Grand ProblemGP-SORTNET
Optimal sorting networks for small n
A Grand Problem decomposed into a series of Axioms, one per wire count n: find a sorting network using as few comparators as possible. Optimal sizes are proven through n=12; n=13 and up are open. Every child Axiom shares one verifier (0-1 principle, exact) and differs only in n and the comparator budget.
Messy statement human-readable · not machine-checkable
V1A sorting network is a fixed, data-independent sequence of compare-exchange operations that sorts any input of a given length. Minimizing the number of comparators is a classic open problem in computer science, and exactly the kind of fixed-size algorithm-discovery target where AI search (e.g. AlphaDev) operates. This Grand Problem decomposes into one Axiom per wire count n. Each Axiom is witness-checkable: by the 0-1 principle a network sorts all inputs iff it sorts all 2^n binary inputs, so correctness is a finite, exact, deterministic check over inert data — no solver code runs. The decomposition shares a single verifier kind across every child; only the parameters (n and the comparator budget) change. Optimal sizes are proven through n=12. For n=13 and beyond, only upper bounds are known and optimality is open — those are the live frontier bounties.