pub fn family_growth(max_n: usize) -> Vec<(usize, usize, Vec<String>)>Expand description
The family growth across n — for each n ≤ max_n: the number of distinct certified families, and
which families are new (absent at n−1). The finding: the cheap families (unit-propagation, parity,
counting) form a fixed menu that saturates early; from then on each increase in n forces exactly one
new family — the degree-n algebraic family (algebraic-d{n}) — because max_ns_degree = n, so a
degree-n certificate becomes necessary at n and was not at n−1. That is the forcing mechanism: the
degree wall. The family count is therefore Θ(n) (fixed cheap menu + one algebraic rung per n), climbing
forever — no finite family set covers all n (bounded-degree incompleteness).