hadamard-b-formal: the bordered Goethals-Seidel characterisation, the s=1 layer, and Theorem D
A Lean 4 and Mathlib formalization of part of the theorem layer of the Hadamard-B note on bordered Goethals-Seidel arrays: twenty-six compared theorems over fifty-eight compared definitions. Theorem A characterises, by an if-and-only-if, when a Goethals-Seidel array of four sign-valued sequences over a finite abelian group extends to a Hadamard matrix through a border of width 4s whose strips are constant on the cosets of a subgroup. Theorem B is its house form, whose hypothesis is exactly a two-tier periodic-autocorrelation profile, and carries two classical degenerations at an arbitrary…
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