{"id":"c433fd98-1192-4181-beb9-d7734e97864c","arxiv_id":"2506.19655","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"In simulated classrooms, trust relationships determine whether students accurately perceive an AI assistant's proficiency: allies-only networks converge correctly unless a single partisan dissenter is present, while opponents-only networks converge to mostly wrong beliefs.","lead":"This paper simulates how students' trust relationships shape their opinions about an AI assistant's skill. It finds that high-trust classrooms converge on the true skill unless one stubborn, wrong student destabilizes everyone, while low-trust classrooms settle on confident but often incorrect beliefs.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'indefinitely' in the single-partisan disruption claim is extrapolated from T=10^4 runs; finite-time nonconvergence has not been distinguished from slow convergence, so the central claim needs a longer-run or stability check.","rationale":"The reader's weakest assumption focuses on external realism: full transparency, static and symmetric trust, and ternary relationships. That is a legitimate limitation, but it is not the most load-bearing threat to the central claim. Even if every modeling assumption is granted, the headline result that one incorrect partisan causes indefinite vacillation is supported only by truncated simulations. The paper's own definitions of asymptotic learning and consensus (Eqs. 7–8) are threshold-based and checked over finite windows, so 'indefinitely' is a strong quantitative statement that outruns the evidence. A longer-run test or an analysis of the underlying stochastic map would settle whether the observed nonconvergence is a genuine asymptotic property or a long-lived transient. This concern reinforces the reader's CONDITIONAL verdict rather than changing it: the model is coherent and the simulations are internally consistent, but the most striking claim needs stronger verification before the paper's conclusions can be relied upon.","tokens_in":31416,"tokens_out":5736,"duration_ms":73307,"concrete_test":"Re-run the Section 4.1 allies-only complete-network configuration (n=10, k=1, θp=0.3, θAI=0.8, μ=0.25) for at least 100 seeds with T=10^6, and compute the Eq. (8) residual at log-spaced checkpoints for every agent. If the residual envelope decays (e.g. approximately as t^-α) and crosses ε=0.01 for all agents before T, the 'indefinite vacillation' claim is refuted and the result reduces to a slow transient; if the residual remains bounded away from zero across all seeds, the finite-run evidence is corroborated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's most load-bearing claim is that one partisan with θp≠θAI makes all students' beliefs vacillate indefinitely between θp and θAI (Abstract and Section 4.1). The support for 'indefinitely' is finite-time nonconvergence in simulations truncated at T=10^4, e.g. Fig. 4 top-left and Section 5.3. No stability or spectral analysis of the update map in Eqs. (1)–(6) is provided, and no run lengths are reported that would separate true nonconvergence from convergence on a timescale much longer than 10^4. The convergence criterion Eq. (8) with ε=0.01 and τmax=99 is only checked within the run; a slowly drifting bimodal PDF could satisfy it for long windows and still fail later. Because the entire 'single obdurate student disrupts the classroom' narrative depends on this extrapolation, the central claim is not yet established by the numerical evidence. This is an internal-model concern: even granting full-transparency, static, symmetric trust networks, the model has not been shown to produce the claimed indefinite vacillation rather than a very long transient.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a multi-agent Monte Carlo model of opinion dynamics in which students form probabilistic beliefs about the proficiency of an AI assistant. Beliefs update via a two-step rule: a Bayesian update from the student's own assessment scores (if the student is an AI-user) and a non-Bayesian linear peer-pressure step that moves beliefs toward the PDFs of trusted allies and away from those of mistrusted opponents (Eqs. 1-6). The authors simulate allies-only, opponents-only, and mixed networks of size n=10, and also larger networks (n=100 to 1000), with and without partisan students or a partisan teacher. The main reported findings are: in allies-only networks all students eventually infer the AI proficiency theta_AI, with AI-avoiders reaching asymptotic learning faster than AI-users; in opponents-only networks a minority infer theta_AI correctly, with a small AI-user advantage; in mixed networks turbulent nonconvergence and intermittency occur; and a single partisan with an incorrect belief theta_p != theta_AI causes persistent vacillation in allies-only networks, described in the abstract as 'indefinite'. The paper concludes with tentative educational policy implications.","tokens_in":31656,"tokens_out":6038,"duration_ms":62444,"significance":"If the central claims hold, the paper offers a striking and counterintuitive result: in a high-trust classroom, one stubbornly misinformed student can prevent the whole cohort from converging on the true proficiency of an AI tool, despite repeated direct evidence. The finding extends the authors' prior media-bias model to an educational context and adds a new, emergent result (AI-avoiders learning faster than AI-users). The model is clearly specified, the simulation methodology is transparent, and the authors are honest about many limitations, explicitly deferring various generalizations. However, the most important claim ('indefinitely' vacillation) rests on finite-horizon simulations only, and at least one numerical result is internally contradictory; these issues currently prevent the paper from establishing its headline conclusions at the level of rigor expected for a physics journal.","major_comments":[{"comment":"The claim that a single partisan with theta_p != theta_AI makes students' beliefs 'vacillate indefinitely' between theta_p and theta_AI is not established by the simulations, which are truncated at T=10^4. The convergence criterion in Eq. (8) with tau_max=99 can be satisfied for long windows by a slowly drifting bimodal PDF, so the observed nonconvergence within the run does not rule out convergence on a longer timescale. The paper should either provide a longer-run stability analysis (e.g., T=10^6, or a spectral/Lyapunov analysis of the update map in Eqs. (1)-(6)) or soften the wording to 'over the simulation horizon' in the abstract and conclusions.","section":"Abstract and Section 4.1"},{"comment":"There is a direct contradiction between the text and the caption of Figure 6 regarding AI-avoiders in large allies-only networks. The text states that AI-avoiders achieve asymptotic learning with ta in the range 49.3 to 66.7 for n=200, while the caption states that AI-avoiders are not plotted because all AI-avoiders fail to achieve asymptotic learning by t=T=10^4. This inconsistency undermines the claimed persistence of the AI-avoider learning-time advantage in larger networks and must be resolved before the large-network results can be accepted.","section":"Section 5.1 and Figure 6"},{"comment":"The choice mu=0.25 is stated 'without loss of generality', but no sensitivity analysis over mu is provided. Since mu controls the strength of peer pressure relative to direct observation, the qualitative outcomes (notably turbulent nonconvergence and the relative learning times of AI-users and AI-avoiders) may depend on mu. Please either demonstrate insensitivity across the allowed range 0<mu<=0.5, or cite a previous systematic study that establishes the robustness of these specific results to mu.","section":"Section 2.2, Eq. (5)"}],"minor_comments":[{"comment":"The prior beliefs are only described as 'randomized', without specifying the distribution (e.g., uniform over the simplex, Dirichlet, etc.). This hampers reproducibility; please specify the prior generation procedure.","section":"Section 3.1"},{"comment":"The sentence 'For example, for n=1, the histogram peaks at ta...' should read 'for k=1' (since n=10 throughout that experiment); as written it is confusing.","section":"Section 3.1, text near Fig. 1"},{"comment":"The statement that 'we do not observe that the modal ta decreases monotonically with k' is unsupported, because the reported partisan simulations use only k=1; no variation of k is presented in that subsection.","section":"Section 4.1, paragraph on the second suite of tests"},{"comment":"The observation that for theta_p=theta_AI in a Barabasi-Albert network with n=1000 no agent achieves asymptotic learning within T=10^4 appears to contradict the small-network result where a correct partisan accelerates learning; the paper defers longer runs but gives no explanation for the discrepancy, leaving the reader to wonder whether the timescale for larger networks simply exceeds T or whether the qualitative behavior differs.","section":"Section 5.3, bottom right panel"},{"comment":"The violin plots in Fig. 2 show distributions of differences in asymptotic learning time; it would be helpful to state explicitly how many simulations had undefined differences (e.g., when no student reaches the right or wrong conclusion), and how those cases are handled in the plot.","section":"Section 3.2, top right panel description"}],"recommendation":"major_revision","confidential_remarks":"The paper is closely based on the authors' previous media-bias model, especially Ref. [31]; the authors are candid about this, but the incremental novelty should be highlighted more clearly in the introduction and conclusion. The 'indefinitely' wording in the abstract and conclusions is the kind of strong claim that invites scrutiny; even if the authors cannot provide an analytic proof, a statement of the finite-horizon nature of the result, together with a more extensive numerical exploration (e.g., longer runs or a scaling analysis), would substantially strengthen the paper. The contradiction in Section 5.1/Fig. 6 must be fixed before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing you should know: this is not a new model. It is the same probabilistic opinion-dynamics framework the authors used in their media-bias papers (Refs [29-31]), re-parameterized for students estimating an AI tool's proficiency. What's new is the application and the domain-specific findings: AI-avoiders asymptotically learn faster than AI-users in allies-only networks, the learning-time asymmetry scales with the number of AI-users, and a single obdurate partisan with a wrong belief appears to prevent convergence altogether. Those are genuinely emergent results, not just relabeled old ones. The AI-avoider result has a nice mechanistic explanation (network averaging reduces fluctuations), and the authors are appropriately cautious about the idealized assumptions throughout.\n\nThat said, the central \"indefinitely\" claim in the abstract and Section 4.1 is on shakier ground than the text suggests. The evidence is finite-time nonconvergence over T=10^4 steps, with no stability analysis of the update map and no longer runs to separate true nonconvergence from a transient on a much longer timescale. A slowly drifting bimodal distribution could satisfy the convergence criterion Eq. (8) over τ_max=99 and still change later. This is an internal-model concern; it doesn't require the full-transparency or static-network assumptions to bite. I'd want the authors to either soften the language to \"for simulated times up to T=10^4\" or provide a spectral or Lyapunov argument. This is the one load-bearing claim that deserves extra scrutiny.\n\nOther soft spots are minor by comparison. μ=0.25 is asserted \"without loss of generality\" but never varied; the prior distribution is described only as \"randomized\"; no code or data are provided, which is a bit frustrating given the storage concerns are discussed but not resolved. And yes, the partisan-disruption result is carried over from the authors' Ref [31] — but they cite it clearly, and the educator-specific version (AI-skeptic vs AI-promoter teachers, smaller vs larger networks) is new enough to stand on its own.\n\nThe paper is honest about its limitations and the simulations are internally consistent. The educational context gives the findings a practical hook, but I wouldn't treat them as policy-ready. Who's it for: people in opinion dynamics wanting a new application, and educators or social scientists interested in how peer networks mediate AI adoption. A serious referee should see it, but I'd ask for the convergence claim to be tightened, μ and prior sensitivity analysis, and a code/data release. If those are addressed, it's publishable.","headline":"Solid reapplication of the authors' opinion-dynamics framework to AI proficiency perceptions, but the key 'indefinite disruption' claim needs longer runs or a stability argument.","tokens_in":32206,"tokens_out":2521,"would_cite":false,"duration_ms":28480,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Trust networks, not just test scores, decide whether students perceive an AI assistant's proficiency correctly, and one stubbornly wrong student can prevent a class from ever converging on the truth.","keywords":["opinion dynamics","perceived AI proficiency","trust networks","multi-agent simulation","Bayesian learning","partisans","asymptotic learning","AI in education"],"falsifier":"Take a real ten-person study group where everyone shares probabilistic beliefs openly and one planted participant never changes a wrong estimate of the AI tool's proficiency; if the group's averaged belief converges to the AI's true proficiency rather than vacillating indefinitely, the paper's main nonconvergence claim is contradicted.","tokens_in":31177,"feed_emoji":"🤖","tokens_out":6871,"duration_ms":79439,"temperature":0.7,"pith_summary":"The paper argues that what students believe about an AI assistant's proficiency is shaped as much by who they trust as by the scores they actually receive. Using Monte Carlo simulations of a probabilistic opinion-dynamics model, it claims that in an all-allies classroom everyone eventually infers the true proficiency $\theta_{\\rm AI}$, that students who do not use AI converge faster than those who do, and that adding a single stubbornly wrong student destroys convergence entirely, leaving everyone's beliefs vacillating indefinitely between the true value and the partisan's value. In low-trust classrooms the opposite holds: everyone settles down, but only a minority lands on the truth. Mixed trust networks produce turbulent nonconvergence and intermittency that depend delicately on network wiring. These results matter because perceived proficiency drives AI adoption, and the model predicts that equal access to the tool is not enough to guarantee accurate shared judgments.","feed_headline":"One stubborn wrong student freezes a class's AI judgment","feed_subtitle":"Simulations show that who students trust, not just their own grades, determines whether they learn the AI's true proficiency.","key_machinery":"Each student's belief is a probability density function $x_i(t,\\theta)$ over a discretized proficiency axis $\\theta\\in\\{0,0.05,\\dots,1\\}$. At every time step the belief is updated in two steps: first, AI-users apply Bayes's theorem to their assessment score, whose Gaussian likelihood is centered on the true $\\theta_{\\rm AI}$; second, all students share their PDFs and mix them linearly through the trust matrix $A_{ij}\\in\\{+1,0,-1\\}$, which pulls a student's belief toward allies and pushes it away from opponents via the average deviation $\\Delta x'_i(t+1/2,\\theta)$, with learning rate $\\mu=0.25$ and renormalization. A partisan is a node whose PDF is fixed at a single value $\\theta_{\\rm p}$. The results come from the competition between the multiplicative Bayesian evidence step and the additive trust-mixing step: a fixed wrong node acts as a permanent source of attraction that direct evidence cannot erase, while opponents-only networks stabilize because repulsion cancels information flow rather than amplifying it.","core_discovery":"The central claim is that perceived proficiency of an AI tool is a socially emergent quantity, not merely an individual inference from direct evidence. Under the model's update rule, an allies-only network converges to the correct $\theta_{\\rm AI}=0.8$ for all students, with AI-avoiders reaching asymptotic learning faster than AI-users because they rely on the network-averaged belief, which fluctuates less than individual scores. However, one partisan student holding a fixed wrong belief $\\theta_{\\rm p}\\neq\\theta_{\\rm AI}$ makes every other student's belief bimodal and nonconvergent, even though AI-users observe repeated direct evidence. In opponents-only networks all students reach asymptotic learning, yet only a minority (about 16 percent in the simulations) correctly infer $\theta_{\\rm AI}$, and AI-users hold a small but real advantage over AI-avoiders. Mixed networks can leave some students never settling, some alternating between stable and unstable phases, and the long-term outcome depends sensitively on the pattern of trust relationships; these qualitative patterns persist in networks up to about 1000 students.","pith_inferences":["If these simulations transfer to real classrooms, publishing independent, unbiased proficiency benchmarks is a necessary but not sufficient remedy: the model implies that one respected wrong voice can outweigh abundant evidence.","The AI-avoiders-learn-faster result suggests a possible second-mover advantage in AI adoption, where students who watch peers' outcomes rather than experimenting directly may form more stable judgments; the paper does not test this adoption implication directly.","A natural, untested extension is to relax full transparency: if students share only summaries of their beliefs rather than complete PDFs, or if trust relationships evolve over time, the partisan disruption could weaken or strengthen; that is an inference beyond the paper's assumptions.","The same machinery could apply to any educational resource whose quality is inferred socially, such as textbooks, but only when students consult it in an oracular way; the paper itself flags this boundary condition."],"forward_implications":["In an allies-only classroom with no partisans, all students eventually learn the AI tool's true proficiency, and AI-avoiders learn it faster than AI-users.","A single stubbornly wrong student or teacher is sufficient to stop the whole network from reaching a settled opinion, even when abundant direct evidence about the true proficiency is available.","In low-trust environments, students reach stable but often wrong conclusions, with only a minority identifying the true proficiency and AI-users enjoying a slight edge over AI-avoiders.","Mixed trust networks can produce individuals who never converge, or who alternate between stable and unstable phases, so the same AI tool can be judged accurately by some students and inaccurately by others within one class.","The main qualitative results persist in larger networks up to about 1000 students, and a partisan teacher allied with everyone is more influential in large sparse networks than in small dense ones."],"supporting_citations":[{"why":"Supplies the probabilistic, linear trust-network opinion-dynamics model with belief PDFs that this paper adapts from media-bias settings to education.","marker":"[29]"},{"why":"Supplies the phenomena of turbulent nonconvergence and intermittency in mixed trust networks, which the paper reproduces for AI-proficiency opinions.","marker":"[30]"},{"why":"Supplies the partisan implementation and the key result that a single obdurate partisan destabilizes an allies-only network of probabilistic learners.","marker":"[31]"},{"why":"Provides the deterministic bounded-confidence mixing model whose probabilistic generalization underlies the linear update rule in Eq. (5).","marker":"[32]"},{"why":"Underpins the single-partisan disruption idea in the voter-model literature, which motivates the paper's study of one partisan in a classroom network.","marker":"[62]"},{"why":"Cited as the social-science analogy for AI-avoiders learning faster: averaging many people's expectations can be more accurate than relying on one's own noisy score.","marker":"[58]"}],"fun_headline_variants":["Trust networks, not just grades, steer AI skill views","One partisan peer wrecks a class's AI judgment","Peer trust can override direct evidence on AI proficiency","Even one stubborn student derails AI learning in class","Who you trust decides if you trust AI in school"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predictions all rest on the assumption that students openly share their complete probability distributions with fixed, symmetric, ternary trust relations; if real students communicate only summaries, hide beliefs, or change whom they trust, the nonconvergence and learning-time results may not appear.","fun_headline_variants_meta":{"raw":{"variants":["Trust networks, not just grades, steer AI skill views","One partisan peer wrecks a class's AI judgment","Peer trust can override direct evidence on AI proficiency","Even one stubborn student derails AI learning in class","Who you trust decides if you trust AI in school"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000178,"raw_usage":{"total_tokens":1367,"prompt_tokens":1087,"completion_tokens":280,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":703,"completion_tokens_details":{"reasoning_tokens":204}},"tokens_in":703,"tokens_out":280,"duration_ms":3868,"temperature":1.0,"reasoning_tokens":204,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T23:05:48.175787+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a real ten-person study group where everyone shares probabilistic beliefs openly and one planted participant never changes a wrong estimate of the AI tool's proficiency; if the group's averaged belief converges to the AI's true proficiency rather than vacillating indefinitely, the paper's main nonconvergence claim is contradicted.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the probabilistic, linear trust-network opinion-dynamics model with belief PDFs that this paper adapts from media-bias settings to education."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the phenomena of turbulent nonconvergence and intermittency in mixed trust networks, which the paper reproduces for AI-proficiency opinions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the partisan implementation and the key result that a single obdurate partisan destabilizes an allies-only network of probabilistic learners."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Cited as the social-science analogy for AI-avoiders learning faster: averaging many people's expectations can be more accurate than relying on one's own noisy score."}],"review_version":1}