1543,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T22:09:28.521711+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same mixture with independently varied age gaps (for example 12, 36, and 60 hours post-fertilization): if the d_hex minimum does not occur at an intermediate gap, or if the traveling-to-fluctuating transition time does not track the time-segmented inferred N, the central claim fails. In simulation, repeating the state diagram with transverse interactions at 100% instead of 10% of the inferred values is a direct check; losing the N=0.5 order dip would show that the peak is an artifact of that rescaling.","supporting_citations":[],"review_version":1}