We present mycelium-index, a streaming approximate nearest neighbor (ANN) index for high-dimensional vector spaces, inspired by the adaptive growth patterns of biological mycelium. The system continuously adapts its topology through myelial edge decay and reinforcement, a traffic-driven living hierarchy, and hybrid deletion combining O(1) bypass for cold nodes with O(k) beam-search repair for hub nodes. Experimental evaluation on SIFT-1M demonstrates that mycelium achieves 0.927 +/- 0.028 recall@5 under FreshDiskANN's 100%-turnover benchmark protocol -- within the measurement confidence interval of FreshDiskANN's ~0.95 -- while using 5.7x less RAM (88 MB vs. >500 MB) and achieving 4.7x higher QPS (2,795 vs. ~600). On the static index, at ef=192, mycelium matches HNSW M=16 recall (0.962 vs. 0.965) at 5.2x less RAM (163 MB vs. 854 MB). Performance optimizations including NEON SIMD distance computation, Vec-backed node storage, and bitset visited tracking yield a cumulative 2.7x QPS improvement. A systematic study of ten streaming repair mechanisms finds that geometric heuristics universally fail in high dimensions, while topological mechanisms succeed -- a principle we term the topological repair invariance of high-dimensional ANN graphs.