This directory contains the operation-specific backend that lowers a tensor contraction to a loop of rank-two GEMM dispatches.

LoopedGemmContractionBackend currently accepts exactly one residual M or N stride group after joint stride merging. Each loop iteration advances copied mdspec metadata to one disjoint output slice, then dispatches gemm_op through the backend's retained execution selector. K remains a single GEMM dimension, so every slice uses the contraction's original beta.

Immediate mdspans are advanced through their accessor offset policy. Deferred mdspecs must provide a descriptor offset_by operation; this preserves the storage and resource identity needed by host, CUDA, and future execution-domain acquisition.

Every projected matrix must still expose a unit-stride axis. Slicing does not materialize or pack a tensor that lacks one; such instances cleanly decline to the next contraction backend.

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