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1. turyn-converseturyn-conversePublic

   A theorem program toward a converse of Turyn's theorem: composites q ≤ 2000 closed, plus unconditional theorems for infinite families.

   TeX

2. p1mod4p1mod4Public

   Hadamard matrices of order 2q(q+1) for prime powers q ≡ 1 (mod 4), built in closed form from the quadratic character.

   Python

3. extremal-eigenvaluesextremal-eigenvaluesPublic

   Settles two conjectures about sparse divisor matrices and extends their analysis to extreme eigenvalues, singular values, and prime-number-theorem encodings.

   Python

4. geometric-difference-familiesgeometric-difference-familiesPublic

   RDS-coarsening lift for partitioned difference families: geometric-block PDF families and optimal constant-composition codes

   Python

5. sparse-mertens-singular-valuessparse-mertens-singular-valuesPublic

   The smallest singular value of a 2.6n-nonzero (0,1) matrix with determinant M(n): sigma_min = |M(n)| n^{-3/2+o(1)}, a two-sided Riemann-hypothesis criterion, via Alladi's estimates for the Mobius f…

   Python

6. convex-framework-cazacconvex-framework-cazacPublic

   Convergence theory for an iterated SOCP relaxation of CAZAC sequence feasibility: unconditional single-point convergence, exact regularity at Zadoff-Chu points, and a transfer to the elliptope of c…

   TeX