This directory adapts normalized CUDA mdspec operands to cuBLAS operation tags. Tensor frontends select the backend while storage policy is available, then lower fixed operands before dispatch. CublasBackend validates their mdspec metadata, blocks for an execution lease, opens synchronized CUDA buffer access, and calls the provider-ready leaf.

The current operations are GEMM plus full inner-product and Euclidean-norm reductions. Direct Tensor dispatch uses the blocking try_kernel entry point. Coroutine dispatch detects the backend's try_make_kernel_task customization, which prepares the same operands, binds a CUDA child to their device, awaits an execution lease, and invokes the prepared provider leaf without redispatching.

The ordinary adapter is gemm.hpp; it has no dependency on coroutine runtime support. Async Tensor lowering additionally includes gemm_task.hpp, keeping task creation and resource awaiters out of synchronous-only targets. reductions.hpp accepts exhaustive raw CUDA descriptors and returns a host scalar through the checked cuBLAS level-one wrappers. Transformed or non-exhaustive descriptors decline rather than bypassing accessor semantics.

CUDA-mdspan recognition, buffer bounds and device validation, completion-ledger access, and the shared blocking/coroutine preparation path are private implementation details under detail/. The adjacent `linalg/cublas/` layer accepts only provider-ready matrix descriptors and an acquired execution lease.

An empty GEMM output succeeds before operand staging. cuBLAS accepts a zero inner extent with null zero-sized input buffers and applies the degenerate C = beta*C operation, so canonical CUDA matrices retain provider execution for that case. CudaReferenceBackend follows CublasBackend in the storage-selected backend list. It currently handles contiguous Tensor transfer; additional fallback kernels remain operation-specific.

assign_product_op may provisionally construct, resize, or relocate its replaceable output before mdspan layout and transform acceptance completes. A decline submits no CUDA work and leaves the prepared output available to a later backend, which may reuse or replace it. Fixed-output gemm_op retains the stronger unchanged-on-decline contract. The adapter receives the normalized readable descriptors, prepares the output, normalizes that output once after preparation, and then calls the private cuBLAS mdspan implementation directly. It does not redispatch the resolved operands through a gemm_op customization.

The Tensor conformance tests share their scalar and canonical-layout cases with the host GEMM backends. cuBLAS-specific tests cover deferred buffer offsets, transpose and conjugate-transpose subviews, padded leading dimensions, clean layout decline before resource acquisition, structured incompatible-device decline, and hard alias contract violations. Unknown accessor semantics are rejected at type probing rather than bypassed through the descriptor.

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