BUG: matmul fails with zero-length broadcast batch dimensions #1007

Bug

Batched sparse.matmul fails when a broadcast batch dimension is zero.

Reproduced on main at d63255057744331b96626a1f1c24504b3a3783cd.

import numpy as np
import sparse

a = sparse.COO.from_numpy(np.zeros((0, 2, 3)))
b = sparse.COO.from_numpy(np.zeros((0, 3, 4)))
sparse.matmul(a, b)
# ValueError: At least one array required.

a = sparse.COO.from_numpy(np.zeros((1, 2, 3)))
sparse.matmul(a, b)
# IndexError: Index is not smaller than dimension 0 >= 0

NumPy returns shape (0, 2, 4) in both cases. The recursive implementation either stacks an empty result list or iterates using max(1, 0), rather than the broadcast result size zero.

A focused empty-batch path and regression coverage are ready. The matrix exercises differing ranks, zero/singleton broadcasting, COO/GCXS/mixed dense inputs, dtype promotion and invalid contraction/batch shapes. Thirty-two new cases fail before the production change.

This is a different path from zero-length contracted axes in tensordot: the contracted dimension here is three and the failure happens in batch recursion.

This is an AI-assisted bug investigation with locally executed reproductions and tests. No assignment is requested.