| --- |
| 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). |
|
|
