We present core attention disaggregation (CAD), a technique that improves long-context LLM training by disaggregating the core attention (CA) -- the parameter-free $\mathrm{softmax}(\mathbf{QK}^{\top})\mathbf{V}$ computation -- and schedules it on an independent pool of resources. Existing systems co-locate core attention with other components. At long context, the quadratic growth of CA computation and near-linear growth of the rest create load imbalance -- hence stragglers across data and pipeline groups. CAD is enabled by two key observations: (i) \emph{statelessness}: CA has no trainable parameters and minimal transient state, so balancing reduces to scheduling compute-bound tasks; and (ii) \emph{composability}: modern attention kernels sustain high utilization on fused batches of arbitrary-length token-level shards. CAD dynamically partitions the core attention computation into token-level tasks (CA-tasks), and dispatches them to a pool of devices specialized for CA computation (attention servers). It then rebatches CA-tasks to equalize CA compute across attention servers without loss of kernel efficiency. We have implemented CAD in a system called DistCA with a ping-pong scheme to completely overlap communication with compute, and in-place attention servers to improve memory utilization. Scaling to 512 H200 GPUs and 512K context length, DistCA eliminates DP/PP stragglers, achieves near-perfect compute and memory balance, and improves end-to-end training throughput by up to 1.9× over Megatron-LM and 1.35× over existing load-balancing methods