A sharp form of Whitney's extension theorem

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The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients (2007, unknown): “Fefferman’s article [18] for related issues).”
Sobolev extension by linear operators (2012, result): “Analogous results for C(R) are given in [8, 12, 14, 15].”
Whitney’s extension problems and interpolation of data (2008, background): “) Building on this work, our recent papers [11]–[16] gave a complete solution to the above problems.”
Fitting a $C^m$-Smooth Function to Data II (2009, methodology): “We refer the reader to works of Whitney, Glaeser, Brudnyi-Shvartsman, Zobin, Bierstone-MilmanPawlucki, as cited in [2,5,7,8,12].”
Interpolation and extrapolation of smooth functions by linear operators (2005, methodology): “By using elementary properties of convex sets, reminiscent of our applications of Helly’s theorem in [8], we show that there exists a subset S ⊂ E, with the following properties: (a) The number of points in S is bounded by a constant depending only on m and n; and (b) Any polynomial P ∈ Γ(y, S) belo”
A Generalized Sharp Whitney Theorem for Jets (2005, methodology): “The next lemma is copied from [9,11], and its proof appears in [9].”