| import OAI.Combinatorics.BooleanFunctions.Amplification | |
| import OAI.Combinatorics.BooleanFunctions.Readout | |
| namespace OAI | |
| open scoped BigOperators | |
| noncomputable section | |
| namespace SquareRootDegree | |
| /-- Every stage and the final sign readout use finitely many actual Boolean inputs. -/ | |
| theorem signed_violations : SignedViolations := by | |
| intro C hC | |
| obtain ⟨F,hF⟩ := Amplification.exists_large_ratio ((C/ReadoutCLT.constant)^2) | |
| exact Observations.violation_of_observation F.map F.cost F.cost_pos F.cell_le | |
| F.variance_pos C hC hF | |
| /-- Unbounded violations for ordinary real Fourier degree and uniform cube averages. -/ | |
| theorem main : SignedViolations ∧ ¬ BddAbove AbsoluteRatios := by | |
| exact ⟨signed_violations,absolute_unbounded_of_signed signed_violations⟩ | |
| end SquareRootDegree | |
| end | |
| end OAI | |