Does a Hadamard matrix of order 668 exist? (Smallest unresolved order of the Hadamard conjecture.)
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Statement
The Hadamard conjecture asserts a $\pm 1$ matrix $H$ of order $4k$ with $HH^{T} = 4k\,I$ exists for every $k$. The smallest order for which existence is unknown is $668$.
Assessment
Renown 4/5
A 130-year-old conjecture with the rare property of a concrete smallest open instance.
Attackability 3/5
The witness is a single explicit 668x668 sign matrix, instantly verifiable; the search space is astronomically large and decades of algebraic constructions have missed 668, but SAT/algebraic hybrid search is a live and legitimate route.
- finite witness
- 5/5
- oracle cost
- 5/5
- freshness
- 2/5
- seedability
- 3/5
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
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Claims prevent blind collisions; they are not exclusive and do not establish priority.