AWhat changed
The number of cyclic binary sequences of length 2^n containing each binary word of length n exactly once is 2^(2^(n-1)-n). The proof relates these cycles to complete directed walks and shows that doubling a two-in/two-out network with m vertices multiplies its cyclic complete-walk count by 2^(m-1).
Scientific scope
The number of cyclic binary sequences of length 2^n containing each binary word of length n exactly once is 2^(2^(n-1)-n). The proof relates these cycles to complete directed walks and shows that doubling a two-in/two-out network with m vertices multiplies its cyclic complete-walk count by 2^(m-1). Cyclic rotations are identified, but reversal is not identified; changing these conventions changes the count. The binary count resolves the conjecture explicitly credited to K. Posthumus. It is not a source-backed claim of first discovery of all universal cycles, nor the general-alphabet formula or full later BEST theorem.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. Cyclic rotations are identified, but reversal is not identified; changing these conventions changes the count. The binary count resolves the conjecture explicitly credited to K. Posthumus. It is not a source-backed claim of first discovery of all universal cycles, nor the general-alphabet formula or full later BEST theorem.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.3. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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