arXiv subjects

John Velkey

Publications and source records attributed to John Velkey.

3 recordsLinked to original sources

arXiv2026

LeanBET: Formally-verified surface area calculations in Lean

The Brunauer--Emmett--Teller (BET) method is a standard tool for estimating surface areas from adsorption isotherms, yet practical implementations involve multiple algorithmic steps whose correctness is rarely made explicit. In this work, we present a fully executable and formally verified BET analysis pipeline implemented in the Lean~4 theorem prover. Our formalization covers the complete BET Surface Identification (BETSI)-style workflow, including window enumeration, monotonicity checks, knee selection, and linear regression. We carry out computations in floating-point arithmetic and develop the corresponding correctness proofs over the real numbers, using a shared polymorphic implementation that supports both. On the proof side, we show that the regression coefficients returned by the algorithm agree with their specification-level definitions and minimize the least-squares error under the stated assumptions. We also formalize the algebraic derivation of the BET linearized expression and connect that result directly to the executable analysis pipeline. We further prove that the window enumeration is sound and complete, and that the admissibility checks and knee-based selection satisfy their formal specifications. We evaluate the implementation against the BETSI reference method on benchmark adsorption isotherms. Compared to BETSI, LeanBET agrees to machine precision for 18 of the 19 isotherms, with only a 0.03\% deviation for the UiO-66 dataset. This demonstrates that a scientific computing workflow can be built in Lean, yielding both formal verification guarantees and numerical agreement with an established Python reference implementation.

cs.LO↗

arXiv2025

Formalizing dimensional analysis using the Lean theorem prover

Dimensional analysis is fundamental to the formulation and validation of physical laws, ensuring that equations are dimensionally homogeneous and scientifically meaningful. In this work, we use Lean 4 to formalize the mathematics of dimensional analysis. We define physical dimensions as mappings from base dimensions to exponents, prove that they form an Abelian group under multiplication, and implement derived dimensions and dimensional homogeneity theorems. Building on this foundation, we introduce a definition of physical variables that combines numeric values with dimensions, extend the framework to incorporate SI base units and fundamental constants, and implement the Buckingham Pi Theorem. Finally, we demonstrate the approach on an example: the Lennard-Jones potential, where our framework enforces dimensional consistency and enables formal proofs of physical properties such as zero-energy separation and the force law. This work establishes a reusable, formally verified framework for dimensional analysis in Lean, providing a foundation for future libraries in formalized science and a pathway toward scientific computing environments with built-in guarantees of dimensional correctness.

physics.chem-ph↗

arXiv2025

Benchmarking Energy Calculations Using Formal Proofs

Traditional approaches for validating molecular simulations rely on making software open source and transparent, incorporating unit testing, and generally employing human oversight. We propose an approach that eliminates software errors using formal logic, providing proofs of correctness. We use the Lean theorem prover and programming language to create a rigorous, mathematically verified framework for computing molecular interaction energies. We demonstrate this in LeanLJ, a package of functions, proofs, and code execution software that implements Lennard Jones energy calculations in periodic boundaries. We introduce a strategy that uses polymorphic functions and typeclasses to bridge formal proofs (about idealized Real numbers) and executable programs (over floating point numbers). Execution of LeanLJ matches the current gold standard NIST benchmarks, while providing even stronger guarantees, given LeanLJ's grounding in formal mathematics. This approach can be extended to formally verified molecular simulations, in particular, and formally verified scientific computing software, in general. Keywords: Formal verification, Lean 4, molecular simulations, functional programming.

cond-mat.stat-mech↗