openAI-math-dataset / lean /OAI /Probability /MatroidSecretary /Transport /TransferSpecification.lean
| import OAI.Probability.MatroidProphet.Main | |
| namespace OAI | |
| /-! Independent specification of source `lem:transfer` / `eq:rank-transfer`. | |
| The fixed filter mask is arbitrary. Every remaining product coordinate and parity | |
| is averaged, and the actual nominal rank statistic is zero when unlisted. -/ | |
| namespace MatroidProphet | |
| open Finset MainAlgorithm | |
| /-- Full sample-to-rank contract for the actual rounded greedy survivor groups. -/ | |
| def TransferClaim : Prop := | |
| ∀ (n : ℕ) (M : Matroid (Fin n)) (hE : M.E = Set.univ) | |
| (w : Weights n), (∀ e, 0 ≤ w e) → | |
| ∀ (H : Finset (Fin n)) (i : ℤ), | |
| let s : Fin n → Option ℤ := fun e => roundedLevel weightBase (w e) | |
| let d : MainMasks n := ⟨H, ∅, ∅, ∅, false⟩ | |
| let U := trueGroup M d s i | |
| let Y := (positiveGreedy M s \ H).filter (fun e => s e = some i) | |
| densityThreshold ≤ (U.card : ℝ) → | |
| ((((2 : ℝ)^16)⁻¹ * Y.card - ((2 : ℝ)^23)⁻¹ * U.card) / (2 : ℝ)^100) ≤ | |
| mainMean d (fun d' => (trueZ M hE d' s i : ℝ)) | |
| end MatroidProphet | |
| end OAI | |