Graph of Thoughts: when a tree of reasoning isn't enough, let the branches merge

Tree of Thoughts was a genuine leap. Instead of reasoning in one straight line, it branches into several lines, scores them, prunes the dead ends, and searches for the best path — so a puzzle that would sink a single chain of thought becomes solvable. But a tree has one restriction baked right into its shape, and once you see it you can't unsee it: every node has exactly one parent. A branch can be extended or abandoned. It can never be combined with another branch. That matters more than it sounds. Real problems decompose, and when they do, different branches each get part of the answer right. Branch A nails the first half; branch B nails the second half; neither is fully correct on its own. A tree is forced to pick one and throw the other's good half away. Graph of Thoughts (GoT) removes exactly that restriction. 🕸️ Interactive demo (a real merge-sort that branches, merges, and refines — with live-verified scores): https://dev48v.infy.uk/prompt/day21-graph-of-thoughts.html The core idea: thoughts are nodes in a graph GoT reframes reasoning as building a graph . Each vertex is a thought — a partial solution or intermediate result. Each edge is an operation that produced one thought from one or more others. Because it's a general graph and not a tree, a thought is allowed to have several parents, and edges can even loop back on themselves. That single change in the data structure is the entire conceptual leap. Everything else is just the operations you're now free to run on that network. The four operations generate (branch) — the familiar move, straight from Tree of Thoughts. From one thought, produce several different next thoughts. This can also be a split : break the input into independent sub-problems solved on separate branches. Diversity matters here — near-duplicates waste budget. score / rank — turn each thought into a number so the controller can compare them. Objective scorers win: a validator, a test, a metric. In the demo, the scorer is deliberately con