Constraint-First Quantum Gravity, machine-checked: the unification is the constraint algebra

Machine-checked (Lean 4 / Mathlib) constraint-first theory of quantum gravity. The forced content is the union of the Born rule (Gleason) and the Einstein equation (Lovelock), joined by the constraint ∇·T = 0, quantized as the Wheeler-DeWitt equation H|ψ⟩ = 0, and closed as the Dirac algebra. Three sharpened, falsifiable statements: SM minimality selects π₁ ≠ 0 (the (1,4) three-generation manifold is a Z₁₂ quotient, not toric; toric χ=±6 starts at h¹¹+h²¹=29); the coupling G is free (not derivable); the BMV entangling phase oscillates with period T=496 s, requiring < 0.1 K. Honest accounting of what is new (the certified chain + three statements) versus textbook (Lovelock, WdW, Dirac, Atiyah-Singer, BMV).