Every connected layer family reduces to a ridge-closed one with loss factor $n-d+1$

For every connected layer family $F$ of rank $d\ge1$ on $n\ge d$ symbols there is a ridge-closed family $G$ (definition Hirsch_clf_ridge_closed) of the same rank on the same symbols with

Hence a polynomial height bound for ridge-closed families gives one for all families with one more degree. Proof. Close every layer by adjoining each $d$-set whose ridges are all present; proper shadows are unchanged, so all subset intervals survive and closure is idempotent. A base occurs in the closed sequence only on the intersection of its ridge intervals, and a ridge interval has at most $n-d+1$ layers (distinct bases above a fixed ridge). Keeping every $(n-d+1)$-st closed layer restores base-disjointness. This restates Hirsch.clf_ridge_closure_reduction (retired: it carried a private copy of the ridge-closed predicate) against the shared definition.