| import OAI.Probability.MatroidProphet.Main | |
| namespace OAI | |
| namespace MatroidProphet | |
| open MainAlgorithm | |
| /-- The source safety guarantee, including the literal constants, all listed | |
| groups, global independent comparison set, and the harmless unlisted zero case. -/ | |
| def SafeSampleClaim : Prop := | |
| ∀ (n : ℕ) (M : Matroid (Fin n)) (hE : M.E = Set.univ) | |
| (d : MainMasks n) (s : Fin n → Option ℤ) (i : ℤ) | |
| (Y : Set (Fin n)), M.Indep Y → | |
| exitThreshold / 4 * | |
| ((d.D : Set (Fin n)) ∩ (Y ∩ (trueGroup M d s i : Set (Fin n)))).ncard - | |
| (d.D ∩ trueGroup M d s i).card / densityThreshold ≤ | |
| bitsExpectation (fun _ => thinningRate) Finset.univ (fun C => | |
| bitsExpectation (fun _ => thinningRate) Finset.univ (fun T => | |
| fairParityExpectation (fun p => | |
| (listedSafeStatistic M hE (2 ^ 100) (withMasks d d.D C T) s i Y | |
| (boolParity p) : ℝ)))) | |
| end MatroidProphet | |
| end OAI | |