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Author

Xavier Callens

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#data science Open access Oct 2026

QuantumFluids: a machine-checked Lean 4 library of quantum-fluid structure, applied to published neutron-scattering work

An open Lean 4 / Mathlib library of 235 machine-checked theorems on the mathematical structure of quantum fluids, with the accompanying paper. Contents. Correctness of the phase-winding algorithm by which Gross-Pitaevskii codes locate quantized vortices, including its exact failure case (a phase step of exactly pi, whe...

Xavier Callens · 0 citations
#software testing Open access Sep 2026

When does self-duality cause physics? A machine-checked criterion, tested across fifteen candidate physical systems, an interventional experiment, and real cosmological data

Physics is full of self-dual points: places where a symmetry exchanges two descriptions of the same system and maps it to itself. Some of these points are physically decisive — the Kramers–Wannier point fixes the Ising critical temperature exactly — and some are not: the free boson's self-dual radius is an ordinary poi...

Xavier Callens · 0 citations
#software testing Open access Sep 2026

When does self-duality cause physics? A machine-checked criterion, tested across sixteen candidate physical systems, an interventional experiment, and real cosmological data

Physics is full of self-dual points: places where a symmetry exchanges two descriptions of the same system and maps it to itself. Some of these points are physically decisive — the Kramers–Wannier point fixes the Ising critical temperature exactly — and some are not: the free boson's self-dual radius is an ordinary poi...

Xavier Callens · 0 citations

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