README.md

metadata

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.