Datasets:
| {"claim": "cvar_is_coherent", "verdict": "REFUTED", "reason": "REFUTED 2026-06-27 - naive tail-integral CVaR fails translation, monotone, subadditive on Fin 3 uniform; use ES (Rockafellar-Uryasev).", "prover": "Lean 4 / Mathlib"} | |
| {"claim": "sharpe_scale_invariant_all_c", "verdict": "REFUTED", "reason": "REFUTED - false for c<0 (sign flips); Sharpe is only scale-invariant under positive scaling.", "prover": "Lean 4 / Mathlib"} | |
| {"claim": "diversification_always_reduces_variance", "verdict": "REFUTED", "reason": "REFUTED - positively correlated assets can exceed either individual variance.", "prover": "Lean 4 / Mathlib"} | |
| {"claim": "kelly_maximizes_expected_wealth", "verdict": "REFUTED", "reason": "REFUTED - Kelly maximizes E[log W], not E[W]; bet-everything dominates E[W] with ruin probability 1.", "prover": "Lean 4 / Mathlib"} | |
| {"claim": "max_sharpe_always_equal_weights", "verdict": "REFUTED", "reason": "REFUTED - max-Sharpe weights depend on inverse covariance and excess returns; equal weights optimal only under full symmetry.", "prover": "Lean 4 / Mathlib"} | |
| {"claim": "all_martingales_bounded", "verdict": "REFUTED", "reason": "REFUTED - symmetric random walk is an unbounded martingale (limsup +inf, liminf -inf a.s.).", "prover": "Lean 4 / Mathlib"} | |
| {"claim": "es_symmetric_in_alpha", "verdict": "REFUTED", "reason": "REFUTED - ES(alpha) != ES(1-alpha) in general; equal only for symmetric zero-mean distributions.", "prover": "Lean 4 / Mathlib"} | |