Add challenge 82: Linear Recurrence (Medium)

[claude]

Summary

• Adds challenge 82: Linear Recurrence (Medium difficulty)
• Computes h[b,t] = a[b,t] * h[b,t-1] + x[b,t] for batched sequences of shape [B, L]
• This is the core primitive of State Space Models (Mamba, S4, H3) used in modern LLM inference
• Naive O(L) sequential scan is correct; solvers are challenged to implement a parallel scan using the associative combine operator (a1,x1)⊕(a2,x2) = (a1·a2, a1·x2+x1) — achieving O(log L) depth
• Teaches a deeper parallel scan pattern than the existing prefix sum challenge, with direct real-world applicability

Test plan

• generate_example_test() uses clean illustrative values (exponential decay + prefix sum rows)
• generate_functional_test() covers: single element, 2-element, zero inputs, a=0 (no recurrence), a=1 (prefix sum), power-of-2 lengths, non-power-of-2 lengths, realistic SSM size
• generate_performance_test() uses B=64, L=16384 (~12 MB total, fits 5× in 16 GB VRAM)
• All tests validated on NVIDIA Tesla T4 via run_challenge.py --action submit ✓
• All 6 starter files present and correct
• pre-commit run --all-files passes
• challenge.html starts with <p>, uses <h2> sections, LaTeX \begin{bmatrix} for matrix examples, includes SVG visualization, performance bullet matches generate_performance_test()

🤖 Generated with Claude Code