| 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 | |