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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 30 31 32 33 34 35 36 37 38 39 40 | import OAI.Probability.MatroidProphet.Main
import Mathlib.Data.Fintype.Prod
namespace OAI
/-! Concrete one-label conditional kernel for the secretary reconstruction.
The boolean records membership in the sacrificed observation mask, not branch choice.
The three coordinates are the original H, D, C coins; the T coin is not sacrificed.
-/
namespace MatroidProphet.Secretary
abbrev MaskTriple := Bool × Bool × Bool
/-- Whether at least one of the three observation coins is set. -/
def tripleRevealed (x : MaskTriple) : Bool := x.1 || x.2.1 || x.2.2
/-- The independent H,D,C law at one label, retaining the thinning parameter. -/
noncomputable def tripleWeight (t : ℝ) (x : MaskTriple) : ℝ :=
(1 / 2) * (if x.2.1 then 1 / 4 else 3 / 4) *
(if x.2.2 then t else 1 - t)
/-- Probability that a label is sacrificed in the main branch. -/
noncomputable def mainRevealRate : ℝ := 5 / 8 + 3 * thinningRate / 8
/-- The source specifies all seven nonzero triple masses divided by the reveal rate.
Outside the observation set the triple is deterministically zero. -/
noncomputable def conditionalTripleWeight (revealed : Bool) (x : MaskTriple) : ℝ :=
if revealed then
if tripleRevealed x then tripleWeight thinningRate x / mainRevealRate else 0
else if x = (false, false, false) then 1 else 0
/-- Probability of a prescribed observation-mask membership bit. -/
noncomputable def revealBitWeight (revealed : Bool) : ℝ :=
if revealed then mainRevealRate else 1 - mainRevealRate
end MatroidProphet.Secretary
end OAI
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