What is reproduced
This first version implements the forward equilibrium problem in Section 2.1, Fig. 2 and Eq. (7). Our four-cable net has one free joint and four fixed supports. Its topology follows the paper; its dimensions and loads are explicitly chosen here, not transcribed from the figure. The paper develops differentiable inverse design; that contribution is outside this version.
The forward method
Force density is axial tension divided by member length. Positive densities give an anchored network a positive-definite equilibrium matrix. The research crate assembles this matrix and uses the production engine’s sparse Cholesky factorization for the three coordinates. Forces follow from f = qℓ.
x* = (Σ qⱼ sⱼ + p) / Σ qⱼ
Supports are (±2, ±2, 0) m. The baseline downward load is 4 kN and every density is 1 kN/m. Eq. (7) then gives z = −1 m, length = 3 m and tension = 3 kN. These are derived targets for our inputs, not published numerical observations.
Evidence and tolerances
Five input cases compare every coordinate and cable force with unmodified jax_fdm in float64. Absolute tolerances are 1e-12 m for coordinates, 1e-12 kN for reference forces and equilibrium residuals, and 1e-9 kN for production truss forces. The validation file records each observed error. The replay is a load sweep computed by the same Rust solver, not convergence iterations.
Maximum reference position error: 2.2 × 10−16 m; Maximum reference force error: 0 kN.
Reference: jax_fdm, MIT, revision 9a17fd379071fb3511ca914f46e8d1e8c286460e. The manifest records the source archive SHA-256, output hashes and installed environment. This revision has not been confirmed as the publication revision.
What the production engine checks
The editor receives the found geometry, fixed support translations and the same vertical load as a 3D linear elastic truss. With equal member stiffnesses, symmetry makes its axial forces match FDM. Tests also check its vertical displacement against the elastic closed form. This is a separate analysis of initially unstressed bars: cable prestress and geometric stiffness are not transferred.
Not yet reproduced
No adjoints, gradients, optimization, shells, mixed tension/compression, shape-dependent loading, buckling or timing claims. No published optimized shapes or table values are reproduced. The preview is a labelled projection; the editor contains the full spatial model.
Research, not a design tool. Agreement with another code is not experimental validation or engineering certification.
Questions for the authors
Which commit and environment generated the paper? Are the exact Fig. 2 inputs available? Which small cable-net benchmark and reference coordinates, forces and gradients would you recommend for a subsequent inverse-design reproduction?
Cite this
Stabileo Research, “Four cables, one equilibrium”, reproduction of Rafael Pastrana, Deniz Oktay, Kai-Uwe Bletzinger, Ryan P. Adams, Sigrid Adriaenssens (2026), doi:10.1016/j.cma.2026.118783. Implementation: research/form-finding/pastrana-2026 at commit 8068cd16ea2c. Engine: the Stabileo engine at the same commit. Permanent links to this exact build are planned.