Stokes' Theorem for Smooth Singular Cubes in Lean 4: True Pullback, Bridges to mathlib4, and Chain-Level d^2=0
Logic in Computer Science
2026-05-05 v1 Differential Geometry
Abstract
We present a sorry-free Lean 4/mathlib4 formalization of Stokes' theorem for smooth singular cubes in arbitrary dimension, using true differential-form pullback via the Frechet derivative. The development also includes a bridge to mathlib4's abstract extDeriv, chain-level Stokes extended by Z-linearity, d^2=0 for singular cubical chains, box Stokes for axis-aligned cubes, dimensional specializations, and a structured comparison with Harrison's HOL Light formalization.
Cite
@article{arxiv.2605.01028,
title = {Stokes' Theorem for Smooth Singular Cubes in Lean 4: True Pullback, Bridges to mathlib4, and Chain-Level d^2=0},
author = {David B. Hulak and Arthur F. Ramos and Ruy J. G. B. de Queiroz},
journal= {arXiv preprint arXiv:2605.01028},
year = {2026}
}