Theorem: Complete finite encoding

The target and every original contact column are

This encodes all $45360$ entries of the $3\times 15120$ matrix.

Proof. The first row is zero by Proposition prop:blind. The second row is exactly (eq:contact-evaluator) specialized to (eq:KH); the diagonal metric gives the printed equality constraints. Exchanging the species in ${\beta }_{+}$ gives ${\beta }_{-}$, which complements the raw species word. The target follows from blindness and Theorem thm:nonzero.

Every species word and every perfect matching is included. No reduced or selected contact list replaces the raw catalogue.