Output
{
"questions": [
{
"id": "q1",
"statement": "The speed of light in vacuum is greater than 300,000 km/s.",
"truth": false,
"category": "physics",
"source": "CODATA 2018 fundamental physical constants",
"rationale": "The exact value is 299,792,458 m/s = 299,792.458 km/s, which is less than 300,000 km/s."
},
{
"id": "q2",
"statement": "The Eiffel Tower is taller than 300 meters including antennas.",
"truth": true,
"category": "geography",
"source": "Société d'Exploitation de la Tour Eiffel",
"rationale": "Height to tip including antennas is ~330 m."
},
{
"id": "q3",
"statement": "Over the last 50 years (to 2024), the US stock market has had more positive calendar years than negative calendar years.",
"truth": true,
"category": "finance-generic",
"source": "S&P / Damodaran annual returns series",
"rationale": "Roughly 73–76% of calendar years are positive over long rolling windows; far more ups than downs."
},
{
"id": "q4",
"statement": "The Great Wall of China is visible to the naked eye from low Earth orbit.",
"truth": false,
"category": "physics",
"source": "NASA — multiple astronaut reports",
"rationale": "It is generally not visible from LEO without aids; this is a common misconception debunked by NASA and astronauts including Chiao."
},
{
"id": "q5",
"statement": "A year on Venus is shorter than a day on Venus.",
"truth": true,
"category": "physics",
"source": "NASA planetary fact sheet",
"rationale": "Venusian orbital period is ~224.7 Earth days; a sidereal day on Venus is ~243 Earth days."
},
{
"id": "q6",
"statement": "Japan has more islands than Greece.",
"truth": true,
"category": "geography",
"source": "Geospatial Information Authority of Japan 2023 recount",
"rationale": "Japan's recount placed islands at ~14,125; Greece has ~1,400–6,000 depending on definition."
},
{
"id": "q7",
"statement": "The global median household income is above USD 15,000.",
"truth": false,
"category": "economics",
"source": "Gallup / World Bank household income surveys",
"rationale": "Global median is closer to $3,000–9,000 USD depending on methodology; nowhere near $15K."
},
{
"id": "q8",
"statement": "The first transatlantic submarine telegraph cable was laid before the American Civil War ended.",
"truth": true,
"category": "history",
"source": "Smithsonian Institution archives",
"rationale": "The first working transatlantic cable began service in August 1858; the Civil War ended April 1865."
},
{
"id": "q9",
"statement": "The Dead Sea is below sea level.",
"truth": true,
"category": "geography",
"source": "Geological Survey of Israel",
"rationale": "Approximately 430 meters below sea level — lowest land elevation on Earth."
},
{
"id": "q10",
"statement": "A bond with a higher yield-to-maturity always has a higher current price than a lower-yield bond of the same maturity and coupon.",
"truth": false,
"category": "finance-generic",
"source": "Standard fixed-income textbook (e.g. Fabozzi)",
"rationale": "Higher YTM corresponds to LOWER price (inverse relationship) for the same cash flows."
},
{
"id": "q11",
"statement": "Pluto is smaller than Mercury.",
"truth": true,
"category": "physics",
"source": "NASA planetary fact sheet",
"rationale": "Pluto diameter ~2,377 km; Mercury diameter ~4,880 km."
},
{
"id": "q12",
"statement": "The EU adopted the euro as a physical currency before the year 2000.",
"truth": false,
"category": "history",
"source": "European Central Bank historical timeline",
"rationale": "Euro banknotes and coins entered circulation on 1 January 2002. The euro existed as an accounting currency from 1 January 1999."
},
{
"id": "q13",
"statement": "In 2023, Norway's sovereign wealth fund crossed USD 1.5 trillion in assets.",
"truth": true,
"category": "finance-generic",
"source": "Norges Bank Investment Management annual report",
"rationale": "Norway's GPFG crossed $1.4T in late 2023, and $1.5T early 2024."
},
{
"id": "q14",
"statement": "Kelly criterion bet sizing is defined as f* = (bp − q) / b where b = odds, p = win probability, q = 1 − p.",
"truth": true,
"category": "finance-generic",
"source": "Kelly 1956, 'A New Interpretation of Information Rate'",
"rationale": "This is the original formula from Kelly's 1956 paper."
},
{
"id": "q15",
"statement": "MCP (Model Context Protocol) was first specified by OpenAI.",
"truth": false,
"category": "tech",
"source": "Anthropic MCP specification repository",
"rationale": "MCP was specified and open-sourced by Anthropic in November 2024."
},
{
"id": "q16",
"statement": "Over the last 100 years, large-cap US equities have had a positive real return in more than 60% of rolling 10-year windows.",
"truth": true,
"category": "finance-generic",
"source": "Damodaran annualised returns series, 1928–present",
"rationale": "Positive real-return share is closer to ~85%+ for rolling 10-year windows; the statement is comfortably true."
},
{
"id": "q17",
"statement": "At a 52% win rate and 1:1 odds, full Kelly recommends a 4% bet of bankroll per trade.",
"truth": true,
"category": "finance-generic",
"source": "Direct Kelly formula: f* = (1 × 0.52 − 0.48) / 1 = 0.04",
"rationale": "Substituting into Kelly's formula gives exactly 0.04 = 4%."
},
{
"id": "q18",
"statement": "The Antarctic Treaty, establishing Antarctica as a scientific preserve, entered force before 1970.",
"truth": true,
"category": "history",
"source": "Secretariat of the Antarctic Treaty",
"rationale": "Signed 1959, entered into force 23 June 1961."
},
{
"id": "q19",
"statement": "A Sharpe ratio of 2.0 on daily returns annualizes to roughly 31.7.",
"truth": true,
"category": "finance-generic",
"source": "Standard Sharpe annualization: SR_annual ≈ SR_daily × √252 ≈ 31.75",
"rationale": "2.0 × √252 ≈ 31.75."
},
{
"id": "q20",
"statement": "The Shannon entropy of a fair coin is 1 bit.",
"truth": true,
"category": "physics",
"source": "Shannon 1948, 'A Mathematical Theory of Communication'",
"rationale": "H(p=0.5, q=0.5) = −(0.5·log₂(0.5) + 0.5·log₂(0.5)) = 1 bit."
},
{
"id": "q21",
"statement": "The Deflated Sharpe Ratio was introduced by Bailey and Lopez de Prado in 2014.",
"truth": true,
"category": "finance-generic",
"source": "Bailey, D. H., & Lopez de Prado, M. (2014). Journal of Portfolio Management 40(5).",
"rationale": "DSR extends Sharpe with a multiple-testing + non-normality correction; original 2014 paper."
},
{
"id": "q22",
"statement": "Most benchmarks of mainstream LLMs on numeric extraction from 10-K filings report accuracy above 99%.",
"truth": false,
"category": "tech",
"source": "Finance-LLM benchmark literature 2023–2025",
"rationale": "Published extraction accuracy on numeric fields from full 10-Ks typically falls in the 80–95% range depending on task and model; 99%+ is not a realistic report."
},
{
"id": "q23",
"statement": "Options pricing via Black-Scholes assumes the underlying follows a geometric Brownian motion.",
"truth": true,
"category": "finance-generic",
"source": "Black & Scholes 1973, Journal of Political Economy",
"rationale": "Geometric Brownian motion (log-normal underlying, constant drift + volatility) is the canonical Black-Scholes assumption."
},
{
"id": "q24",
"statement": "Cointegration between two price series is the same as high Pearson correlation between them.",
"truth": false,
"category": "finance-generic",
"source": "Engle & Granger 1987, Econometrica 55(2)",
"rationale": "Cointegration is about a stationary linear combination of non-stationary series; two series can be highly correlated without being cointegrated, and vice versa."
}
],
"hint": "POST {op:'score', answers:[{probability, actual}, ...]} to score a session."
}