The Topological Gap in Neuromorphic Hardware: Why Current Chips Are Von Neumann-Adjacent and How to Fix It

Neuromorphic computing architectures (Intel Loihi, IBM TrueNorth) promise to escape the von Neumann bottleneck by co-locating memory and computation. We apply the capped alternative-path action S(e) — shown in a companion paper to be the formal topological signature of in-memory computing — to the routing topologies of current neuromorphic chips and find that all exhibit exactly 0% S(e)=3 connections. This is mathematically necessary: square and torus meshes are bipartite graphs, and the Von Neumann Obstruction Theorem (companion paper, Proposition 1) proves that bipartite graphs cannot contain triangles, making S(e)=3 structurally impossible. Current neuromorphic chips are therefore topologically von Neumann-adjacent in their routing fabric, despite their in-memory synaptic compute model. We compute S(e) for two alternative routing topologies: triangular lattice (100% S=3) and Watts-Strogatz small-world with p=0.1 (89.3% S=3), both entering the biological target zone (77–95% observed across four biological connectomes). Markov chain simulations show an 11% baseline latency reduction from triangular routing, expanding to 44–45% under 20% edge failure rates — a direct consequence of S=3 providing local bypass paths. All computations were validated on a mobile ARM device using NEON 128-bit SIMD intrinsics (BFS frontier expansion via vorrq_u8, 0.1 ms per topology). A reference C++ NEON implementation is included as an appendix. The fix is architecturally concrete: replace square mesh inter-core routing with triangular lattice routing (6 ports per core instead of 4), or add sparse Watts-Strogatz rewiring (p=0.1) to an existing mesh.