The explicit family and the shared-control coefficient

The existing balanced Chattopadhyay--Liao family requires more than (C-ε)n signed unbounded AND/OR/XOR gates eventually, with C approximately 1.22148505965. The signature permits arbitrary fan-in, fanout, depth, and repeated signed literals.

theorem Algebraic.Cutwidth.Aggregate.Geometry.Shared.sourceReductionHardFamily_eventually_lt_size {ε : ℝ} (hε : 0 < ε) : ∀ᶠ (n : ℕ) in Filter.atTop, ∀ (c : Circuit Aggregate.Geometry.signature n 1), (c.Computes Aggregate.Geometry.interpretation fun (x : Fin n → Bool) (x_1 : Fin 1) => Extractor.sourceReductionHardFamily n x) → (gateCoefficient - ε) * ↑n < ↑c.size

The fixed explicit family attains the stronger shared-control coefficient without depth, fanout, fan-in, or placement restrictions.