Frontroad gee(c/acc)🇨🇻🇳🇴

I came across this post I made in 2024, suggesting that blockchain networks might be better understood as curved, hyperbolic spaces. Two years later, I used Claude to test it in four rounds of simulation, using Ollivier-Ricci curvature to measure the shape of each network. Scoring: Distance in time behaves differently from distance in hops, and that matters: this held. Curvature, measured on hops, points to a network's bottlenecks: this held. Gossip spreads better in curved spaces: not supported. New nodes can plug in at the edges easily: only with hubs. Real network delays fit curved space better than flat: needs real data. Setup for the simulation: 4 networks (random, peer-capped, scale-free and hyperbolic)
 500 nodes each (average of 8 peers per node) 
3 seeds x 150 broadcasts (results averaged)
 Flood gossip (40ms average link latency, 2ms per send) The first round compared four network shapes and how fast a block spreads through each of them. The hyperbolic network turned out to be genuinely hyperbolic, and curvature did point to where the bottlenecks were. But the idea that gossip spreads better in curved space didn't hold. With busy hubs it was about 40 to 60% slower to reach most of the network, mostly because everything funnels through a few large hubs, some with around 180 peers, and those hubs get stuck. So in the second round I removed the hubs by capping every node at 16 peers, and compared curved against flat. Curvature marked the bottlenecks more clearly here, with the most negatively curved links carrying blocks about 37% of the time against 13% for the most positive. The problem was the edge. Without hubs, up to 31% of nodes in the curved network were left stranded, and none in the flat one. The hubs were what kept the edge connected, and they were also what slowed everything down. The third round tried to fix that. Giving each node six nearby links and two random ones worked well. Nobody was stranded and blocks spread roughly three to six times faster. I also tried two changes to how nodes pass blocks along, and neither helped. The last round placed nodes roughly where validators actually are, with delays based on real distance. Choosing peers by distance, plus a couple of random ones, was about 29% faster than picking peers at random. So shape does matter. What I couldn't settle is whether that shape is curved or flat, since both performed the same. That needs real measured delays. There are limits to all this. These were 500 simulated nodes, not a real network running one simple gossip protocol. The last round also sends traffic in straight lines, which the real internet doesn't do. These are simulation results btw. Longer writing and code in the comments:)