Authoritative order and data

Rows are $({\beta }_0,{\beta }_{+},{\beta }_{-})$. Columns are ordered lexicographically by species word and then by the recursive matching order below. That recursion pairs the smallest remaining slot with each possible partner and recurses.

The blind covariant tensor is

The time-gauge tensor is $G_t=H_1$ in (eq:KH). The fit always refers to the original labels ${\ell }_a,{\ell }_b$, regardless of computational ordering.

The listing uses only Python's standard library. It reconstructs all raw contact responses, checks the original pivots and minor, and checks the finite fit. Its target arithmetic implements the proved diagonal cubic formula, not an independent Einstein-vertex library. Inclusion is not a claim of execution.