Stokes' Theorem for Smooth Singular Cubes in Lean 4: True Pullback, Bridges to mathlib4, and Chain-Level d^2=0
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| Format: | Preprint |
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2026
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| _version_ | 1866918477828194304 |
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| author | Hulak, David B. Ramos, Arthur F. de Queiroz, Ruy J. G. B. |
| author_facet | Hulak, David B. Ramos, Arthur F. de Queiroz, Ruy J. G. B. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01028 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stokes' Theorem for Smooth Singular Cubes in Lean 4: True Pullback, Bridges to mathlib4, and Chain-Level d^2=0 Hulak, David B. Ramos, Arthur F. de Queiroz, Ruy J. G. B. Logic in Computer Science Differential Geometry 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. |
| title | Stokes' Theorem for Smooth Singular Cubes in Lean 4: True Pullback, Bridges to mathlib4, and Chain-Level d^2=0 |
| topic | Logic in Computer Science Differential Geometry |
| url | https://arxiv.org/abs/2605.01028 |