BackendOps Array API substrate

BackendOps remains SpaceCore’s declared numerical API. Users and internals should continue to call explicit methods such as ops.matmul, ops.reshape, and ops.eigh rather than reaching through to backend libraries directly.

Concrete backends expose an Array API compatible xp namespace as the shared implementation substrate for common dense-array operations. NumPy and PyTorch use array-api-compat wrappers; JAX uses jax.numpy, which already exposes the Array API spellings SpaceCore relies on. xp is intentionally an escape hatch for advanced backend-specific code; it is not the preferred portable SpaceCore API.

Audit categories

Category	Methods	Notes
Direct xp delegation	reshape, broadcast_to, stack, conj, real, imag, abs, sign, sqrt, exp, log, where, isfinite, isnan	Implemented once in BackendOps.
Delegation with name or namespace adaptation	transpose, concatenate, trace, take, eigh, eigvalsh, solve, svd, cholesky, norm	SpaceCore keeps existing method names while adapting to names such as concat or backend linalg namespaces where needed.
Common Array API delegation	sum, mean, min, max, prod, sort, argsort, argmin, argmax, diag, diagonal, tril, triu	The base method uses Array API spellings such as axis, keepdims, concat, and permute_dims.
Deliberately backend-specific	sanitize_dtype, assparse, sparse_matmul, logsumexp, index_set, index_add, ix_, fori_loop, while_loop, scan, cond, allclose_sparse, sparse/dense type predicates	These operations have sparse formats, mutation semantics, tracing rules, or dtype/device behavior that is not captured by the common dense-array namespace.

Backend tuning arguments

Portable mathematical options stay as explicit method arguments. Backend tuning should be passed only to selected heavier methods, currently through a backend_kwargs dictionary on operations such as matmul, eigh, solve, eigvalsh, svd, and cholesky. Exotic backend features belong behind ops.xp or the backend-specific handles such as ops.np and ops.jax.