Step a point stencil

:cite:`goswamiEnhancedClimbingImage2026,henkelmanDimer1999,malekArtNouveau2000`

Stencil::point builds a minimiser, a dimer, Lanczos, ART, or eigen following. The defaults match MinModeConfig: forward difference, dr = 1e-3, rotation tolerance 1e-4, rotation angle five degrees (zero disables it), 20 rotations, Krylov dimension 12, FIRE, maximum move 0.2. When the per-atom cap shortens a negative-curvature FIRE step and the arrival is no longer negative, that step is replaced from the last negative point by 0.01 times the reflected force. Dimer and Lanczos are a MinModeSession. Dimer rotational conjugate-gradient history crosses translations. A negative curvature reflects the parallel force. A curvature that is not negative takes one full per-atom maximum move along the mode and drops the perpendicular force. Henkelman and Jónsson (1999), https://doi.org/10.1063/1.480097. Goswami, Gunde, and Jónsson, Front. Chem. (2026), https://doi.org/10.3389/fchem.2026.1807063, Eq. 9.

let mut search = Stencil::point(x0)
    .preset(Preset::Dimer)
    .mode(seed)
    .build()?;
let report = search.step(&surface)?;

ART pushes along the seed until the curvature falls under art_threshold (default 0), then climbs with Lanczos. Malek and Mousseau (2000), https://doi.org/10.1103/PhysRevE.62.7723. Eigen following builds a central-difference Hessian, calls exact_eigh, and makes the largest-magnitude component of the lowest mode positive. build rejects Climb::Reflect on a minimiser, a window on a point, a zero thread count, and ART without a mode solver.

Stencil::band checks the array and then returns band presets stay on feat/band-methods-zoom. Zoom, energy-weighted springs, and the band side of the builder are that branch. The chain, the mesh (remesh, insert, window), and the point controller are on this branch.

From C, rgsaddle_stencil_config_new takes the preset discriminant. Unknown keys return RGSADDLE_INVALID_PARAMETER. rgsaddle_last_error is thread-local. rgsaddle_stencil_run loops over rgsaddle_stencil_step. The report opens with struct_size. The older band and min-mode entries stay step-only, and the ABI minor stays 16.

From Python, rgsaddle.Stencil.point(x, preset”dimer”)= takes a C-contiguous float64 vector. step(surface) releases the thread, and the surface callback re-attaches. rgsaddle.ase.Point(atoms, preset”dimer”).run(fmax, steps)= is an ASE Optimizer whose step is one stencil step. A second thread that enters the same handle raises RuntimeError.

Chain::evaluate writes each image from a block of one. Threads 1, 2, 3, and 8 produce the same bytes. A point preset is one row, so its thread count does not change the bytes either.