OpenAI reports graph decomposition at the integral expectation threshold

Every graph can be partitioned into a universally bounded number of fixed edge pieces, each with ordinary random-graph containment threshold at most a universal constant times the original graph’s integral expectation threshold.

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Understanding the problem

Read the background

Every graph can be partitioned into a universally bounded number of fixed edge pieces, each with ordinary random-graph containment threshold at most a universal constant times the original graph’s integral expectation threshold.

Why it matters

If correct, resolves the graph-decomposition conjecture and removes the logarithmic threshold loss for each piece.

What counts as progress

Can every graph be split into a bounded number of pieces whose thresholds match its integral expectation threshold?

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