High-contrast homogenization: Provider.Regularity.CorrectorIdentificationQuantitativeData

Imported from the Apache-2.0 HighContrastHomogenization development at commit 7a13dbcd8d6609264a713373f5c69ceeac870472.

Quantitative data for corrector identification

One good-tail threshold supplies the intrinsic slope and the scale-linear value growth of every canonical joint corrector. Both conclusions are independent of the physical coefficient field: the value row comes from the coarse-grained Poincare inequality at a good scale, so no ellipticity pair enters here.

theorem HCPolySupport.HighContrast.exists_scalarIdentityGoodTailCorrectorIdentificationDataConstant (d : ℕ) [NeZero d] (s : ℝ) (hs : 0 < s) (hsLt : s < 1 / 2) : ∃ c ∈ Set.Ioo 0 1, ∀ (a : Book.Ch02.TriadicCoeffFamily d) (delta : ℝ) (n : ℤ), delta ∈ Set.Ioc 0 c → ScalarIdentityGoodTail a s delta n → ∀ (hCauchy : FiniteAffineCorrectionLocalCauchy a) (e : Vec d), HasIntrinsicNormalizedSlope e (finiteAffineCorrectionJointLocalLimit a hCauchy e) ∧ ∃ (C : ℝ), 0 ≤ C ∧ ∀ (q : ℕ), n.toNat ≤ q → cubeLpNorm (originCube d ↑q) 2 (finiteAffineCorrectionJointLocalLimit a hCauchy e).globalValueRepresentative ≤ C * 3 ^ q

A common scalar-identity good-tail threshold produces the two coefficient-free corrector facts consumed by translated-gradient identification.