{"id":"751a1152-a5b7-48aa-99dc-781e18ca7ba7","arxiv_id":"2601.05801","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":2,"one_line_summary":"Risk-driven local behavioral adaptation suppresses bistable explosive transitions in hypergraph contagion, and sufficiently strong group-based awareness makes the transition continuous and indistinguishable from pairwise contagion.","lead":"The paper shows that when people adjust their behavior because they see infected neighbors or infected groups, explosive 'group-spread' epidemic transitions can shrink or vanish. This turns a sudden, bistable outbreak into a smooth, gradual one—an effect that does not occur for ordinary pairwise contagion.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The pairwise-equivalence claim rests on χ_e^{i_e>1}≈0, which the SM shows can fail: ng does not completely suppress bistability for all empirical hypergraphs, so the universality of 'transforming into a pairwise one' is unsupported.","rationale":"The reader identified the χ≈0 assumption as the weakest point, and I agree that it is the crucial condition for the analytical reduction. However, I found stronger evidence than the reader's hypothetical 'correlations might persist': the paper's own Supplementary Material shows that for several empirical hypergraphs, ng does not completely suppress bistability, implying χ>0 in those cases. This makes the 'complete neutralization' claim dataset-dependent rather than a general property of the ng strategy. The analytical derivation conditional on χ=0 is correct and the simulations support it where it applies, so the paper's core mechanism stands, but the abstract and the reader's strongest claim overgeneralize. I therefore keep the reader's CONDITIONAL verdict unchanged, while emphasizing that the universality of the pairwise-transformation language must be hedged. The concrete test I propose would settle the issue by systematically correlating χ with residual bistability across all datasets, using data already present in the SM.","tokens_in":30305,"tokens_out":7881,"duration_ms":84493,"concrete_test":"Using the SM data already reported, compute for each empirical and synthetic hypergraph the quantity max_{r<r_C^{NAD,p}} ⟨χ_e^{i_e>1}⟩_m for the ng strategy (from the curves in SM Fig. 4 and Supplementary Figs. 8-11), and correlate it with the bistability width ΔB for ng (from SM Fig. 13 and phase diagrams). If the datasets with ΔB>0 are exactly those with χ>0, the χ=0 condition is the decisive criterion and the claim must be restricted to hypergraphs where χ=0 holds. If any dataset has ΔB>0 despite χ=0 for all r<r_C, the mechanism is incomplete.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The Appendix's reduction of higher-order to pairwise dynamics (Eq. 23) assumes χ_e^{i_e>1}≈0 — no hyperedge with a susceptible node has more than one infected. This is the mechanism for 'complete neutralization' under ng: if χ=0 for all r<r_C^{NAD,p}, the nonlinear group terms vanish and the transition becomes continuous at the pairwise threshold. But the paper does not prove χ=0 for ng; it only integrates the IBMF equations for LH10 (θ=0.3, ν=4). The SM (Section II) explicitly notes that for some empirical hypergraphs, 'both nn and ng strategies completely suppress the bistability region, while in other cases both lead to a still discontinuous transition with a shrinked but still finite bistability.' Thus in those datasets χ>0 for r<r_C, so the ng strategy does not generically 'transform' the process into a pairwise one. The abstract's unqualified phrasing ('effectively transforming a higher-order contagion process into a pairwise one') and the reader's strongest claim overstate a dataset-dependent outcome. The conditional derivation is sound, but the antecedent is not established beyond specific cases.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies SIS contagion on static hypergraphs with two risk-based adaptive strategies (nn and ng) that reduce node transmission/reception rates λ_i(t) when local infectious neighbors/groups are present. Using individual-based mean-field equations and Monte Carlo simulations on empirical and synthetic hypergraphs, the authors show: (i) for pairwise contagion, the adaptive strategies do not shift the epidemic threshold (Eq. 5), a result derived by linearization; (ii) for higher-order nonlinear contagion, adaptation shrinks the bistability region and can, on the hospital dataset, completely eliminate it—making the transition continuous at the pairwise threshold. The mechanism is quantified by χ_e^{i_e>1}, the probability that a hyperedge with a susceptible node contains >1 infected; the Appendix gives a conditional reduction to pairwise dynamics when χ≈0. The SM shows the complete suppression is dataset-dependent, with some empirical hypergraphs retaining a finite bistable region under ng.","tokens_in":30563,"tokens_out":11427,"duration_ms":121520,"significance":"The paper's pairwise threshold equality is a clean, exact linearization result and is a useful reference for adaptive SIS models. The higher-order result—that local awareness can defuse the non-linear group contagion responsible for explosive transitions—is interesting and well-supported by the IBMF/simulation agreement on LH10. The χ diagnostic is a valuable tool for quantifying when higher-order effects are suppressed. The conditional analytical reduction (Eq. 23) is a strength, but its antecedent is only verified numerically for one dataset; the SM's explicit counterexamples mean the 'transforming into a pairwise one' language overstates the generality. With appropriate qualification the paper would be a solid contribution to the adaptive higher-order contagion literature.","major_comments":[{"comment":"The abstract's 'effectively transforming a higher-order contagion process into a pairwise one' and the main text's 'Strikingly, the ng strategy completely neutralizes the bistability regime...' are stated without dataset qualification. SM Section II explicitly reports that 'for some datasets both nn and ng strategies completely suppresses the bistability region, while in other cases both lead to a still discontinuous transitions with a shrinked but still finite bistability.' Thus the ability of ng to make χ_e^{i_e>1}=0 for all r<r_C^{NAD,p} is not a general property of the strategy; it holds only for the hospital dataset shown. The 'transforming into a pairwise one' language should be made conditional, e.g., 'in cases where the strategy drives χ to zero,' and the abstract should be aligned with the SM's dataset-dependent outcome.","section":"Abstract; Results (discussion of Fig. 2b and Fig. 3c)"},{"comment":"The analytical reduction is a conditional statement: if χ_e^{i_e>1}≈0, then near r_C the higher-order mean-field equations reduce to the pairwise ones (Eqs. 23–26). The paper does not prove that the ng strategy realizes this condition; the only evidence is the IBMF integration and simulations for LH10 (Fig. 3c). Since the SM shows counterexamples on other empirical hypergraphs, the mechanism by which ng 'transforms' the process is incomplete. I ask the authors to either provide an analytical argument bounding χ under ng (e.g., via the linearized equations for the multi-infected probability) or to explicitly frame the pairwise equivalence as a dataset/strategy-dependent phenomenon rather than a property of ng.","section":"Appendix, 'From higher-order transition to a pairwise one' (Eq. 23)"},{"comment":"The sentence 'for adaptive strategies efficient enough to make χ_e^{i_e>1}=0 ∀e for all r<r_C^{NAD,p}, such as the ng strategy' is contradicted by the SM's observation that ng does not always achieve this. Even though the main text focuses on LH10, the phrase 'such as the ng strategy' reads as a general claim. This should be reformulated to 'such as the ng strategy on the datasets considered here' or, more precisely, 'when the strategy succeeds in making χ=0.' Otherwise the reader is left with an internal inconsistency between the main text and the SM.","section":"Main text, paragraph after Fig. 3"}],"minor_comments":[{"comment":"The definition of β_i^e(i_e,ν) contains garbled notation ('λ0iν e'). Please clarify the exponent structure and show explicitly how it reduces to the prefactor λ0 λ_i(t)(λ_j(t)/λ0)^ν used in Eq. (24) for i_e=1.","section":"Contagion models, Eq. (4)"},{"comment":"The abstract states that 'adaptive mechanisms based on local (pairwise or group-based) risk perception impact only the endemic state, without affecting the epidemic phase transition' for pairwise contagion. This is a general statement, but only the nn and ng mechanisms are studied here; please qualify it to 'the mechanisms considered.'","section":"Abstract"},{"comment":"Supp. Fig. 2 uses θ=0 for the ng strategy, while the main text uses θ=0.3. The caption should explain this choice or explicitly state that the local-impact quantification is done at θ=0 for that figure.","section":"SM Section II, Supp. Fig. 2"},{"comment":"Several important details and extensions are deferred to the companion paper [45], which is listed as 'In preparation.' Please indicate clearly which results in the present manuscript are self-contained, since the reader cannot access [45].","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely to be of interest to the higher-order contagion community, but the abstract and main text overstate the generality of the ng-induced pairwise equivalence; this is internally contradicted by the SM. The authors should qualify the claims and possibly adjust the title/abstract. The dependence on the unpublished companion paper [45] for key strategy variants is also a concern for a stand-alone publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this paper is worth a serious referee. It shows that risk-based adaptive behaviors (neighbor-based nn and group-based ng) leave the pairwise epidemic threshold untouched but can shrink or even eliminate the bistable explosive transition in higher-order contagion, with a clear mechanism: adaptation suppresses hyperedges containing multiple infected individuals. That's a genuinely new organizing result, and the support is strong.\n\nThe strongest part is the analytical result for pairwise contagion. The proof that the threshold equals 1/Λ_w for both adaptive strategies is a direct linearization, not a fit. For the higher-order case, the authors use IBMF and stochastic simulations across six empirical and many synthetic hypergraphs, and the agreement is good. The χ-statistic (probability a susceptible-containing hyperedge has >1 infected) is a nice explanatory tool: when adaptation drives χ to zero, the nonlinear group terms vanish and the dynamics reduce to pairwise near criticality. The reduction is derived conditionally in the appendix (Eq. 23) and then checked numerically.\n\nNow the soft spots, in roughly increasing order of importance.\n\nFirst, no code is released. The datasets are public, but the IBMF solver is not, which limits reproducibility.\n\nSecond, the paper fixes θ=0.3 and ν=4; other values are deferred to a companion paper. That's fine for a first report, but it means we don't know how robust the 'complete suppression' is to parameter changes.\n\nThird, the claim in the abstract that ng 'effectively transforms a higher-order contagion process into a pairwise one' is too strong. The appendix's reduction is conditional on χ_e^{i_e>1}≈0, and that condition is not proven analytically. More tellingly, the SM itself states that in some empirical hypergraphs both nn and ng still leave a discontinuous transition with a finite (though shrunk) bistability region. So ng does not always neutralize bistability; it depends on the structure. The main text does include the caveat that the equivalence applies only for r≤r_C^{NAD,p}, but the abstract and the 'Strikingly' sentence in the results overgeneralize the hospital-dataset result.\n\nNone of this undermines the core finding—adaptive behaviors generically shrink bistability and can eliminate it when χ drops to zero. What needs fixing is the phrasing, and ideally a sharper condition for when χ=0 actually holds.\n\nWho is this for? Anyone working on higher-order contagion, adaptive networks, or epidemic phase transitions. It's a solid contribution that deserves peer review; with a revised abstract and a more careful statement of when 'pairwise-equivalence' happens, it should be publishable. I'd bring it to the reading group.","headline":"A solid study of adaptive risk perception in higher-order contagion, with a clean pairwise threshold result and a conditional higher-order suppression; the 'transform to pairwise' claim outruns the data.","tokens_in":31046,"tokens_out":3136,"would_cite":true,"duration_ms":34774,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["05C82","92D30"],"pacs":["89.75.Hc"],"model":"deepseek-v4-flash","headline":"When individuals adapt their behavior to perceived infection risk, the explosive, bistable transition characteristic of higher-order group contagion can be completely neutralized, leaving a continuous phase transition with the same epidemic","keywords":["higher-order contagion","hypergraphs","adaptive behavior","bistability","discontinuous phase transition","SIS epidemic model","risk perception","mean-field approximation"],"falsifier":"Simulate the ng strategy on a hypergraph with strong within-group infection-state correlations (e.g., by adding a small infection bias to group members of infected individuals) and measure, at r < r_C^{NAD,p}, the stationary probability that a hyperedge with a susceptible node contains two or more infected individuals; if this probability is clearly above zero while the phase diagram still shows a discontinuous jump, the conversion-to-pairwise mechanism is not universal. Equivalently, look for any empirical dataset where the ng strategy leaves a nonzero bistability width.","tokens_in":30181,"feed_emoji":"🦠","tokens_out":6278,"duration_ms":62240,"temperature":0.7,"pith_summary":"This paper asks what happens when people adjust their behavior based on perceived infection risk during a contagion that spreads through group interactions as well as pairwise contacts. In a standard pairwise (link-based) epidemic model, such adaptive behaviors change the endemic prevalence but leave the continuous phase transition and its threshold untouched. In contrast, for a higher-order (group-based) contagion process—where infection probability is nonlinear in the number of infected group members—risk-driven adaptation shrinks the bistability region and the size of the discontinuous jump, and can eliminate both entirely. The central result is that a group-aware strategy, which makes an individual reduce exposure whenever a group they belong to contains a risky number of infected members, converts the higher-order process into an effectively pairwise one below the pairwise threshold, restoring a continuous transition at the pairwise critical rate. A sympathetic reader would care because it identifies a concrete mechanism—suppressing groups with more than one infected member—by which behavioral flexibility can defend against explosive outbreak dynamics.","feed_headline":"Adaptive behavior can erase explosive group-contagion transitions","feed_subtitle":"Under a group-aware risk strategy, the bistable window vanishes and the outbreak threshold matches ordinary pairwise spread.","key_machinery":"The central object is χ_e^{i_e>1}, the probability (in the asymptotic stationary state) that a hyperedge containing at least one susceptible node has more than one infected member; this quantity controls how often the nonlinear, reinforcement-driven group contagion events occur. The argument runs through individual-based mean-field (IBMF) equations for the infection probabilities P_i(t), in which the awareness functions f_i^{nn}(t) and f_i^{ng}(t) enter as exponential reductions of the per-node transmission/susceptibility parameters λ_i. Two analytic results carry the weight: (i) a linear-stability analysis of the absorbing state shows that adaptive strategies leave the Jacobian unchanged at","core_discovery":"The paper establishes that for an SIS process on a hypergraph with nonlinear group reinforcement (infection probability within a hyperedge scaling as the ν-th power of average infected-node transmission rates), the discontinuous phase transition and bistable regime are driven by hyperedges containing more than one infected individual. Adaptive behaviors reduce transmission rates of both susceptible and infected individuals locally, via λ_i(t)=λ_0 e^{-f_i(t)}, with awareness f_i based either on the number of infectious neighbors (nn) or the number of 'infectious groups' perceived by i (ng, where a group counts as infectious if its infected members exceed a threshold fraction θ of the group).","pith_inferences":["A testable extension is to track χ_e^{i_e>1} in real-time during an outbreak: the prediction is that under an effective group-aware strategy, the population should rarely (if ever) observe groups containing more than one infected member while prevalence is below the pairwise critical value.","The mechanism suggests a design principle for intervention: interventions that specifically break up 'multi-infection groups' (e.g., capping group sizes, discouraging mixing within groups when one member is infected) may convert explosive dynamics into smooth ones even without global awareness.","If correlations between infection states within hyperedges persist (e.g., due to temporal clustering in empirical contact patterns), the χ≈0 assumption could fail; one could test this by time-resolved analysis of the hospital data in the regime where ng yields a continuous transition.","The result may transfer to other higher-order dynamical processes (opinion dynamics, adoption cascades) where nonlinear reinforcement drives bistability; behavioral adaptation based on group-level information could analogously suppress tipping cascades."],"forward_implications":["In pairwise SIS contagion, adaptive behaviors based on local risk perception do not shift or alter the continuous epidemic phase transition; they only reduce the endemic prevalence.","In higher-order contagion, both the 'infectious neighbors' (nn) and 'infectious groups' (ng) strategies shrink the bistability region; the ng strategy can eliminate it entirely, making the transition continuous at the pairwise threshold r_C = 1/Λ_w.","The upper boundary of the bistability region is invariant under these adaptive strategies because the stability of the disease-free state is determined solely by pairwise interactions.","The suppression of the transition is mediated by the reduction of the probability χ_e^{i_e>1} that a group containing a susceptible node has multiple infected members; when this probability vanishes below the pairwise threshold, higher-order effects are replaced by pairwise ones.","These findings hold across several empirical face-to-face interaction hypergraphs and a range of synthetic hypergraphs, including ones with tunable hyperdegree heterogeneity and hyperedge overlap."],"fun_headline_variants":["Cautious crowds tame explosive group contagion","Group-aware caution quashes bistable epidemic jumps","Adaptive behavior flattens higher-order contagion spikes","Risk perception suppresses discontinuous outbreak transitions"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The proof that the higher-order process becomes pairwise near criticality assumes that a hyperedge containing a susceptible node has at most one infected member (χ_e^{i_e>1}≈0); this is checked numerically and via mean-field integration rather than proven rigorously, and if correlations kept multi-infected groups common under adaptation, the suppression could be incomplete.","fun_headline_variants_meta":{"raw":{"variants":["Cautious crowds tame explosive group contagion","Group-aware caution quashes bistable epidemic jumps","Adaptive behavior flattens higher-order contagion spikes","Risk perception suppresses discontinuous outbreak transitions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000209,"raw_usage":{"total_tokens":1214,"prompt_tokens":685,"completion_tokens":529,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":429,"completion_tokens_details":{"reasoning_tokens":471}},"tokens_in":429,"tokens_out":529,"duration_ms":6345,"temperature":1.0,"reasoning_tokens":471,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T11:32:00.206549+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the ng strategy on a hypergraph with strong within-group infection-state correlations (e.g., by adding a small infection bias to group members of infected individuals) and measure, at r < r_C^{NAD,p}, the stationary probability that a hyperedge with a susceptible node contains two or more infected individuals; if this probability is clearly above zero while the phase diagram still shows a discontinuous jump, the conversion-to-pairwise mechanism is not universal. Equivalently, look for any empirical dataset where the ng strategy leaves a nonzero bistability width.","supporting_citations":[],"review_version":1}