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1base_model: Qwen/Qwen3-32B
2gate_mode: hidden
3dtype: bfloat16
4
5experts:
6 - source_model: Qwen/Qwen3-32B
7 positive_prompts:
8 - "Consider the ∞-topos Sh_∞(X) of ∞-sheaves on a topological space X = K(π, 2) where π = Z/3Z × Z/3Z. Let F: Sh_∞(X) → Spaces be the global sections functor and G: Sh_∞(X) → Spaces be the functor of compactly supported cohomology with coefficients in the sphere spectrum. Compute the homotopy type of the mapping space Map_Fun(Sh_∞(X),Spaces)(F, G) in the ∞-category of functors, and determine π_2 of this mapping space."
9 - "Let C be the dg-nerve of the A_∞-category of twisted complexes over the Fukaya category of T^4 with its standard symplectic structure. Consider the Yoneda embedding y: C → Fun(C^op, Ch_k) where Ch_k is the dg-category of chain complexes over a field k of characteristic 2. Define the weighted colimit ∫^A y(A) ⊗ Hom_C(-, A) as a functor C^op → Ch_k. Calculate the Hochschild homology HH_*(∫^A y(A) ⊗ Hom_C(-, A)) and identify its E_2-algebra structure."
10 - "Let Span_2(Gpd_fin) be the (∞,2)-category of spans of finite groupoids. Consider the lax 2-functor F: Span_2(Gpd_fin) → 2Vect_C given by taking groupoid algebras and the strict 2-functor G: Span_2(Gpd_fin) → 2Vect_C given by linearization of the correspondence category. Compute the homotopy fiber of the natural transformation α: F ⇒ G over the object BZ/5Z × BZ/5Z, where the transformation is induced by the canonical comparison map. Express your answer as a 2-groupoid and determine its π_0 and π_1."
11 - "Consider the cyclotomic spectrum THH(BP⟨2⟩) with its natural S^1-action, where BP⟨2⟩ is the truncated Brown-Peterson spectrum. Let F = (THH(BP⟨2⟩)^{hC_p})^{tC_{p^2}} and G = (THH(BP⟨2⟩)^{tC_p})^{hC_{p^2}} be two different mixed Tate-homotopy fixed point constructions for p = 3. The canonical comparison maps induce a diagram in the stable ∞-category. Calculate the cofiber of the natural map F → G, identify it as a wedge of suspensions of Eilenberg-MacLane spectra, and determine the complete list of suspension degrees that appear."
12 - source_model: LLMcompe-Team-Watanabe/Qwen3-32B-openmathreasoning-sft
13 positive_prompts:
14 - "A double pendulum consists of two identical masses m connected by rigid, massless rods of equal length L. The upper rod is pivoted at a fixed point, and the lower rod is pivoted at the first mass. The system starts from rest with both rods horizontal and aligned (pointing in the same direction). After release, when the upper rod first becomes vertical (pointing downward), the kinetic energy of the system is K₁. When both rods first become vertical and aligned (both pointing downward), the kinetic energy is K₂. What is the ratio K₁/K₂? Express your answer in terms of a simple fraction."
15 - "A hollow cylinder of mass M and radius R contains a point mass m that can slide freely along a diameter. The cylinder is placed on a horizontal surface with coefficient of static friction μ. Initially, the mass m is at the center of the cylinder. The cylinder is given an initial angular velocity ω₀ about its axis while the center of mass remains stationary. As the system evolves, the internal mass moves radially outward due to 'centrifugal force.' Find the critical value of μ (in terms of m, M, and no other parameters) such that the cylinder just begins to slip when the internal mass reaches the cylinder wall. Assume the cylinder rolls without slipping until this critical moment."
16 - "Let G be a graph. A vertex-pair selector of G is a function f: {1,2} → V(G) such that dist(f(1), f(2)) ≤ 2 in G. Consider the following Markov Chain N = N(G): The state space of N is the set of all vertex-pair selectors of G, and transitions are defined as follows: Given Nt = f, (1) pick i ∈ {1,2} u.a.r.; (2) pick v ∈ V(G) such that dist(v, f(3-i)) ≤ 2 u.a.r.; (3) set f'(i) = v and f'(3-i) = f(3-i); (4) Set Nt+1 = f'. We say a graph G is distance-regular if N(G) is irreducible and its stationary distribution π satisfies π(f) ∝ deg(f(1)) · deg(f(2)) for all vertex-pair selectors f. Which of the following is true?"
17 - "Let G = (V,E) be a connected graph. Define a triangle-configuration as a function t: {a,b,c} → V such that at least two of {t(a),t(b)}, {t(b),t(c)}, {t(c),t(a)} are edges in E. Consider the Markov chain T(G) with state space all triangle-configurations and transitions: Given state t, (1) pick x ∈ {a,b,c} u.a.r.; (2) let {y,z} = {a,b,c} \\ {x}; (3) pick vertex v such that at least one of {v,t(y)} or {v,t(z)} is an edge, u.a.r.; (4) set t'(x) = v, t'(y) = t(y), t'(z) = t(z). We say G is triangle-mixing if T(G) is ergodic and rapidly mixing (mixing time polynomial in |V|). Which condition guarantees that a graph is NOT triangle-mixing?"
18 - source_model: LLMcompe-Team-Watanabe/Qwen3-32B-textbookreasoning-UGPhysics-AoPsInstruct-sft
19 positive_prompts:
20 - "A patient presents with a novel gain-of-function mutation in the PIEZO1 mechanosensitive channel causing constitutive Ca²⁺ influx. Analysis reveals secondary upregulation of TRPV4 channels and altered phosphorylation of myosin light chain kinase. Given that red blood cells show 40% reduction in deformability index, endothelial cells exhibit 2.3-fold increase in VE-cadherin internalization rate, and plasma shows elevated sphingosine-1-phosphate (S1P) levels, calculate the expected change in transcapillary filtration coefficient (Kf,c) using the revised Starling equation. Consider the coupling between PIEZO1-mediated cortical actin reorganization and glycocalyx shedding kinetics."
21 - "In examining the epistemological foundations of Kantian synthetic a priori judgments versus Quinean holistic empiricism, construct a formal model using modal logic that demonstrates why the analytic-synthetic distinction collapses under scrutiny of mathematical physics. Specifically, show how gauge invariance in Yang-Mills theory challenges the notion of purely analytic truths by requiring that: (1) the fiber bundle structure over spacetime manifolds introduces non-trivial topological constraints, (2) the principle of local gauge symmetry emerges as both mathematically necessary and empirically contingent, and (3) the holonomy group classification bridges pure mathematics and physical observation. Resolve this tension using category-theoretic semantics."
22 - "A CRISPR-engineered organoid model combines human iPSC-derived cortical neurons with primary astrocytes harboring ApoE4/4 genotype. Under conditions of chronic intermittent hypoxia (8% O₂ for 8h/day), measure the spatiotemporal dynamics of tau hyperphosphorylation propagation using a modified Kermack-McKendrick model that incorporates: (1) prion-like tau seeding efficiency as a function of post-translational modifications at residues S396/S404, (2) ApoE4-mediated disruption of heparan sulfate proteoglycan internalization, (3) exosome-mediated trans-synaptic spread with direction-dependent transmission rates. Derive the basic reproduction number R₀ for pathological tau and predict the critical intervention window."
23 - "Analyze the hermeneutical implications of Gadamer's fusion of horizons (Horizontverschmelzung) when applied to the interpretation of Tang dynasty regulated verse (lüshi) by contemporary AI language models. Consider how the formal constraints of tonal parallelism and semantic couplets in classical Chinese poetry create what Ricoeur would call a 'surplus of meaning' that resists algorithmic reduction. Using Peirce's triadic semiotic framework, demonstrate why the indexical relationship between classical allusions (diangu) and their cultural referents cannot be fully captured by distributional semantics. Propose a neo-structuralist model that preserves both the archaeological and teleological dimensions of meaning."
24 - source_model: LLMcompe-Team-Watanabe/Qwen3-32B-merge-base2-math3-science3-submath05-med05-other1
25 positive_prompts:
26 - "Design a metamaterial cloaking device operating at 10 GHz using transformation optics. The cloak must render a cylindrical object of radius 5λ invisible to TM-polarized waves. Starting from the coordinate transformation r' = (b/(b-a))(r-a) for a < r < b, derive the required constitutive parameters εr, εθ, and μz as functions of position. Account for dispersion using a Drude-Lorentz model and calculate the scattering cross-section reduction when the metamaterial is implemented using split-ring resonators with Q-factor = 50. Determine the bandwidth over which the cloaking efficiency exceeds 90%, considering both material losses and discretization effects from the finite unit cell size (λ/20)."
27 - "A hypersonic waverider vehicle operates at Mach 8 at 30 km altitude. The leading edge uses ultra-high temperature ceramic (UHTC) composite of HfB₂-SiC-TaSi₂ with graded porosity from 5% to 35%. During atmospheric entry, the stagnation point reaches 2800 K with heat flux of 12 MW/m². Model the coupled aerothermochemical problem including: (1) non-equilibrium boundary layer with finite-rate surface catalysis, (2) oxidation kinetics forming a multilayer scale (HfO₂/SiO₂/Ta₂O₅), (3) thermal stress evolution considering CTE mismatch and creep above 0.6Tm. Calculate the critical thickness of the oxidation layer that triggers spallation and determine the vehicle's maximum survivable flight time."
28 - "Design an active noise control system for a turbofan engine (bypass ratio 9:1) using a ring of 32 actuators around the nacelle. The target is 15 dB reduction of the blade passage frequency (BPF) and its first two harmonics. Implement a distributed MIMO feedforward controller using the multichannel filtered-x LMS algorithm with leaky integration. Given that the acoustic field exhibits spinning modes (m,n) with azimuthal order m ≤ 15 and radial order n ≤ 3, derive the optimal actuator placement to minimize spatial aliasing. Account for flow effects (M = 0.3) on sound propagation and calculate the convergence rate considering the correlation between turbulence-induced reference signals. Determine the required sampling rate and filter length for stable adaptation."
29 - "A soft robotics gripper uses dielectric elastomer actuators (DEA) with a prestretched VHB 4910 membrane (λpre = 4) and compliant electrodes of carbon grease. The gripper must manipulate objects ranging from raw eggs (failure force 30 N) to steel bearings (weight 500 g). Model the electromechanical instability considering: (1) neo-Hookean hyperelasticity with Gent correction for strain-stiffening (Jm = 100), (2) Maxwell stress including fringing fields at electrode edges, (3) viscoelastic relaxation using a 5-element generalized Maxwell model, (4) dielectric breakdown following Weibull statistics. Design a charge-controlled actuation strategy that prevents pull-in instability while achieving 200% area strain. Calculate the gripper's specific energy density and compare with McKibben pneumatic actuators."1export HF_HUB_DOWNLOAD_TIMEOUT=120
2export HF_HUB_ETAG_TIMEOUT=120
3vllm serve weblab-llm-competition-2025-bridge/team-watanabe-4xQwen3-32B \
4 --tensor-parallel-size 4 \
5 --max-model-len 40960 \
6 ・・・max_completion_tokens: 36275