| query,label | |
| "What is the capital of France?",low | |
| "Who wrote Romeo and Juliet?",low | |
| "How many days are in a leap year?",low | |
| "What is the chemical symbol for Gold?",low | |
| "Who was the first president of the United States?",low | |
| "What is the largest ocean on Earth?",low | |
| "How many planets are in our solar system?",low | |
| "What color is the sky on a clear day?",low | |
| "What is the boiling point of water in Celsius?",low | |
| "Who painted the Mona Lisa?",low | |
| "What is the capital of Japan?",low | |
| "In what year did World War II end?",low | |
| "What is the currency of the United Kingdom?",low | |
| "What is the main ingredient in guacamole?",low | |
| "Who discovered penicillin?",low | |
| "What is the tallest mountain in the world?",low | |
| "What is the freezing point of water?",low | |
| "How many continents are there?",low | |
| "Who is the author of Harry Potter?",low | |
| "What is the capital of Canada?",low | |
| "What is the largest organ in the human body?",low | |
| "How many sides does a hexagon have?",low | |
| "What planet is known as the Red Planet?",low | |
| "What is the national animal of Australia?",low | |
| "Who invented the telephone?",low | |
| "What is the hardest natural substance on Earth?",low | |
| "What is the capital of Germany?",low | |
| "How many teeth does an adult human typically have?",low | |
| "What gas do plants absorb from the atmosphere?",low | |
| "Who wrote the Odyssey?",low | |
| "What is the chemical formula for water?",low | |
| "What is the capital of Italy?",low | |
| "How many states are there in the United States?",low | |
| "What is the primary language spoken in Brazil?",low | |
| "What year did the Titanic sink?",low | |
| "What is the speed of light in vacuum?",low | |
| "Who was the second president of the United States?",low | |
| "What is the capital of Spain?",low | |
| "What is the largest planet in our solar system?",low | |
| "How many rings are on the Olympic flag?",low | |
| "What instrument is used to measure temperature?",low | |
| "Who painted the Sistine Chapel ceiling?",low | |
| "What is the smallest country in the world?",low | |
| "What is the main component of natural gas?",low | |
| "What is the capital of Australia?",low | |
| "How many colors are in a rainbow?",low | |
| "What currency is used in Japan?",low | |
| "Who wrote Pride and Prejudice?",low | |
| "What is the atomic number of Carbon?",low | |
| "What is the capital of Egypt?",low | |
| "What is the square root of 64?",low | |
| "What is 15 multiplied by 4?",low | |
| "How many hours are in a day?",low | |
| "What is the freezing point of water in Fahrenheit?",low | |
| "What is 100 divided by 5?",low | |
| "Convert 5 kilometers to meters.",low | |
| "What is 20 percent of 150?",low | |
| "How many minutes are in 3 hours?",low | |
| "What is 9 squared?",low | |
| "What is 50 minus 18?",low | |
| "What does CPU stand for?",low | |
| "What does HTML stand for?",low | |
| "What does URL stand for?",low | |
| "What is a synonym for big?",low | |
| "What is the opposite of hot?",low | |
| "Define the word biology.",low | |
| "What does HTTP stand for?",low | |
| "What is the plural form of child?",low | |
| "What does RAM stand for in computing?",low | |
| "What is an antonym for bright?",low | |
| "Translate hello to French.",low | |
| "Capitalize the first letter of this word.",low | |
| "Spell check the word receive.",low | |
| "Say hello to the user.",low | |
| "Convert this string to uppercase.",low | |
| "Good morning, how are you?",low | |
| "What time is it right now?",low | |
| "Who is the current Prime Minister of the UK?",low | |
| "What is the capital of India?",low | |
| "What ocean lies between America and Europe?",low | |
| "What is the symbol for Sodium on the periodic table?",low | |
| "How many bones are in the human body?",low | |
| "What is the capital of Russia?",low | |
| "Who discovered gravity?",low | |
| "What is the longest river in the world?",low | |
| "What is the capital of China?",low | |
| "What is the main language spoken in Mexico?",low | |
| "What is the national currency of India?",low | |
| "Who wrote Hamlet?",low | |
| "What is the capital of South Korea?",low | |
| "What is the symbol for Iron?",low | |
| "What gas do humans exhale?",low | |
| "What is the capital of Brazil?",low | |
| "How many weeks are in a year?",low | |
| "What is the capital of Argentina?",low | |
| "What is the chemical symbol for Silver?",low | |
| "What is the capital of Turkey?",low | |
| "What is the boiling point of water in Fahrenheit?",low | |
| "What is the largest desert in the world?",low | |
| "What is the capital of South Africa?",low | |
| "Explain how a hash map works internally.",medium | |
| "Write a Python function to check if a string is a palindrome.",medium | |
| "What is the difference between TCP and UDP?",medium | |
| "How do I filter a Pandas dataframe by column values?",medium | |
| "Explain the concept of Dependency Injection in software design.",medium | |
| "Write a SQL query to find the top 5 highest paid employees.",medium | |
| "How does garbage collection work in Java?",medium | |
| "Explain the difference between process and thread in operating systems.",medium | |
| "Write a Python script to scrape table data from a webpage using BeautifulSoup.",medium | |
| "How do CSS flexbox alignment properties work?",medium | |
| "Explain how Git rebase differs from Git merge.",medium | |
| "Write a JavaScript function to debounce a user input event.",medium | |
| "What is the difference between REST and GraphQL APIs?",medium | |
| "How do I set up a CORS header in an Express.js backend?",medium | |
| "Explain the concept of virtual memory and paging in OS.",medium | |
| "Write a Dockerfile for a basic Node.js web application.",medium | |
| "How do Python decorators work under the hood?",medium | |
| "Explain how asymmetric encryption works using public and private keys.",medium | |
| "Write a Python function to compute the Fibonacci sequence using memoization.",medium | |
| "What is the difference between inner join and outer join in SQL?",medium | |
| "How do I handle file uploads in a FastAPI application?",medium | |
| "Explain the Model-View-Controller (MVC) architecture pattern.",medium | |
| "Write a Rust function to read a text file line by line.",medium | |
| "What is the difference between a stack and a queue data structure?",medium | |
| "How to implement a binary search algorithm in Python?",medium | |
| "Explain how HTTP/2 multiplexing works compared to HTTP/1.1.",medium | |
| "Write a C program to implement a singly linked list with insert and delete operations.",medium | |
| "How does the Event Loop work in Node.js?",medium | |
| "Explain the difference between abstract classes and interfaces in C#.",medium | |
| "Write a regex pattern to validate email addresses.",medium | |
| "How to set up JWT authentication in a Django REST Framework app?",medium | |
| "Explain how a B-tree index improves database search performance.",medium | |
| "Write a Python script to resize images in a directory using Pillow.",medium | |
| "What is the difference between synchronous and asynchronous I/O?",medium | |
| "How do I configure Nginx as a reverse proxy for a Gunicorn app?",medium | |
| "Explain the SOLID principles of object-oriented design with examples.",medium | |
| "Write a JavaScript function to deep clone an object.",medium | |
| "How to implement pagination in a PostgreSQL query using LIMIT and OFFSET?",medium | |
| "Explain how Redis pub/sub messaging works.",medium | |
| "Write a Bash script to monitor system CPU usage and log it to a file.",medium | |
| "What is the difference between microservices and monolithic architecture?",medium | |
| "How do I configure Prometheus to monitor a Go application?",medium | |
| "Explain how TLS handshake works step by step.",medium | |
| "Write a Python script to send an automated email with attachments using smtplib.",medium | |
| "What is the difference between optimistic and pessimistic locking in databases?",medium | |
| "How do I mock an API call in Pytest using unittest.mock?",medium | |
| "Explain how CSS Grid layout works with template areas.",medium | |
| "Write a TypeScript interface for a user profile object.",medium | |
| "How to parse JSON in C++ using nlohmann/json library?",medium | |
| "Explain the concept of tail call optimization in recursion.",medium | |
| "Write a Python function to flatten a nested list.",medium | |
| "How does connection pooling work in database drivers?",medium | |
| "Explain the difference between mutable and immutable types in Python.",medium | |
| "Write a Golang HTTP handler that returns JSON response.",medium | |
| "How to resolve git merge conflicts in a team project?",medium | |
| "Explain how webhooks work for real-time notifications.",medium | |
| "Write a SQL query using window functions like ROW_NUMBER() and RANK().",medium | |
| "What is the difference between a shallow copy and a deep copy?",medium | |
| "How to configure environment variables in Docker Compose?",medium | |
| "Explain how sliding window pattern works for array problems.",medium | |
| "Write a Python script to merge multiple CSV files into one.",medium | |
| "How to implement rate limiting in a Flask API using Redis?",medium | |
| "Explain the difference between HTTP GET and POST requests.",medium | |
| "Write a C# method to serialize an object to JSON using System.Text.Json.",medium | |
| "How does DNS resolution work from browser to server?",medium | |
| "Explain the concept of closures in JavaScript with code examples.",medium | |
| "Write a Python function to count word frequencies in a text file.",medium | |
| "How do I handle global state management in React using Context API?",medium | |
| "Explain how A/B testing works in web analytics.",medium | |
| "Write a Shell script to backup a MySQL database daily.",medium | |
| "What is the difference between SQL and NoSQL databases?",medium | |
| "How to implement custom middleware in Express.js?",medium | |
| "Explain how garbage collection in Python uses reference counting and generational GC.",medium | |
| "Write a Java method to check if two trees are isomorphic.",medium | |
| "How do I configure SSL certificates using Let's Encrypt and Certbot?",medium | |
| "Explain the concept of micro-frontends in web applications.",medium | |
| "Write a Python script to interact with AWS S3 using boto3.",medium | |
| "What is the difference between hard links and symbolic links in Linux?",medium | |
| "How to implement dynamic programming solution for the knapsack problem?",medium | |
| "Explain how OAuth 2.0 authorization code grant flow works.",medium | |
| "Write a Rust function to parse command line arguments using clap.",medium | |
| "How to implement soft deletion in ORMs like SQLAlchemy?",medium | |
| "Explain how deadlocks occur in operating systems and how to prevent them.",medium | |
| "Write a TypeScript generic function for sorting arrays of objects.",medium | |
| "How to set up CI/CD pipeline using GitHub Actions for a Python package?",medium | |
| "Explain the mechanics of a LSM-tree (Log-Structured Merge-tree) vs B-tree.",medium | |
| "Write a Python script to parse log files and extract IP addresses using regex.",medium | |
| "How to implement custom validation in Pydantic models?",medium | |
| "Explain how cache invalidation strategies (write-through, write-back, cache-aside) work.",medium | |
| "Write a Go routine program with channels to perform parallel matrix multiplication.",medium | |
| "How to configure CORS in Spring Boot backend?",medium | |
| "Explain how dynamic linking works in C/C++ Linux executables.",medium | |
| "Write a Python script to compute TF-IDF scores for a collection of documents.",medium | |
| "How to optimize SQL queries using EXPLAIN ANALYZE?",medium | |
| "Explain how reactive programming works with RxJS observables.",medium | |
| "Write a C++ class implementing RAII memory management for a dynamic resource.",medium | |
| "How to configure Kubernetes ingress controller with Nginx?",medium | |
| "Explain the difference between thread starvation and deadlock.",medium | |
| "Write a Python function to solve the N-Queens problem using backtracking.",medium | |
| "How to implement a custom LRU Cache in Python using OrderedDict?",medium | |
| "Implement a lock-free multi-producer multi-consumer bounded queue in C++20 using atomic operations, memory order acquire/release semantics, and ABA prevention with epoch counters.",hard | |
| "Derive the Navier-Stokes equations for incompressible fluid flow in spherical coordinates and prove the uniqueness of weak solutions under boundary conditions.",hard | |
| "Design a fault-tolerant distributed consensus protocol based on Raft, including leader election, log compaction with snapshotting, dynamic membership changes, and proof of safety guarantees.",hard | |
| "Calculate the contour integral of f(z) = e^(iz)/(z^2 + 1)^2 along the upper half-plane contour using the residue theorem and Jordan's Lemma.",hard | |
| "Architect a zero-trust end-to-end encrypted messaging system with double-ratchet key exchange, post-quantum ML-KEM key encapsulation, out-of-order message handling, and perfect forward secrecy.",hard | |
| "Write a custom eBPF kernel program using libbpf and XDP layer to perform high-speed packet filtering, SYN flood protection, and ring buffer event propagation to userspace in C.",hard | |
| "Implement a lock-free SPMC (Single Producer Multiple Consumer) work-stealing deque in C++ using std::atomic and hazard pointers to prevent use-after-free during concurrent stealing.",hard | |
| "Derive the complete backpropagation gradient equations for Multi-Head Attention with FlashAttention tiled online softmax optimization, showing memory savings during forward and backward passes.",hard | |
| "Design a high-throughput LSM-tree storage engine in Go featuring SSTable block compression with zstd, sparse index filtering with Bloom filters, WAL recovery, and size-tiered compaction.",hard | |
| "Analyze this x86-64 assembly dump for AVX-512 vectorization bottlenecks, identifying cache line bouncing, false sharing, and branch mispredictions under high thread contention.",hard | |
| "Implement a custom tracing garbage collector in C using tri-color marking, write barriers for concurrent mutation, and compacting sweep phase to eliminate heap fragmentation.",hard | |
| "Derive the general relativity field equations from the Hilbert-Einstein action using variational calculus with respect to the metric tensor g_uv.",hard | |
| "Architect a multi-region distributed database system supporting serializable multi-document transactions using Hybrid Logical Clocks (HLC) and two-phase commit across Raft groups.",hard | |
| "Write a Rust macro that parses a custom domain-specific language (DSL) at compile time, constructing zero-cost abstract syntax trees and static type assertions.",hard | |
| "Prove the convergence rate of stochastic gradient descent (SGD) for non-convex optimization under PL (Polyak-Lojasiewicz) inequality conditions.",hard | |
| "Implement a complete WebAssembly JIT compiler backend in C++ targeting x86-64, including register allocation using graph coloring and SSA form construction.",hard | |
| "Derive the analytical solution to the 3D Time-Dependent Schrödinger Equation for a particle in an asymmetric double-well potential using perturbation theory.",hard | |
| "Design a zero-copy network architecture using Linux io_uring, splice, and kTLS to achieve 100Gbps line-rate HTTPS proxying with minimal CPU overhead.",hard | |
| "Write a lock-free memory allocator in C featuring thread-local arenas, slab allocation for small objects, and atomic lock-free freelists using double-width CAS operations.",hard | |
| "Derive the Black-Scholes partial differential equation from first principles using Ito's Lemma and arbitrage-free pricing arguments, and solve it for European call options.",hard | |
| "Implement a high-performance SIMD-accelerated JSON parser in C++ using AVX2 instructions to vectorize structural character identification and quote mask processing.",hard | |
| "Prove that the Traveling Salesperson Problem (TSP) decision version is NP-complete by reduction from the Hamiltonian Cycle problem.",hard | |
| "Design a distributed vector database indexing system using Hierarchical Navigable Small World (HNSW) graphs with product quantization and SIMD distance search.",hard | |
| "Derive the variational inference updates for Latent Dirichlet Allocation (LDA) using mean-field approximation and ELBO optimization.",hard | |
| "Write a CUDA C++ kernel for sparse matrix-matrix multiplication (SpGEMM) using warp-level cooperative groups, shared memory tiling, and atomic hash collating.",hard | |
| "Implement a distributed lock manager using Chubby/Zookeeper-style lease mechanisms, fencing tokens, and heartbeat failure detectors in Rust.",hard | |
| "Derive the stress-energy tensor for a massive scalar field minimally coupled to gravity in curved spacetime.",hard | |
| "Design an operating system microkernel IPC mechanism featuring zero-copy capability-based message passing, thread migration, and fastpath assembly context switches.",hard | |
| "Write a custom LLVM compiler optimization pass in C++ that detects and vectorizes non-stride memory access patterns into gather/scatter instructions.",hard | |
| "Prove the correctness and safety properties of the Paxos consensus algorithm using TLA+ temporal logic specification and model checking proofs.",hard | |
| "Derive the exact closed-form expression for the option pricing under Heston stochastic volatility model using characteristic function inversion.",hard | |
| "Implement a lock-free skip list data structure in C++ with concurrent insertion, deletion, and search using atomic pointer mark bits.",hard | |
| "Design a fault-tolerant event streaming engine featuring partitioned append-only commit logs, zero-copy socket transfer, and distributed transactional producers.",hard | |
| "Calculate the stress tensor distribution and stress intensity factor K_I for a semi-infinite crack in an elastic solid under Mode I loading.",hard | |
| "Write a Linux kernel module in C implementing a custom block device driver with asynchronous request queueing and bio structure dispatch.",hard | |
| "Derive the policy gradient theorem and show equivalence between REINFORCE, Actor-Critic, and PPO objective functions with generalized advantage estimation (GAE).",hard | |
| "Implement a complete B+ Tree with concurrent optimistic lock coupling (latch crabbing) and page split rebalancing in C++.",hard | |
| "Design a distributed ledger system utilizing Directed Acyclic Graphs (DAG) with asynchronous Byzantine Fault Tolerance (aBFT) consensus.",hard | |
| "Derive the Renormalization Group equations for phi^4 scalar field theory at two-loop order using dimensional regularization and MS-bar scheme.",hard | |
| "Write an optimizing garbage-collected virtual machine in Rust with generational copying collector, inline caches, and Bytecode JIT compilation.",hard | |
| "Prove the tight lower bound for comparison-based sorting algorithms using decision tree height arguments.",hard | |
| "Design a real-time ray tracing engine in C++/Vulkan with hardware-accelerated BVH traversal, path guiding, and spatio-temporal reservoir resampling (ReSTIR).",hard | |
| "Derive the exact steady-state distribution of a M/M/c/K queueing network with customer balking and server breakdown/repair dynamics.",hard | |
| "Implement a lock-free ring buffer in Rust supporting SPMC streaming with cache-aligned atomic sequence numbers and relaxed memory ordering.",hard | |
| "Architect a secure enclave application using Intel SGX/AMD SEV featuring remote attestation, sealed storage key derivation, and enclave-to-enclave TLS channel.",hard | |
| "Derive the Euler-Lagrange equations for a relativistic charged particle in an arbitrary electromagnetic field tensor F_uv.",hard | |
| "Write a C++ static analyzer pass using Clang LibTooling to enforce custom memory safety rules and detect potential use-after-free bugs.",hard | |
| "Prove the existence and uniqueness of strong solutions to the stochastic differential equation with non-Lipschitz drift coefficient using Yamada-Watanabe theorem.",hard | |
| "Design a distributed graph processing framework based on the Pregel bulk synchronous parallel (BSP) model in Go with fault-tolerant vertex checkpointing.",hard | |
| "Derive the optimal Kalman filter state estimation equations for a non-linear system using Extended Kalman Filtering (EKF) and Unscented Transform (UKF).",hard | |
| "Implement a BFT consensus engine using Tendermint engine architecture in Rust, featuring 2-step voting (prevote/precommit), block proposal verification, and WAL commit.",hard | |
| "Calculate the differential cross-section for Moller scattering (e- e- -> e- e-) at tree level in Quantum Electrodynamics using Feynman rules and trace technology.",hard | |
| "Write a custom memory-mapped virtual file system (VFS) layer in C for FUSE with extent-based file allocation and copy-on-write (CoW) snapshots.",hard | |
| "Derive the backpropagation algorithm for Recurrent Neural Networks (BPTT) with LSTM gates, showing explicit handling of vanishing and exploding gradients.",hard | |
| "Design a zero-knowledge proof circuit using Groth16/Plonk for verifying SHA-256 hash preimages without revealing the input secret.",hard | |
| "Implement a distributed key-value store with Multi-Paxos replication, automatic node membership reconfiguration, and vector clock conflict resolution in C++.",hard | |
| "Derive the thermodynamic properties and Bose-Einstein condensation temperature for an ideal Bose gas in a 3D harmonic trap potential.",hard | |
| "Write a high-performance C++20 coroutine-based asynchronous network framework using io_uring submit queues and zero-alloc awaitables.",hard | |
| "Prove NP-completeness of the 3-SAT problem by reduction from Circuit-SAT using Tseitin transformation.",hard | |
| "Design a distributed time-series database with specialized delta-of-delta timestamp compression, Gorilla float XOR compression, and inverted index search.",hard | |
| "Derive the Green's function for the wave equation in 3D unbounded domain and solve the inhomogeneous wave equation using retarded potentials.",hard | |
| "Implement a lock-free hash map using hopscotch hashing with atomic atomic_compare_exchange loops and hazard pointers in C++.",hard | |
| "Architect a multi-tenant database system with row-level security, tenant isolation at storage layer, and dynamic schema migration execution.",hard | |
| "Derive the gradient of the ELBO with respect to variational parameters using the reparameterization trick for Variational Autoencoders (VAEs).",hard | |
| "Write an eBPF program using bcc to hook kernel TCP functions and compute per-socket RTT distribution in real time.",hard | |
| "Prove the safety and liveness properties of the Raft consensus algorithm under network partitions using formal TLA+ specifications.",hard | |
| "Design a compiler auto-vectorizer pass that converts scalar loops into SIMD instructions using polyhedral loop transformation algorithms.",hard | |
| "Derive the analytical solution for the quantum harmonic oscillator using ladder operators (creation and annihilation operators).",hard | |
| "Implement a distributed file system (DFS) in Go featuring chunkservers, metadata master with lease-based chunk locking, and automatic re-balancing.",hard | |
| "Calculate the anomalous magnetic moment of the electron at one-loop order in QED (Schwinger term alpha / 2 pi).",hard | |
| "Write a custom lock-free memory pool in Rust using atomic CAS operations and ABA-resistant tagged pointers.",hard | |
| "Derive the exact probability density function of the spectral radius of GUE (Gaussian Unitary Ensemble) random matrices using Wigner surmise.",hard | |
| "Design an autonomous database query optimizer featuring cost estimation using learned neural cardinality estimators and dynamic programming join ordering.",hard | |
| "Implement a real-time physics engine solver for rigid body dynamics using Projected Gauss-Seidel (PGS) impulse contact resolution in C++.",hard | |
| "Derive the general equations for gravitational waves in linearized gravity and compute the energy flux radiated by a compact binary system.",hard | |
| "Write a C++ source-to-source transformation tool using Clang AST Matchers to automatically insert bounds checking on raw pointer arithmetic.",hard | |
| "Prove the security of RSA encryption under the Strong RSA Assumption in the Random Oracle Model.",hard | |
| "Design a distributed stream processing engine based on Chandy-Lamport lightweight asynchronous snapshotting for exactly-once processing guarantees.",hard | |
| "Derive the partition function and critical temperature of the 2D Ising model on a square lattice using Onsager's exact solution method.",hard | |
| "Implement a SIMD-accelerated String Distance (Levenshtein / Hamming) calculator in Rust using AVX-512 byte-level comparisons.",hard | |
| "Architect a global DNS authoritative server capable of serving 10 Million QPS using XDP kernel bypass, eBPF routing, and lockless memory tables.",hard | |
| "Derive the backpropagation equations for Graph Neural Networks (GNNs) using Message Passing Neural Networks (MPNN) framework.",hard | |
| "Write a custom Linux kernel LSM (Linux Security Module) in C to enforce mandatory access control policies on file execution.",hard | |
| "Prove that the 3-Coloring graph problem is NP-complete by reduction from 3-SAT.",hard | |
| "Design a high-frequency trading (HFT) order book engine in C++ featuring sub-microsecond matching latency, LMAX Disruptor ring buffer, and lockless execution.",hard | |
| "Derive the variational equations of motion for a constrained mechanical system using D'Alembert's principle and Lagrange multipliers.",hard | |
| "Implement a lock-free MPMC queue using atomic ring buffer, sequence counters, and double CAS operations in C++17.",hard | |
| "Calculate the loop corrections to the Higgs boson self-energy from top quark loops in the Standard Model.",hard | |
| "Write a CUDA C++ kernel for 3D Fast Fourier Transform (FFT) using Cooley-Tukey algorithm with shared memory transposition.",hard | |
| "Prove the security of the Diffie-Hellman key exchange protocol under the Decisional Diffie-Hellman (DDH) assumption.",hard | |
| "Design a distributed ledger using DAG consensus with SPECTRE/PHANTOM protocol to order arbitrary transactions with high throughput.",hard | |
| "Derive the exact solution to the Fokker-Planck equation for a Brownian particle in a harmonic potential (Ornstein-Uhlenbeck process).",hard | |
| "Implement an optimizing JIT compiler for a Lisp dialect in C using libgccjit or LLVM C API.",hard | |
| "Architect a zero-downtime database migration tool capable of schema changes on multi-terabyte tables without table locks.",hard | |
| "Derive the exact expression for the Casimir force between two parallel conducting plates using quantum field theory zero-point energy summation.",hard | |
| "Write an eBPF program to trace kernel page allocation failures and export stack traces to userspace via perf event buffer.",hard | |
| "Prove the convergence of the Expectation-Maximization (EM) algorithm to a local maximum of the log-likelihood function.",hard | |
| "Design a fault-tolerant distributed object store featuring erasure coding (Reed-Solomon 8+4), scrubbers, and automated disk repair.",hard | |
| "Derive the Einstein field equations in the presence of a cosmological constant Lambda from the modified Einstein-Hilbert action.",hard | |
| "Implement a custom memory allocator in C++ with TLSF (Two-Level Segregated Fit) strategy for real-time embedded systems.",hard | |
| "Calculate the partition function and heat capacity of a 3D Einstein solid using quantum statistical mechanics.",hard | |