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


reason: REFUTED - false for c<0 (sign flips); Sharpe is only scale-invariant under positive scaling.


reason: REFUTED - positively correlated assets can exceed either individual variance.


reason: REFUTED - Kelly maximizes E[log W], not E[W]; bet-everything dominates E[W] with ruin probability 1.


reason: REFUTED - max-Sharpe weights depend on inverse covariance and excess returns; equal weights optimal only under full symmetry.


reason: REFUTED - symmetric random walk is an unbounded martingale (limsup +inf, liminf -inf a.s.).


reason: REFUTED - ES(alpha) != ES(1-alpha) in general; equal only for symmetric zero-mean distributions.