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Mathematics / Lean 4 / Research supplements

A handbook of
copula verification.

From mathematical statements to inspectable proofs. Explore the definitions, follow an article’s verification map, and read the Lean behind it.

Start with copulas Open the Lean reference ↗
10 article supplements4 handbook chaptersLean 4 generated API
Verification is recorded result by result.

Consult each supplement’s coverage map for its verified results and remaining gaps. A passing build checks the included code; it does not certify an entire article.

A reading path

Understand the mathematics.
Then inspect the proof.

Definitions → conventions → coverage
01

Copulas & conventions

Probability measures, distribution functions, and the basic examples.

02

Dependence measures

The normalizations and directions behind the rank coefficients.

03

Attainable regions

Bounds, extremizers, and what an exact region requires.

04

Reading a verification

Coverage, hypotheses, axiom reports, and reproducible snapshots.

The collection

Article supplements

Browse all 10 articles →

Built to be checked. Written to be cited.

Each article has a permanent folder, a versioned source, and an explicit coverage map. Cite an immutable commit for a publication; use this handbook to explore the current collection.

Reproduce and cite a supplement →