| import Mathlib |
| import OAI.Probability.SKGap.Stability.OrdinaryClosure |
| import OAI.Probability.SKGap.Localization.RecipeCoefficientClosure |
|
|
| namespace OAI |
|
|
| section |
|
|
| noncomputable section |
| open scoped BigOperators |
| namespace SKGapCutoff.Recipe |
| open SKGap.Noncrossing.Primary |
| variable {n : ℕ} {ι κ σ τ : Type*} [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] [Fintype σ] [Fintype τ] |
|
|
| namespace LocalConstants |
| def withCoefficient (c : LocalConstants) (K S : ℝ) (hK : 1≤K) (hS : 0≤S) : LocalConstants := |
| {c with A:=K,C:=K,S:=S,one_le_A:=hK,C_nonneg:=le_trans (by norm_num) hK,C_le_A:=le_rfl,S_nonneg:=hS} |
| end LocalConstants |
|
|
| theorem LocalOrdinaryInput.with_coefficients {D : OrdinaryData n ι κ σ} {N : ℕ} |
| {T : ι→SourceTree (Fin n→ℝ)} {x : Spin n} {c : LocalConstants} |
| (h : LocalOrdinaryInput D T x N c) (E : OrdinaryData n ι κ τ) |
| (hJ : E.J=D.J) (hj : E.j=D.j) (hH : E.H=D.H) (hp : E.predecessor=D.predecessor) (hθ : E.θ=D.θ) |
| (A : ℕ) (K S : ℝ) (hK : 1≤K) (hS : 0≤S) |
| (hs : (∑s,vectorNorm (E.seed s))≤S) (hc : E.CoefficientClass A x K) : |
| LocalOrdinaryInput E T x A (c.withCoefficient K S hK hS) := by |
| refine ⟨h.dimension,?_,?_,?_,?_,?_,?_,hs,?_,hc.seedRegular,hc.auxRegular,?_,?_⟩ |
| · simpa only [hJ,LocalConstants.withCoefficient] using h.interaction |
| · simpa only [hH,LocalConstants.withCoefficient] using h.primaryShape |
| · simpa only [hH,hj,hJ,LocalConstants.withCoefficient] using h.primaryFieldError |
| · simpa only [hp,hj,hJ,LocalConstants.withCoefficient] using h.primarySourceError |
| · simpa only [hp] using h.primaryValue |
| · simpa only [hp,LocalConstants.withCoefficient] using h.primaryDerivative |
| · simpa only [hθ,LocalConstants.withCoefficient] using h.parameter |
| · intro a ha s i; exact (hc.seedValue a ha s).at i |
| · intro a ha b i; exact (hc.auxValue a ha b).at i |
|
|
| end SKGapCutoff.Recipe |
|
|
| end |
| end |
|
|
| end OAI |
|
|
