Explicit lower bounds for vertices of hollow simplicial lattice polytopes

We record explicit hollow simplicial lattice polytopes with 7, 11, 16 and 22 vertices in dimensions 3, 4, 5 and 6, respectively. Exact facet enumeration and complete coordinate-box lattice-point tests verify these finite inputs. A denominator-two affine free sum combines blocks while preserving hollowness, simpliciality and an interior half-lattice point. Consequently H(d) >= 22 floor(d/6) + c_(d mod 6), where H(d) is the largest number of vertices of a hollow simplicial lattice d-polytope and (c_0,...,c_5) = (0,2,4,7,11,16), and liminf as d tends to infinity of H(d)/d >= 11/3. The composition lemma is a short consequence of the affine free-sum framework of Beck-Jayawant-McAllister; the quantitative application and explicit certified blocks are the subject of this note. The displayed coefficient is the ratio of a particular certified block found in a short exploratory search, not a proposed optimal constant. No superlinear growth or preservation of affine general position is claimed. The principal conclusions are presented as provisional candidate results; the finite inputs have exact facet enumerations, lattice-point censuses and anchor checks, while the general arguments have conventional written proofs and have not received full mechanical verification.