k-index

Quantity	k_index — position in the ordered table of meshes
Model	none yet
Setting	k-point mesh

Core keeps every mesh a structure can have in one ordered ladder. A k-index is a rung on that ladder: mesh 0 is the coarsest, and each step up is the next mesh that is meaningfully denser.

Predicting the rung directly is a different problem from predicting a k-distance, which is why the two are separate quantities under one setting rather than one model with two outputs.

Why it is a separate quantity

A k-distance is a physical spacing in Å⁻¹, and Core converts it to a mesh with the crystal's reciprocal lattice: N_i = ceil(|b_i| / k_distance). Two structures with the same k-distance can get very different meshes.

A k-index is an integer into a table Core already built. There is no conversion — the answer is the mesh, once you know which table it indexes.

So the two need different conversions and different guarantees, and a consumer must know which it is being given. That is what the quantity segment of a release name records:

k_points.k_distance.qrf.goldilocks_kdist_ultra.v1
k_points.k_index.<family>.<dataset>.v1
└ setting  └ quantity

Status

No model here predicts a k-index. Goldilocks Core has a k-index path of its own that does its own feature extraction and inference inline; the inference seam is what a model published here would plug into instead.