{
    "Exam Name": "CAT Demo Exam - Adaptive Testing",
    "EnableCAT": true,
    "minQuestions": 10,
    "maxQuestions": 30,
    "percentPass": 70,
    "Number of Questions": 100,
    "Default Time": 0,
    "BackNavigation": false,
    "Questions": [
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is 2 + 2?",
            "Choices": [
                "3",
                "4",
                "5",
                "6"
            ],
            "AnswerKey": "4",
            "Explanation": "Basic addition: 2 + 2 = 4",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is 5 + 3?",
            "Choices": [
                "6",
                "7",
                "8",
                "9"
            ],
            "AnswerKey": "8",
            "Explanation": "5 + 3 = 8",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What does 'big' mean?",
            "Choices": [
                "Small",
                "Large",
                "Fast",
                "Slow"
            ],
            "AnswerKey": "Large",
            "Explanation": "Big means large in size",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "If A > B and B > C, then A __ C",
            "Choices": [
                "> (greater than)",
                "< (less than)",
                "= (equal to)",
                "Cannot determine"
            ],
            "AnswerKey": "> (greater than)",
            "Explanation": "Transitive property: if A > B and B > C, then A > C",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the main source of energy for Earth?",
            "Choices": [
                "Moon",
                "Sun",
                "Stars",
                "Wind"
            ],
            "AnswerKey": "Sun",
            "Explanation": "The Sun provides most of Earth's energy",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is 10 - 4?",
            "Choices": [
                "4",
                "5",
                "6",
                "7"
            ],
            "AnswerKey": "6",
            "Explanation": "10 - 4 = 6",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is the opposite of 'hot'?",
            "Choices": [
                "Warm",
                "Cool",
                "Cold",
                "Freezing"
            ],
            "AnswerKey": "Cold",
            "Explanation": "Cold is the opposite of hot",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "Which comes next: 2, 4, 6, 8, __?",
            "Choices": [
                "9",
                "10",
                "11",
                "12"
            ],
            "AnswerKey": "10",
            "Explanation": "Pattern increases by 2",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "How many legs does a spider have?",
            "Choices": [
                "6",
                "8",
                "10",
                "12"
            ],
            "AnswerKey": "8",
            "Explanation": "Spiders have 8 legs",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is 3 × 3?",
            "Choices": [
                "6",
                "9",
                "12",
                "15"
            ],
            "AnswerKey": "9",
            "Explanation": "3 × 3 = 9",
            "difficultyLevel": 1
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is 15 + 27?",
            "Choices": [
                "40",
                "41",
                "42",
                "43"
            ],
            "AnswerKey": "42",
            "Explanation": "15 + 27 = 42",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is 12 × 5?",
            "Choices": [
                "50",
                "55",
                "60",
                "65"
            ],
            "AnswerKey": "60",
            "Explanation": "12 × 5 = 60",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What does 'ancient' mean?",
            "Choices": [
                "New",
                "Modern",
                "Very old",
                "Future"
            ],
            "AnswerKey": "Very old",
            "Explanation": "Ancient means very old",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "If all cats are animals, and some animals are pets, which is true?",
            "Choices": [
                "All cats are pets",
                "Some cats might be pets",
                "No cats are pets",
                "All pets are cats"
            ],
            "AnswerKey": "Some cats might be pets",
            "Explanation": "We only know cats are animals and some animals are pets",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What state is water at 0°C?",
            "Choices": [
                "Gas",
                "Liquid",
                "Solid",
                "Plasma"
            ],
            "AnswerKey": "Solid",
            "Explanation": "Water freezes at 0°C (ice)",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is 50% of 80?",
            "Choices": [
                "30",
                "35",
                "40",
                "45"
            ],
            "AnswerKey": "40",
            "Explanation": "50% of 80 = 80/2 = 40",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "A synonym for 'happy' is:",
            "Choices": [
                "Sad",
                "Joyful",
                "Angry",
                "Tired"
            ],
            "AnswerKey": "Joyful",
            "Explanation": "Joyful means happy",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "Which number doesn't fit: 2, 4, 6, 9, 10?",
            "Choices": [
                "2",
                "4",
                "9",
                "10"
            ],
            "AnswerKey": "9",
            "Explanation": "9 is the only odd number",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What do plants need for photosynthesis?",
            "Choices": [
                "Darkness",
                "Moonlight",
                "Sunlight",
                "Artificial light only"
            ],
            "AnswerKey": "Sunlight",
            "Explanation": "Plants need sunlight for photosynthesis",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is 144 ÷ 12?",
            "Choices": [
                "10",
                "11",
                "12",
                "13"
            ],
            "AnswerKey": "12",
            "Explanation": "144 ÷ 12 = 12",
            "difficultyLevel": 2
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "Solve: 3x + 7 = 22",
            "Choices": [
                "x = 3",
                "x = 5",
                "x = 7",
                "x = 9"
            ],
            "AnswerKey": "x = 5",
            "Explanation": "3x = 15, so x = 5",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is 17²?",
            "Choices": [
                "289",
                "299",
                "279",
                "269"
            ],
            "AnswerKey": "289",
            "Explanation": "17 × 17 = 289",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What does 'ephemeral' mean?",
            "Choices": [
                "Lasting forever",
                "Very large",
                "Short-lived",
                "Beautiful"
            ],
            "AnswerKey": "Short-lived",
            "Explanation": "Ephemeral means lasting for a very short time",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "If P implies Q, and Q implies R, what can we conclude?",
            "Choices": [
                "R implies P",
                "P implies R",
                "R is false",
                "Cannot determine"
            ],
            "AnswerKey": "P implies R",
            "Explanation": "Transitive property of implication",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the chemical symbol for gold?",
            "Choices": [
                "Go",
                "Gd",
                "Au",
                "Ag"
            ],
            "AnswerKey": "Au",
            "Explanation": "Au comes from Latin 'aurum'",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the area of a circle with radius 5? (use π ≈ 3.14)",
            "Choices": [
                "78.5",
                "31.4",
                "15.7",
                "62.8"
            ],
            "AnswerKey": "78.5",
            "Explanation": "A = πr² = 3.14 × 25 = 78.5",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "An antonym for 'verbose' is:",
            "Choices": [
                "Wordy",
                "Talkative",
                "Concise",
                "Lengthy"
            ],
            "AnswerKey": "Concise",
            "Explanation": "Verbose means wordy, concise is the opposite",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "In a group of 100 people, 60 speak English, 40 speak French, 10 speak both. How many speak neither?",
            "Choices": [
                "0",
                "10",
                "20",
                "30"
            ],
            "AnswerKey": "10",
            "Explanation": "60 + 40 - 10 = 90 speak at least one, so 10 speak neither",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is Newton's First Law?",
            "Choices": [
                "F=ma",
                "Objects in motion stay in motion unless acted upon",
                "Every action has a reaction",
                "E=mc²"
            ],
            "AnswerKey": "Objects in motion stay in motion unless acted upon",
            "Explanation": "Law of inertia",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "Factor: x² - 9",
            "Choices": [
                "(x-3)(x-3)",
                "(x+3)(x+3)",
                "(x-3)(x+3)",
                "Cannot factor"
            ],
            "AnswerKey": "(x-3)(x+3)",
            "Explanation": "Difference of squares: a² - b² = (a-b)(a+b)",
            "difficultyLevel": 3
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "Integrate: ∫2x dx",
            "Choices": [
                "x² + C",
                "2x² + C",
                "x²/2 + C",
                "2x + C"
            ],
            "AnswerKey": "x² + C",
            "Explanation": "∫2x dx = 2(x²/2) + C = x² + C",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is log₂(64)?",
            "Choices": [
                "4",
                "5",
                "6",
                "7"
            ],
            "AnswerKey": "6",
            "Explanation": "2⁶ = 64, so log₂(64) = 6",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What does 'ubiquitous' mean?",
            "Choices": [
                "Rare",
                "Present everywhere",
                "Ancient",
                "Mysterious"
            ],
            "AnswerKey": "Present everywhere",
            "Explanation": "Ubiquitous means existing everywhere",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "Which statement is the contrapositive of 'If P then Q'?",
            "Choices": [
                "If Q then P",
                "If not Q then not P",
                "If not P then not Q",
                "P and Q"
            ],
            "AnswerKey": "If not Q then not P",
            "Explanation": "Contrapositive: if A→B, then ¬B→¬A",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the Heisenberg Uncertainty Principle about?",
            "Choices": [
                "Energy conservation",
                "Position and momentum cannot both be precisely measured",
                "Speed of light limit",
                "Time dilation"
            ],
            "AnswerKey": "Position and momentum cannot both be precisely measured",
            "Explanation": "Fundamental limit of quantum mechanics",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "Solve for x: e^x = 7.389 (approximately)",
            "Choices": [
                "x = 1",
                "x = 2",
                "x = 3",
                "x = 4"
            ],
            "AnswerKey": "x = 2",
            "Explanation": "e² ≈ 7.389",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is a 'tautology'?",
            "Choices": [
                "A contradiction",
                "A statement that's always true",
                "A circular argument",
                "A false premise"
            ],
            "AnswerKey": "A statement that's always true",
            "Explanation": "A tautology is logically true in all cases",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "In propositional logic, what is ¬(P ∧ Q) equivalent to?",
            "Choices": [
                "¬P ∨ ¬Q",
                "¬P ∧ ¬Q",
                "P ∨ Q",
                "P ∧ Q"
            ],
            "AnswerKey": "¬P ∨ ¬Q",
            "Explanation": "De Morgan's Law",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the unit of electrical resistance?",
            "Choices": [
                "Ampere",
                "Volt",
                "Ohm",
                "Watt"
            ],
            "AnswerKey": "Ohm",
            "Explanation": "Resistance is measured in Ohms (Ω)",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the derivative of sin(x)?",
            "Choices": [
                "cos(x)",
                "-cos(x)",
                "sin(x)",
                "-sin(x)"
            ],
            "AnswerKey": "cos(x)",
            "Explanation": "d/dx[sin(x)] = cos(x)",
            "difficultyLevel": 4
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "Evaluate: lim(x→0) (sin(x)/x)",
            "Choices": [
                "0",
                "1",
                "∞",
                "Undefined"
            ],
            "AnswerKey": "1",
            "Explanation": "Famous limit: lim(x→0) sin(x)/x = 1",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the sum of an infinite geometric series with a=1 and r=1/2?",
            "Choices": [
                "1",
                "2",
                "3",
                "Diverges"
            ],
            "AnswerKey": "2",
            "Explanation": "S = a/(1-r) = 1/(1-0.5) = 2",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What does 'soliloquy' mean?",
            "Choices": [
                "Dialogue between two people",
                "A speech given alone",
                "A type of poem",
                "Musical performance"
            ],
            "AnswerKey": "A speech given alone",
            "Explanation": "A soliloquy is when someone speaks their thoughts aloud alone",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What is the principle of explosion in logic?",
            "Choices": [
                "From contradiction, anything follows",
                "Truth implies truth",
                "False implies nothing",
                "Axioms must be consistent"
            ],
            "AnswerKey": "From contradiction, anything follows",
            "Explanation": "Ex falso quodlibet: from falsehood, anything",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is Schrödinger's equation used for?",
            "Choices": [
                "Classical mechanics",
                "Relativity",
                "Quantum mechanics",
                "Thermodynamics"
            ],
            "AnswerKey": "Quantum mechanics",
            "Explanation": "Fundamental equation of quantum mechanics",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is ∫e^x cos(x) dx?",
            "Choices": [
                "e^x(sin(x)+cos(x))/2 + C",
                "e^x sin(x) + C",
                "e^x cos(x) + C",
                "Cannot integrate"
            ],
            "AnswerKey": "e^x(sin(x)+cos(x))/2 + C",
            "Explanation": "Integration by parts twice",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'apotheosis'?",
            "Choices": [
                "A downfall",
                "The highest point or culmination",
                "A beginning",
                "A repetition"
            ],
            "AnswerKey": "The highest point or culmination",
            "Explanation": "Apotheosis means the peak or highest development",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "In modal logic, □P means:",
            "Choices": [
                "P is possible",
                "P is necessary",
                "P is contingent",
                "Not P"
            ],
            "AnswerKey": "P is necessary",
            "Explanation": "□ (box) represents necessity in modal logic",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What does the Second Law of Thermodynamics state about entropy?",
            "Choices": [
                "Decreases over time",
                "Remains constant",
                "Increases in isolated systems",
                "Can be reversed"
            ],
            "AnswerKey": "Increases in isolated systems",
            "Explanation": "Entropy always increases in an isolated system",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the Laplace transform of t?",
            "Choices": [
                "1/s",
                "1/s²",
                "s",
                "s²"
            ],
            "AnswerKey": "1/s²",
            "Explanation": "L{t} = 1/s²",
            "difficultyLevel": 5
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "Solve the differential equation: y'' + 4y = 0",
            "Choices": [
                "y = C₁cos(2x) + C₂sin(2x)",
                "y = C₁e^(2x) + C₂e^(-2x)",
                "y = C₁cos(x) + C₂sin(x)",
                "y = C₁x + C₂"
            ],
            "AnswerKey": "y = C₁cos(2x) + C₂sin(2x)",
            "Explanation": "Characteristic equation r² + 4 = 0, r = ±2i",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the residue of f(z) = 1/z² at z = 0?",
            "Choices": [
                "0",
                "1",
                "-1",
                "Undefined"
            ],
            "AnswerKey": "0",
            "Explanation": "Pole of order 2, coefficient of 1/z term is 0",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'prolegomenon'?",
            "Choices": [
                "A conclusion",
                "A preliminary discussion",
                "A middle section",
                "An appendix"
            ],
            "AnswerKey": "A preliminary discussion",
            "Explanation": "Prolegomenon is an introductory or preliminary discussion",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What is Gödel's Incompleteness Theorem about?",
            "Choices": [
                "Geometry",
                "Arithmetic systems have unprovable true statements",
                "All statements are provable",
                "Logic is complete"
            ],
            "AnswerKey": "Arithmetic systems have unprovable true statements",
            "Explanation": "No consistent system can prove all truths about arithmetic",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the Pauli Exclusion Principle?",
            "Choices": [
                "Particles can share quantum states",
                "No two fermions can have identical quantum numbers",
                "Energy is conserved",
                "Momentum is conserved"
            ],
            "AnswerKey": "No two fermions can have identical quantum numbers",
            "Explanation": "Fundamental principle of quantum mechanics for fermions",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the dimension of the vector space of n×n matrices over ℝ?",
            "Choices": [
                "n",
                "2n",
                "n²",
                "n!"
            ],
            "AnswerKey": "n²",
            "Explanation": "Each entry is independent, n rows × n columns",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What does 'apophenia' mean?",
            "Choices": [
                "Fear of heights",
                "Seeing patterns where none exist",
                "Love of knowledge",
                "Speaking truth"
            ],
            "AnswerKey": "Seeing patterns where none exist",
            "Explanation": "Apophenia is perceiving connections in random data",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "In set theory, what is the cardinality of the power set of ℕ?",
            "Choices": [
                "ℵ₀",
                "2^ℵ₀",
                "ℵ₁",
                "Finite"
            ],
            "AnswerKey": "2^ℵ₀",
            "Explanation": "|P(A)| = 2^|A|, so |P(ℕ)| = 2^ℵ₀",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is renormalization in quantum field theory?",
            "Choices": [
                "Making calculations finite",
                "Increasing energy",
                "Decreasing mass",
                "Time reversal"
            ],
            "AnswerKey": "Making calculations finite",
            "Explanation": "Technique to handle infinities in QFT",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the Fourier transform of a Gaussian?",
            "Choices": [
                "Another Gaussian",
                "Sinc function",
                "Delta function",
                "Exponential"
            ],
            "AnswerKey": "Another Gaussian",
            "Explanation": "Gaussians are eigenfunctions of Fourier transform",
            "difficultyLevel": 6
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the Riemann Hypothesis about?",
            "Choices": [
                "Prime numbers",
                "Zeros of zeta function",
                "Continuous functions",
                "Metric spaces"
            ],
            "AnswerKey": "Zeros of zeta function",
            "Explanation": "Concerns non-trivial zeros of ζ(s) having Re(s) = 1/2",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "In algebraic topology, what is π₁(S¹)?",
            "Choices": [
                "0",
                "ℤ",
                "ℤ₂",
                "ℝ"
            ],
            "AnswerKey": "ℤ",
            "Explanation": "Fundamental group of circle is integers",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'tmesis'?",
            "Choices": [
                "Repetition",
                "Insertion of word into another word",
                "Omission",
                "Inversion"
            ],
            "AnswerKey": "Insertion of word into another word",
            "Explanation": "Tmesis is separating a word with another (e.g., 'abso-bloody-lutely')",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What is the axiom of choice equivalent to?",
            "Choices": [
                "Continuum hypothesis",
                "Zorn's lemma",
                "Axiom of infinity",
                "Power set axiom"
            ],
            "AnswerKey": "Zorn's lemma",
            "Explanation": "AC, Zorn's lemma, and well-ordering theorem are equivalent",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the Yang-Mills existence and mass gap problem?",
            "Choices": [
                "Solved problem",
                "Millennium Prize Problem about quantum field theory",
                "Classical mechanics problem",
                "Statistical problem"
            ],
            "AnswerKey": "Millennium Prize Problem about quantum field theory",
            "Explanation": "Unsolved problem worth $1 million",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the Hodge conjecture concerned with?",
            "Choices": [
                "Number theory",
                "Algebraic cycles in algebraic geometry",
                "Differential equations",
                "Graph theory"
            ],
            "AnswerKey": "Algebraic cycles in algebraic geometry",
            "Explanation": "Millennium problem about algebraic geometry",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'aporia'?",
            "Choices": [
                "Logical certainty",
                "State of puzzlement or doubt",
                "Clear understanding",
                "Simple truth"
            ],
            "AnswerKey": "State of puzzlement or doubt",
            "Explanation": "Aporia is an irresolvable internal contradiction",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What does 'intuitionistic logic' reject?",
            "Choices": [
                "Modus ponens",
                "Law of excluded middle",
                "Law of identity",
                "Modus tollens"
            ],
            "AnswerKey": "Law of excluded middle",
            "Explanation": "Intuitionistic logic doesn't accept P ∨ ¬P universally",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the holographic principle in physics?",
            "Choices": [
                "3D can be described by 2D surface",
                "Light behaves as particles",
                "Energy equals mass",
                "Time is relative"
            ],
            "AnswerKey": "3D can be described by 2D surface",
            "Explanation": "Information in volume encoded on boundary",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the Taniyama-Shimura conjecture (now theorem)?",
            "Choices": [
                "About elliptic curves and modular forms",
                "About prime distribution",
                "About topology",
                "About logic"
            ],
            "AnswerKey": "About elliptic curves and modular forms",
            "Explanation": "Key to proving Fermat's Last Theorem",
            "difficultyLevel": 7
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the Langlands program about?",
            "Choices": [
                "Connecting number theory and harmonic analysis",
                "Solving polynomials",
                "Prime factorization",
                "Matrix theory"
            ],
            "AnswerKey": "Connecting number theory and harmonic analysis",
            "Explanation": "Vast web of conjectures relating different areas",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "In category theory, what is a topos?",
            "Choices": [
                "A type of group",
                "A category behaving like Set",
                "A topological space",
                "A number field"
            ],
            "AnswerKey": "A category behaving like Set",
            "Explanation": "Topos is a category with specific properties generalizing Set",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'hapax legomenon'?",
            "Choices": [
                "Common word",
                "Word appearing once in a text",
                "Repeated phrase",
                "Title"
            ],
            "AnswerKey": "Word appearing once in a text",
            "Explanation": "A word that occurs only once in a written record",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What is linear logic concerned with?",
            "Choices": [
                "Linear algebra",
                "Resource-sensitive reasoning",
                "Lines and points",
                "Sequential thinking"
            ],
            "AnswerKey": "Resource-sensitive reasoning",
            "Explanation": "Logic that tracks resource usage",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is supersymmetry in particle physics?",
            "Choices": [
                "Particles move symmetrically",
                "Fermions and bosons are related",
                "Atoms are symmetric",
                "Forces are equal"
            ],
            "AnswerKey": "Fermions and bosons are related",
            "Explanation": "Theoretical relation between two particle types",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is a scheme in algebraic geometry?",
            "Choices": [
                "A plan",
                "Generalization of algebraic varieties",
                "A function",
                "A graph"
            ],
            "AnswerKey": "Generalization of algebraic varieties",
            "Explanation": "Fundamental object in modern algebraic geometry",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'parapraxis'?",
            "Choices": [
                "Perfect action",
                "Freudian slip",
                "Logical conclusion",
                "Medical condition"
            ],
            "AnswerKey": "Freudian slip",
            "Explanation": "Error revealing unconscious thoughts",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What is homotopy type theory?",
            "Choices": [
                "Study of shapes",
                "Foundations of math based on homotopy",
                "Theory of functions",
                "Number theory"
            ],
            "AnswerKey": "Foundations of math based on homotopy",
            "Explanation": "Connects type theory with homotopy theory",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the firewall paradox in black hole physics?",
            "Choices": [
                "Black holes are hot",
                "Conflict between quantum mechanics and general relativity at horizon",
                "Black holes have firewalls",
                "Stars burn forever"
            ],
            "AnswerKey": "Conflict between quantum mechanics and general relativity at horizon",
            "Explanation": "Paradox about information and horizons",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the Birch and Swinnerton-Dyer conjecture about?",
            "Choices": [
                "Rational points on elliptic curves",
                "Prime numbers",
                "Topology",
                "Analysis"
            ],
            "AnswerKey": "Rational points on elliptic curves",
            "Explanation": "Millennium problem relating L-functions to curves",
            "difficultyLevel": 8
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the classification of finite simple groups?",
            "Choices": [
                "5 groups",
                "26 sporadic groups plus infinite families",
                "Infinite list",
                "Unsolved"
            ],
            "AnswerKey": "26 sporadic groups plus infinite families",
            "Explanation": "Enormous theorem classifying all finite simple groups",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is a motive in algebraic geometry?",
            "Choices": [
                "Purpose",
                "Universal cohomology theory",
                "Function",
                "Shape"
            ],
            "AnswerKey": "Universal cohomology theory",
            "Explanation": "Conjectural object unifying cohomology theories",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'catachresis'?",
            "Choices": [
                "Correct usage",
                "Misuse of words creating new meaning",
                "Repetition",
                "Rhyming"
            ],
            "AnswerKey": "Misuse of words creating new meaning",
            "Explanation": "Creative misuse of language (e.g., 'leg of a table')",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What is the curry-howard correspondence?",
            "Choices": [
                "Recipes",
                "Proofs are programs",
                "Logic is math",
                "Sets are types"
            ],
            "AnswerKey": "Proofs are programs",
            "Explanation": "Deep connection between logic and computation",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the measurement problem in quantum mechanics fundamentally about?",
            "Choices": [
                "Accuracy",
                "How observation causes wave function collapse",
                "Instrument calibration",
                "Human perception"
            ],
            "AnswerKey": "How observation causes wave function collapse",
            "Explanation": "Fundamental interpretational issue in QM",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is derived algebraic geometry?",
            "Choices": [
                "Simple algebra",
                "Homotopy-theoretic enhancement of algebraic geometry",
                "Calculus",
                "Number patterns"
            ],
            "AnswerKey": "Homotopy-theoretic enhancement of algebraic geometry",
            "Explanation": "Modern approach using ∞-categories",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'zeugma' as a rhetorical device?",
            "Choices": [
                "Repetition",
                "Using one word to govern multiple others in different senses",
                "Exaggeration",
                "Understatement"
            ],
            "AnswerKey": "Using one word to govern multiple others in different senses",
            "Explanation": "E.g., 'She broke his car and his heart'",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What is a large cardinal in set theory?",
            "Choices": [
                "Big number",
                "Cardinal with strong axioms beyond ZFC",
                "Infinite set",
                "Countable set"
            ],
            "AnswerKey": "Cardinal with strong axioms beyond ZFC",
            "Explanation": "Cardinals whose existence cannot be proven in ZFC",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is the AdS/CFT correspondence?",
            "Choices": [
                "Alphabet codes",
                "Duality between gravity and quantum field theories",
                "Chemical formulas",
                "Astronomical mapping"
            ],
            "AnswerKey": "Duality between gravity and quantum field theories",
            "Explanation": "Profound connection in string theory",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is perfectoid space theory used for?",
            "Choices": [
                "Cooking",
                "Studying p-adic geometry",
                "Classical mechanics",
                "Statistics"
            ],
            "AnswerKey": "Studying p-adic geometry",
            "Explanation": "Recent breakthrough in arithmetic geometry",
            "difficultyLevel": 9
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is anabelian geometry?",
            "Choices": [
                "Study without coordinates",
                "Recovering schemes from fundamental groups",
                "Non-abelian groups",
                "Abstract algebra"
            ],
            "AnswerKey": "Recovering schemes from fundamental groups",
            "Explanation": "Grothendieck's program on étale fundamental groups",
            "difficultyLevel": 10
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the étale cohomology used for primarily?",
            "Choices": [
                "Calculus",
                "Studying algebraic varieties over finite fields",
                "Statistics",
                "Trigonometry"
            ],
            "AnswerKey": "Studying algebraic varieties over finite fields",
            "Explanation": "Cohomology theory for algebraic geometry",
            "difficultyLevel": 10
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'sesquipedalian'?",
            "Choices": [
                "Half-measure",
                "Given to using long words",
                "Walk slowly",
                "Ancient"
            ],
            "AnswerKey": "Given to using long words",
            "Explanation": "Ironically, a long word meaning 'using long words'",
            "difficultyLevel": 10
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What is forcing in set theory?",
            "Choices": [
                "Coercion",
                "Technique to prove consistency and independence results",
                "Strong axioms",
                "Proof by contradiction"
            ],
            "AnswerKey": "Technique to prove consistency and independence results",
            "Explanation": "Paul Cohen's method for independence proofs",
            "difficultyLevel": 10
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What does the black hole information paradox concern?",
            "Choices": [
                "Data storage",
                "Whether information is destroyed in black holes",
                "Hawking radiation temperature",
                "Black hole size"
            ],
            "AnswerKey": "Whether information is destroyed in black holes",
            "Explanation": "Conflict between QM unitarity and GR",
            "difficultyLevel": 10
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is the geometric Langlands program?",
            "Choices": [
                "Mapping geography",
                "Geometric analogue of number-theoretic Langlands",
                "Land surveying",
                "Graph theory"
            ],
            "AnswerKey": "Geometric analogue of number-theoretic Langlands",
            "Explanation": "Deep connections in algebraic geometry",
            "difficultyLevel": 10
        },
        {
            "DomainOfKnowledge": "Vocabulary",
            "Question": "What is 'apocatastasis'?",
            "Choices": [
                "Medical term",
                "Restoration to original condition",
                "Destruction",
                "Evolution"
            ],
            "AnswerKey": "Restoration to original condition",
            "Explanation": "Theological/philosophical concept of universal reconciliation",
            "difficultyLevel": 10
        },
        {
            "DomainOfKnowledge": "Logic",
            "Question": "What is incompatible with the axiom of choice in some models?",
            "Choices": [
                "Addition",
                "Axiom of determinacy",
                "Subtraction",
                "Multiplication"
            ],
            "AnswerKey": "Axiom of determinacy",
            "Explanation": "AD and AC are inconsistent",
            "difficultyLevel": 10
        },
        {
            "DomainOfKnowledge": "Science",
            "Question": "What is M-theory in string theory?",
            "Choices": [
                "Theory of mass",
                "Unifying theory of all string theories",
                "Magnetic theory",
                "Mathematical theory"
            ],
            "AnswerKey": "Unifying theory of all string theories",
            "Explanation": "11-dimensional theory unifying 5 string theories",
            "difficultyLevel": 10
        },
        {
            "DomainOfKnowledge": "Math",
            "Question": "What is a condensed mathematics?",
            "Choices": [
                "Summary",
                "New foundations using condensed sets",
                "Compressed data",
                "Simple math"
            ],
            "AnswerKey": "New foundations using condensed sets",
            "Explanation": "Recent Scholze-Clausen approach to topology",
            "difficultyLevel": 10
        }
    ]
}