Correspondence between the external local computation and the neighborhood theorem

Establish whether the external local computation cited in connection with the maximum-number preprint corresponds, with a checked correspondence covering the entire closed neighborhood \(\mathcal U\) of the reference Hadamard matrix, to the local nonextension result proved for \(\mathcal U\).

Background

The paper proves an independent computer-assisted theorem for every exact complex Hadamard matrix in the closed entrywise neighborhood $\mathcal U$ of a fixed reference matrix. The theorem establishes an exact count of 48 common-unbiased rays and rules out a third mutually unbiased orthonormal basis in that neighborhood.

A separate maximum-number preprint is described as using related candidate-vector and orthogonality-graph computations. However, the paper states that comparing that external local computation with its own neighborhood theorem requires a matching output record and a verified correspondence over the whole neighborhood. That comparison is explicitly left unresolved and is not used as a premise of the paper's proof.