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a2ee19a | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | 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
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