The wall: Baker/Matveev requires transcendence theory (~1000 lines not in Lean).
The replacement: SOS certificates require polynomial arithmetic only.
Key formula:
gap(x,m) = s₀(x,m) + Σᵢ sᵢ(x,m)·gᵢ(x,m)
where sᵢ = Σⱼ qᵢⱼ² (sum of squares)
and gᵢ are BMS domain constraints
Verification: expand and compare. No transcendence theory needed.
No Baker. No Matveev. Pure polynomial arithmetic.
Formula-first: zero English in formulas.
