Problem dossier · Number Theory
Hadamard conjecture
A Hadamard matrix — a ±1 matrix with pairwise orthogonal rows — exists for every order divisible by 4.
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Status
Open. The smallest order with no known construction is 668.
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The Angle of Attack
Generate constructions (Paley, Sylvester, Williamson-type composition) for unresolved orders; run structured search over cocyclic or symmetric candidates for order 668.
Tags: matrices · orthogonality · combinatorial designs · construction
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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Related Problems
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