Xavier Callens

A topological proxy for the ill-conditioning of the discrete inverse conductance problem, and an independent integrator check of a resistor-capacitor bench

The Jacobian of the Dirichlet-to-Neumann map of a resistor network with respect to its edge conductances has one column per edge; the exponential growth of its condition number with the depth of the unknowns is the central finding of the companion preprints. This preprint asks wh...

A kernel-checked symmetric-square structure theorem for Cooper's sporadic Apéry-like operators, and the monodromy lattice of the s₇ family

Stream 1 of the Dual-Scale program: a Lean 4 formalization, kernel-checked with Lean's three standard axioms (propext, Classical.choice, Quot.sound), no sorry, no native_decide outside the golden tests. Principal results. (i) The order-3 Picard–Fuchs operator of Cooper's sporadic...

A kernel-checked symmetric-square structure theorem for Cooper's sporadic Apéry-like operators, and the monodromy lattice of the s₇ family

Stream 1 of the Dual-Scale program: a Lean 4 formalization, kernel-checked with Lean's three standard axioms (propext, Classical.choice, Quot.sound), no sorry, no native_decide outside the golden tests. Principal results. (i) The order-3 Picard–Fuchs operator of Cooper's sporadic...

Logarithmic boundary depth and the conditioning of the discrete inverse conductance problem on hyperbolic lattices

Version 1.1 (revised after peer review; the review and the point-by-point response are included in code.zip under paper/reviews). Changes from v1.0: (a) the flat-lattice condition numbers that are singular in double precision are now computed in 512-bit ball arithmetic with certi...

Claims vs. Evidence: A Measured Audit of an AI-Assisted Rust Kernel and an Oracle-Gated Workflow for LLM Proof Completion

Large language model (LLM) agents can now generate operating-system code, formal specifications, benchmark reports, and papers faster than a human can check them. We report what happened when we measured one such artifact against its own claims. RunuX is a Rust reimplementation o...

The Frontier Triad: Swampland Distance Bounds, Tachyon Condensation, and Non-Perturbative Vacuum Decay on K3 × T²

Revision (2026-09-18): orientifold bookkeeping. The tadpole configuration is placed in the orientifold K3 × T²/Z2, with the 4 O7-planes at the fixed points of T²/Z2, and the charges are stated in units of μ7/4 (+1 and −4 in D7 units; Sen hep-th/9605150, Tripathy–Trivedi hep-th/03...