I need you to write a paged attention decode kernel for the RTX PRO 6000 (SM120 Blackwell, GDDR7, 1.8 TB/s). The reference implementation is in reference.py and your kernel goes in solution.py. You can make whatever mess you want in this directory — scratch files, intermediate kernels, build artifacts, profiling traces — but the final answer has to be in solution.py with the same Model, get_inputs, and get_init_inputs interface as reference.py.

This is single-query decode: each batch element has a query of shape (num_heads, head_dim) and attends over a KV cache of seq_len[b] tokens stored as fixed-size pages in a global pool, with block_table[b] listing which pages belong to batch element b. The KV cache is laid out as (num_blocks, page_size, num_kv_heads, head_dim * 2) where the last dim packs [K | V] so a single gather pulls both. You return the bf16 output of shape (batch, num_heads, head_dim). Correctness tolerance is 0.02 abs/rel on bf16/fp16. The shapes you have to handle are batch=8 num_heads=32 num_kv_heads=8 head_dim=128 seq_len=1024 page_size=16 (Llama-3 8B-style decode), batch=32 num_heads=32 num_kv_heads=8 head_dim=128 seq_len=2048 page_size=16 (server-batched decode), batch=4 num_heads=64 num_kv_heads=8 head_dim=128 seq_len=4096 page_size=16 (Llama-3 70B GQA wide ratio with long context), batch=16 num_heads=32 num_kv_heads=8 head_dim=128 seq_len=1535 page_size=16 (non-power-of-two seq_len that forces predicated tails), and batch=8 num_heads=16 num_kv_heads=4 head_dim=64 seq_len=2000 page_size=16 (small head_dim, non-pow2).

This needs to be a real custom kernel. Don't import or call vllm.attention, flashinfer.batch_decode_with_paged_kv_cache, flashinfer.decode, torch.nn.functional.scaled_dot_product_attention, or F.scaled_dot_product_attention — they're off-limits, including the trick of gathering pages first and then dispatching to SDPA. Try CUDA C++ via load_inline, Triton, inline PTX, or CUTLASS — whatever fits. Anything you're uncertain about, look up PTX docs, clone CUTLASS or vLLM or FlashInfer or other reference repos, read library headers, and investigate.

Your flywheel is implement, profile (ncu, nsys, torch.profiler — whatever's useful) and time it with benchmark.py, verify correctness by running `python check.py` and reading the output, then iterate. Don't substitute your own one-off correctness snippets for check.py — it iterates over every shape, your spot-check almost certainly won't. If `python check.py` hasn't printed PASS, you're not done. Take as long as you need to actually push the number up.