---
license: apache-2.0
language:
- en
tags:
- formal-verification
- quantitative-finance
- lean4
- mathlib
- negative-results
size_categories:
- n<1K
task_categories:
- text-classification
pretty_name: Formally Verified Financial-Engineering Claims
---

# Formally Verified Financial-Engineering Claims

A small, machine-checked database of quantitative-finance claims that were either
**refuted by a formal counterexample** or **confirmed by a formal proof** in
Lean 4 / Mathlib. The point is discipline over folklore: each entry is settled by
a kernel-checked artifact, not an appeal to authority.

## Contents

- `refutations.jsonl` — 7 widely-repeated claims that are **false as usually stated**,
  each with the counterexample that breaks it (e.g. naive tail-integral CVaR is not
  coherent; Kelly maximizes `E[log W]`, not `E[W]`; a symmetric random walk is an
  unbounded martingale).
- `confirmations.jsonl` — 40 standard results **confirmed** by formal proof
  (ES/Rockafellar–Uryasev coherence, put–call parity, Cramér–Rao, Gale–Shapley
  stability, VCG strategy-proofness, …).

Each row: `{ "claim", "verdict", "reason"?, "prover" }`.

## Why

Practitioner intuition is often *almost* right in a way that fails at the edge —
the sign flip, the negative-`c` scaling, the unbounded tail. Publishing the
refutations, not just the confirmations, is the honest half of the ledger. All
verdicts are reproducible against the Lean 4 / Mathlib sources.

## Scope and limitations

This is a curated slice of standard, publicly-known results — a demonstration of
the formal-verification method applied to quant finance, not an exhaustive library.
Claims are settled relative to their stated hypotheses; a "REFUTED" verdict means
the claim is false *as commonly stated*, and the reason names the missing condition.

## Citation

> Formally Verified Financial-Engineering Claims. Lean 4 / Mathlib. 2026.
> https://sunlitmoon.online

Companion CLI: [`SMC17/formal-counterex-zig`](https://github.com/SMC17/formal-counterex-zig).