pub fn family_tower(n: usize) -> Vec<String>Expand description
The family tower — proven complete and finite at every n, without enumeration. The constructive
Nullstellensatz completeness of crate::polycalc::build_ns_certificate (every UNSAT formula over n
variables has a degree-≤ n GF(2) refutation, so nothing is beyond budget) pins the weakest crushing
rung of every minimal-UNSAT formula to a FIXED, parametric set: the three cheap families (unit
propagation, counting, parity) and the algebraic degrees d = 2..=n. No family lies outside this tower.
So the complete list of families at scale n is produced in O(n) here — not read off the
super-exponential orbit census. This is the “we do not iterate — we PROVED the families” statement, and
family_census (which does enumerate) is always a subset of it. The size is Θ(n), climbing forever:
no finite family set covers all n, because the degree wall forces a fresh algebraic-d{n} at each n.