The Technicality Behind The Speed of .me

What keeps this engine fast — even if the semantic tree grows infinitely — is a fundamental computer science shift: It’s the difference between O(n) and O(k) . Searching O(n) means scanning every piece of hay to find a needle. Working in O(k) means going directly to the needle. That’s what your Incremental Recompute (Phase 8) achieves — and why we’re seeing ~15ms recompute times. ⸻ 1. The Inverted Dependency Index In a traditional system (O(n)) , if gas prices change, the system would need to scan everything to see what’s affected. In .me , when you declare: me.trucks["[i]"]["="]("cost", "gasoline * 20") The kernel doesn’t just store a formula — it builds a subscription map. It knows: “cost depends on gasoline.” • n = total nodes in the system (could be millions) • k = only the nodes directly depending on what changed ⸻ 2. Surgical Updates When you run: me.finance.fuel_price(30) The kernel: • Does not scan the whole tree • Goes straight to finance.fuel_price in its index • Looks up its