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ea76aac | 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 | import Mathlib
import OAI.Computability.MaxCut.Estimates.Dictator
namespace OAI
noncomputable section
namespace OptimalMaxCut.LongCode.InstanceAdapter
open scoped BigOperators
open MaxCutGames.Foundations.Target MaxCutGames.Foundations.Hastad
/-- Fixed binary radix indexing, rather than a chosen `Fintype.equivFin`. -/
def cubeEquiv (q : ℕ) : Cube (Fin q) ≃ Fin (2 ^ q) :=
(Equiv.arrowCongr (Equiv.refl (Fin q)) finTwoEquiv.symm).trans finFunctionFinEquiv
/-- Row-major indexing before the explicit finite-field blowup. -/
def vertexEquiv (n q : ℕ) : (Fin n × Cube (Fin q)) ≃ Fin (n * 2 ^ q) :=
(Equiv.prodCongr (Equiv.refl (Fin n)) (cubeEquiv q)).trans finProdFinEquiv
noncomputable def output {q : ℕ} (g : Instance q) (t : ℚ)
(ht : t ∈ Set.Icc (-1 : ℚ) 1) (K : ℕ) : ScaledGraph :=
(ofInstance g).output t ht (vertexEquiv g.vertices q) K
theorem output_vertex_bound {q : ℕ} (g : Instance q) (t : ℚ)
(ht : t ∈ Set.Icc (-1 : ℚ) 1) (K : ℕ) :
(output g t ht K).graph.vertices ≤
(g.vertices * 2 ^ q) * (2 * (K * (g.vertices * 2 ^ q + 1) ^ 2 + 1)) ^ 6 :=
Game.output_vertex_bound _ _ _ _ _
end OptimalMaxCut.LongCode.InstanceAdapter
end
end OAI
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